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In_II this_DD1 study_NN1 ,_, we_PPIS2 briefly_RR review_VV0 the_AT formulation_NN1 of_IO moment_NN1 models_NN2 for_IF electron_NN1 transport_NN1 in_II gases_NN2 and_CC liquids_NN2 in_II section_NN1 2_MC ,_, elaborating_VVG on_II the_AT modifications_NN2 needed_VVN for_IF electron_NN1 transport_NN1 in_II liquids_NN2 ._. 
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However_RR ,_, the_AT nanoparticles_NN2 in_II the_AT composite_JJ usually_RR tend_VV0 to_TO aggregate_VVI during_II charge-discharge_JJ process_NN1 ,_, and_CC therefore_RR a_AT1 stronger_JJR force_NN1 is_VBZ required_VVN to_TO combine_VVI the_AT nanoparticles_NN2 and_CC graphene_NN1 ._. 
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There_EX are_VBR two_MC highly_RR non-trivial_JJ problems_NN2 that_CST eventually_RR modified_JJ gravity_NN1 might_VM provide_VVI consistent_JJ answers_NN2 ._. 
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Vertical_JJ displacement_NN1 then_RT proceeds_VVZ on_II the_AT resistive_JJ wall_NN1 time_NNT1 ,_, wt_NN1 as_CSA eddy_NN1 currents_NN2 decay_VV0 ,_, which_DDQ is_VBZ the_AT case_NN1 whenever_RRQV the_AT wall_NN1 slows_VVZ the_AT displacement_NN1 ._. 
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Then_RT <Equation>_FO will_VM be_VBI zero_NN1 at_II <Equation>_FO and_CC <Professional_FO Term>_FO will_VM diverge_VVI at_II <Equation>_FO ,_, as_CSA we_PPIS2 require_VV0 for_IF the_AT extrapolated_JJ tail_NN1 field_NN1 ._. 
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One_MC1 of_IO the_AT key_JJ inputs_NN2 in_II the_AT proof_NN1 &lsqb;_( She16_FO ,_, Thm._NP1 2.5_MC &rsqb;_) is_VBZ a_AT1 tail_NN1 bound_VVN for_IF the_AT law_NN1 of_IO the_AT length_NN1 of_IO the_AT reduced_JJ word_NN1 |_NULL X_ZZ1 (_( 1_MC1 ,_, n_ZZ1 )_) |_NULL (_( see_VV0 &lsqb;_( She16_FO ,_, Lem_NP1 ._. 
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Both_DB2 results_NN2 are_VBR identical_JJ up_II21 to_II22 this_DD1 point_NN1 after_II neglecting_VVG the_AT difference_NN1 in_II initial_NN1 and_CC final_JJ Coulomb_NN1 potentials_NN2 ._. 
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This_DD1 produces_VVZ an_AT1 extended_JJ low_JJ energy_NN1 tail_NN1 in_II the_AT iron_NN1 line_NN1 ._. 
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Figure_NN1 47_MC (_( a_ZZ1 )_) Snapshot_NN1 of_IO single_JJ lamellar_JJ crystal_NN1 raised_VVN by_II the_AT template_NN1 seed_NN1 in_II the_AT center_NN1 at_II a_AT1 high_JJ crystallization_NN1 temperature_NN1 ,_, obtained_VVN in_II dynamic_JJ Monte_NP1 Carlo_NP1 simulations_NN2 ._. 
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It_PPH1 generated_VVD 17ps_FO mode-locked_JJ pulses_NN2 with_IW an_AT1 average_JJ power_NN1 of_IO only_JJ 38mW.128_FO Two_MC years_NNT2 later_RRR ,_, Ma_NP1 et_RA21 al_RA22 ._. 
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presented_VVD the_AT first_MD diode-_NN1 pumped_VVD femtosecond_NN1 operation_NN1 of_IO a_AT1 2lm_FO mode-locked_JJ solid-state_JJ laser_NN1 using_VVG a_AT1 Tm3t:CLNGG_FO disordered_JJ crystal_NN1 as_II the_AT gain_NN1 medium.129_FO The_AT laser_NN1 generated_VVD stable_JJ 479fs_RA ultrashort_VV0 mode-locked_JJ pulses_NN2 with_IW average_JJ output_NN1 power_NN1 as_RG high_JJ as_CSA 288mW_FO at_II 1994nm_FO ._. 
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The_AT smart_JJ materials_NN2 or_CC HNCs_NP1 reviewed_VVD here_RL can_VM integrate_VVI "_" controlled_JJ "_" cancer_NN1 theranostics_NN2 into_II a_AT1 solitary_JJ platform_NN1 ,_, which_DDQ is_VBZ a_AT1 revolutionary_JJ advancement_NN1 in_II the_AT path_NN1 toward_II highly_RR safe_JJ and_CC effec-_JJ tive_JJ personalized_JJ cancer_NN1 therapy_NN1 ._. 
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Published_VVN under_II license_NN1 by_II AIP_NP1 Publishing_NN1 ._. 
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Figure_NN1 5_MC shows_VVZ these_DD2 data_NN for_IF the_AT case_NN1 of_IO the_AT <professional_FO term>_FO ratio_NN1 populated_VVN via_II 56Fe_NN1 (_( p_ZZ1 ,_, n_ZZ1 )_) measured_VVD via_II stacked-target_JJ activation_NN1 at_II the_AT LBNL_NP1 88-Inch_NNU1 Cyclotron_NN1 in_II comparison_NN1 to_II TALYS_NP2 calculations_NN2 for_IF different_JJ values_NN2 of_IO the_AT spin_NN1 cutoff_NN1 parameter_NN1 (_( Figure_NN1 5a_FO )_) and_CC the_AT six_MC level_JJ density_NN1 models_NN2 available_JJ for_IF use_NN1 in_II TALYS_NP2 (_( Figure_NN1 5b_FO )_) ._. 
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In_II practice_NN1 ,_, each_DD1 additional_JJ observable_JJ reduces_VVZ statistics_NN ,_, making_VVG such_DA measurements_NN2 exceedingly_RR challenging_VVG ._. 
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The_AT cross_NN1 correlation_NN1 XC_MC 1_MC1 shows_VVZ that_CST P_ZZ1 1_MC1 is_VBZ abruptly_RR formed_VVN at_II time-zero_NN1 ._. 
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For_IF the_AT modified_JJ Gaussian_JJ model_NN1 for_IF the_AT charge_NN1 distribution_NN1 (_( Sirlin_NP1 ,_, 1987_MC )_) more_RGR extended_JJ expressions_NN2 are_VBR obtained_VVN ._. 
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This_DD1 leads_VVZ to_II unusual_JJ magnetic_JJ field_NN1 dependences_NN2 of_IO the_AT classical_JJ and_CC quantum_NN1 correlations_NN2 between_II the_AT fictitious_JJ spins_NN2 ._. 
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This_DD1 limits_VVZ the_AT computational_JJ cost_NN1 because_CS it_PPH1 drastically_RR reduces_VVZ the_AT number_NN1 of_IO virtual_JJ quark-antiquark_JJ loops_NN2 that_CST have_VH0 to_TO be_VBI taken_VVN into_II account_NN1 ._. 
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However_RR ,_, for_IF a_AT1 system_NN1 with_IW strong_JJ variations_NN2 in_II density_NN1 the_AT differential_JJ motion_NN1 of_IO the_AT neutrons_NN2 and_CC protons_NN2 is_VBZ more_RGR complicated_JJ ._. 
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Parameters_NN2 such_II21 as_II22 Rsym_NP1 are_VBR unavailable_JJ ._. 
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High_JJ harmonics_NN2 having_VHG their_APPGE spectral_JJ phase_NN1 locked_VVN demonstrate_VV0 the_AT emission_NN1 of_IO attosecond_NN1 duration_NN1 pulses_NN2 ._. 
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Using_VVG these_DD2 amplitudes_NN2 ,_, the_AT Bose_NP1 symmetrized_VVD decay_NN1 amplitude_NN1 is_VBZ given_VVN by_II <EQUATION>_FO ._. 
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The_AT terms_NN2 quadratic_JJ in_II the_AT auxiliary_JJ field_NN1 encapsulate_VV0 the_AT second_MD moment_NN1 of_IO the_AT Gaussian_JJ white_JJ noise_NN1 with_IW zero_MC mean_JJ ._. 
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The_AT final_JJ aim_NN1 is_VBZ to_TO provide_VVI a_AT1 good_JJ toolbox_NN1 and_CC starting_VVG set_NN1 of_IO procedures_NN2 for_IF readers_NN2 interested_JJ in_II starting_VVG their_APPGE own_DA microstructuring_JJ projects_NN2 ._. 
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Therefore_RR ,_, our_APPGE results_NN2 support_VV0 the_AT possible_JJ use_NN1 of_IO the_AT PCP_NP1 embedded_VVD in_II the_AT substrate_NN1 chuck_NN1 or_CC a_AT1 dummy_JJ wafer_NN1 before_II real_JJ processing_NN1 ._. 
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If_CS we_PPIS2 allow_VV0 such_DA interactions_NN2 ,_, then_RT approaches_VVZ reminiscent_JJ of_IO the_AT Froggatt–Nielsen_NP1 approach_NN1 can_VM explain_VVI the_AT fermion_NN1 mass_NN1 hierarchy_NN1 by_II making_VVG the_AT Yukawa_NP1 couplings_NN2 Higgs-dependent_JJ &lsqb;_( 49_MC &rsqb;_) ,_, which_DDQ also_RR breaks_VVZ the_AT SM_NP1 relation_NN1 m_ZZ1 v_ZZ1 which_DDQ holds_VVZ irrespective_II21 of_II22 the_AT particle_NN1 species_NN ._. 
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To_TO follow_VVI the_AT evolution_NN1 of_IO this_DD1 peak_NN1 across_II the_AT phase_NN1 transition_NN1 ,_, we_PPIS2 adopt_VV0 a_AT1 fit_JJ procedure_NN1 to_TO extract_VVI the_AT most_RGT relevant_JJ parameters_NN2 from_II the_AT experimental_JJ spectra_NN2 ,_, namely_REX ,_, the_AT intensity_NN1 of_IO the_AT FM_NN1 peak_NN1 and_CC the_AT temperature_NN1 T._NP1 In_II Fig._NN1 3(a)_FO ,_, we_PPIS2 show_VV0 the_AT fit_JJ results_NN2 for_IF the_AT spectrum_NN1 measured_VVN at_II 430_MC K._NP1 We_PPIS2 refer_VV0 the_AT reader_NN1 to_II Ref_NN1 ._. 
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Moreover_RR ,_, the_AT appearance_NN1 of_IO single-valued_JJ MZVs_NP1 in_II the_AT sigma-model_NN1 approach_NN1 to_II effective_JJ gauge_NN1 interactions_NN2 of_IO type-I_NN1 and_CC heterotic_JJ strings_NN2 has_VHZ been_VBN studied_VVN in_II &lsqb;_( 23_MC &rsqb;_) ._. 
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Similarly_RR to_II what_DDQ is_VBZ done_VDN in_II Ref_NN1 ._. 
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The_AT reason_NN1 for_IF this_DD1 ,_, as_CSA discussed_VVN in_II Sec_NNU ._. 
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II.C.4_FO ,_, is_VBZ the_AT existence_NN1 of_IO the_AT vDVZ_NNU discontinuity_NN1 ._. 
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The_AT subsystems_NN2 A_ZZ1 and_CC B_ZZ1 are_VBR left_VVN and_CC right_RR spins_VVZ ,_, respectively_RR ._. 
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We_PPIS2 also_RR restrict_VV0 our_APPGE classification_NN1 to_II PWIs_NN1 that_CST are_VBR easily_RR parameterizable_JJ ._. 
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The_AT end_NN1 result_NN1 is_VBZ that_CST one_PN1 may_VM consider_VVI only_RR the_AT modification_NN1 for_IF the_AT helicity-2_MC modes_NN2 but_CCB neglect_VV0 the_AT non-helicity-2_MC modes_NN2 ,_, which_DDQ is_VBZ the_AT assumption_NN1 for_IF the_AT mass_JJ bounds_NN2 discussed_VVN in_II Sec_NNU ._. 
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V._NNU In_II Fig._NN1 5(b)_FO ,_, we_PPIS2 show_VV0 the_AT total_JJ EVDF_NN1 covering_VVG the_AT region_NN1 from<Equation>_FO to_II about<Equation>_FO ,_, well_RR beyond_II the_AT sheath_NN1 region_NN1 ,_, which_DDQ remains_VVZ approximately_RR Maxwellian_JJ ._. 
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Equations_NN2 (_( 1_MC1 )_) –_- (_( 3_MC )_) define_VV0 the_AT model_NN1 via_II a_AT1 set_NN1 of_IO chemical-like_JJ reactions_NN2 ._. 
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While_CS the_AT area_NN1 of_IO a_AT1 hard_JJ particle_NN1 jet_NN1 could_VM be_VBI treated_VVN analytically_RR ,_, this_DD1 is_VBZ not_XX the_AT case_NN1 for_IF the_AT pure-ghost_JJ jet_NN1 area_NN1 ._. 
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Many-body_JJ localized_JJ (_( MBL_NP1 )_) systems_NN2 remain_VV0 perfect_JJ insulators_NN2 at_II nonzero_NN1 temperature_NN1 ,_, which_DDQ do_VD0 not_XX thermalize_VVI and_CC therefore_RR can_VM not_XX be_VBI described_VVN using_VVG statistical_JJ mechanics_NN2 ._. 
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The_AT averaging_NN1 in_II Eqs._NP1 (_( 113_MC )_) and_CC (_( 114_MC )_) is_VBZ over_II the_AT azimuth_NN1 ._. 
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In_II the_AT limit_NN1 R_ZZ1 R0_FO ,_, we_PPIS2 have_VH0 F_NP1 (_( R_ZZ1 )_) R2_FO ,_, and_CC hence_RR the_AT model_NN1 mimics_VVZ the_AT CDM_NP1 model_NN1 ._. 
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When_CS the_AT condition_NN1 above_RL holds_VVZ we_PPIS2 say_VV0 that_CST p_ZZ1 thermomajorizes_VVZ q_ZZ1 ._. 
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The_AT technical_JJ aspects_NN2 of_IO the_AT evolution_NN1 of_IO the_AT ATLAS_NN1 detector_NN1 over_II many_DA2 years_NNT2 are_VBR discussed_VVN in_II Section_NN1 4.1_MC ._. 
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As_CSA BB_NP1 p_ZZ1 in_II most_DAT tokamaks_NN2 ,_, the_AT associated_JJ momentum_NN1 flux_NN1 is_VBZ likely_RR an_AT1 order_NN1 of_IO magnitude_NN1 larger_JJR than_CSN the_AT values_NN2 obtained_VVN here_RL ._. 
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This_DD1 material_NN1 is_VBZ based_VVN upon_II work_NN1 supported_VVN by_II the_AT Department_NN1 of_IO Energy_NN1 National_JJ Nuclear_JJ Security_NN1 Administration_NN1 under_II Award_NN1 No_UH ._. 
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DE-NA0003856_NP1 ,_, the_AT University_NN1 of_IO Rochester_NP1 ,_, and_CC the_AT New_NP1 York_NP1 State_NN1 Energy_NN1 Research_NN1 and_CC Development_NN1 Authority_NN1 ._. 
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Ar_UH Br_NP1 ,_, and_CC let_VV0 m_ZZ1 be_VBI the_AT size_NN1 of_IO C1_FO ._. 
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For_IF emphasis_NN1 ,_, we_PPIS2 explicitly_RR write_VV0 that_CST the_AT steady_JJ state_NN1 transport_NN1 properties_NN2 are_VBR functions_NN2 of_IO the_AT mean_JJ electron_NN1 energy_NN1 ,_, <equation>_FO ._. 
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Both_DB2 the_AT pseudomagnetic_JJ field_NN1 and_CC the_AT injecting_VVG proton_NN1 are_VBR applied_VVN at_II <EQUATION_FO >_FO ._. 
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When_CS graded_VVN by_II the_AT charges_NN2 of_IO the_AT ghost_NN1 U_ZZ1 (_( 1_MC1 )_) current_JJ in_II a_AT1 specific_JJ way_NN1 ,_, its_APPGE twined_JJ partition_NN1 function_NN1 coincides_VVZ with_IW ,_, g_ZZ1 ._. 
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In_II Fig._NN1 1(c)_FO we_PPIS2 show_VV0 the_AT evolution_NN1 of_IO the_AT number_NN1 of_IO principal_JJ components_NN2 Npc_NP1 ._. 
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We_PPIS2 now_RT move_VV0 on_RP to_II the_AT case_NN1 of_IO fermionic_JJ topological_JJ orders_NN2 with_IW U(1)_FO ZT_NP1 2_MC symmetry_NN1 ._. 
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Additionally_RR ,_, they_PPHS2 stated_VVD that_CST these_DD2 electrospun_VV0 nanofifibrous_JJ scaffolds_NN2 of_IO Gel/HA_FU obtained_VVN by_II the_AT spin–spray_NN1 method_NN1 are_VBR promising_JJ superior_JJ biocomposites_NN2 suitable_JJ for_IF bone_NN1 tissue_NN1 regeneration_NN1 ._. 
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Although_CS a_AT1 vanishing_JJ overlap_NN1 does_VDZ not_XX necessarily_RR result_VVI in_II a_AT1 vanishing_JJ Coulomb_NP1 integral_JJ ,_, it_PPH1 can_VM be_VBI assumed_VVN to_TO be_VBI at_RR21 least_RR22 considerably_RR smaller_JJR than_CSN in_II the_AT other_JJ cases_NN2 ._. 
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However_RR ,_, these_DD2 techniques_NN2 pose_VV0 certain_JJ limitations_NN2 such_II21 as_II22 lower_JJR productivity_NN1 and_CC large_JJ time_NNT1 frames_NN2 required_VVN to_TO produce_VVI adequate_JJ quantities_NN2 of_IO nanoscale_NN1 materials_NN2 ._. 
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The_AT RRPA_NN1 presents_VVZ rather_RG similar_JJ ij_JJ distributions_NN2 &lsqb;_( Fig._NN1 8(d)_FO &rsqb;_) as_CSA low-packing-fraction_JJ RIPAs_NN2 ,_, going_VVG through_II a_AT1 minimum_NN1 for_IF i5_FO ._. 
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The_AT progress_NN1 in_II the_AT field_NN1 is_VBZ in_II a_AT1 considerable_JJ way_NN1 due_II21 to_II22 instrumental_JJ developments_NN2 in_II high_JJ pressure_NN1 physics_NN1 and_CC technique_NN1 in_II 1990s_MC2 and_CC 2000s_MC2 ,_, including_II high-pressure_JJ neutron_NN1 technique_NN1 ,_, high-pressure_JJ magnetic_JJ susceptibility_NN1 measurements_NN2 technique_NN1 ,_, the_AT technique_NN1 of_IO ultrahigh_NN1 (_( 100_MC T_ZZ1 range_NN1 )_) magnetic_JJ fields_NN2 ,_, the_AT technique_NN1 developed_VVN for_IF high-pressure_JJ high-temperature_JJ studies_NN2 of_IO highly_RR reactive_JJ (_( like_II hydrogen_NN1 and_CC oxygen_NN1 )_) substances_NN2 ,_, etc_RA ._. 
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Under_II certain_JJ conditions_NN2 ,_, the_AT residue_NN1 can_VM be_VBI approximated_VVN as_CSA follows_VVZ :_: <Equation>_FO (_( B.8_FO )_) ._. 
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Ishihara_NP1 et_RA21 al_RA22 ._. 
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&lsqb;_( 8_MC &rsqb;_) found_VVD that_CST the_AT oxygen_NN1 ion_NN1 conductivity_NN1 of_IO Pr2NiO4+δincreases_FO by_II substitution_NN1 of_IO Ni_NP1 with_IW Ga_NP1 and_CC Cu_FO ,_, but_CCB also_RR by_II introducing_VVG Pr_NP1 deficiency_NN1 ._. 
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The_AT base_NN1 case_NN1 <Equation>_FO is_VBZ trivial_JJ ._. 
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Any_DD subjective_JJ views_NN2 or_CC opinions_NN2 that_CST might_VM be_VBI expressed_VVN in_II the_AT paper_NN1 do_VD0 not_XX necessarily_RR represent_VVI the_AT views_NN2 of_IO the_AT U.S._NP1 Department_NN1 of_IO Energy_NN1 or_CC the_AT U.S._NP1 Government_NN1 ._. 
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Similar_JJ to_II G-invariant_JJ states_NN2 ,_, a_AT1 quantum_NN1 channel_NN1 is_VBZ G_ZZ1 covariant_JJ if_CS and_CC only_RR if_CS it_PPH1 commutes_VVZ with_IW Ug_NN1 for_IF all_DB g_ZZ1 ∈_FO G._NNU When_CS the_AT photogenerated_JJ electrons_NN2 reach_VV0 the_AT boundary_NN1 of_IO the_AT P-N_JJ junction_NN1 ,_, the_AT photogenerated_JJ electrons_NN2 will_VM drift_VVI under_II the_AT built-in_JJ electric_JJ field_NN1 force_NN1 ,_, then_RT will_VM pass_VVI through_II the_AT depletion_NN1 layer_NN1 and_CC finally_RR enter_VV0 the_AT MoS2_FO in_II the_AT N_ND1 region_NN1 ._. 
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It_PPH1 is_VBZ intriguing_JJ to_TO note_VVI that_DD1 for_IF the_AT boron_NN1 and_CC beryllium_NN1 fragments_NN2 it_PPH1 appears_VVZ that_CST the_AT more_RGR neutron-rich_JJ systems_NN2 result_VV0 in_II more_RGR neutron-rich_JJ fragments_NN2 ,_, while_CS for_IF the_AT helium_NN1 fragments_NN2 this_DD1 trend_NN1 is_VBZ reversed_VVN ;_; the_AT lithium_NN1 fragments_NN2 exhibit_VV0 intermediate_JJ behavior_NN1 ._. 
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The_AT faster_JJR the_AT rotation_NN1 of_IO the_AT inner_JJ cylinder_NN1 ,_, therefore_RR ,_, the_AT more_DAR energy_NN1 is_VBZ stored_VVN in_II the_AT no_NN1 axisymmetric_JJ modes_NN2 of_IO the_AT instability_NN1 ._. 
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Besides_II the_AT accuracy_NN1 of_IO the_AT studied_JJ models_NN2 ,_, also_RR their_APPGE predictive_JJ power_NN1 has_VHZ been_VBN considered_VVN ._. 
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As_II a_AT1 way_NN1 to_TO increase_VVI distance_NN1 ,_, the_AT trusted_JJ noise_NN1 concept_NN1 was_VBDZ proposed_VVN ,_, in_II which_DDQ a_AT1 noise_NN1 is_VBZ added_VVN in_II a_AT1 specific_JJ way_NN1 to_TO increase_VVI security_NN1 &lsqb;_( 16_MC &rsqb;_) ._. 
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We_PPIS2 apologize_VV0 to_II the_AT many_DA2 colleagues_NN2 whose_DDQGE work_NN1 could_VM not_XX be_VBI cited_VVN owing_II21 to_II22 space_NN1 constraints_NN2 ._. 
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For_IF particles_NN2 in_II the_AT quasi-bound_JJ regime_NN1 of_IO doughnut_NN1 scattering_VVG the_AT distribution_NN1 maximum_NN1 position_NN1 of_IO the_AT vertical_JJ deflection_NN1 angles_NN2 is_VBZ at_II <Equation>_FO as_CSA in_II the_AT case_NN1 presented_VVN in_II Fig._NN1 81_MC ._. 
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For_IF this_DD1 reason_NN1 ,_, microchip_NN1 based_VVN drug_NN1 delivery_NN1 devices_NN2 have_VH0 become_VVN a_AT1 potent_JJ technology_NN1 owing_II21 to_II22 their_APPGE capability_NN1 of_IO containing_VVG drugs_NN2 for_IF extended_JJ periods_NN2 of_IO time_NNT1 ._. 
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Then_RT <Equation>_FO is_VBZ the_AT same_DA as_CSA the_AT time_NNT1 <Equation>_FO from_II Lemma_NN1 3.22_MC and_CC by_II the_AT strong_JJ Markov_NP1 property_NN1 the_AT increments_NN2 <Equation>_FO for_IF <Equation>_FO are_VBR i.i.d_NNU ._. 
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This_DD1 could_VM also_RR explain_VVI the_AT near_JJ spherical_JJ symmetry_NN1 of_IO most_DAT supernova_NN1 remnants_NN2 of_IO SNe_NP1 Ia_NP1 ._. 
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The_AT volume_NN1 integral_JJ in_II the_AT numerator_NN1 of_IO (_( 15_MC )_) is_VBZ taken_VVN only_RR over_II the_AT space_NN1 that_CST the_AT plasma_NN1 occupies_VVZ ._. 
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Therefore_RR ,_, a_AT1 mathematical_JJ isomorphism_NN1 between_II two_MC Hilbert_NP1 spaces_NN2 ,_, such_II21 as_II22 C2_FO C2_FO C4_FO ,_, does_VDZ not_XX necessarily_RR translate_VVI into_II the_AT same_DA set_NN1 of_IO Free_JJ states_NN2 (_( or_CC free_JJ operations_NN2 )_) for_IF the_AT two_MC spaces_NN2 ._. 
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A_AT1 fast_JJ readout_NN1 pnCCD_NNU detector_NN1 (_( Strüder_NP1 et_RA21 al._RA22 ,_, 2010_MC )_) measures_VVZ the_AT elastically_RR scattered_JJ photons_NN2 from_II single_JJ xenon_NN1 clusters_NN2 (_( Rupp_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) ._. 
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The_AT orientation_NN1 of_IO the_AT two_MC clusters_NN2 with_II31 respect_II32 to_II33 the_AT scattering_NN1 plane_NN1 ,_, The_AT distance_NN1 between_II two_MC clusters_NN2 ,_, i.e._REX separation_NN1 in_II the_AT case_NN1 of_IO Newton_NP1 rings_NN2 (_( figure_NN1 24_MC (_( b_ZZ1 )_) )_) and_CC fusion_NN1 for_IF twin_NN1 clusters_NN2 ,_, Sizes_NN2 of_IO both_DB2 the_AT particles_NN2 ._. 
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To_TO go_VVI higher_JJR in_II energy_NN1 O._NP1 Svelto_NP1 and_CC his_APPGE group_NN1 (_( Nisoli_NP1 ,_, De_NP1 Silvestri_NP1 ,_, and_CC Svelto_NP1 ,_, 1996_MC )_) introduced_VVD a_AT1 compression_NN1 technique_NN1 based_VVN on_II a_AT1 fused_JJ silica_NN1 hollow-core_NN1 capillary_NN1 ,_, filled_VVN with_IW noble_JJ gases_NN2 to_TO broaden_VVI the_AT pulse_NN1 spectrum_NN1 before_II efficiently_RR compressing_VVG to_II the_AT 100_MC J_ZZ1 level_JJ with_IW chirped_JJ mirrors_NN2 that_CST introduce_VV0 negative_JJ dispersion_NN1 to_II the_AT pulse_NN1 phase_NN1 ._. 
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It_PPH1 was_VBDZ shown_VVN that_CST (_( for_IF solitary_JJ waves_NN2 of_IO different_JJ amplitudes_NN2 )_) the_AT measurements_NN2 of_IO the_AT force_NN1 scaled_VVN by_II the_AT incident_NN1 force_NN1 as_II a_AT1 function_NN1 of_IO time_NNT1 (_( normalized_VVN by_II the_AT duration_NN1 of_IO the_AT pulse_NN1 )_) fall_VV0 on_II31 top_II32 of_II33 each_PPX221 other_PPX222 ._. 
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NSI_NN2 provide_VV0 a_AT1 possible_JJ solution_NN1 to_II this_DD1 discrepancy_NN1 ._. 
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This_DD1 is_VBZ in_II fact_NN1 a_AT1 limitation_NN1 of_IO the_AT process_NN1 ._. 
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Since_CS the_AT dawn_NNT1 of_IO the_AT laser_NN1 in_II 1960_MC ,_, scientists_NN2 focused_VVD them_PPHO2 to_TO create_VVI nonlinear_JJ effects_NN2 and_CC very_RG quickly_RR ,_, as_CSA intensity_NN1 increased_VVD ,_, plasmas_NN2 ._. 
</s>
<s>
By_II the_AT definition_NN1 of_IO U_ZZ1 =_FO U_ZZ1 (_( r_ZZ1 ,_, r_ZZ1 |_NULL 2r_FO )_) ,_, the_AT boson-boson_JJ part_NN1 Y00_FO of_IO Y_ZZ1 is_VBZ a_AT1 Hermitian_JJ matrix_NN1 while_CS the_AT fermion-fermion_JJ part_NN1 Y11_FO is_VBZ anti-Hermitian_JJ ._. 
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<s>
As_CSA listed_VVN in_II Table_NN1 1_MC1 ,_, the_AT x_ZZ1 value_NN1 (_( atomic_JJ ratio_NN1 of_IO O/Si_FU )_) can_VM be_VBI obtained_VVN to_TO be_VBI ca_VM ._. 
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<s>
Therefore_RR ,_, in_II the_AT specimen_NN1 heated_VVN at_II temperatures_NN2 higher_JJR than_CSN the_AT exothermic_JJ peak_NN1 temperature_NN1 ,_, the_AT LPS–NMC_NP1 composites_NN2 are_VBR transformed_VVN into_II aggregations_NN2 of_IO Li3PO4_FO ,_, CoNi2S4_FO ,_, and_CC MnS_NP1 nanocrystallites_NN2 ._. 
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<s>
These_DD2 photo_NN1 neutrons_NN2 are_VBR usually_RR measured_VVN to_TO diagnose_VVI the_AT interaction_NN1 rather_II21 than_II22 being_VBG optimized_VVN to_TO investigate_VVI their_APPGE potential_NN1 as_II a_AT1 source_NN1 and_CC so_RR yields_NN2 tend_VV0 to_TO be_VBI low_JJ (_( ?100_FO neutrons_NN2 per_II shot_NN1 )_) ._. 
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<s>
This_DD1 expression_NN1 is_VBZ only_RR valid_JJ assuming_JJ isospin_NN1 invariance_NN1 ,_, and_CC much_DA1 work_NN1 has_VHZ been_VBN done_VDN &lsqb;_( see_VV0 Gorringe_NN1 and_CC Fearing_VVG (_( 2003_MC )_) and_CC Bhattacharya_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2012_MC )_) and_CC references_NN2 therein_RR &rsqb;_) to_TO provide_VVI higher-order_JJ corrections_NN2 to_II this_DD1 result_NN1 ._. 
</s>
<s>
In_II fact_NN1 ,_, the_AT authors_NN2 of_IO Ref_NN1 ._. 
</s>
<s>
Controllability_NN1 of_IO quantum_NN1 dynamics_NN is_VBZ of_IO fundamental_JJ as_II31 well_II32 as_II33 practical_JJ importance_NN1 since_CS it_PPH1 determines_VVZ the_AT extent_NN1 to_II which_DDQ a_AT1 quantum_NN1 system_NN1 can_VM be_VBI manipulated_VVN and_CC brought_VVN to_II a_AT1 desired_JJ target_NN1 state_NN1 ._. 
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<s>
Within_II the_AT FCS_NP2 formalism_NN1 ,_, in_II the_AT long_JJ time_NNT1 limit_NN1 ,_, one_PN1 can_VM obtain_VVI the_AT PBp_NP1 contributions_NN2 from_II scaled_JJ cumulant_JJ generating_JJ function_NN1 given_VVN by_II additively_RR separable_JJ into_II a_AT1 dynamic_JJ and_CC a_AT1 geometric_JJ part_NN1 ,_, <equation>_FO ,_, <equation>_FO (_( 4_MC )_) <equation>_FO (_( 5_MC )_) In_II the_AT above_JJ equation_NN1 ,_, Sd()_NP1 and_CC Sg()_NP1 represent_VV0 the_AT dynamic_JJ and_CC geometric_JJ cumulant_JJ generating_JJ functions_NN2 ,_, respectively_RR ._. 
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<s>
No_AT 3d_NNU element_NN1 needs_VVZ to_TO be_VBI involved_VVN ._. 
</s>
<s>
We_PPIS2 round_VV0 off_RP the_AT review_NN1 with_IW a_AT1 summary_NN1 of_IO several_DA2 applications_NN2 in_II diverse_JJ fields_NN2 of_IO science_NN1 ._. 
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<s>
We_PPIS2 will_VM study_VVI what_DDQ effect_VV0 the_AT dynamic_JJ disorder_NN1 has_VHZ on_II the_AT CDR_NP1 and_CC how_RRQ it_PPH1 depends_VVZ on_II the_AT density_NN1 of_IO defects_NN2 and_CC the_AT timescale_NN1 of_IO defect_NN1 turnover_NN1 ._. 
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<s>
In_II this_DD1 section_NN1 ,_, a_AT1 method_NN1 is_VBZ introduced_VVN by_II which_DDQ one_PN1 can_VM convert_VVI the_AT uncertainty_NN1 relations_NN2 in_II the_AT absence_NN1 of_IO quantum_NN1 memory_NN1 to_II those_DD2 in_II the_AT presence_NN1 of_IO it_PPH1 ._. 
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<s>
We_PPIS2 impose_VV0 the_AT following_JJ regularity_NN1 conditions_NN2 on_II <Professional_FO terms>_FO ,_, <Professional_FO terms>_FO ,_, <Professional_FO terms>_FO ,_, We_PPIS2 take_VV0 such_DA a_AT1 local_JJ Gibbs_NP1 state_NN1 as_CSA initial_JJ state_NN1 ._. 
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<s>
This_DD1 phenomenon_NN1 links_VVZ the_AT polarity_NN1 of_IO the_AT domain_NN1 walls_NN2 with_IW their_APPGE direction_NN1 of_IO motion_NN1 ._. 
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<s>
A_AT1 seed_NN1 pulse_NN1 provided_VVN by_II an_AT1 oscillator_NN1 was_VBDZ stretched_VVN amplified_VVN to_II several_DA2 tens_MC2 of_IO joules_NNU2 and_CC compressed_VVN to_II its_APPGE initial_JJ value_NN1 with_IW the_AT grating_JJ pair_NN compressor_NN1 ._. 
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<s>
Cylindrical_JJ microparticles_NN2 interact_VV0 over_RP distances_NN2 comparable_JJ with_IW 10_MC particle_NN1 lengths_NN2 ,_, with_IW excellent_JJ agreement_NN1 with_IW the_AT power_NN1 law_NN1 for_IF interacting_VVG polar_JJ quadrupoles_NN2 in_II the_AT far_JJ field_NN1 ,_, as_CSA presented_VVN in_II Figure_NN1 5d–e_NN1 (_( 63_MC )_) ._. 
</s>
<s>
Finally_RR ,_, the_AT heat_NN1 currents_NN2 are_VBR obtained_VVN in_II Eqs_NN2 ._. 
</s>
<s>
J._NP1 Sotor_NP1 ,_, G._NP1 Sobon_NP1 ,_, W._NP1 Macherzynski_NP1 ,_, and_CC K._NP1 M._NN1 Abramski_NN1 ,_, Laser_NN1 Phys_NN2 ._. 
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<s>
The_AT "_" cap_NN1 "_" of_IO a_AT1 puff_NN1 of_IO turbulence_NN1 ._. 
</s>
<s>
The_AT periods_NN2 of_IO the_AT expansional_JJ and_CC shear-rotational_JJ distortion_NN1 ,_, Texpansion_NN1 and_CC Tshear-rot_NN1 ,_, are_VBR given_VVN by_II the_AT roundtrip_NN1 time_NNT1 of_IO the_AT acoustic_JJ waves_NN2 propagating_VVG between_II the_AT two_MC faces_NN2 of_IO the_AT membrane_NN1 ._. 
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<s>
In_II this_DD1 paper_NN1 ,_, we_PPIS2 propose_VV0 to_TO estimate_VVI the_AT parameter_NN1 spaces_NN2 of_IO target_NN1 systems_NN2 without_IW PCA_NP1 and_CC to_TO plot_VVI the_AT BDs_NP1 in_II the_AT estimated_JJ parameter_NN1 spaces_NN2 by_II using_VVG the_AT PFB_NP1 algorithm_NN1 ._. 
</s>
<s>
This_DD1 is_VBZ a_AT1 hypothetical_JJ situation_NN1 since_CS in_II the_AT actual_JJ protocol_NN1 Alice_NP1 and_CC Bob_NP1 measure_VV0 their_APPGE qubits_NN2 after_II every_AT1 round_JJ ._. 
</s>
<s>
Note_VV0 that_CST Pm_NP1 =_FO 0.1_MC already_RR belongs_VVZ to_II the_AT small_JJ Pm_NP1 regime_NN1 where_CS the_AT subcritical_JJ excitations_NN2 are_VBR very_RG weak_JJ ._. 
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<s>
For_IF F_ZZ1 1_MC1 ,_, geometrical_JJ optics_NN1 is_VBZ a_AT1 good_JJ approximation_NN1 for_IF wave_NN1 optics_NN1 that_CST are_VBR applicable_JJ for_IF imaging_VVG typical_JJ ICF_NN1 implosions_NN2 with_IW soft_JJ x_ZZ1 rays_NN2 ._. 
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<s>
Ideas_NN2 in_II this_DD1 direction_NN1 go_VV0 back_RP at_RR21 least_RR22 to_II the_AT late_JJ 1960s_MC2 when_CS the_AT effect_NN1 of_IO quantum_NN1 noise_NN1 on_II the_AT estimation_NN1 of_IO classicalparameters_NN2 started_VVD to_TO be_VBI studied_VVN in_II a_AT1 systematic_JJ way_NN1 usingappropriate_VV0 mathematical_JJ tools_NN2 (_( Helstrom_NP1 ,_, 1969_MC ;_; Holevo_NP1 ,_, 1982_MC )_) ._. 
</s>
<s>
PEO_NP1 (_( Poly_NN1 (_( ethylene_NN1 oxide_NN1 )_) )_) is_VBZ a_AT1 familiar_JJ polymer_NN1 matrix_NN1 used_VVN in_II SEs_NP2 and_CC extends_VVZ to_II the_AT GPE_NN1 field_NN1 currently_RR ._. 
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<s>
Combustion_NN1 method_NN1 ,_, Magnetic_JJ properties_NN2 ,_, XRD_NP1 ,_, PL_NP1 ,_, SEM_NP1 ._. 
</s>
<s>
Therefore_RR ,_, for_IF the_AT 4e_FO pathways_NN2 and_CC 2e_FO pathways_NN2 ,_, n_ZZ1 =_FO 4_MC and_CC n_ZZ1 =_FO 2_MC ,_, respectively_RR ._. 
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<s>
Second_MD order_NN1 weak_JJ interactions_NN2 also_RR generate_VV0 the_AT crossed_JJ channel_NN1 transition_NN1 <Professional_FO Term>_FO ._. 
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<s>
However_RR ,_, since_CS is_VBZ everywhere_RL nilpotent_JJ ,_, clearly_RR it_PPH1 does_VDZ not_XX correspond_VVI to_II a_AT1 nondegenerate_JJ critical_JJ point_NN1 ._. 
</s>
<s>
In_II this_DD1 paper_NN1 we_PPIS2 show_VV0 that_CST there_EX are_VBR only_RR four_MC classes_NN2 of_IO non-equivalent_JJ non-degenerated_JJ non-skew-symmetric_JJ so(3)_FO so(3)-valued_JJ classical_JJ r_ZZ1 -matrices_NN2 diagonal_JJ in_II the_AT standard_JJ basis_NN1 ._. 
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<s>
Typically_RR ,_, this_DD1 is_VBZ because_CS they_PPHS2 represent_VV0 calculations_NN2 where_RRQ is_VBZ so_RG small_JJ that_CST is_VBZ essentially_RR ill-defined_JJ ,_, or_CC because_CS the_AT low-inclination_JJ component_NN1 of_IO the_AT distant_JJ belt_NN1 is_VBZ so_RR depleted_VVN that_CST the_AT statistical_JJ measures_NN2 and_CC become_VV0 unintelligible_JJ ._. 
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<s>
In_II all_DB cases_NN2 ,_, obtained_VVD states_NN2 are_VBR solely_RR dependent_JJ on_II the_AT signs_NN2 of_IO b_ZZ1 and_CC ,_, being_VBG the_AT eigenstates_NN2 of_IO the_AT chirality_NN1 operator_NN1 ,_, thus_RR confirming_VVG its_APPGE essential_JJ role_NN1 ._. 
</s>
<s>
The_AT important_JJ physics_NN1 that_CST is_VBZ made_VVN apparent_JJ in_II such_DA a_AT1 construction_NN1 is_VBZ at_RR21 least_RR22 three-fold_JJ ._. 
</s>
<s>
The_AT first_MD definition_NN1 corresponds_VVZ to_II an_AT1 effective_JJ nuclear_JJ potential_NN1 due_II21 to_II22 a_AT1 quantum_NN1 nucleus_NN1 a_AT1 which_DDQ is_VBZ approximated_VVN by_II the_AT classical_JJ point_NN1 like_II nuclei_NN2 having_VHG the_AT charge_NN1 Za_NP1 ._. 
</s>
<s>
CMS_NP1 considered_VVD four_MC options_NN2 :_: a_AT1 lead/scintillator_NN1 sampling_NN1 calorimeter_NN1 (_( known_VVN as_II a_AT1 shashlik_NN1 )_) and_CC three_MC fully_RR active_JJ dense_JJ scintillating_JJ materials_NN2 ,_, namely_REX cerium_NN1 fluoride_NN1 ,_, lead_VV0 tungstate_NN1 (_( PbWO4_FO )_) crystals_NN2 ,_, and_CC hafnium_NN1 fluoride_NN1 glass_NN1 ._. 
</s>
<s>
Extinction_NN1 coefficient_NN1 is_VBZ related_VVN with_IW total_JJ optical_JJ losses_NN2 caused_VVN by_II both_RR absorption_NN1 and_CC scattering_VVG ._. 
</s>
<s>
The_AT formation_NN1 of_IO NaF_NN1 as_II part_NN1 of_IO ionic_JJ structures_NN2 clearly_RR is_VBZ critical_JJ ._. 
</s>
<s>
Then_RT ,_, we_PPIS2 evaluated_VVD the_AT fast_JJ 3He_FO ion_NN1 slowing-down_NN1 distributions_NN2 with_IW the_AT OFMC_NN1 code_NN1 using_VVG the_AT birth_NN1 distributions_NN2 and_CC compared_VVD the_AT distributions_NN2 between_II the_AT cases_NN2 when_RRQ the_AT ICE(3He)_FO is_VBZ observed_VVN and_CC not_XX ._. 
</s>
<s>
J.B.D._NP1 is_VBZ indebted_JJ to_II the_AT Deutscher_NP1 Akademischer_NP1 Austauschdienst_NP1 (_( DAAD_NP1 )_) for_IF a_AT1 research_NN1 fellowship_NN1 and_CC Hartwick_NP1 College_NN1 for_IF a_AT1 Faculty_NN1 Travel_NN1 Grant_NP1 ._. 
</s>
<s>
The_AT cold-ion_JJ version_NN1 of_IO the_AT drift-reduced_JJ Braginskii_NN1 '_NULL s_ZZ1 set_NN1 of_IO equations_NN2 used_VVN for_IF this_DD1 work_NN1 can_VM be_VBI written_VVN as_CSA ._. 
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<s>
The_AT most_RGT striking_JJ result_NN1 is_VBZ the_AT surprisingly_RR different_JJ ion_NN1 signal_NN1 from_II atom_NN1 and_CC cluster_VV0 beams_NN2 ._. 
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<s>
The_AT free_JJ boxes_NN2 in_II this_DD1 theory_NN1 are_VBR those_DD2 satisfying_JJ Eq_NN1 ._. 
</s>
<s>
(_( 37_MC )_) ,_, and_CC the_AT allowed_JJ conversions_NN2 are_VBR built_VVN using_VVG three_MC ingredients_NN2 :_: pre-LOSR_JJ ,_, post-LOSR_JJ ,_, and_CC local_JJ side_NN1 channels_NN2 ._. 
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<s>
By_II comparing_VVG the_AT left_JJ and_CC right-hand_JJ sides_NN2 of_IO Eq_NN1 ._. 
</s>
<s>
(_( 11_MC )_) and_CC noting_VVG that_CST the_AT logarithm_NN1 is_VBZ a_AT1 monotonic_JJ function_NN1 ,_, we_PPIS2 see_VV0 that_DD1 Eq_NN1 ._. 
</s>
<s>
(_( 11_MC )_) implies_VVZ (_( 1_MC1 )_) ,_, and_CC hence_RR so_RR does_VDZ (_( 4_MC )_) ._. 
</s>
<s>
We_PPIS2 have_VH0 then_RT applied_VVN this_DD1 general_JJ formalism_NN1 to_II random_JJ cascades_NN2 on_II trees_NN2 ,_, where_CS particles_NN2 are_VBR injected_VVN at_II the_AT root_NN1 via_II a_AT1 '_NULL source_NN1 reservoir_NN1 '_NULL ,_, while_CS the_AT particles_NN2 are_VBR removed_VVN at_II the_AT leaves_NN2 of_IO the_AT last_MD generation_NN1 of_IO the_AT tree_NN1 via_II '_NULL sink_NN1 reservoirs_NN2 '_NULL ,_, again_RT both_RR for_IF discrete-time_JJ dynamics_NN and_CC for_IF continuous-time_JJ jump_NN1 dynamics_NN ._. 
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<s>
The_AT Hilbert_NP1 space_NN1 is_VBZ formed_VVN by_II the_AT L-functions_NN2 dened_VVD on_II L_ZZ1 ._. 
</s>
<s>
This_DD1 symmetry_NN1 leads_VVZ to_II a_AT1 Lagrangian_NN1 of_IO the_AT form_NN1 <equation>_FO where_RRQ ,_, as_CSA above_RL ,_, Zr_NP1 is_VBZ the_AT new_JJ gauge_NN1 boson_NN1 ,_, gZr_NNU is_VBZ the_AT new_JJ gauge_NN1 coupling_NN1 ,_, and_CC <equation>_FO gives_VVZ the_AT <equation>_FO charges_NN2 ._. 
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<s>
Tetrahedrons_NN2 in_II the_AT bounding_JJ mesh_NN1 connect_VV0 to_II the_AT convex_JJ hull_NN1 of_IO the_AT simulation_NN1 domain_NN1 ._. 
</s>
<s>
Most_DAT first-principles_NN2 calculations_NN2 of_IO phonon_NN1 dispersion_NN1 relations_NN2 in_II metals_NN2 have_VH0 been_VBN carried_VVN out_RP using_VVG this_DD1 strategy_NN1 ._. 
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<s>
If_CS (_( X_ZZ1 ,_, )_) Is_VBZ A_AT1 Torus_NN1 With_IW A_AT1 Slit_NN1 ,_, Then_RT The_AT Accumulation_NN1 Point_NN1 Of_IO The_AT Set_NN1 Of_IO Cylinder_NN1 Directions_NN2 Of_IO Cylinders_NN2 Disjoint_JJ From_II The_AT Slit_NN1 Must_VM Lie_VV0 Exactly_RR In_II The_AT Direction_NN1 Of_IO The_AT Slit_NN1 ._. 
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<s>
Implicit_JJ in_II this_DD1 advance_NN1 is_VBZ a_AT1 casting_NN1 off_II21 of_II22 the_AT twin_NN1 chains_NN2 of_IO classical_JJ thermodynamics_NN1 ._. 
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<s>
Now_CS21 that_CS22 the_AT vast_JJ array_NN1 of_IO possible_JJ distributed_JJ sensing_NN1 system_NN1 configurations_NN2 that_CST have_VH0 been_VBN studied_VVN are_VBR summarized_VVN ,_, the_AT applications_NN2 of_IO these_DD2 systems_NN2 to_II real-world_JJ measurement_NN1 problems_NN2 will_VM be_VBI reviewed_VVN ._. 
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<s>
Over_II these_DD2 short_JJ distances_NN2 ,_, pulse_NN1 broadening_NN1 effects_NN2 are_VBR minimal_JJ ._. 
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<s>
Parameter_NN1 modulation_NN1 also_RR provided_VVN a_AT1 pathway_NN1 to_TO increase_VVI the_AT complexity_NN1 of_IO the_AT optical_JJ chaotic_JJ carriers_NN2 ._. 
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<s>
The_AT newly_RR introduced_VVN wireless_NN1 video_NN1 capsule_NN1 endoscopes_NN2 with_IW camera_NN1 sensor_NN1 ,_, a_AT1 light_JJ source_NN1 ,_, a_AT1 battery_NN1 ,_, and_CC a_AT1 wireless_NN1 radio_NN1 frequency_NN1 transmitter_NN1 can_VM be_VBI considered_VVN alternative_NN1 to_II conventional_JJ light_JJ delivery_NN1 carriers_NN2 for_IF diagnosis_NN1 and_CC therapy_NN1 of_IO deep_JJ seated_JJ tumors_NN2 ._. 
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<s>
We_PPIS2 show_VV0 that_CST transitions_NN2 to_II the_AT self-excitatory_JJ state_NN1 can_VM lead_VVI to_II complex_JJ oscillation_NN1 modes_NN2 (_( COM_NN1 )_) ._. 
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<s>
The_AT accuracy_NN1 of_IO these_DD2 theoretical_JJ predictions_NN2 is_VBZ enhanced_VVN by_II scanning_VVG a_AT1 realistic_JJ spread_NN1 in_II secondary_JJ emission_NN1 energies_NN2 ._. 
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<s>
For_IF illumination_NN1 with_IW different_JJ types_NN2 of_IO source_NN1 fields_NN2 ,_, e.g._REX ,_, dipole_NN1 sources_NN2 ,_, also_RR the_AT remaining_JJ eigen_NN1 modes_NN2 of_IO the_AT rich_JJ spectrum_NN1 can_VM be_VBI excited_VVN ._. 
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<s>
The_AT range_NN1 of_IO its_APPGE applications_NN2 has_VHZ been_VBN considerable_JJ starting_NN1 from_II the_AT eV_NN1 ,_, the_AT visible_JJ photon_NN1 energy_NN1 ,_, and_CC extending_VVG to_II the_AT GeV_NP1 ,_, possibly_RR the_AT TeV_NP1 ._. 
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<s>
For_REX21 example_REX22 ,_, if_CS the_AT individual_JJ rods_NN2 of_IO the_AT cluster_NN1 are_VBR oriented_JJ parallel_NN1 to_II the_AT force_NN1 ,_, the_AT cluster_NN1 is_VBZ easily_RR destroyed_VVN due_II21 to_II22 velocity_NN1 fluctuations_NN2 ._. 
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<s>
On_II the_AT other_JJ hand_NN1 ,_, case_NN1 (_( d_ZZ1 )_) has_VHZ the_AT optimum_JJ pre-plasma_JJ condition_NN1 at_II both_DB2 sides_NN2 for_IF the_AT foot-pulse_JJ intensity_NN1 of_IO 1012_MC Wcm2_FO ._. 
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<s>
Further_JJR developments_NN2 are_VBR required_VVN to_TO properly_RR account_VVI for_IF the_AT impact_NN1 of_IO the_AT initial_JJ non-thermal_JJ phonon_NN1 distribution_NN1 and_CC mode_NN1 specific_JJ phonon-phonon_JJ interactions_NN2 on_II ultrafast_NN1 transport_NN1 processes_NN2 and_CC the_AT transient_JJ local_JJ lattice_NN1 stress_NN1 ,_, particularly_RR relevant_JJ for_IF the_AT nanoscale_NN1 geometries_NN2 considered_VVN here_RL ._. 
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<s>
The_AT dependence_NN1 of_IO the_AT beam_NN1 fraction_NN1 deflected_VVD in_II the_AT DSB_NP1 regime_NN1 on_II the_AT crystal_NN1 orientation_NN1 was_VBDZ obtained_VVN ._. 
</s>
<s>
Observe_VV0 also_RR that_CST the_AT notion_NN1 of_IO strict_JJ YM-convexity_NN1 depends_VVZ on_II the_AT adjoint_JJ orbit_NN1 O_ZZ1 that_CST we_PPIS2 have_VH0 fixed_VVN ._. 
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<s>
Free-electron_JJ lasers_NN2 produce_VV0 extremely_RR brief_JJ ,_, coherent_JJ ,_, and_CC brilliant_JJ laser-like_JJ photon_NN1 pulses_NN2 that_CST allow_VV0 to_II image_NN1 matter_NN1 at_II atomic_JJ resolution_NN1 and_CC at_II timescales_NN2 faster_RRR than_CSN the_AT characteristic_JJ atomic_JJ motions_NN2 ._. 
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<s>
However_RR ,_, mY_APPGE continues_NN2 to_TO increase_VVI until_CS pY_JJ ,_, so_CS21 that_CS22 A_ZZ1 ?_? 1_MC1 ?_? 
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<s>
This_DD1 paper_NN1 is_VBZ organised_VVN as_CSA follows_VVZ :_: Leveraging_VVG previous_JJ derivations_NN2 by_II Myra_NP1 et_RA21 al._RA22 ,_, 37_MC we_PPIS2 provide_VV0 the_AT analytical_JJ scaling_NN1 to_TO estimate_VVI the_AT velocity_NN1 of_IO blobs_NN2 in_II diverted_JJ configurations_NN2 in_II Sec.II_NP1 ._. 
</s>
<s>
Recently_RR a_AT1 breakthrough_NN1 in_II the_AT description_NN1 of_IO the_AT Hoyle_NP1 state_NN1 was_VBDZ achieved_VVN by_II two_MC groups_NN2 (_( Epelbaum_NP1 et_RA21 al._RA22 ,_, 2012_MC ;_; Carlson_NP1 et_RA21 al._RA22 ,_, 2015_MC )_) using_VVG Monte_NP1 Carlo_NP1 techniques_NN2 ._. 
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<s>
Another_DD1 interesting_JJ property_NN1 of_IO networks_NN2 is_VBZ that_CST there_EX are_VBR also_RR intermediate_JJ scales_NN2 that_CST might_VM play_VVI a_AT1 key_JJ role_NN1 for_IF the_AT functioning_NN1 of_IO the_AT system_NN1 at_II the_AT global_JJ level_NN1 ._. 
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<s>
The_AT remaining_JJ slow_JJ logarithmic_JJ rise_NN1 of_IO the_AT cross_NN1 section_NN1 can_VM be_VBI attributed_VVN to_II multiple_JJ Pomeron_NN1 poles_NN2 &lsqb;_( 87_MC &rsqb;_) ._. 
</s>
<s>
Theoretical_JJ analysis_NN1 of_IO the_AT generalization_NN1 of_IO deep_JJ learning_NN1 is_VBZ difficult_JJ because_CS it_PPH1 involves_VVZ a_AT1 complicated_JJ interaction_NN1 between_II the_AT specifics_NN2 of_IO the_AT model_NN1 <Professional_FO Term>_FO ,_, the_AT optimization_NN1 algorithms_NN2 ,_, the_AT loss_NN1 function_NN1 ,_, regularization_NN1 techniques_NN2 ,_, and_CC the_AT specifics_NN2 of_IO the_AT finite_JJ training_NN1 samples_NN2 and_CC the_AT true_JJ underlying_JJ distribution_NN1 <Professional_FO Term>_FO ._. 
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<s>
This_DD1 appeals_VVZ for_IF a_AT1 brief_JJ discussion_NN1 of_IO travel_NN1 in_II time_NNT1 on_II the_AT exploration_NN1 of_IO 2D_NNU ._. 
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<s>
In_II this_DD1 section_NN1 ,_, we_PPIS2 consider_VV0 whether_CSW the_AT involvement_NN1 of_IO water_NN1 molecules_NN2 in_II assisting_VVG N–H_NN1 bond_NN1 formation_NN1 lowers_VVZ elementary_JJ reduction_NN1 barriers_NN2 ._. 
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<s>
The_AT first_MD choice_NN1 is_VBZ the_AT natural_JJ one_PN1 for_IF the_AT numerical_JJ scheme_NN1 ._. 
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<s>
If_CS m_ZZ1 is_VBZ odd_JJ ,_, we_PPIS2 can_VM choose_VVI the_AT complex_JJ structure_NN1 to_TO be_VBI a_AT1 product_NN1 on_II <Equation>_FO ._. 
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<s>
Neither_RR measuring_VVG a_AT1 single_JJ quadrature_NN1 ,_, nor_CC making_VVG a_AT1 homodyne_JJ measurement_NN1 are_VBR sucient_JJ for_IF this_DD1 purpose_NN1 &lsqb;_( 137_MC &rsqb;_) ._. 
</s>
<s>
The_AT decomposition_NN1 of_IO the_AT system_NN1 into_II a_AT1 subsystem_NN1 A_ZZ1 shown_VVN in_II blue_JJ (_( light_JJ gray_JJ )_) and_CC its_APPGE complement_NN1 B._NP1 (_( a_ZZ1 )_) Two_MC spin_NN1 systems_NN2 ._. 
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<s>
We_PPIS2 thank_VV0 Daniel_NP1 Twitchen_NP1 for_IF insights_NN2 into_II literature_NN1 variation_NN1 in_II irradiation_NN1 outcomes_NN2 ._. 
</s>
<s>
Such_DA sensors_NN2 ,_, which_DDQ operate_VV0 in_II the_AT visible_JJ ,_, can_VM be_VBI used_VVN for_IF naked_JJ eye_NN1 measurement_NN1 of_IO stress_NN1 and_CC strain_NN1 ._. 
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<s>
In_RR21 addition_RR22 ,_, Bagarinao_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
have_VH0 proposed_VVN to_II reconstructBDs_NN2 using_VVG autoregressive_JJ models_NN2 as_CSA tme-series_JJ predictors_NN2 ,_, based_VVN on_II the_AT PBR_NP1 algorithm_NN1 &lsqb;_( 7,8_MC &rsqb;_) ._. 
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<s>
Repeatedly_RR construct_VV0 and_CC measure_VV0 the_AT state_NN1 <Professional_FO Term>_FO to_TO get_VVI a_RR21 bit_RR22 string_VV0 x_ZZ1 ,_, and_CC evaluate_VV0 c(x)_MC ._. 
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<s>
Jet_NN1 grooming_VVG techniques_NN2 are_VBR substructure_NN1 tools_NN2 extensively_RR used_VVN in_II the_AT context_NN1 of_IO boosted_JJ fat_JJ jets_NN2 at_II the_AT LHC_NP1 ,_, and_CC we_PPIS2 have_VH0 briefly_RR studied_VVN this_DD1 in_II the_AT second_MD part_NN1 of_IO this_DD1 document_NN1 ._. 
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The_AT resulting_JJ dynamical_JJ equation_NN1 for_IF the_AT TKC_NP1 resonator_NN1 modes_NN2 is_VBZ <EQUATION>_FO ._. 
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<s>
The_AT most_RGT striking_JJ feature_NN1 in_II Fig._NN1 56_MC is_VBZ a_AT1 step_NN1 or_CC local_JJ maximum_NN1 at_II n_ZZ1 =_FO 32_MC for_IF helium_NN1 ,_, hydrogen_NN1 (_( or_CC deuterium_NN1 )_) ,_, CH4_FO ,_, C2H4_FO ,_, and_CC N2_FO ._. 
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<s>
We_PPIS2 derive_VV0 a_AT1 linear_JJ equation_NN1 that_CST contains_VVZ both_RR coverage_NN1 dependence_NN1 and_CC Stark_NP1 effect_NN1 and_CC allows_VVZ us_PPIO2 to_TO extract_VVI numerical_JJ values_NN2 to_TO compare_VVI with_IW the_AT experimental_JJ data_NN ._. 
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<s>
In_BCL21 order_BCL22 to_TO prove_VVI this_DD1 theorem_NN1 ,_, we_PPIS2 first_MD establish_VV0 (_( 5.43_MC )_) ,_, (_( 5.44_MC )_) ,_, and_CC (_( 5.45_MC )_) for_IF a_AT1 subsequential_JJ limit_NN1 of_IO the_AT sequence_NN1 <Equation>_FO ,_, then_RT prove_VV0 the_AT above_JJ sequence_NN1 has_VHZ a_AT1 unique_JJ subsequential_JJ limit_NN1 ,_, and_CC finally_RR justify_VV0 (_( 5.46_MC )_) and_CC (_( 5.47_MC )_) ._. 
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<s>
According_II21 to_II22 this_DD1 definition_NN1 ,_, orbiting_VVG resonances_NN2 are_VBR much_RR more_RGR diffuse_JJ than_CSN shape_NN1 resonances_NN2 ._. 
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The_AT resulting_JJ image_NN1 shows_VVZ only_RR the_AT wavelength_NN1 and_CC thickness_NN1 dependent_JJ absorption_NN1 of_IO the_AT object_NN1 ._. 
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<s>
Clusters_NN2 up_II21 to_II22 approximately_RR 100_MC nm_FU appear_VV0 mostly_RR spherical_JJ with_IW a_AT1 significant_JJ fraction_NN1 of_IO twinned_JJ clusters_NN2 ._. 
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<s>
Almost_RR surely_RR this_DD1 event_NN1 will_VM occur_VVI for_IF some_DD k_ZZ1 ._. 
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<s>
Since_CS Nh_NP1 (_( X_ZZ1 (_( n_ZZ1 ,_, 1_MC1 )_) )_) is_VBZ monotone_NN1 increasing_VVG in_II n_ZZ1 ,_, almost_RR surely_RR <Professional_FO Term>_FO ._. 
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Figure_NN1 2(a)_FO shows_VVZ a_AT1 typical_JJ spatial_JJ profile_NN1 of_IO the_AT electron_NN1 beam_NN1 recorded_VVN for_IF bare_JJ mylar_JJ foil_NN1 ._. 
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<s>
Using_VVG equation_NN1 (_( 11_MC )_) ,_, the_AT expression_NN1 (_( 10_MC )_) becomes_VVZ <Equation>_FO The_AT factors_NN2 (_( <Equation>_FO )_) can_VM be_VBI expanded_VVN in_RP and_CC give_VV0 typical_JJ finite_JJ contributions_NN2 ln(<Equation>)_FO ._. 
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<s>
Specifically_RR ,_, we_PPIS2 say_VV0 that_CST a_AT1 pair_NN of_IO distributions_NN2 ep_VV0 ;_; qT_NNU is_VBZ more_RGR distinguishable_JJ than_CSN another_DD1 pair_NN of_IO distributions_NN2 ep0_FO ;_; q0T_FO if_CS there_EX exists_VVZ a_AT1 column_NN1 stochastic_JJ matrix_NN1 M_ZZ1 such_CS21 that_CS22 <Equation>_FO ._. 
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<s>
At_II variance_NN1 with_IW the_AT Migdal-Eliashberg_NP1 theory_NN1 ,_, the_AT gap_NN1 function_NN1 in_II the_AT density-functional_JJ theory_NN1 for_IF superconductors_NN2 does_VDZ not_XX carry_VVI an_AT1 explicit_JJ frequency_NN1 dependence_NN1 ._. 
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<s>
Before_II cycling_NN1 ,_, two-dimensional_JJ sheet-like_JJ morphology_NN1 can_VM be_VBI clearly_RR observed_VVN in_II the_AT electrodes_NN2 ;_; after_II cycling_VVG ,_, there_EX appeared_VVD many_DA2 cracks_NN2 on_II the_AT surface_NN1 of_IO the_AT particles_NN2 ._. 
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<s>
Next_MD ,_, we_PPIS2 observe_VV0 that_CST since_CS f_ZZ1 is_VBZ -measurable_JJ ,_, and_CC is_VBZ a_AT1 measure-preserving_JJ transformation_NN1 of_IO the_AT probability_NN1 space_NN1 (_( S2_FO ,_, )_) ,_, it_PPH1 is_VBZ clear_JJ that_CST f_ZZ1 is_VBZ also_RR -measurable_JJ ,_, and_CC is_VBZ a_AT1 measure-preserving_JJ transformation_NN1 of_IO the_AT probability_NN1 space_NN1 (_( S2_FO ,_, )_) ._. 
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Ribera_NP1 et_RA21 al_RA22 ._. 
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<s>
&lsqb;_( 363_MC &rsqb;_) proposed_VVD an_AT1 explanation_NN1 of_IO urban_JJ scaling_NN1 '_NULL s_ZZ1 based_VVN on_II the_AT interactions_NN2 between_II individuals_NN2 and_CC the_AT fractal_JJ dimension_NN1 of_IO cities_NN2 ._. 
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In_II31 terms_II32 of_II33 easy_JJ observational_JJ access_NN1 ,_, Eu_NP1 has_VHZ a_AT1 prominent_JJ role_NN1 ,_, with_IW its_APPGE two_MC main_JJ stable_JJ isotopes_NN2 151Eu_FO and_CC 153Eu_FO ._. 
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These_DD2 two_MC effects_NN2 tend_VV0 to_TO cancel_VVI each_PPX221 other_PPX222 ._. 
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<s>
One_MC1 of_IO the_AT few_DA2 physical_JJ properties_NN2 of_IO cuprates_NN2 found_VVD to_TO exhibit_VVI a_AT1 sharp_JJ anomaly_NN1 at_II Hc2_FO is_VBZ the_AT thermal_JJ conductivity_NN1 ._. 
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Note_VV0 also_RR that_CST detectors_NN2 may_VM effectively_RR introduce_VVI low-pt_JJ cutoffs_NN2 of_IO their_APPGE own_DA ._. 
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<s>
A_AT1 Lie_NN1 Derivative_NN1 Of_IO The_AT Euclidean_JJ Background_NN1 Metric_JJ (_( Arising_VVG From_II A_AT1 Well-Known_JJ Obstruction_NN1 Explained_VVN In_II The_AT Proof_NN1 Of_IO Lemma_NN1 2.8_MC )_) ._. 
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<s>
Once_RR this_DD1 path_NN1 reaches_VVZ fissionable_JJ nuclei_NN2 the_AT resulting_JJ fission_NN1 products_NN2 continue_VV0 capturing_VVG neutrons_NN2 ,_, potentially_RR repeating_VVG the_AT cycle_NN1 a_AT1 number_NN1 of_IO times_NNT2 &lsqb;_( 69,70_MC &rsqb;_) ._. 
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<s>
The_AT trajectory_NN1 of_IO a_AT1 particle_NN1 being_VBG reflected_VVN with_IW a_AT1 turning_JJ point_NN1 in_II the_AT fourth_MD channel_NN1 is_VBZ shown_VVN ._. 
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<s>
In_II contrast_NN1 ,_, for_IF the_AT TRAPPIST-1_MC1 system_NN1 ,_, it_PPH1 has_VHZ been_VBN found_VVN that_CST the_AT innermost_JJ planet_NN1 (_( with_IW Ps_NP1 1_MC1 atm_NN1 assumed_VVD throughout_RL )_) may_VM lose_VVI its_APPGE atmosphere_NN1 over_II atime_NNT1 scale_NN1 of_IO O108_FO yr_NNU ,_, while_CS the_AT duration_NN1 of_IO atmospheric_JJ retention_NN1 for_IF the_AT outermost_JJ planet_NN1 is_VBZ O1010_FO yr_NNU (_( Dong_NP1 ,_, Jin_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) ._. 
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<s>
Extrinsic_JJ iSGE_NN1 mechanisms_NN2 related_VVD to_TO spin_VVI scattering_NN1 were_VBDR also_RR theoretically_RR shown_VVN to_TO generate_VVI a_AT1 dampinglike_JJ component_NN1 of_IO the_AT SOT_NN1 ._. 
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<s>
Responding_VVG to_II both_DB2 the_AT observations_NN2 of_IO anomalous_JJ phenomena_NN2 and_CC the_AT theoretical_JJ model_NN1 '_NULL to_TO describe_VVI them_PPHO2 ,_, the_AT theoretical_JJ notions_NN2 were_VBDR revisited_VVN and_CC advanced_VVN by_II taking_VVG proper_JJ account_NN1 of_IO the_AT complicated_JJ experimental_JJ geometry_NN1 ._. 
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<s>
Pawliszeska_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
reported_VVN a_AT1 290_MC MHz_NNU (_( 10th_MD harmonic_JJ )_) repetition_NN1 rate_NN1 with_IW 1.3_MC ps_NNU2 using_VVG BP_NP1 as_II an_AT1 SA_NP1 in_II mode-locked_JJ fiber_NN1 lasers_NN2 at_II a_AT1 2094_MC nm_FU central_JJ wavelength_NN1 ._. 
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<s>
We_PPIS2 have_VH0 already_RR shown_VVN above_RL that_CST any_DD radial_JJ Gibbs_NP1 measure_NN1 for_IF f_ZZ1 ,_, d_ZZ1 ,_, and_CC must_VM be_VBI a_AT1 Gibbs_NP1 measure_NN1 for_IF f_ZZ1 ,_, C_ZZ1 ,_, and_CC ._. 
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<s>
It_PPH1 is_VBZ possible_JJ to_TO extend_VVI the_AT method_NN1 to_II jet_NN1 constituents_NN2 ,_, using_VVG the_AT fact_NN1 that_CST Sudakov_NP1 factors_NN2 are_VBR nothing_PN1 but_II no-splitting_JJ probabilities_NN2 ._. 
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<s>
The_AT ideas_NN2 of_IO device-independent_JJ quantum_NN1 random_JJ number_NN1 generators_NN2 can_VM be_VBI extended_VVN to_II an_AT1 even_RR more_RGR general_JJ model_NN1 where_CS quantum_NN1 mechanics_NN2 needs_VVZ not_XX to_TO be_VBI true_JJ ,_, following_VVG the_AT example_NN1 of_IO the_AT device-independent_JJ quantum_NN1 key_JJ distribution_NN1 protocols_NN2 (_( Barrett_NP1 ,_, Hardy_NP1 ,_, and_CC Kent_NP1 ,_, 2005_MC ;_; Barrett_NP1 ,_, Colbeck_NP1 ,_, and_CC Kent_NP1 ,_, 2012_MC )_) that_CST only_RR require_VV0 the_AT no-signaling_JJ principle_NN1 to_TO hold_VVI ._. 
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Other_JJ unconventional_JJ memory_NN1 and_CC logic_NN1 architectures_NN2 can_VM be_VBI envisaged_VVN based_VVN on_II purely_RR planar_JJ structures_NN2 ._. 
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<s>
The_AT different_JJ methods_NN2 for_IF this_DD1 summation_NN1 were_VBDR used_VVN ,_, apart_II21 from_II22 the_AT direct_JJ summation_NN1 over_II discrete_JJ spectrum_NN1 and_CC integration_NN1 over_II the_AT continuous_JJ spectrum_NN1 ,_, as_CSA in_II &lsqb;_( 23,24_MC &rsqb;_) ._. 
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<s>
We_PPIS2 found_VVD that_CST the_AT ignition_NN1 beam_VV0 that_CST initiates_VVZ the_AT ignition_NN1 and_CC burn_VV0 wave_NN1 is_VBZ in_II the_AT range_NN1 of_IO 250–400_MCMC kJ_NNU at_II a_AT1 pulse_NN1 duration_NN1 of_IO 0.2_MC ns_FO ._. 
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<s>
The_AT light_JJ signal_NN1 is_VBZ read_VVN by_II photo_NN1 detectors_NN2 optically_RR coupled_VVN to_II the_AT bar_NN1 lateral_JJ edges_NN2 ._. 
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This_DD1 will_VM then_RT allow_VVI the_AT players_NN2 to_TO share_VVI a_AT1 secure_JJ key_NN1 among_II the_AT players_NN2 ._. 
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<s>
As_CSA mentioned_VVN above_RL ,_, for_IF localization_NN1 of_IO the_AT electron_NN1 bubble_NN1 at_II the_AT dopant_NN1 the_AT electron_NN1 affinity_NN1 of_IO the_AT dopant_NN1 must_VM be_VBI positive_JJ ._. 
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<s>
It_PPH1 was_VBDZ based_VVN on_II a_AT1 dual-OEO_JJ architecture_NN1 where_CS two_MC pump_NN1 signals_NN2 are_VBR multiplexed_VVN in_II the_AT same_DA feedback_NN1 loop_NN1 ,_, while_CS two_MC electric_JJ branches_NN2 process_VV0 the_AT baseband_NN1 signal_NN1 and_CC perform_VV0 the_AT distance-to-frequency_JJ conversion_NN1 ._. 
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<s>
Thus_RR ,_, in_II this_DD1 review_NN1 ,_, we_PPIS2 focus_VV0 on_II the_AT bene_NN1 ?_? cial_NN1 impact_NN1 of_IO porcine-derived_JJ tissue_NN1 specific_JJ ECM_NP1 (_( pECM_NN1 )_) on_II the_AT expansion_NN1 and_CC retention_NN1 of_IO the_AT regenerative_JJ potential_NN1 of_IO human_JJ MPCs_NP1 in_RR21 vitro_RR22 ._. 
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<s>
Results_NN2 on_II the_AT computed_JJ DC_NN1 values_NN2 for_IF the_AT Ag(100)_FO surface_NN1 are_VBR then_RT presented_VVN in_II Sec_NNU ._. 
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<s>
III_MC ._. 
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<s>
In_RR21 particular_RR22 ,_, the_AT various_JJ electrolyte_NN1 models_NN2 are_VBR illustratively_RR compared_VVN under_II vacuum_NN1 conditions_NN2 in_II Sec_NNU ._. 
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III_MC A_ZZ1 ,_, while_CS their_APPGE performance_NN1 is_VBZ better_RRR validated_VVN in_II Sec_NNU ._. 
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III_MC B_ZZ1 by_II comparing_VVG the_AT results_NN2 to_II experimental_JJ data_NN ._. 
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<s>
However_RR ,_, the_AT main_JJ advantages_NN2 of_IO the_AT in-situ_JJ TEM-SIMS_NP1 technique_NN1 are_VBR the_AT possibility_NN1 to_TO do_VDI atomic_JJ resolution_NN1 imaging_NN1 ,_, nanoscale_NN1 electron_NN1 diffraction_NN1 ,_, and_CC complementary_JJ chemical_NN1 and_CC even_RR electronic-structure_JJ analysis_NN1 using_VVG EELS_NN2 ._. 
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<s>
Since_CS for_IF the_AT usual_JJ weak_JJ collisionality_NN1 case_NN1 the_AT new_JJ term_NN1 will_VM only_RR be_VBI noticeable_JJ for_IF times_NNT2 much_RR longer_RRR than_CSN the_AT initial_JJ transient_JJ time_NNT1 ,_, it_PPH1 may_VM be_VBI appropriate_JJ to_TO neglect_VVI collisions_NN2 until_CS a_AT1 reasonable_JJ steady_JJ state_NN1 is_VBZ reached_VVN and_CC only_RR then_RT to_TO turn_VVI collisions_NN2 on_II and_CC allow_VVI the_AT gradual_JJ relaxation_NN1 to_II the_AT final_JJ steady_JJ state_NN1 ._. 
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<s>
If_CS the_AT same_DA argument_NN1 can_VM be_VBI applied_VVN to_II superclusters_NN2 or_CC filaments_NN2 ,_, which_DDQ were_VBDR not_XX known_VVN in_II the_AT 1970s_MC2 ,_, the_AT mass_JJ bound_NN1 may_VM be_VBI raised_VVN by_II a_AT1 few_DA2 orders_NN2 of_IO magnitude_NN1 ._. 
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<s>
When_CS modeling_VVG electrocatalytic_JJ systems_NN2 ,_, the_AT potential_NN1 is_VBZ often_RR only_RR taken_VVN into_II account_NN1 in_II the_AT cases_NN2 of_IO faradic_JJ reactions_NN2 ._. 
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<s>
Here_RL for_IF general_JJ Rashba_NP1 and_CC Dresselhaus_NP1 parameters_NN2 ,_, the_AT spin_NN1 is_VBZ rapidly_RR randomized_VVN via_II the_AT Dyakonov-Perel_NP1 spin_NN1 relaxation_NN1 mechanism_NN1 (_( Dyakonov_NP1 and_CC Perel_NP1 ,_, 1972_MC )_) ._. 
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<s>
Lemma_NN1 1.5_MC &lsqb;_( 53_MC ,_, Lemma_NN1 6.8_MC &;_NULL Proposition_NN1 6.10_MC &rsqb;_) ._. 
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<s>
Quantum_NN1 Hall_NN1 ferromagnets_NN2 (_( QHFMs_NP1 )_) furnish_VV0 one_MC1 such_DA example_NN1 ,_, where_CS the_AT formation_NN1 of_IO a_AT1 topological_JJ QH_NP1 state_NN1 is_VBZ driven_VVN by_II interaction-induced_JJ spontaneous_JJ breaking_NN1 of_IO a_AT1 globalsymmetry_NN1 ,_, such_II21 as_II22 that_DD1 associated_VVN with_IW electron_NN1 spin_NN1 ,_, or_CC valley_NN1 or_CC layer_NN1 pseudospin_NN1 &lsqb;_( 1_MC1 &rsqb;_) ._. 
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The_AT neutron_NN1 pluse_NN1 length_NN1 is_VBZ less_DAR than_CSN 10_MC ns_FO ._. 
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Thus_RR ,_, it_PPH1 is_VBZ interesting_JJ to_TO design_VVI multiparty_JJ QSDC_NP1 protocols_NN2 against_II collective_JJ noise_NN1 ._. 
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<s>
Their_APPGE dengue_NN1 early_JJ warning_NN1 system_NN1 combining_VVG DBSI_NN2 with_IW traditional_JJ surveillance_NN1 and_CC meteorological_JJ data_NN can_VM improve_VVI the_AT capability_NN1 of_IO dengue_NN1 case_NN1 prediction_NN1 ._. 
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<s>
The_AT direction_NN1 of_IO the_AT electric_JJ field_NN1 is_VBZ represented_VVN by_II E._NP1 (_( d_ZZ1 )_) Coefficients_NN2 of_IO the_AT cos_CS θ_NULL mE_PPIO1 and_CC sin_VV0 θ_NULL mE_PPIO1 fits_VVZ to_II the_AT angle_NN1 dependence_NN1 of_IO the_AT out-of-plane_JJ SOT_NN1 field_NN1 for_IF the_AT sample_NN1 set_NN1 ._. 
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<s>
Structurally_RR ,_, graphene_NN1 can_VM be_VBI visualized_VVN as_II a_AT1 monoatomic_JJ layer_NN1 of_IO sp_NNU carbon_NN1 atoms_NN2 arranged_VVN on_II a_AT1 honey_NN1 comb_NN1 lattice_NN1 ._. 
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<s>
This_DD1 paper_NN1 investigates_VVZ the_AT OTOC_NN1 in_II the_AT quantum_NN1 bakers_NN2 map_VV0 which_DDQ is_VBZ the_AT quantum_NN1 version_NN1 of_IO a_AT1 simple_JJ and_CC exactly_RR solvable_JJ model_NN1 of_IO deterministic_JJ chaos_NN1 that_CST caricatures_NN2 the_AT action_NN1 of_IO kneading_VVG dough_NN1 ._. 
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Eu_NP1 abundance_NN1 ratios_NN2 of_IO stars_NN2 in_II dwarf_NN1 galaxies_NN2 as_II a_AT1 function_NN1 of_IO metallicity_NN1 (_( &lsqb;_( Fe/H_NP1 &rsqb;_) )_) ._. 
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<s>
N_ZZ1 doped_JJ biomass_NN1 derived_VVD porous_JJ carbon_NN1 (_( N/C_ZZ1 )_) with_IW a_AT1 3D_NNU framework_NN1 and_CC large_JJ specific_JJ surface_NN1 area_NN1 was_VBDZ obtained_VVN by_II carbonizing_VVG bagasse_NN1 biomass_NN1 waste_NN1 with_IW melamine_NN1 as_CSA nitrogen_NN1 source_NN1 ._. 
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<s>
In_II this_DD1 review_NN1 ,_, we_PPIS2 instead_RR discuss_VV0 the_AT "_" (_( jet_NN1 )_) fragmentation_NN1 function_NN1 "_" which_DDQ describes_VVZ the_AT momentum-fraction_JJ distribution_NN1 of_IO hadrons_NN2 inside_II a_AT1 jet_NN1 ._. 
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<s>
However_RR ,_, in_II a_AT1 properly_RR renormalized_VVD EFT_NP1 ,_, the_AT scaling_NN1 is_VBZ modified_VVN to_II <Professional_FO Term>_FO ._. 
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<s>
Grad1_FO first_MD proposed_VVD that_CST smooth_JJ 3D_NNU MHD_NP1 equilibria_NN2 with_IW nested_JJ toroidal_JJ flux_NN1 surfaces_NN2 generally_RR do_VD0 not_XX exist_VVI ,_, due_II21 to_II22 the_AT pathologies_NN2 that_CST arise_VV0 at_II rational_JJ sur-faces_NN2 ._. 
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<s>
One_PN1 sees_VVZ that_CST the_AT ghost_NN1 always_RR undergoes_VVZ its_APPGE clustering_NN1 before_II either_DD1 of_IO the_AT perturbative_JJ particles_NN2 p1_FO and_CC p2_FO ._. 
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<s>
The_AT prerequisites_NN2 for_IF light-emitting_JJ applications_NN2 are_VBR chiefly_RR lumi-nescence_JJ properties_NN2 and_CC charge-transport_JJ characteristics_NN2 where_RRQ in-depth_JJ understanding_NN1 and_CC thorough_JJ investigation_NN1 are_VBR needed_VVN ._. 
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<s>
With_IW the_AT increasing_JJ LHC_NP1 luminosity_NN1 ,_, one_PN1 might_VM wonder_VVI if_CS further_JJR gains_NN2 can_VM be_VBI found_VVN ._. 
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<s>
The_AT preparation_NN1 procedure_NN1 and_CC electrochemical_JJ properties_NN2 of_IO the_AT In/LPS/NMC_FU all-solid-state_JJ cell_NN1 (_( NMC:SE_FO =75:25_FO wt%_FO )_) have_VH0 been_VBN described_VVN elsewhere_RL &lsqb;_( 4_MC &rsqb;_) ._. 
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<s>
To_TO prove_VVI Lemma_NN1 3.3_MC ,_, we_PPIS2 first_MD explain_VV0 why_RRQ (_( 3.4_MC )_) implies_VVZ that_CST xs(x)_NNU is_VBZ identified_VVN in_II <Professional_FO Term>_FO and_CC that_CST the_AT word_NN1 <Professional_FO Term>_FO must_VM take_VVI the_AT form_NN1 Cn_NP1 hm_UH for_IF some_DD <Professional_FO Term>_FO (_( where_CS here_RL Cn_NP1 denotes_VVZ the_AT word_NN1 which_DDQ is_VBZ a_AT1 concatenation_NN1 of_IO n_ZZ1 C_ZZ1 '_NULL s_ZZ1 ,_, etc._RA )_) ;_; see_VV0 (_( 3.6_MC )_) ._. 
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<s>
These_DD2 large_JJ plasmon_NN1 amplitudes_NN2 reveal_VV0 the_AT strong_JJ nonlinear_JJ effect_NN1 in_II the_AT nonlinear_JJ hydrodynamic_JJ model_NN1 ,_, where_CS linear_JJ response_NN1 theory_NN1 is_VBZ not_XX applicable_JJ because_CS a_AT1 small_JJ plasmon_NN1 amplitude_NN1 is_VBZ assumed_VVN <PROFESSIONAL_FO TERM>_FO in_II the_AT latter_DA case_NN1 ._. 
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<s>
Before_II proceeding_VVG with_IW the_AT results_NN2 ,_, it_PPH1 is_VBZ useful_JJ to_TO detail_VVI the_AT terminology_NN1 and_CC simulation_NN1 tools_NN2 that_CST we_PPIS2 have_VH0 used_VVN ._. 
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<s>
While_CS it_PPH1 is_VBZ natural_JJ that_CST the_AT normalisation_NN1 of_IO D_ZZ1 and_CC P_ZZ1 (_( k_ZZ1 )_) changes_NN2 towards_II the_AT Galactic_JJ centre_NN1 ,_, it_PPH1 is_VBZ surprising_JJ that_CST the_AT type_NN1 of_IO turbulence_NN1 depends_VVZ on_II the_AT Galactocentric_JJ distance_NN1 R._NP1 As_CSA described_VVN in_II the_AT introduction_NN1 ,_, the_AT dominant_JJ process_NN1 upon_II UV-excitation_NN1 of_IO both_DB2 molecules_NN2 is_VBZ neutral_JJ C–I_JJ bond_NN1 cleavage_NN1 ._. 
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<s>
Since_CS the_AT law_NN1 of_IO the_AT bi-infinite_JJ word_NN1 X_ZZ1 is_VBZ translation_NN1 invariant_JJ ,_, we_PPIS2 also<Professional_FO Term>_FO in_II law_NN1 for_IF each_DD1 <Equation>_FO ._. 
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<s>
For_REX21 example_REX22 ,_, the_AT capacity_NN1 of_IO a_AT1 channel_NN1 can_VM be_VBI expressed_VVN in_II31 terms_II32 of_II33 its_APPGE mutual_JJ information_NN1 (_( Shannon_NP1 ,_, 1948_MC )_) ,_, that_REX21 is_REX22 ,_, in_II31 terms_II32 of_II33 the_AT correlations_NN2 between_II a_AT1 receiver_NN1 and_CC a_AT1 sender_NN1 ._. 
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<s>
We_PPIS2 believe_VV0 that_DD1 part_NN1 of_IO the_AT reason_NN1 for_IF this_DD1 is_VBZ that_CST the_AT hadronisation_NN1 process_NN1 for_IF low_JJ <Equation>_FO particles_NN2 intrinsically_RR tends_VVZ to_TO produce_VVI hadrons_NN2 separated_VVN by_II large_JJ angles_NN2 ,_, as_CSA illustrated_VVN concretely_RR in_II the_AT case_NN1 of_IO ±_FO resonance_NN1 decay_NN1 ._. 
</s>
<s>
Ex_II situ_NN1 XRD_NP1 measurements_NN2 were_VBDR then_RT conducted_VVN using_VVG an_AT1 airtight_JJ sample_NN1 holder_NN1 and_CC a_AT1 diffractometer_NN1 (_( SmartLab_NP1 ;_; Rigaku_NP1 Corp._NP1 )_) equipped_VVN with_IW a_AT1 Cu_FO K_ZZ1 radiation_NN1 source_NN1 ._. 
</s>
<s>
The_AT peak_NN1 observed_VVD only_RR for_IF PMMA/GO/WO3_NP1 ,_, around_RG 740_MC <Professional_FO Term>_FO corresponds_VVZ to_II <Professional_FO Term>_FO stretching_VVG vibrations_NN2 ._. 
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<s>
Nevertheless_RR ,_, a_AT1 Harris_NP1 sheet_NN1 is_VBZ a_AT1 standard_JJ initial_JJ condition_NN1 for_IF two-dimensional_JJ studies_NN2 of_IO magnetic_JJ reconnection_NN1 ._. 
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<s>
In_II Fig._NN1 9_MC (_( a_ZZ1 )_) –_- (_( b_ZZ1 )_) ,_, the_AT simulated_JJ oxide_NN1 thickness_NN1 with_IW parameter_NN1 set_VVD 2_MC shows_NN2 better_RRR or_CC comparable_JJ agreement_NN1 with_IW the_AT experimental_JJ data_NN than_CSN that_DD1 with_IW parameter_NN1 set_VVD 1_MC1 and_CC the_AT currently_RR established_VVN atomic_JJ mobility_NN1 is_VBZ reliable_JJ at_II high_JJ temperatures_NN2 (_( electrical_JJ potential_NN1 of_IO ions_NN2 is_VBZ ignored_VVN )_) ._. 
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By_II contrast_NN1 ,_, a_AT1 solid_JJ IE_REX with_IW reverse_JJ polarity_NN1 has_VHZ the_AT worst_JJT variability_NN1 of_IO 60.9%_FO ,_, much_RR larger_JJR than_CSN any_DD other_JJ cases_NN2 ._. 
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<s>
Trajectory_NN1 looping_VVG performed_VVN multiple_JJ times_NNT2 enables_VVZ recurrent_JJ trajectory_NN1 reuse_NN1 and_CC simulation_NN1 of_IO chemical_JJ processes_NN2 on_II timescales_NN2 several_DA2 orders_NN2 of_IO magnitude_NN1 longer_RRR than_CSN the_AT original_JJ diffusion_NN1 trajectory_NN1 ._. 
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<s>
Also_RR ,_, though_CS we_PPIS2 have_VH0 not_XX discussed_VVN that_CST into_II details_NN2 ,_, a_AT1 grid_NN1 cell_NN1 size_NN1 of_IO 0.55_MC is_VBZ a_AT1 good_JJ default_NN1 as_CSA is_VBZ the_AT use_NN1 of_IO <Equation>_FO jets_NN2 with_IW <Equation>_FO ._. 
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<s>
These_DD2 two_MC distinct_JJ signatures_NN2 are_VBR attributed_VVN to_II highly_RR efficient_JJ recombination_NN1 that_CST eventually_RR leads_VVZ to_II the_AT dominant_JJ formation_NN1 of_IO neutral_JJ atoms_NN2 in_II the_AT cluster_NN1 ._. 
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<s>
Monogamy_NN1 relations_NN2 were_VBDR first_MD established_VVN by_II (_( CKW_NP1 )_) in_II &lsqb;_( 4_MC &rsqb;_) ,_, where_CS a_AT1 <Professional_FO Term>_FO system_NN1 consisted_VVN of_IO the_AT subsystems_NN2 A_ZZ1 ,_, B_ZZ1 ,_, and_CC C_NP1 was_VBDZ considered_VVN ._. 
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<s>
However_RR ,_, at_II <Equation>_FO ,_, and_CC for_IF repulsive_JJ <Equation>_FO J<Equation>_FO ._. 
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<s>
In_RR21 addition_RR22 ,_, both_DB2 the_AT quality_NN1 factor_NN1 of_IO angular_JJ momentum_NN1 storage_NN1 and_CC the_AT efficiency_NN1 of_IO wave_NN1 driven_VVN angular_JJ momentum_NN1 generation_NN1 are_VBR calculated_VVN and_CC shown_VVN to_TO be_VBI independent_JJ of_IO the_AT details_NN2 of_IO the_AT charge_NN1 separation_NN1 processes_NN2 ._. 
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<s>
In_II31 light_II32 of_II33 these_DD2 results_NN2 ,_, we_PPIS2 now_RT believe_VV0 that_CST the_AT laser_NN1 heating_NN1 phase_NN1 is_VBZ responsible_JJ for_IF the_AT generation_NN1 and_CC subsequent_JJ transport_NN1 of_IO this_DD1 material_NN1 into_II the_AT fuel_NN1 ._. 
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<s>
To_TO compute_VVI this_DD1 effect_NN1 ,_, we_PPIS2 take_VV0 a_AT1 slightly_RR different_JJ approach_NN1 than_CSN the_AT one_PN1 we_PPIS2 have_VH0 adopted_VVN before_RT to_TO calculate_VVI the_AT average_JJ effect_NN1 ._. 
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<s>
Support_VV0 by_II the_AT Polish-JINR_NP1 (_( Dubna_NP1 )_) Cooperation_NN1 Programme_NN1 ,_, the_AT GSI_JJ Helmholtzzentrum_NN1 für_NN1 Schwerionenforschung_VVD GmbH_NP1 ,_, the_AT European_JJ Science_NN1 Foundation_NN1 (_( within_II the_AT EuroGenesis_NN1 programme_NN1 )_) ,_, the_AT European_JJ Research_NN1 Council_NN1 (_( ERC_NP1 )_) under_II the_AT European_JJ Union_NN1 '_NULL s_ZZ1 Horizon_NN1 2020_MC research_NN1 and_CC innovation_NN1 programme_NN1 (_( Grant_NP1 Agreement_NN1 No._NN1 682841_MC "_" ASTRUm_NP1 "_" )_) ,_, and_CC the_AT Helmholtz-CAS_NP2 Joint_JJ Re-search_NN1 Group_NN1 (_( HCJRG-108_MC )_) is_VBZ gratefully_RR acknowledged_VVN ._. 
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<s>
The_AT probability_NN1 of_IO this_DD1 process_NN1 can_VM typically_RR be_VBI reduced_VVN to_II integrals_NN2 of_IO the_AT radial_JJ wave_NN1 functions_NN2 of_IO initial_NN1 and_CC final_JJ bound_JJ states_NN2 ,_, where_CS the_AT shake_NN1 off_RP probability_NN1 can_VM simply_RR be_VBI calculated_VVN as_II the_AT deviation_NN1 from_II unity_NN1 when_CS summing_VVG all_DB aforementioned_JJ probabilities_NN2 ._. 
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<s>
As_CSA discussed_VVN in_II more_DAR detail_NN1 later_RRR ,_, this_DD1 is_VBZ not_XX the_AT strongest_JJT bound_NN1 on_II the_AT graviton_NN1 mass_NN1 ,_, but_CCB it_PPH1 is_VBZ certainly_RR a_AT1 very_RG solid_JJ bound_NN1 for_IF several_DA2 reasons_NN2 ._. 
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<s>
Several_DA2 active_JJ methods_NN2 that_CST employ_VV0 chemical_NN1 &lsqb;_( 18_MC &rsqb;_) ,_, electrical_JJ &lsqb;_( 11,19–21_MCMC &rsqb;_) ,_, X-ray_NN1 Photoelectron_NP1 Spectroscopy_NP1 (_( XPS_NP1 )_) measurements_NN2 were_VBDR performed_VVN in_II UHV_NP1 chamber_NN1 equipped_VVN with_IW a_AT1 Phoibos_NP1 150_MC Specs_NP2 charged_VVD particle_NN1 analyzer_NN1 and_CC a_AT1 conventional_JJ X-ray_NN1 source_NN1 (_( Al_NP1 K_NP1 and_CC Mg_FO K_ZZ1 )_) ._. 
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<s>
The_AT upper_JJ bound_NN1 for_IF performance_NN1 can_VM be_VBI known_VVN from_II the_AT start_NN1 ,_, and_CC this_DD1 can_VM help_VVI manage_VVI expectations_NN2 ._. 
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<s>
Apart_II21 from_II22 the_AT constraints_NN2 ,_, the_AT ultimate_JJ goal_NN1 in_II modified_JJ gravity_NN1 is_VBZ to_TO offer_VVI a_AT1 self-consistent_JJ theoretical_JJ framework_NN1 in_II the_AT context_NN1 of_IO which_DDQ the_AT early-time_NNT1 and_CC late-time_JJ acceleration_NN1 will_VM be_VBI described_VVN by_II the_AT same_DA theory_NN1 ._. 
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<s>
The_AT null_JJ hypothesis_NN1 for_IF the_AT surrogates_NN2 used_VVD was_VBDZ that_CST all_DB structures_NN2 in_II the_AT EEG_NN1 ,_, in_II the_AT time_NNT1 and_CC in_II the_AT spatial_JJ domain_NN1 ,_, can_VM be_VBI adequately_RR described_VVN by_II a_AT1 linear_JJ model_NN1 ._. 
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<s>
In_II31 addition_II32 to_II33 single_JJ electron_NN1 transfer_NN1 from_II atomic_JJ helium_NN1 anions_NN2 to_II dopants_NN2 ,_, double_JJ electron_NN1 transfer_NN1 has_VHZ recently_RR been_VBN observed_VVN &lsqb;_( 239_MC &rsqb;_) ._. 
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<s>
Studies_NN2 of_IO how_RRQ jsw_NNU scales_NN2 as_II a_AT1 function_NN1 of_IO dot_NN1 size_NN1 have_VH0 been_VBN performed_VVN for_IF Ta_UH and_CC W=CoFeB=MgO_FO dots_NN2 (_( C._NP1 Zhang_NP1 et_RA21 al._RA22 ,_, 2015_MC ;_; Zhang_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) ._. 
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<s>
In_II figure_NN1 4(a)_FO ,_, the_AT count_NN1 rate_NN1 corresponding_VVG to_II the_AT maxima_NN2 of_IO the_AT spectra_NN2 has_VHZ been_VBN considered_VVN ._. 
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<s>
As_II a_AT1 result_NN1 ,_, the_AT modified_JJ network_NN1 is_VBZ spanned_VVN by_II a_AT1 single_JJ cactus_NN1 ,_, thus_RR controllable_JJ by_II a_AT1 single_JJ root_NN1 ._. 
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<s>
One_MC1 manifestation_NN1 of_IO this_DD1 is_VBZ that_DD1 Figure_NN1 5b_FO includes_VVZ an_AT1 infinite_JJ series_NN of_IO diagrams_NN2 that_CST are_VBR all_RR31 the_RR32 same_RR33 order_NN1 of_IO magnitude_NN1 ._. 
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PCA_NN1 of_IO crystallographic_JJ coordinate_NN1 sets_NN2 has_VHZ particular_JJ utility_NN1 for_IF the_AT analysis_NN1 of_IO large_JJ structural_JJ data_NN sets_NN2 ._. 
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Usage_NN1 of_IO a_AT1 bent_JJ crystal_NN1 for_IF effective_JJ focusing_NN1 of_IO channeled_JJ fraction_NN1 of_IO high_JJ energy_NN1 positive_JJ particle_NN1 beams_NN2 with_IW a_AT1 short_JJ focal_JJ length_NN1 of10_FO cm_NNU was_VBDZ shown.6_FO ._. 
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<s>
These_DD2 parameters_NN2 resulted_VVN in_II a_AT1 deposition_NN1 rate_NN1 of_IO about_RG 0.03–0.04_MCMC nm/pulse_FU ,_, determined_VVN by_II profilometry_NN1 ._. 
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<s>
Not_XX only_RR do_VD0 these_DD2 deep_JJ networks_NN2 have_VH0 more_RGR expressive_JJ capacity_NN1 ,_, but_CCB also_RR the_AT layers_NN2 can_VM be_VBI interpreted_VVN as_CSA building_VVG up_RP a_AT1 hierarchical_JJ representation_NN1 of_IO the_AT data_NN ._. 
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<s>
Here_RL ,_, we_PPIS2 will_VM show_VVI that_DD1 for_IF different_JJ class_NN1 of_IO entangled_JJ states_NN2 explicit_JJ relations_NN2 between_II some_DD measures_NN2 of_IO entanglement_NN1 and_CC Riemannian_JJ metric_JJ exist_VV0 ._. 
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<s>
Concomitantly_RR ,_, an_AT1 increase_NN1 of_IO the_AT characteristic_JJ mound_NN1 sizes_NN2 is_VBZ observed_VVN ,_, which_DDQ is_VBZ reflected_VVN by_II an_AT1 increasing_JJ of_IO the_AT correlation_NN1 length_NN1 ._. 
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<s>
It_PPH1 can_VM be_VBI shown_VVN that_CST Rrel_NP1 is_VBZ asymptotically_RR continuous_JJ in_II any_DD convex_JJ QRT_NP1 for_IF which_DDQ the_AT maximally_RR mixed_VVN state_NN1 is_VBZ free_JJ ._. 
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<s>
Their_APPGE waveforms_NN2 are_VBR monitored_VVN and_CC recorded_VVN using_VVG an_AT1 oscilloscope_NN1 (_( Tektronix_NP1 ,_, DPO4104_FO )_) ._. 
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<s>
Convergence_NN1 of_IO the_AT expectations_NN2 implies_VVZ that_CST <Equation>_FO for_IF each_DD1 <Equation>_FO ,_, and_CC convergence_NN1 of_IO variances_NN2 implies_VVZ with_IW Proposition_NN1 3.21_MC implies_VVZ Z_ZZ1 (_( t_ZZ1 )_) has_VHZ finite_JJ variance_NN1 ._. 
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<s>
Likewise_RR ,_, the_AT strong_JJ drops_NN2 after_CS n_ZZ1 =_FO 2_MC and_CC 6_MC in_II the_AT calculated_JJ dissociation_NN1 energies_NN2 of_IO Na+Hen_FO agree_VV0 with_IW measured_JJ ion_NN1 abundances_NN2 ._. 
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<s>
Nevertheless_RR ,_, for_IF <Equation>_FO ,_, it_PPH1 is_VBZ not_XX too_RG unreasonable_JJ to_TO take_VVI <Equation>_FO and_CC examine_VVI the_AT consequences_NN2 ._. 
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<s>
Far_RR away_II21 from_II22 the_AT boundary_NN1 ,_, the_AT bulk_NN1 plasma_NN1 potential_NN1 should_VM be_VBI zero_NN1 which_DDQ requires_VVZ that_CST the_AT fluxes_NN2 for_IF primary_JJ electrons_NN2 ,_, ions_NN2 ,_, and_CC secondary_JJ elec_NN1 trons_NN2 ,_, which_DDQ in_II our_APPGE case_NN1 are_VBR photoelectrons_NN2 ,_, balance_VV0 to_TO have_VHI the_AT net_JJ plasma_NN1 current_JJ density_NN1 zero<Equation>_FO (_( 28_MC )_) ,_, where<Equation>_FO (_( 29_MC )_) <Equation>_FO (_( 30_MC )_) <Equation>_FO (_( 31_MC )_) ,_, where_CS Js_NP2 are_VBR the_AT respective_JJ current_JJ densities_NN2 in_II the_AT bulk_NN1 plasma_NN1 due_II21 to_II22 the_AT primary_JJ plasma_NN1 electrons_NN2 ,_, photoelectrons_NN2 ,_, and_CC ions_NN2 ._. 
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<s>
We_PPIS2 study_VV0 the_AT existence_NN1 and_CC non-existence_NN1 of_IO flux_NN1 tubes_NN2 both_RR below_RL and_CC above_II the_AT deconfinement_NN1 phase_NN1 transition_NN1 temperature_NN1 Tc_NP1 ._. 
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At_II the_AT end_NN1 of_IO this_DD1 section_NN1 ,_, it_PPH1 is_VBZ worth_II returning_VVG to_II the_AT subject_NN1 of_IO the_AT Debye-Waller_NP1 self-energy_NN1 ._. 
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The_AT remainder_NN1 of_IO this_DD1 review_NN1 is_VBZ structured_VVN as_CSA follows_VVZ ._. 
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<s>
In_II pulses_NN2 of_IO about_RG 50_MC fs_FO duration_NN1 it_PPH1 provides_VVZ as_RG many_DA2 photons_NN2 as_CSA one_PN1 gets_VVZ in_II 1_MC1 sec_NNU from_II modern_JJ storage_NN1 ring_NN1 synchrotron_NN1 radiation_NN1 facilities_NN2 ._. 
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<s>
In_RR21 particular_RR22 ,_, a_AT1 relative_JJ shift_NN1 of_IO the_AT s_ZZ1 level_NN1 of_IO atom_NN1 l_ZZ1 by_II jl_NNU matched_VVN by_II a_AT1 sideband_NN1 of_IO the_AT Raman_NN1 laser_NN1 (_( shown_VVN in_II gray_JJ )_) ,_, selectively_RR creates_VVZ an_AT1 interaction_NN1 between_II these_DD2 two_MC atoms_NN2 ._. 
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The_AT data_NN is_VBZ found_VVN to_TO accurately_RR obey_VVI the_AT WF_NP1 law_NN1 ._. 
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<s>
Since_CS the_AT lowest_JJT energy_NN1 vibronic_JJ excited_JJ state_NN1 <Equation>_FO lies_VVZ <Equation>_FO above_II the_AT ground_NN1 state_NN1 ,_, energy_NN1 considerations_NN2 restrict_VV0 all_DB ions_NN2 that_CST all_DB ions_NN2 formed_VVN must_VM be_VBI in_II the_AT ground_NN1 vibronic_JJ state_NN1 ,_, which_DDQ is_VBZ the_AT eEDM_JJ sensitive_JJ state_NN1 ._. 
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Moreover_RR ,_, suicide_NN1 estimates_NN2 based_VVN on_II GTs_NP1 are_VBR much_RR better_RRR than_CSN predictions_NN2 based_VVN on_II previous_JJ suicide_NN1 data_NN ._. 
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<s>
Experimentally_RR ,_, it_PPH1 was_VBDZ found_VVN that_CST ,_, as_CSA the_AT electrode_NN1 gap_NN1 length_NN1 is_VBZ increased_VVN ,_, the_AT light_JJ emission_NN1 intensity_NN1 of_IO an_AT1 atomic_JJ oxygen_NN1 line_NN1 decreases_VVZ gradually_RR and_CC the_AT plasma_NN1 density_NN1 increases_VVZ abruptly_RR ._. 
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Furthermore_RR ,_, to_TO enable_VVI the_AT quantitative_JJ extraction_NN1 of_IO the_AT N-V_NP1 -to-N-V_JJ charge-state_JJ ratio_NN1 from_II these_DD2 PL_NN1 measurements_NN2 ,_, we_PPIS2 also_RR empirically_RR determine_VV0 the_AT relative_JJ PL_NN1 rate_NN1 of_IO N-V_NP1 compared_VVD with_IW that_DD1 of_IO N-V_NP1 ,_, findings_NN2 532_MC =_FO 2.5_MC ±_FO 0.5_MC under_II low-intensity_JJ 532-nm_FU excitation_NN1 ._. 
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By_II solving_VVG Eq_NN1 ._. 
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<s>
(_( 48_MC )_) for_IF each_DD1 occupied_JJ state_NN1 v_ZZ1 and_CC each_DD1 wave_NN1 vector_NN1 k_ZZ1 using_VVG standard_JJ linear_JJ algebra_NN1 techniques_NN2 ,_, one_PN1 obtains_VVZ the_AT induced_JJ density_NN1 in_II Eq_NN1 ._. 
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(_( 49_MC )_) ._. 
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<s>
A_AT1 nontrivial_JJ example_NN1 of_IO a_AT1 and_CC b_ZZ1 either_RR satisfying_VVG the_AT required_JJ equations_NN2 for_IF an_AT1 ideal_JJ evolution_NN1 ,_, or_CC not_XX ,_, is_VBZ given_VVN by_II a_AT1 toroidal_JJ plasma_NN1 with_IW magnetic_JJ surfaces_NN2 ._. 
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<s>
This_DD1 stage_NN1 transforms_VVZ to_II a_AT1 slow_JJ decrease_NN1 in_II the_AT shock_NN1 velocity_NN1 gradually_RR approaching_VVG the_AT speed_NN1 of_IO sound_NN1 in_II undisturbed_JJ water_NN1 ._. 
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<s>
In_II 2009_MC ,_, an_AT1 InGaAsSb-based_JJ quantum_NN1 well_RR SESAM_NP1 was_VBDZ developed_VVN ,_, in_II which_DDQ GaSb/AlAsSb_NP1 distributed_VVD Bragg_NP1 reflectors_NN2 and_CC Te-doped_JJ GaSb_NN1 substrates_NN2 were_VBDR adopted_VVN to_TO avoid_VVI lattice_NN1 mismatch_NN1 ,_, significantly_RR improving_VVG the_AT SESAM_NN1 quality_NN1 around_II the_AT operating_NN1 wavelength_NN1 of_IO 2.0lm_FO ._. 
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However_RR ,_, the_AT actual_JJ relaxation_NN1 time_NNT1 could_VM be_VBI longer_JJR since_CS Alfvén_JJ waves_NN2 undergo_VV0 enhanced_JJ damping_NN1 in_II a_AT1 region_NN1 of_IO stochastic_JJ magnetic_JJ field_NN1 lines_NN2 &lsqb;_( 26_MC &rsqb;_) ._. 
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However_RR ,_, this_DD1 claim_NN1 has_VHZ been_VBN challenged_VVN in_II academia_NN1 and_CC is_VBZ still_RR in_II debate_NN1 ,_, for_IF the_AT same_DA reason_NN1 mentioned_VVD before_RT :_: (_( 1_MC1 )_) the_AT problem_NN1 artificial_JJ nature_NN1 and_CC (_( 2_MC )_) suboptimal_JJ annealing_JJ time_NNT1 on_II easier_JJR cases_NN2 may_VM be_VBI hiding_VVG the_AT exponential_NN1 scaling_NN1 ._. 
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Alternatively_RR ,_, consider_VV0 the_AT emission_NN1 from_II a_AT1 high-energy_JJ parton_NN1 of_IO a_AT1 gluon_NN1 with_IW a_AT1 pt_NNU of_IO the_AT order_NN1 of_IO 1_MC1 GeV_NP1 :_: this_DD1 gluon_NN1 can_VM only_RR be_VBI considered_VVN perturbative_JJ if_CS its_APPGE transverse_JJ momentum_NN1 relative_II21 to_II22 the_AT emitter_NN1 is_VBZ at_RR21 least_RR22 of_IO order_NN1 a_AT1 GeV_NP1 ,_, i.e._REX if_CS it_PPH1 has_VHZ an_AT1 angle_NN1 relative_II21 to_II22 the_AT emitted_JJ of_IO order_NN1 1_MC1 ._. 
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<s>
Following_VVG that_DD1 convention_NN1 ,_, we_PPIS2 define_VV0 a_AT1 '_NULL lattice_NN1 surface_NN1 '_NULL to_TO be_VBI simply_RR a_AT1 2-chain_NN1 in_II the_AT standard_JJ cell_NN1 complex_NN1 of_IO Zd_NP1 ._. 
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Such_DA a_AT1 variation_NN1 in_II QD_NP1 levels_NN2 can_VM be_VBI engineered_VVN by_II considering_VVG suitable_JJ diameter_NN1 variation_NN1 of_IO QDs_NP1 in_II the_AT SLNW_NP1 shown_VVN in_II Fig._NN1 1(a)_FO ,_, which_DDQ can_VM be_VBI realized_VVN by_II advanced_JJ etching_NN1 and_CC lithography_NN1 techniques_NN2 ._. 
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In_II this_DD1 case_NN1 we_PPIS2 can_VM analytically_RR calculate_VVI the_AT mean_JJ value_NN1 and_CC the_AT complete_JJ distribution_NN1 function_NN1 of_IO the_AT run_NN1 duration_NN1 and_CC tumble_VV0 duration_NN1 ._. 
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<s>
Based_VVN on_II survey_NN1 data_NN ,_, Feely_NP1 &lsqb;_( 539_MC &rsqb;_) found_VVD that_CST the_AT employees_NN2 with_IW large_JJ degrees_NN2 and_CC between_RL are_VBR less_RGR likely_JJ to_TO leave_VVI their_APPGE jobs_NN2 ._. 
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<s>
Next_MD ,_, we_PPIS2 varied_VVD the_AT quadratic_JJ coupling_NN1 parameter_NN1 12_MC to_TO study_VVI its_APPGE influence_NN1 on_II the_AT interfaces_NN2 between_II the_AT two_MC crystalline_JJ phases_NN2 and_CC on_II the_AT heterostructures_NN2 as_II a_AT1 whole_NN1 ._. 
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<s>
It_PPH1 can_VM be_VBI shown_VVN that_CST in_II the_AT long_JJ time_NNT1 limit_NN1 the_AT probability_NN1 of_IO finding_VVG the_AT random_JJ walk_NN1 at_II node_NN1 i_ZZ1 is_VBZ proportional_JJ to_II its_APPGE degree_NN1 ,_, <equation>where_FO m_ZZ1 is_VBZ the_AT number_NN1 of_IO links_NN2 in_II the_AT network_NN1 ._. 
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<s>
The_AT second_MD rule_NN1 for_IF combing_VVG circuit_NN1 elements_NN2 tells_VVZ us_PPIO2 how_RRQ to_TO determine_VVI the_AT unit_NN1 that_CST describes_VVZ a_AT1 network_NN1 in_II which_DDQ the_AT outputs_NN2 of_IO a_AT1 unit_NN1 G1_FO are_VBR connected_VVN to_II the_AT inputs_NN2 of_IO a_AT1 unit_NN1 G2_FO ._. 
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<s>
Thus_RR ,_, even_RR for_IF kP_NNU kS_FO (_( provided_VVN )_) the_AT entire_JJ velocity_NN1 distribution_NN1 can_VM be_VBI addressed_VVN if_CS the_AT laser_NN1 intensity_NN1 is_VBZ sufficiently_RR high_JJ ._. 
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<s>
Glauber_NN1 '_NULL s_ZZ1 method_NN1 to_TO calculate_VVI the_AT reaction_NN1 cross_NN1 section_NN1 is_VBZ a_AT1 semiclassical_JJ (_( eikonal_JJ )_) approximation_NN1 to_II the_AT standard_JJ sum_NN1 over_II partial_JJ wave_NN1 formula_NN1 that_CST can_VM be_VBI found_VVN in_II every_AT1 Quantum_NN1 Mechanics_NN2 (_( QM_FO )_) book_NN1 &lsqb;_( 60_MC &rsqb;_) ._. 
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<s>
What_DDQ will_VM be_VBI studied_VVN in_II this_DD1 paper_NN1 is_VBZ the_AT nature_NN1 of_IO magnetic_JJ reconnection_NN1 in_II the_AT limit_NN1 as_CSA nonideal_JJ effects_NN2 go_VV0 to_TO zero_VVI ,_, the_AT limit_NN1 as_CSA <equation>goes_FO to_TO zero_VVI ._. 
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<s>
Schematic_JJ presentation_NN1 of_IO an_AT1 acetylene-vinylidene_JJ reaction_NN1 observed_VVN by_II an_AT1 XUV-pump_NN1 /_FO XUV-probe_JJ experiment_NN1 ._. 
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The_AT simple_JJ chain_NN1 model_NN1 in_II Eq_NN1 ._. 
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<s>
(_( 7_MC )_) is_VBZ justi_NN2 ?_? ed_NN1 because_CS the_AT reflection_NN1 phase_NN1 shift_NN1 can_VM be_VBI brie_NN1 ?_? y_ZZ1 and_CC algebraically_RR summarized_VVN with_IW the_AT external_JJ force_NN1 terms_NN2 on_II boundary_NN1 atoms_NN2 ._. 
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<s>
Most_RGT prominently_RR ,_, collapse_NN1 models_NN2 (_( Bassi_NP1 et_RA21 al._RA22 ,_, 2013_MC )_) including_II gravitationally_RR induced_VVN collapse_NN1 (_( Diósi_NP1 ,_, 1989_MC ;_; Penrose_NP1 ,_, 1996_MC )_) or_CC continuous_JJ spontaneous_JJ localization_NN1 (_( Ghirardi_NP1 ,_, Rimini_NP1 ,_, and_CC Weber_NP1 ,_, 1986_MC ;_; Gisin_NP1 ,_, 1989_MC ;_; Ghirardi_NP1 ,_, Pearle_NP1 ,_, and_CC Rimini_NP1 ,_, 1990_MC )_) has_VHZ been_VBN suggested_VVN ._. 
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<s>
For_IF the_AT very_RG small_JJ magnetic_JJ Prandtl_NP1 number_NN1 Pm_NP1 =_FO 105_MC and_CC for_IF stationary_JJ cylinders_NN2 the_AT TI_NN1 for_IF increasing_VVG electrical_JJ currents_NN2 have_VH0 been_VBN numerically_RR simulated_VVN ._. 
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<s>
The_AT beat_NN1 between_II a_AT1 frequency-swept_JJ sinusoidal_JJ optical_JJ sig_NN1 nal_JJ and_CC a_AT1 time-delayed_JJ version_NN1 of_IO the_AT same_DA signal_NN1 determines_VVZ the_AT location_NN1 of_IO reflection_NN1 points_VVZ along_II the_AT optical_JJ path_NN1 ._. 
</s>
<s>
Explicit_JJ and_CC large_JJ GO_VV0 layers_NN2 on_II the_AT surface_NN1 of_IO FTO/GO/WO3_NP1 film_NN1 caused_VVD high_JJ tungsten_NN1 absorption_NN1 on_II the_AT structure_NN1 ._. 
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<s>
This_DD1 would_VM benefit_VVI experiments_NN2 aiming_VVG to_TO observe_VVI neutrinoless_JJ double-_JJ β_NULL decay_NN1 ,_, which_DDQ enrich_VV0 the_AT 136Xe_FO of_IO their_APPGE target_NN1 mass_NN1 ,_, and_CC thus_RR produce_VV0 significant_JJ quantities_NN2 of_IO depleted_JJ xenon_NN1 as_II a_AT1 by-product_NN1 ._. 
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<s>
Guessing_VVG Xi1_FO from_II Xi_NN1 is_VBZ computationally_RR hard_RR unless_CS the_AT quadratic_JJ residuosity_NN1 problem_NN1 can_VM be_VBI solved_VVN in_II polynomial_NN1 time_NNT1 ._. 
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<s>
The_AT surface_NN1 morphology_NN1 of_IO the_AT precursor_NN1 and_CC final_JJ products_NN2 <Chart>Fig._FO 2_MC ._. 
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<s>
Implementing_VVG this_DD1 we_PPIS2 find_VV0 that_CST the_AT correction_NN1 to_II the_AT OPE_NN1 where_RRQ by<Equation>we_FO mean_VV0 an_AT1 equality_NN1 of_IO double_JJ discontinuities_NN2 ._. 
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<s>
This_DD1 "_" created_JJ mass_NN1 "_" actually_RR comes_VVZ from_II the_AT chain_NN1 ,_, so_CS there_EX is_VBZ no_AT problem_NN1 here_RL ._. 
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<s>
For_IF the_AT present_JJ protocol_NN1 ,_, there_EX are_VBR seven_MC Lindblad_NP1 operators_NN2 :_: <Equation>_FO where_RRQ <Professional_FO Term>_FO are_VBR the_AT spontaneous_JJ emission_NN1 rate_NN1 for_IF the<Professional_FO Term>_FO atom_NN1 ,_, <Professional_FO Term>_FO are_VBR the_AT decay_NN1 rate_NN1 for_IF the_AT nth_MD cavity_NN1 ,_, and_CC is_VBZ the_AT decay_NN1 rate_NN1 for_IF the_AT fiber_NN1 ._. 
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<s>
WO3_FO and_CC NiO_NP1 can_VM be_VBI colored_VVN and_CC bleached_VVN instantaneously_RR under_II the_AT applied_JJ voltage_NN1 to_II the_AT device_NN1 ._. 
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<s>
First_MD ,_, a_AT1 photon_NN1 propagates_VVZ some_DD distance_NN1 before_II interacting_VVG (_( <Euqation>_FO cm_NNU in_II LAr_NP1 )_) ,_, so_RR if_CS a_AT1 vertex_NN1 can_VM be_VBI identified_VVN ,_, then_RT the_AT gap_NN1 between_II the_AT vertex_NN1 and_CC the_AT start_NN1 of_IO an_AT1 electromagnetic_JJ shower_NN1 is_VBZ a_AT1 clear_JJ photon_NN1 signature_NN1 ._. 
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<s>
The_AT discrete_JJ points_NN2 from_II simulations_NN2 show_VV0 excellent_JJ agreement_NN1 with_IW continuous_JJ lines_NN2 from_II analytics_NN1 ._. 
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<s>
For_IF completeness_NN1 we_PPIS2 emphasize_VV0 that_CST the_AT underestimation_NN1 of_IO the_AT EPI_JJ matrix_NN1 elements_NN2 by_II semilocal_JJ DFT_NP1 functionals_NN2 does_VDZ not_XX propagate_VVI in_II the_AT same_DA way_NN1 into_II different_JJ materials_NN2 properties_NN2 ._. 
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<s>
Moreover_RR ,_, people_NN affected_VVN by_II emergencies_NN2 propagate_VV0 the_AT emergency_NN1 information_NN1 rapidly_RR and_CC globally_RR through_II social_JJ networks_NN2 ._. 
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<s>
Based_VVN on_II these_DD2 visual_JJ features_NN2 ,_, they_PPHS2 developed_VVD a_AT1 classification_NN1 method_NN1 to_TO predict_VVI personality_NN1 traits_NN2 ,_, exhibiting_VVG a_AT1 mean_JJ classification_NN1 accuracy_NN1 of_IO about_RG 0.60_MC for_IF each_DD1 of_IO the_AT five_MC traits_NN2 ._. 
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<s>
A_AT1 second_MD notion_NN1 of_IO feedback_NN1 control_NN1 without_IW explicit_JJ measurements_NN2 was_VBDZ introduced_VVN by_II Lloyd_NP1 in_II 2000_MC &lsqb;_( 57_MC &rsqb;_) ._. 
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<s>
During_II the_AT clustering_NN1 the_AT ghosts_NN2 may_VM cluster_VVI both_RR with_IW each_PPX221 other_PPX222 and_CC with_IW the_AT hard_JJ particles_NN2 ._. 
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<s>
In_II the_AT bibliography_NN1 a_AT1 list_NN1 of_IO articles_NN2 concerning_II the_AT research_NN1 in_II Japan_NP1 is_VBZ available_JJ ._. 
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<s>
To_TO compute_VVI the_AT characters_NN2 of_IO the_AT theory_NN1 ,_, consider_VV0 the_AT conformal_JJ mapping_NN1 from_II the_AT complex_JJ plane_NN1 to_II the_AT cylinder_NN1 given_VVN by_II z_ZZ1 =_FO ew_NN1 ._. 
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<s>
For_IF that_DD1 reason_NN1 ,_, we_PPIS2 are_VBR going_VVGK to_TO apply_VVI (_( actually_RR ,_, adapt_VV0 )_) the_AT symmetry_NN1 doubling_NN1 argument_NN1 to_II the_AT U(1)_FO conserved_JJ current_NN1 of_IO the_AT network_NN1 model_NN1 instead_RR ._. 
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<s>
The_AT reason_NN1 only_RR even_RR powers_NN2 of_IO the_AT extrinsic_JJ curvatures_NN2 appear_VV0 in_II Eq_NN1 ._. 
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<s>
(_( 170_MC )_) is_VBZ that_CST the_AT entanglement_NN1 entropy_NN1 for_IF a_AT1 region_NN1 A_ZZ1 is_VBZ equal_JJ to_II that_DD1 of_IO its_APPGE complement_NN1 A_ZZ1 while_CS their_APPGE extrinsic_JJ curvatures_NN2 have_VH0 opposite_JJ signs_NN2 ,_, hence_RR the_AT odd_JJ powers_NN2 of_IO K_ZZ1 vanish_VV0 ._. 
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<s>
Background_NN1 c_ZZ1 has_VHZ attracted_VVN particular_JJ interest_NN1 because_CS it_PPH1 does_VDZ not_XX come_VVI directly_RR from_II measurements_NN2 but_CCB rather_RR is_VBZ based_VVN on_II nonperturbative_JJ theoretical_JJ calculations_NN2 (_( e.g._REX ,_, 20_MC ,_, 21_MC )_) ._. 
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<s>
After_II collecting_VVG 12.84_MC (_( 11.27_MC )_) ×_II 1020_MC protons_NN2 on_II target_NN1 (_( POT_NN1 )_) in_II neutrino_NN1 (_( antineutrino_NN1 )_) modes_NN2 ,_, the_AT MiniBooNE_NN1 Collaboration_NN1 (_( 5_MC ,_, 6_MC )_) observed_VVD excesses_NN2 of_IO electron-like_JJ events_NN2 in_II both_DB2 modes_NN2 ,_, leading_VVG to_II a_AT1 4.7_MC deviation_NN1 from_II the_AT expected_JJ background_NN1 ._. 
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<s>
Again_RT ,_, experimental_JJ evidence_NN1 ,_, including_II GW-power_JJ radiation_NN1 ,_, agreed_VVD well_RR with_IW the_AT theoretical_JJ expectations_NN2 ,_, and_CC was_VBDZ registered_VVN with_IW relief_NN1 by_II everybody_PN1 worldwide_RL working_VVG on_II FELs_NN2 at_II even_RR shorter_JJR wavelengths_NN2 ._. 
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<s>
In_II the_AT L-S_NP2 coupling_NN1 scheme_NN1 ,_, the_AT spins_NN2 of_IO the_AT qq_NNU '_NULL pair_NN couple_VV0 to_II the_AT total_JJ intrinsic_JJ spin_NN1 <EQUAION>_FO ._. 
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<s>
After_CS the_AT transition_NN1 lines_NN2 belonging_VVG to_II the_AT DFE_NN1 monomer_NN1 &lsqb;_( 43_MC &rsqb;_) ,_, DFE_NP1 dimer_NN1 &lsqb;_( 28_MC &rsqb;_) ,_, and_CC DFM_NP1 trimer_NN1 &lsqb;_( 26_MC &rsqb;_) were_VBDR removed_VVN from_II the_AT spectrum_NN1 ,_, several_DA2 groups_NN2 of_IO lines_NN2 belonging_VVG for_IF isomer_JJR II_MC were_VBDR observed_VVN and_CC assigned_VVN first_MD ._. 
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<s>
In_II contrast_NN1 ,_, the_AT related_JJ diamond_NN1 lattice_NN1 of_IO ,_, e.g._REX ,_, Si_FW &lsqb;_( Fig._NN1 7(b)_FO &rsqb;_) has_VHZ global_JJ inversion_NN1 symmetry_NN1 and_CC therefore_RR can_VM not_XX promote_VVI a_AT1 net_JJ iSGE_NN1 spin_NN1 density_NN1 when_CS integrated_VVN over_II the_AT unit_NN1 cell_NN1 ._. 
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<s>
Although_CS the_AT scattering_NN1 matrix_NN1 S_ZZ1 does_VDZ not_XX appear_VVI in_II the_AT master_NN1 equation_NN1 (_( 3.16_MC )_) ,_, it_PPH1 affects_VVZ the_AT input-output_NN1 relation_NN1 of_IO the_AT system_NN1 as_CSA shown_VVN in_II Eq_NN1 ._. 
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<s>
(_( 3.14_MC )_) and_CC thus_RR will_VM affect_VVI the_AT dynamics_NN of_IO more_RGR complex_JJ quantum_NN1 input-output_NN1 systems_NN2 ,_, such_II21 as_II22 the_AT quantum_NN1 cascade_NN1 systems_NN2 which_DDQ will_VM be_VBI specified_VVN below_RL ._. 
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<s>
As_CS31 long_CS32 as_CS33 these_DD2 aspects_NN2 are_VBR taken_VVN into_II account_NN1 ,_, the_AT relatively_RR high_JJ rate_NN1 of_IO QRNGs_NP1 makes_VVZ them_PPHO2 also_RR a_AT1 viable_JJ option_NN1 to_TO directly_RR generate_VVI keys_NN2 ,_, probably_RR after_CS some_DD kind_NN1 of_IO postprocessing_VVG ._. 
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<s>
Its_APPGE higher_JJR duty_NN1 cycle_NN1 allows_VVZ one_PN1 to_TO extend_VVI the_AT energy_NN1 range_NN1 ,_, while_CS the_AT energy_NN1 calibration_NN1 using_VVG FD_NP1 data_NN avoids_VVZ the_AT use_NN1 of_IO hadronic_JJ interaction_NN1 models_NN2 ._. 
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<s>
Extensive_JJ simulations_NN2 have_VH0 been_VBN performed_VVN by_II the_AT quasi-1D_NNU model_NN1 to_TO ignite_VVI a_AT1 precompressed_JJ fuel_NN1 which_DDQ has_VHZ a_AT1 length_NN1 of_IO 1_MC1 mm_NNU at_II different_JJ initial_JJ temperatures_NN2 ._. 
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<s>
This_DD1 follows_VVZ from_II the_AT observation_NN1 that_CST if_CS the_AT two_MC branches_NN2 can_VM be_VBI distinguished_VVN by_II measuring_VVG only_RR a_AT1 small_JJ number_NN1 of_IO subsystems_NN2 ,_, then_RT even_RR a_AT1 small_JJ amount_NN1 of_IO loss_NN1 leaks_VVZ enough_DD particle_NN1 to_II the_AT environment_NN1 to_TO allow_VVI it_PPH1 to_TO fully_RR collapse_VVI the_AT state_NN1 to_II one_MC1 of_IO the_AT two_MC branches_NN2 ._. 
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<s>
Different_JJ conclusions_NN2 are_VBR reported_VVN concerning_II the_AT volcano_NN1 simulation_NN1 ._. 
</s>
<s>
This_DD1 insight_NN1 motivates_VVZ a_AT1 second_MD avenue_NN1 of_IO future_JJ colliders_NN2 ,_, namely_REX another_DD1 (_( possibly_RR ultimately_RR final_JJ )_) push_VV0 for_IF a_AT1 hadron–_JJ hadron_NN1 collider_NN1 extrapolated_VVD from_II existing_JJ LHC_NP1 technology_NN1 ._. 
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<s>
This_DD1 <Equation>_FO ,_, N_ZZ1 relationship_NN1 depends_VVZ to_II some_DD extent_NN1 on_II the_AT shape_NN1 of_IO the_AT fragmentation_NN1 function_NN1 and_CC it_PPH1 is_VBZ given_VVN for_IF the_AT same_DA Pythia_NP1 6_MC fragmentation_NN1 function_NN1 that_CST was_VBDZ used_VVN in_II Fig_NN1 ._. 
</s>
<s>
B.1_FO ._. 
</s>
<s>
The_AT remaining_JJ two_MC stars_NN2 have_VH0 the_AT lowest_JJT metallicity_NN1 (_( &lsqb;_( Fe/H_NP1 &rsqb;_) <_FO 3_MC )_) of_IO the_AT observed_JJ sample_NN1 ._. 
</s>
<s>
For_IF Korsbakken_NP1 ,_, Wilhelm_NP1 ,_, and_CC Whaley_NP1 (_( 2009_MC )_) ,_, it_PPH1 matters_VVZ whether_CSW a_AT1 single_JJ electron_NN1 makes_VVZ the_AT difference_NN1 between_II the_AT <Equation>_FO and<Equation>_FO or_CC whether_CSW all_RR electrons_NN2 behave_VV0 differently_RR in_II the_AT two_MC branches_NN2 ._. 
</s>
<s>
This_DD1 is_VBZ the_AT case_NN1 in_II the_AT QRT_NP1 of_IO multipartite_JJ entanglement_NN1 under_II LOCC_NP1 ._. 
</s>
<s>
High-resolution_JJ TEM_NN1 (_( HRTEM_NP1 )_) images_NN2 recorded_VVN during_II the_AT in-situ_JJ experiment_NN1 were_VBDR analyzed_VVN with_IW the_AT CrystalMatch_NN1 software_NN1 &lsqb;_( 28_MC &rsqb;_) ._. 
</s>
<s>
In_II our_APPGE PIC_NN1 simulations_NN2 ,_, neutrons_NN2 were_VBDR generated_VVN using_VVG the_AT D-D_NNA fusion_NN1 cross-sections_NN2 and_CC the_AT relative_JJ velocity_NN1 between_II individual_JJ macro_JJ particles_NN2 ._. 
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<s>
For_IF N_ZZ1 =_FO 500_MC ,_, the_AT network_NN1 oscillation_NN1 has_VHZ the_AT same_DA frequency_NN1 as_CSA in_II Fig._NN1 9_MC at_II the_AT corresponding_JJ values_NN2 of_IO ext_NN1 ._. 
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<s>
Naturally_RR ,_, R0_FO would_VM imply_VVI large_JJ quantum_NN1 effects_NN2 ._. 
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<s>
On_II data_NN transmission_NN1 request_NN1 ,_, the_AT arbitrator_NN1 generates_VVZ GHZ_NNU states_NN2 and_CC posts_NN2 single_JJ particles_NN2 to_II communicating_JJ peers_NN2 ._. 
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<s>
The_AT right_JJ panel_NN1 of_IO Fig._NN1 12_MC shows_VVZ the_AT neutral_JJ stability_NN1 curves_NN2 ._. 
</s>
<s>
The_AT ultimate_JJ goal_NN1 for_IF theoristsa_NN1 comprehensive_JJ description_NN1 of_IO fission_NN1 starting_VVG from_II protons_NN2 ,_, neutrons_NN2 ,_, and_CC their_APPGE interactions_NN2 that_CST provides_VVZ accurate_JJ values_NN2 for_IF all_DB fission_NN1 data_NN of_IO interest_NN1 remains_VVZ elusive_JJ ._. 
</s>
<s>
The_AT particlehole_NN1 symmetry_NN1 itself_PPX1 is_VBZ realized_VVN as_II an_AT1 approximate_JJ symmetry_NN1 in_II the_AT Bogoliubov–de_NP1 Gennes_NP2 Hamiltonian_JJ ,_, which_DDQ describes_VVZ microscopic_JJ low-energy_JJ physics_NN1 of_IO superconductors_NN2 around_II the_AT Fermi_NP1 energy_NN1 at_II the_AT mean-field_JJ level_NN1 ._. 
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<s>
The_AT pulse_NN1 width_NN1 of_IO the_AT as_RG observed_JJ flflat_NN1 top_NN1 solitonsincreased_VVN as_II the_AT pump_NN1 power_NN1 increased_VVD ._. 
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<s>
In_II a_AT1 recent_JJ study_NN1 ,_, 21_MC we_PPIS2 demonstrated_VVD a_AT1 quantitative_JJ approach_NN1 to_II choosing_VVG the_AT right_JJ descriptor_NN1 for_IF maximizing_VVG the_AT activity_NN1 prediction_NN1 efficiency_NN1 given_VVN a_AT1 threshold_NN1 activity_NN1 of_IO interest_NN1 ._. 
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<s>
These_DD2 calculations_NN2 have_VH0 facilitated_VVN the_AT identification_NN1 of_IO the_AT 214.25_MC ,_, 216.79_MC ,_, and_CC 227.66_MC nm_FU spectral_JJ lines_NN2 of_IO Pb_FO V._NNU In_II the_AT absence_NN1 of_IO experimental_JJ results_NN2 of_IO oscillator_NN1 strengths_NN2 and_CC transition_NN1 probabilities_NN2 ,_, we_PPIS2 could_VM not_XX make_VVI a_AT1 direct_JJ comparison_NN1 with_IW our_APPGE results_NN2 ._. 
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<s>
In_RR21 general_RR22 ,_, it_PPH1 is_VBZ required_VVN to_TO identify_VVI high-Z_NP1 materials_NN2 in_II concrete_JJ filled_JJ containers_NN2 ._. 
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<s>
But_CCB in_II conversations_NN2 ,_, those_DD2 who_PNQS publish_VV0 work_NN1 based_VVN on_II two-dimensional_JJ analysis_NN1 claim_NN1 agreement_NN1 with_IW obser_NN1 vations_NN2 shows_VVZ correctness_NN1 ._. 
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<s>
It_PPH1 was_VBDZ deduced_VVN that_CST the_AT Ga-doped_JJ phagraphene_NN1 may_VM be_VBI a_AT1 promising_JJ work_NN1 function_NN1 type_NN1 sensor_NN1 for_IF CO_NP1 molecule_NN1 with_IW a_AT1 short_JJ recovery_NN1 time_NNT1 ._. 
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<s>
In_II 1826_MC ,_, captain_NN1 d_ZZ1 '_NULL Urville_NP1 ,_, a_AT1 French_JJ naval_JJ staff_NN ,_, reported_VVD the_AT first_MD extreme_JJ sea_NN1 wave_NN1 having_VHG an_AT1 amplitude_NN1 of_IO 100_MC ft_NNU ._. 
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<s>
In_RR21 addition_RR22 ,_, observations_NN2 of_IO SN_NN1 2011fe_FO implied_VVD a_AT1 size_NN1 of_IO R_ZZ1 0.1_MC R_ZZ1 for_IF the_AT exploding_JJ star_NN1 (_( Bloom_NP1 et_RA21 al._RA22 ,_, 2012_MC ;_; and_CC Piro_NP1 and_CC Nakar_NP1 ,_, 2014_MC )_) ,_, suggesting_VVG either_RR a_AT1 degenerate_JJ star_NN1 or_CC at_RR21 least_RR22 an_AT1 unusual_JJ star_NN1 (_( such_II21 as_II22 a_AT1 carbon_NN1 star_NN1 )_) ._. 
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<s>
Then_RT for_IF each_DD1 set_VVD the_AT total_JJ projection_NN1 Me_PPIO1 should_VM be_VBI defined_VVN and_CC all_DB Me_PPIO1 values_NN2 should_VM be_VBI distributed_VVN between_II possible_JJ values_NN2 of_IO Je_NP1 ._. 
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<s>
Our_APPGE procedure_NN1 ,_, in_II31 addition_II32 to_II33 being_VBG mathematically_RR justifiable_JJ ,_, is_VBZ consistent_JJ with_IW the_AT general_JJ methodology_NN1 used_VVN in_II treatment_NN1 of_IO data_NN for_IF ENSDF_NN1 database_NN1 and_CC horizontal_JJ evaluations_NN2 ._. 
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<s>
In_II direct-drive_JJ inertial_JJ confinement_NN1 fusion_NN1 (_( ICF_NP1 )_) implosions_NN2 ,_, 1,2_MC a_AT1 spherical_JJ target_NN1 (_( plastic_NN1 shell_NN1 )_) containing_VVG the_AT fusion_NN1 fuel_NN1 &lsqb;_( deuterium_NN1 (_( D_ZZ1 )_) and_CC tritium_NN1 (_( T_ZZ1 )_) &rsqb;_) is_VBZ irradiated_VVN directly_RR with_IW nominally_RR identical_JJ laser_NN1 beams_NN2 with_IW the_AT goal_NN1 of_IO achieving_VVG sufficient_JJ compression_NN1 needed_VVN for_IF ignition_NN1 ._. 
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<s>
If_CS ,_, instead_RR ,_, we_PPIS2 use_VV0 <Equation>_FO ,_, for_IF which_DDQ <Equation>_FO ,_, one_PN1 obtains_VVZ <Equation>_FO and_CC <Equation>_FO ._. 
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<s>
Here_RL ,_, the_AT constraints_NN2 on_II |_NULL U4_FO |_NULL 2_MC are_VBR driven_VVN by_II MINOS_NP1 &MINOS+;_NULL (_( 46_MC )_) ,_, the_AT IceCube_NP1 atmospheric_JJ neutrino_NN1 sample_NN1 (_( 47_MC )_) ,_, CDHS_NP1 (_( 48_MC )_) ,_, and_CC the_AT MiniBooNE/SciBooNE_NN1 disappearance_NN1 analyses_NN2 (_( 49_MC ,_, 50_MC )_) ._. 
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<s>
We_PPIS2 can_VM thus_RR extract_VVI precession_NN1 frequencies_NN2 of_IO (_( equawhich_NN1 are_VBR identical_JJ to_II those_DD2 obtained_VVN by_II FFT_NP1 analysis_NN1 ._. 
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However_RR ,_, it_PPH1 is_VBZ not_XX at_RR21 all_RR22 clear_VV0 that_CST a_AT1 single_JJ temperature_NN1 can_VM adequately_RR describe_VVI all_DB aspects_NN2 of_IO the_AT dynamics_NN of_IO a_AT1 glassy_JJ material_NN1 ._. 
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<s>
In_II the_AT presence_NN1 of_IO an_AT1 AC_NN1 elec-tric_JJ field_NN1 resonant_JJ with_IW the_AT Mott_NP1 gap_NN1 ,_, the_AT system_NN1 evolves_VVZ to_II a_AT1 photoinduced_JJ metallic_JJ state_NN1 within_II a_AT1 short_JJ time_NNT1 ._. 
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Therefore_RR this_DD1 '_NULL ridge_NN1 '_NULL is_VBZ not_XX indicated_VVN in_II Fig._NN1 17_MC ._. 
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<s>
Noting_VVG from_II figure_NN1 4_MC that_DD1 without_IW wall_NN1 contact_NN1 ,_, the_AT plasma_NN1 current_NN1 continues_VVZ with_IW a_AT1 relatively_RR slow_JJ decay_NN1 after_II thermal_JJ energy_NN1 is_VBZ diminished_VVN ,_, the_AT characterization_NN1 of_IO major_JJ versus_II minor_JJ disruption_NN1 &lsqb;_( 24_MC &rsqb;_) generally_RR describes_VVZ the_AT different_JJ behavior_NN1 in_II our_APPGE 3D_NNU computations_NN2 with_IW and_CC without_IW vertical_JJ forcing_NN1 ._. 
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In_II Fig._NN1 4(b)_FO ,_, the_AT band_NN1 intensities_NN2 between_II 350_MC and_CC 700_MC cm1_FO increase_VV0 strongly_RR for_IF lowering_NN1 of_IO the_AT electric_JJ potential_NN1 ,_, which_DDQ is_VBZ opposite_JJ to_II the_AT expected_JJ behavior_NN1 ._. 
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Thus_RR ,_, tuning_VVG only_RR the_AT interlayer_NN1 Coulomb_NP1 interaction_NN1 parameter_NN1 W_ZZ1 could_VM lead_VVI to_II the_AT transition_NN1 from_II the_AT metallic_JJ into_II the_AT semiconducting_JJ state_NN1 in_II the_AT tBLG_NNU system_NN1 (_( here_RL ,_, we_PPIS2 have_VH0 kept_VVN the_AT intralayer_NN1 Coulomb_NP1 interaction_NN1 parameter_NN1 at_II the_AT same_DA value_NN1 ,_, equal_JJ to_II <EQUATION>_FO ._. 
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Optimized_JJ ferrite_NN1 NP_NP1 was_VBDZ successfully_RR coated_VVN with_IW PEG_NP1 and_CC the_AT non-cytotoxic_JJ nature_NN1 of_IO the_AT particles_NN2 was_VBDZ then_RT confirmed_VVN ._. 
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This_DD1 demonstrates_VVZ <Picture>Figure_FO 3_MC :_: (_( A_ZZ1 )_) Fourier_NP1 spectra_NN2 of_IO first_MD order_NN1 autoregressive_JJ noise_NN1 as_CSA calculated_VVN in_II Eq_NN1 ._. 
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3_MC with_IW varying_JJ values_NN2 of_IO ._. 
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<s>
As_CSA Kendal_NP1 '_NULL s_ZZ1 tau_NN1 requires_VVZ a_AT1 large_JJ number_NN1 of_IO pair_NN comparison_NN1 ,_, its_APPGE computational_JJ complexity_NN1 is_VBZ higher_JJR than_CSN the_AT previous_JJ two_MC coefficients_NN2 ._. 
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<s>
The_AT center_NN1 frequency_NN1 is_VBZ 34.0_MC GHz_NNU ,_, which_DDQ agrees_VVZ with_IW the_AT cold_JJ test_NN1 frequency_NN1 of_IO the_AT <Professional_FO Term>_FO mode_NN1 in_II <Professional_FO Term>_FO ._. 
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<s>
Strikingly_RR enough_RR ,_, it_PPH1 should_VM be_VBI noted_VVN that_CST the_AT original_JJ system_NN1 proposed_VVN by_II Ikeda_NP1 was_VBDZ not_XX an_AT1 optoelectronic_JJ oscillator_NN1 because_CS the_AT feedback_NN1 loop_NN1 was_VBDZ all_DB optical_JJ (_( Ikeda_NP1 ,_, 1979_MC )_) ._. 
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<s>
Nuclear_JJ emulsion_NN1 detectors_NN2 were_VBDR among_II the_AT first_MD tracking_JJ devices_NN2 to_TO be_VBI used_VVN &lsqb;_( 48_MC &rsqb;_) ._. 
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<s>
Further_RRR ,_, mesostate_VV0 transitions_NN2 are_VBR treated_VVN as_CSA discontinuous_JJ '_NULL jumps_NN2 '_NULL occurring_VVG at_II specific_JJ ,_, but_CCB probabilistically_RR determined_VVN ,_, times_NNT2 (_( though_CS variants_NN2 of_IO the_AT theory_NN1 have_VH0 been_VBN developed_VVN in_II which_DDQ mesostate_VV0 transitions_NN2 are_VBR modeled_VVN as_CSA continuous_JJ '_NULL diffusive_JJ '_NULL processes_NN2 ._. 
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<s>
Figure_NN1 4(a)_FO shows_VVZ the_AT resulting_JJ contribution_NN1 ratio_NN1 and_CC cumulative_JJ contribution_NN1 ratio_NN1 for_IF the_AT logistic_JJ map_NN1 ,_, in_II continuation_NN1 of_IO the_AT numerical_JJ experiment_NN1 of_IO Sec_NNU ._. 
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III_MC C._ZZ1 <chart>_FO <chart>_FO FIG._NN1 4_MC ._. 
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<s>
Contribution_NN1 ratio_NN1 and_CC cumulative_JJ contribution_NN1 ratio_NN1 for_IF (_( a_ZZ1 )_) logistic_JJ map_NN1 and_CC (_( b_ZZ1 )_) Hénon_NN1 map_NN1 ._. 
</s>
<s>
The_AT formula_NN1 was_VBDZ developed_VVN for_IF free_JJ electron_NN1 metals_NN2 and_CC neglects_VVZ so-called_JJ "_" umklapp_NN1 "_" (_( folding_NN1 )_) processes_NN2 ,_, i.e._REX ,_, scattering_VVG events_NN2 whereby_RRQ k_ZZ1 goes_VVZ into_II <Equation>_FO with_IW G_NP1 being_VBG a_AT1 reciprocal_JJ lattice_NN1 vector_NN1 ._. 
</s>
<s>
The_AT resultant_JJ optical_JJ pulses_NN2 in_II the_AT FUT_NN1 are_VBR backscattered_VVN and_CC detected_VVN in_II a_AT1 photodiode_NN1 (_( PD_NP1 )_) via_II a_AT1 circulator_NN1 or_CC splitter_NN1 ._. 
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<s>
RS_NN1 technology_NN1 can_VM produce_VVI high-resolution_JJ flood_NN1 hazard_NN1 maps_NN2 for_IF regions_NN2 lacking_VVG of_IO ground_NN1 based_VVN system_NN1 to_TO monitor_VVI rainfall_NN1 and_CC river_NN1 discharge_NN1 ._. 
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<s>
The_AT membranes_NN2 were_VBDR used_VVN in_II batteries_NN2 and_CC the_AT possibility_NN1 of_IO further_JJR improvement_NN1 was_VBDZ referred_VVN from_II the_AT results_NN2 of_IO their_APPGE over_JJ potentials_NN2 and_CC surface_NN1 analyses_NN2 ._. 
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<s>
It_PPH1 should_VM be_VBI noted_VVN here_RL that_CST the_AT identification_NN1 of_IO these_DD2 generated_VVN solitary_JJ waves_NN2 ,_, i.e._REX ,_, whether_CSW they_PPHS2 are_VBR EASWs_NN2 or_CC IASWs_NN2 ,_, is_VBZ verified_VVN through_II their_APPGE dispersion_NN1 characteristics_NN2 in_II a_AT1 later_JJR part_NN1 of_IO this_DD1 section_NN1 ._. 
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<s>
The_AT other_JJ type_NN1 of_IO hybrid_JJ entanglement_NN1 of_IO the_AT form_NN1 of_IO Eq_NN1 ._. 
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<s>
(_( 16_MC )_) can_VM be_VBI obtained_VVN by_II using_VVG two-photon_JJ four-mode_JJ state_NN1 as_CSA in_II Eq_NN1 ._. 
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<s>
(_( 14_MC )_) as_II the_AT target_NN1 one_MC1 ._. 
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<s>
The_AT apparent_JJ simplicity_NN1 of_IO the_AT systems_NN2 can_VM lead_VVI to_II the_AT impression_NN1 that_CST the_AT research_NN1 is_VBZ trivial_JJ ,_, easy_JJ ,_, or_CC unimportant_JJ ._. 
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<s>
The_AT connecting_JJ links_NN2 are_VBR visible_JJ from_II which_DDQ it_PPH1 is_VBZ possible_JJ to_TO determine_VVI which_DDQ spheres_NN2 are_VBR attached_VVN together_RL in_II each_DD1 chain_NN1 ._. 
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<s>
The_AT only_JJ parameter_NN1 that_CST matters_NN2 is_VBZ the_AT bare_JJ charge_NN1 density_NN1 of_IO the_AT ionic_JJ planes_NN2 ._. 
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<s>
Each_DD1 type_NN1 of_IO experiment_NN1 is_VBZ presented_VVN as_II a_AT1 separate_JJ dataset_NN1 ._. 
</s>
<s>
From_II an_AT1 analysis_NN1 of_IO the_AT peak-to-peak_JJ distances_NN2 in_II the_AT time_NNT1 series_NN we_PPIS2 determined_VVD the_AT frequencies_NN2 f_ZZ1 of_IO the_AT oscillating_JJ spots_NN2 ,_, and_CC we_PPIS2 assigned_VVD f_ZZ1 =_FO 0_MC to_II the_AT units_NN2 showing_VVG no_AT oscillations_NN2 ._. 
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<s>
The_AT improvement_NN1 in_II the_AT electrochromic_JJ activity_NN1 of_IO the_AT porous_JJ inorganic_JJ oxides_NN2 has_VHZ been_VBN reported_VVN in_II the_AT literature_NN1 &lsqb;_( 4,38_MC &rsqb;_) ._. 
</s>
<s>
Non-reciprocal_JJ transport_NN1 properties_NN2 and_CC entanglement_NN1 in_II non-Hermitian_JJ system_NN1 of_IO SP_NN1 interacting_VVG withs_NN2 coupled_VVN to_II 1D_NNU waveguide_NN1 have_VH0 not_XX been_VBN considered_VVN yet_RR ._. 
</s>
<s>
If_CS there_EX are_VBR k_ZZ1 emissions_NN2 belonging_VVG to_II the_AT second_MD category_NN1 ,_, the_AT median_NN1 will_VM be_VBI shifted_VVN by_II (_( still_RR working_VVG in_II the_AT large_JJ number_NN1 of_IO cell_NN1 N_ZZ1 limit_NN1 )_) <Equation>_FO ._. 
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<s>
Consequently_RR ,_, the_AT effective_JJ interaction_NN1 vanishes_VVZ identically_RR at_II the_AT point_NN1 of_IO the_AT quantum_NN1 phase_NN1 transition_NN1 ._. 
</s>
<s>
All_DB chemicals_NN2 were_VBDR of_IO reagent_JJ grade_NN1 and_CC purchased_VVN from_II Thermo_NP1 Fisher_NP1 Scienti_NP1 ?_? c_ZZ1 (_( Waltham_NP1 ,_, MA_NNA )_) unless_CS otherwise_RR noted_VVN ._. 
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<s>
Fy_NP1 (_( 34_MC )_) have_VH0 been_VBN studied_VVN successfully_RR using_VVG FIB_NN1 contacting_VVG ._. 
</s>
<s>
It_PPH1 is_VBZ instructive_JJ to_TO consider_VVI what_DDQ preparation_NN1 uncertainty_NN1 means_VVZ in_II the_AT most_RGT general_JJ setting_NN1 ._. 
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<s>
The_AT generic_JJ fibre_NN1 is_VBZ a_AT1 2-dimensional_JJ torus_NN1 ._. 
</s>
<s>
Its_APPGE study_NN1 forms_VVZ an_AT1 invaluable_JJ tool_NN1 in_II the_AT search_NN1 for_IF physics_NN1 beyond_II the_AT standard_JJ electroweak_NN1 model_NN1 and_CC the_AT weak_JJ magnetism_NN1 recoil_NN1 term_NN1 ._. 
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<s>
Nevertheless_RR ,_, this_DD1 derivation_NN1 of_IO the_AT r_ZZ1 -process_JJ abundances_NN2 is_VBZ not_XX without_IW problems_NN2 :_: Strictly_RR speaking_VVG ,_, those_DD2 abundances_NN2 are_VBR just_RR the_AT "_" not_XX from_II the_AT s-process_JJ "_" abundances_NN2 ,_, and_CC could_VM be_VBI a_AT1 combination_NN1 of_IO nucleosynthesis_NN1 processes_NN2 (_( and_CC sites_NN2 )_) ._. 
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<s>
We_PPIS2 study_VV0 anomalies_NN2 in_II time-reversal-_NN1 (_( ZT_NP1 2_MC )_) andU(1)-symmetric_JJ topological_JJ orders_NN2 ._. 
</s>
<s>
As_CSA ,_, in_RR21 general_RR22 ,_, a_AT1 roto-translation_NN1 of_IO one_MC1 detector_NN1 with_II31 respect_II32 to_II33 the_AT other_NN1 determines_VVZ non-zero_JJ expected_JJ values_NN2 for_IF these_DD2 residuals_NN2 ,_, the_AT estimation_NN1 of_IO parameter_NN1 of_IO interest_NN1 xD_NNU and_CC θ_NULL D_ZZ1 can_VM be_VBI obtained_VVN from_II a_AT1 minimum_NN1 2_MC estimation_NN1 method_NN1 ,_, using_VVG the_AT following_JJ 2_MC definition_NN1 :_: <EQUATION>_FO (_( 55_MC )_) where_RRQ x0_FO and_CC θ_NULL are_VBR respectively_RR the_AT errors_NN2 on_II the_AT reconstructed_JJ x0_FO and_CC θ_NULL respectively_RR ,_, the_AT subscripts_NN2 h_ZZ1 and_CC l_ZZ1 refer_VV0 to_II the_AT higher_JJR and_CC lower_JJR detectors_NN2 ,_, and_CC the_AT i_MC1 index_NN1 runs_VVZ over_RP all_DB the_AT reconstructed_JJ muons_NN2 in_II the_AT data_NN sample_NN1 ._. 
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<s>
It_PPH1 will_VM be_VBI very_RG beneficial_JJ if_CS the_AT microscopic_JJ images_NN2 can_VM be_VBI recorded_VVN with_IW a_AT1 temporal_JJ resolution_NN1 ranging_VVG from_II the_AT second_NNT1 to_TO attosecond_VVI range_NN1 ._. 
</s>
<s>
They_PPHS2 have_VH0 found_VVN that_CST such_DA WO3_FO nanoparticles_NN2 optimized_VVN in_II CA_NP1 exhibited_VVD 1055_MC F/g_ZZ1 capacitance_NN1 at_II 5_MC <Professional_FO Term>_FO &lsqb;_( 14_MC &rsqb;_) ._. 
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<s>
The_AT filling_NN1 factor_NN1 of_IO the_AT grating_JJ is_VBZ fixed_VVN to_TO be_VBI 0.55_MC ._. 
</s>
<s>
Thus_RR ,_, M0_FO and_CC M1_FO are_VBR equivalent_JJ and_CC only_RR one_MC1 map_NN1 is_VBZ needed_VVN to_TO describe_VVI the_AT system_NN1 (_( as_II seen_VVN in_II Sec_NNU ._. 
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<s>
II_MC )_) ._. 
</s>
<s>
It_PPH1 gives_VVZ a_AT1 higher_JJR negative_JJ value_NN1 of_IO ._. 
</s>
<s>
<Table>_FO ._. 
</s>
<s>
In_II fact_NN1 ,_, we_PPIS2 perform_VV0 a_AT1 stochastic_JJ optimisation_NN1 ,_, i.e._REX we_PPIS2 optimise_VV0 the_AT sublimation_NN1 rate_NN1 for_IF Gauss_NN1 distributions_NN2 of_IO shifts_NN2 around_II each_DD1 pair_NN of_IO nominal_JJ (_( h1_FO ,_, h2_FO )_) values_NN2 ,_, with_IW standard_JJ deviations_NN2 of_IO 0.2mm_NNU ._. 
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<s>
These_DD2 mixed_JJ state_NN1 results_NN2 also_RR suggest_VV0 that_CST the_AT intermediate_JJ is_VBZ real_JJ and_CC not_XX the_AT result_NN1 of_IO averaging_NN1 of_IO the_AT two_MC endpoint_NN1 conformations_NN2 and_CC implies_VVZ that_CST the_AT time-resolved_JJ ligand_NN1 and_CC protein_NN1 conformational_JJ changes_NN2 are_VBR finitely_RR coupled_VVN in_II the_AT crystalline_JJ state_NN1 of_IO the_AT tetrahydrofolate_NN1 bound_VVD complex_JJ ._. 
</s>
<s>
One_MC1 excited_JJ helium_NN1 atom_NN1 transfers_VVZ its_APPGE internal_JJ energy_NN1 to_II the_AT embedded_JJ methyl_NN1 iodide_NN1 ,_, and_CC a_AT1 molecular_JJ or_CC atomic_JJ cation_NN1 is_VBZ produced_VVN according_II21 to_II22 the_AT reaction_NN1 sequence_NN1 above_RL ._. 
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<s>
For_IF a_AT1 recent_JJ review_NN1 on_II the_AT physics_NN1 of_IO free-electron_JJ lasers_NN2 see_VV0 (_( Pellegrini_NP1 et_RA21 al._RA22 ,_, 2016_MC )_) ._. 
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<s>
It_PPH1 has_VHZ also_RR been_VBN suggested_VVN that_CST the_AT presence_NN1 of_IO a_AT1 companion_NN1 might_VM leave_VVI a_AT1 signature_NN1 on_II the_AT supernova_NN1 remnant_NN1 (_( e.g._REX ,_, Papish_NN1 et_RA21 al._RA22 ,_, 2015_MC )_) ._. 
</s>
<s>
The_AT main_JJ difference_NN1 with_IW the_AT case_NN1 <EQUATION>_FO is_VBZ that_CST the_AT position_NN1 of_IO the_AT point_NN1 <EQUATION>_FO on_II the_AT <EQUATION>_FO ,_, leading_VVG to_II the_AT additional_JJ rightshift_NN1 in_II the_AT energy_NN1 spectrum_NN1 at_II the_AT point_NN1 <EQUATION>_FO ._. 
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<s>
They_PPHS2 suggested_VVD to_TO integrate_VVI remote_JJ sensing_NN1 ,_, computer_NN1 vision_NN1 and_CC machine_VV0 learning_VVG for_IF better_JJR urban_JJ observation_NN1 ._. 
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<s>
The_AT magnetic_JJ energy_NN1 exceeds_VVZ the_AT kinetic_JJ energy_NN1 only_RR for_IF Rm_NP1 200_MC ._. 
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<s>
Parameters_NN2 that_CST are_VBR constrained_VVN to_TO be_VBI positive_JJ ,_, such_II21 as_II22 velocity_NN1 distribution_NN1 location_NN1 and_CC scale_NN1 parameters_NN2 (_( e.g._REX ,_, lC_NNU ;_; rM_NNU )_) ,_, are_VBR given_VVN exponential_NN1 distributions_NN2 as_CSA priors_NN2 while_CS most_DAT other_JJ parameters_NN2 are_VBR given_VVN normal_JJ distributions_NN2 as_CSA priors_NN2 ._. 
</s>
<s>
The_AT authors_NN2 have_VH0 no_AT conflicts_NN2 to_TO declare_VVI ._. 
</s>
<s>
This_DD1 paper_NN1 theoretically_RR aims_VVZ to_TO provide_VVI a_AT1 new_JJ route_NN1 to_TO realize_VVI real-time_JJ blackout_NN1 communication_NN1 encountered_VVN during_II spacecraft_NN reentry_NN1 based_VVN on_II the_AT laser-plasma-induced_JJ X-ray_NN1 emission_NN1 ._. 
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<s>
In_II our_APPGE cases_NN2 ,_, the_AT moduli_NN2 spaces_NN2 under_II consideration_NN1 are_VBR hyperk?hler_NN1 ,_, with_IW complex_JJ structures_NN2 I_PPIS1 ,_, J_ZZ1 ,_, K_ZZ1 of_IO the_AT following_JJ type_NN1 ._. 
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<s>
To_TO better_RRR understand_VVI the_AT interpretation_NN1 in_II31 terms_II32 of_II33 loop_NN1 structure_NN1 we_PPIS2 compare_VV0 the_AT above_JJ results_NN2 with_IW the_AT case_NN1 where_CS the_AT epidemic_NN1 is_VBZ initiated_VVN with_IW two_MC singly_RR infected_JJ nodes_NN2 ,_, chosen_VVN randomly_RR ,_, but_CCB constrained_VVD to_TO be_VBI at_II a_AT1 minimum_JJ distance_NN1 from_II each_PPX221 other_PPX222 ._. 
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<s>
Depending_II21 on_II22 the_AT context_NN1 ,_, the_AT partial-wave_JJ index_NN1 i_ZZ1 has_VHZ two_MC meanings_NN2 ._. 
</s>
<s>
A_AT1 Lagrangian_JJ ,_, involutive_JJ sub-bundle_NN1 L_ZZ1 T_ZZ1 MC_NN1 is_VBZ also_RR called_VVN a_AT1 Dirac_JJ structure_NN1 ,_, and_CC generalized_JJ complex_JJ structures_NN2 correspond_VV0 in_II a_AT1 one-to-one_JJ fashion_NN1 with_IW Dirac_JJ structures_NN2 L_ZZ1 satisfying_VVG the_AT additional_JJ non-degeneracy_JJ condition_NN1 <Equation>_FO ._. 
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<s>
These_DD2 and_CC similar_JJ effects_NN2 can_VM be_VBI understood_VVN to_II some_DD degree_NN1 by_II employing_VVG computational_JJ models_NN2 of_IO oscillatory_JJ and_CC state-dependent_JJ dynamics_NN (_( Alagapan_NP1 et_RA21 al._RA22 ,_, 2016_MC )_) ._. 
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<s>
It_PPH1 turned_VVD out_RP that_CST the_AT changes_NN2 of_IO the_AT unquenched_JJ gluon_NN1 due_II21 to_II22 the_AT different_JJ up/down_II quark_NN1 masses_NN2 in_II the_AT DSE_NN1 result_NN1 were_VBDR smaller_JJR than_CSN the_AT (_( statistical_JJ )_) error_NN1 bars_NN2 of_IO the_AT lattice_NN1 data_NN ,_, such_CS21 that_CS22 both_DB2 comparisons_NN2 have_VH0 been_VBN meaningful_JJ and_CC delivered_VVD a_AT1 similar_JJ result_NN1 ,_, shown_VVN in_II Fig._NN1 4.7_MC ._. 
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<s>
In_BCL21 order_BCL22 to_TO tackle_VVI this_DD1 problem_NN1 ,_, scientists_NN2 attempt_VV0 chemical_JJ modification_NN1 of_IO electron-withdrawing_JJ groups_NN2 on_II molecular_JJ terminals_NN2 based_VVN on_II typical_JJ molecular_JJ frameworks_NN2 to_TO produce_VVI n-type_JJ organic_JJ semiconductor_NN1 materials_NN2 ._. 
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<s>
Type_NN1 II_MC PDT_NP1 is_VBZ a_AT1 form_NN1 of_IO phototherapy_NN1 involving_VVG light_JJ and_CC a_AT1 photosensitizer_NN1 ._. 
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<s>
A_AT1 mor_NN1 complete_JJ study_NN1 must_VM also_RR include_VVI the_AT effective_JJ collisionalit_JJ eff_NN1 ,_, which_DDQ normalizes_VVZ the_AT electron–ion_NN1 collision_NN1 frequency_NN1 e_ZZ1 to_II the_AT curvature_NN1 drift_NN1 frequency_NN1 De_NP1 ._. 
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<s>
We_PPIS2 would_VM allow_VVI for_IF larger_JJR tolerances_NN2 of_IO the_AT targets_NN2 ,_, compatible_JJ with_IW the_AT assembly_NN1 time_NNT1 schedule_NN1 ,_, but_CCB would_VM measure_VVI the_AT resulting_JJ step_NN1 height_NN1 along_II the_AT gaps_NN2 between_II TEs_NP1 ._. 
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<s>
Over_II the_AT years_NNT2 ,_, this_DD1 work_NN1 has_VHZ been_VBN supported_VVN by_II many_DA2 institutions_NN2 (_( the_AT LPTHE_NN1 at_II the_AT University_NN1 Pierre_NP1 et_NP1 Marie_NP1 Curie_NP1 ,_, the_AT Brookhaven_JJ National_JJ Laboratory_NN1 ,_, CERN_NP1 ,_, the_AT French_JJ CNRS_NP1 and_CC the_AT IPhT_NN1 at_II the_AT CEA_NP1 Saclay_NP1 )_) and_CC several_DA2 grants_NN2 (_( Contract_NN1 No_UH ._. 
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<s>
DE-_JJ AC02-98CH10886_NN1 with_IW the_AT U.S._NP1 Department_NN1 of_IO Energy_NN1 ,_, the_AT French_JJ ANR_NN1 grant_NN1 Jets4LHC_FO under_II number_NN1 ANR-10-CEXC-009-01_NP1 ,_, the_AT ERC_NP1 advanced_JJ grant_NN1 Higgs@LHC_FO and_CC the_AT French_JJ ANR_NN1 grant_NN1 OptimalJets_VVZ under_II number_NN1 ANR-15-CE31-0016_NP1 )_) ._. 
</s>
<s>
The_AT initial_JJ resources_NN2 placed_VVN on_II objects_NN2 are_VBR first_MD evenly_RR divided_VVN among_II neighboring_VVG users_NN2 and_CC then_RT evenly_RR divided_VVN among_II those_DD2 users_NN2 '_NULL neighboring_VVG objects_NN2 ._. 
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<s>
In_II this_DD1 section_NN1 ,_, we_PPIS2 will_VM briefly_RR introduce_VVI literature_NN1 that_CST map_NN1 poverty_NN1 from_II satellite_NN1 imagery_NN1 ,_, infer_VV0 socioeconomic_JJ status_NN1 from_II mobile_JJ phone_NN1 (_( MP_NN1 )_) data_NN and_CC fight_VV0 against_II poverty_NN1 with_IW combined_JJ data_NN ._. 
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<s>
Geometry_NN1 of_IO the_AT magnetic_JJ nozzle._NNU )_) section_NN1 3_MC ._. 
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<s>
The_AT Facility_NN1 for_IF Rare_JJ Isotope_NN1 Beams_NN2 (_( FRIB_NP1 )_) ,_, located_VVN at_II the_AT site_NN1 of_IO the_AT NSCL_NN1 in_II Michigan_NP1 ,_, USA_NP1 ,_, is_VBZ currently_RR undergoing_VVG construction_NN1 with_IW a_AT1 target_NN1 completion_NN1 date_NN1 of_IO 2020_MC ._. 
</s>
<s>
These_DD2 quantized_JJ maps_NN2 are_VBR studied_VVN as_CSA models_NN2 of_IO relaxation_NN1 in_II classical_JJ mixing_NN1 systems_NN2 &lsqb;_( 37_MC &rsqb;_) ._. 
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<s>
For_IF <Equation>_FO ,_, this_DD1 again_RT only_RR leads_VVZ to_II splittings_NN2 ._. 
</s>
<s>
The_AT agreement_NN1 between_II the_AT two_MC techniques_NN2 is_VBZ ,_, however_RR ,_, a_AT1 good_JJ result_NN1 to_TO believe_VVI in_II the_AT robustness_NN1 of_IO the_AT two_MC measurements_NN2 ._. 
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<s>
In_II the_AT simple_JJ case_NN1 ,_, for_REX21 example_REX22 ,_, when_CS ATP_NN1 hydrolysis_NN1 is_VBZ driving_VVG an_AT1 exergonic_JJ reduction_NN1 (_( as_CSA in_II Nitrogenases_NP1 &lsqb;_( 94_MC &rsqb;_) )_) ,_, the_AT reduction_NN1 '_NULL s_ZZ1 completion_NN1 precedes_VVZ ,_, and_CC triggers_NN2 ,_, the_AT hydrolysis_NN1 ._. 
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<s>
We_PPIS2 thank_VV0 the_AT X-ray_NN1 CoreLab_NP1 and_CC BER_NP1 II_MC at_II Helmholtz-Zentrum_NP1 Berlin_NP1 ,_, Germany_NP1 for_IF providing_VVG the_AT experiment_NN1 times_NNT2 and_CC beam_NN1 times_NNT2 ,_, respectively_RR ,_, and_CC Dr._NNB Michael_NP1 Tovar_NP1 ,_, Rene_NP1 Gunder_NP1 and_CC Dr._NNB Alexandra_NP1 Franz_NP1 for_IF the_AT technical_JJ support_NN1 in_II the_AT diffraction_NN1 experiments_NN2 ._. 
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<s>
Relative_JJ velocity_NN1 between_II target-like_JJ fragments_NN2 and_CC intermediate_JJ mass_JJ fragments_NN2 (_( normalized_VVN to_II fission_NN1 systematics_NN2 )_) versus_II relative_JJ velocity_NN1 between_II projectile-like_JJ fragments_NN2 and_CC intermediate_JJ mass_JJ fragments_NN2 (_( also_RR normalized_VVN )_) for_IF collisions_NN2 of_IO <Professional_FO Term>_FO ._. 
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<s>
For_IF the_AT other_JJ U3_FO state_VV0 from_II configuration_NN1 D_ZZ1 ,_, the_AT hyperfine_JJ parameter_NN1 will_VM be_VBI too_RG high_JJ whatever_DDQV the_AT composition_NN1 of_IO the_AT 4p_NNU MO_NP1 ._. 
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<s>
We_PPIS2 also_RR assume_VV0 that_CST all_DB three_MC nanorods_NN2 are_VBR identical_JJ and_CC therefore_RR have_VH0 the_AT same_DA LSP_NP1 resonance_NN1 frequency_NN1 R_ZZ1 ,_, loss_NN1 terms_NN2 ,_, and_CC eigenfunction_NN1 dipole_NN1 moments_NN2 |_NULL p1_FO |_NULL =_FO |_NULL p2_FO |_NULL =_FO |_NULL p3_FO |_NULL ,_, where_CS we_PPIS2 assume_VV0 one_MC1 dominant_JJ LSP_NP1 mode_NN1 on_II each_DD1 and_CC drop_VV0 the_AT mode_NN1 superscript_NN1 ._. 
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<s>
For_IF Pm_NP1 of_IO order_NN1 unity_NN1 ,_, the_AT spectrum_NN1 is_VBZ rather_RG flat_JJ on_II the_AT low_JJ m_ZZ1 side_NN1 ,_, and_CC rather_RG steep_JJ for_IF small_JJ Pm_NP1 ._. 
</s>
<s>
The_AT fitted_JJ in-plane_NN1 field_NN1 coefficients_NN2 (_( representing_VVG the_AT fieldlike_JJ torque_NN1 )_) for_IF a_AT1 set_NN1 of_IO devices_NN2 in_II different_JJ crystal_NN1 directions_NN2 ._. 
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<s>
The_AT same_DA approach_NN1 used_VMK to_TO analyze_VVI the<Equation>_FO case_NN1 was_VBDZ also_RR used_VVN for<Equation>_FO ,_, with_IW reasonably_RR good_JJ agreement_NN1 with_IW numerical_JJ simulations_NN2 &lsqb;_( 36_MC &rsqb;_) ._. 
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<s>
It_PPH1 is_VBZ seen_VVN that_CST there_EX is_VBZ long_RR charge_VV0 potential_JJ plateau_NN1 at_II 1.2_MC V_NNU with_IW negligible_JJ discharge_NN1 capacity_NN1 ._. 
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<s>
The_AT First_MD Application_NN1 Of_IO The_AT Linearized_JJ Solution_NN1 Operator_NN1 Will_VM Be_VBI To_II The_AT Homogeneous_JJ Problem_NN1 With_IW Inhomogeneous_JJ Boundary_NN1 Data_NN ._. 
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<s>
Spitzer_NN1 gives_VVZ expressions_NN2 for_IF the_AT slow-down_NN1 time_NNT1 of_IO a_AT1 test_NN1 particle_NN1 entering_VVG a_AT1 field_NN1 of_IO electrons_NN2 ._. 
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<s>
Suppose_VV0 that_CST there_EX exists_VVZ <Equation>_FO such_CS21 that_CS22 <Equation>_FO for_IF some_DD <Equation>_FO and_CC <Equation>_FO ._. 
</s>
<s>
The_AT fact_NN1 that_CST even_RR these_DD2 "_" extreme_JJ "_" triangles_NN2 obey_VV0 the_AT Y_NP1 law_NN1 is_VBZ explicitly_RR demonstrated_VVN in_II Fig._NN1 11_MC (_( instead_RR ,_, the_AT most_RGT outlying_JJ data_NN points_NN2 turn_VV0 out_RP to_TO be_VBI the_AT ones_NN2 with_IW smallest_JJT triangle_NN1 base_NN1 )_) ,_, where_CS the_AT caption_NN1 qqq_NNU (_( Y_ZZ1 →_NULL )_) implies_VVZ that_CST for_IF such_DA triangles_NN2 the_AT Fermat-Torricelli_JJ point_NN1 coincides_VVZ with_IW one_MC1 of_IO the_AT vertices_NN2 turning_VVG the_AT Y_NP1 law_NN1 into_II the_AT law_NN1 ._. 
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<s>
Rochester_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2016_MC )_) suggested_VVD using_VVG an_AT1 additional_JJ degenerate_JJ ensemble_NN1 3_MC of_IO states_NN2 ,_, serving_VVG as_II shelf_NN1 states_NN2 ._. 
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<s>
This_DD1 region_NN1 is_VBZ dominated_VVN by_II the_AT c-type_JJ R-branch_JJ rotational_JJ transitions_NN2 ._. 
</s>
<s>
Throughout_II this_DD1 review_NN1 we_PPIS2 adopt_VV0 the_AT convention_NN1 that_CST HX_NP1 denotes_VVZ a_AT1 classical_JJ system_NN1 whose_DDQGE states_NN2 are_VBR always_RR diphase_VV0 in_II some_DD a_JJ21 priori_JJ22 fixed_JJ orthonormal_JJ basis_NN1 fjiigi_NN2 ._. 
</s>
<s>
The_AT exactly_RR identical_JJ mass_JJ density_NN1 tensors_NN2 <EQUATION>_FO <FIGURE>_FO and_CC <EQUATION>_FO and_CC bulk_VV0 modulus_NN1 ,_, B_ZZ1 ,_, in_II the_AT local_JJ coordinate_NN1 systems_NN2 should_VM be_VBI satisfied_VVN ._. 
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<s>
The_AT <Equation>_FO and_CC the_AT C/A_ZZ1 algorithms_NN2 are_VBR not_XX shown_VVN for_IF clarity_NN1 ,_, but_CCB they_PPHS2 share_VV0 the_AT behavior_NN1 of_IO C/A_ZZ1 (_( filt_NN1 )_) ._. 
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Additionally_RR ,_, development_NN1 and_CC usage_NN1 of_IO materials_NN2 which_DDQ exhibit_VV0 better_JJR performance_NN1 such_II21 as_II22 Al_NP1 will_VM also_RR improve_VVI performance_NN1 and_CC cost_NN1 ._. 
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Particles_NN2 in_II the_AT DSB_NP1 regime_NN1 move_NN1 along_II the_AT bent_JJ atomic_JJ strings_NN2 ._. 
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Therefore_RR ,_, these_DD2 undetermined_JJ parameters_NN2 are_VBR commonly_RR estimated_VVN by_II calibration_NN1 via_II Rayleigh_NP1 or_CC Raman_NN1 scattering_VVG ._. 
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The_AT derivative_NN1 of_IO the_AT magnetization_NN1 curve_NN1 of_IO the_AT samples_NN2 ._. 
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The_AT wind_NN1 tunnel_NN1 was_VBDZ equipped_VVN with_IW four_MC sapphire_NN1 widows_NN2 ,_, one_MC1 on_II each_DD1 side_NN1 ,_, for_IF the_AT laser_NN1 beam_NN1 ,_, imaging_VVG and_CC light_JJ collection_NN1 of_IO the_AT LIB_NN1 ._. 
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If_CS the_AT matching_JJ number_NN1 is_VBZ larger_JJR than_CSN five_MC ,_, this_DD1 reference_NN1 spectrum_NN1 can_VM be_VBI remained_VVN as_II a_AT1 candidate_NN1 spectrum_NN1 ._. 
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Brelsford_NP1 et_RA21 al_RA22 ._. 
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&lsqb;_( 426_MC &rsqb;_) explored_VVD the_AT topology_NN1 and_CC spatial_JJ evolution_NN1 of_IO neighborhoods_NN2 based_VVN on_II a_AT1 diverse_JJ set_NN1 of_IO detailed_JJ urban_JJ maps_NN2 ._. 
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This_DD1 comparison_NN1 is_VBZ presented_VVN in_II Table_NN1 I._NP1 Evidently_RR ,_, as_CSA already_RR displayed_VVN in_II Fig._NN1 9_MC ,_, the_AT DCC_MC bare-Roper_JJ mass_NN1 agrees_VVZ with_IW the_AT quark-core_JJ results_NN2 obtained_VVD using_VVG both_RR a_AT1 QCD-kindred_JJ interaction_NN1 (_( Segovia_NP1 et_RA21 al._RA22 ,_, 2015_MC )_) and_CC refined_JJ treatments_NN2 of_IO a_AT1 vector_NN1 contact_NN1 interaction_NN1 (_( Wilson_NP1 et_RA21 al._RA22 ,_, 2012_MC ;_; Lu_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
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What_DDQ are_VBR the_AT possible_JJ routes_NN2 of_IO escaping_JJ thermalization_NN1 As_CSA discussed_VVN in_II the_AT Introduction_NN1 ,_, the_AT absence_NN1 of_IO transport_NN1 would_VM be_VBI sufficient_JJ ,_, and_CC therefore_RR ,_, Anderson_NP1 localization_NN1 in_II single_JJ particle_NN1 disordered_JJ systems_NN2 provides_VVZ a_AT1 natural_JJ starting_NN1 point_NN1 to_TO look_VVI for_IF no_AT thermalizing_JJ systems_NN2 ._. 
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Because_II21 of_II22 its_APPGE large_JJ amount_NN1 of_IO calculation_NN1 ,_, we_PPIS2 use_VV0 GGA-PBE_JJ methods_NN2 to_TO analyse_VVI photocurrent_NN1 ._. 
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Thus_RR the_AT bulk_NN1 electrolyte_NN1 is_VBZ not_XX reached_VVN even_RR far_RR away_II21 from_II22 the_AT electrode_NN1 ,_, and_CC situations_NN2 are_VBR not_XX ideal_JJ for_IF the_AT electrochemical_JJ setup_NN1 ._. 
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HS-LEIS_NP1 for_IF the_AT LSF-YSZ_JJ electrode_NN1 ,_, before_CS and_CC after_II adding_VVG 5_MC and_CC 10_MC ALD_NN1 cycles_NN2 Co3O4_FO ,_, are_VBR shown_VVN in_II Fig._NN1 3_MC ._. 
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The_AT beam_NN1 of_IO 400_MC GeV/c_FU protons_NN2 enters_VVZ the_AT central_JJ ultrathin_NN1 crystal_NN1 area_NN1 ._. 
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Also_RR as_II part_NN1 of_IO this_DD1 study_NN1 ,_, we_PPIS2 characterized_VVD a_AT1 series_NN of_IO "_" off_JJ pathway_NN1 "_" complexes_NN2 of_IO XcPGM_NP1 ._. 
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Our_APPGE studies_NN2 demonstrated_VVD that_CST a_AT1 simple_JJ method_NN1 using_VVG a_AT1 combination_NN1 of_IO serum_NN1 and_CC water_NN1 washes_NN2 (_( Fig._NN1 1_MC1 )_) shortens_VVZ the_AT process_NN1 of_IO muscle_NN1 ECM_NP1 decellularization_NN1 to_TO further_RRR protect_VVI native_JJ bioactive_JJ proteins_NN2 ,_, as_CSA compared_VVN to_II other_JJ methods_NN2 that_CST commonly_RR use_VV0 DNase_NN1 as_II a_AT1 degradation_NN1 method_NN1 ._. 
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If_CS a_AT1 resonance_NN1 is_VBZ formed_VVN during_II the_AT scattering_NN1 process_NN1 ,_, E_ZZ1 becomes_VVZ the_AT energy_NN1 of_IO the_AT resonance_NN1 in_II its_APPGE rest_NN1 frame_NN1 ._. 
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In_RR21 particular_RR22 ,_, β_NULL fells_NN2 into_II a_AT1 narrow_JJ band_NN1 <Equation>_FO ,_, where<Equation>_FO for_IF the_AT AIDS/HIV_FU prevalence_NN1 in_II the_AT US_NP1 cities_NN2 and_CC <Equation>_FO for_IF the_AT total_JJ GDP_NN1 per_II square_JJ kilometer_NNU1 in_II the_AT European_JJ cities_NN2 ._. 
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In_RR21 addition_RR22 ,_, if_CS the_AT Compton_NP1 length_NN1 of_IO the_AT scalar_JJ particle_NN1 becomes_VVZ smaller_JJR that_CST the_AT interatomic_JJ distance_NN1 ,_, the_AT matter_NN1 fluids_NN2 can_VM not_XX be_VBI approximated_VVN in_II the_AT general_JJ relativistic_JJ way_NN1 ,_, that_DD1 is_VBZ as_RG perfect_JJ fluids_NN2 ,_, and_CC hence_RR ,_, the_AT Chameleon_NN1 mechanism_NN1 can_VM not_XX work_VVI in_II this_DD1 case_NN1 ._. 
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At_II a_AT1 conceptual_JJ level_NN1 ,_, marginally_RR coordinated_JJ critical_JJ motion_NN1 can_VM be_VBI hypothesized_VVN to_TO constitute_VVI an_AT1 optimal_JJ trade-off_NN1 to_TO deal_VVI with_IW conflicting_JJ imperatives_NN2 such_II21 as_II22 (_( i_ZZ1 )_) the_AT need_NN1 to_TO behave_VVI cohesively_RR as_II a_AT1 unique_JJ entity_NN1 and_CC (_( ii_MC )_) being_VBG highly_RR responsive_JJ to_II informtion_NN1 from_II transitorily_RR well-informed_JJ individuals_NN2 (_( Couzin_NP1 et_RA21 al._RA22 ,_, 2005_MC ,_, 2011_MC ;_; Vanni_NP1 ,_, Lukovi_NP1 ?_? ,_, and_CC Grigolini_NP1 ,_, 2011_MC ;_; De_NP1 Vincenzo_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
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In_BCL21 order_BCL22 to_TO bound_VVI the_AT first_MD term_NN1 ,_, we_PPIS2 use_VV0 the_AT following_JJ general_JJ inequality_NN1 for_IF s_ZZ1 ,_, <Equation>_FO ,_, <Equation>_FO ._. 
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Once_RR tightly_RR focused_VVD it_PPH1 could_VM produce_VVI easily_RR ,_, intensity_NN1 at_II or_CC above_II the_AT Schwinger_JJR limit_NN1 ._. 
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The_AT strong_JJ ,_, short-range_JJ nuclear_JJ force_NN1 acts_VVZ in_II a_AT1 failing_JJ attempt_NN1 to_TO hold_VVI them_PPHO2 together_RL ,_, but_CCB the_AT relative_JJ velocity_NN1 and_CC angular_JJ momentum_NN1 will_VM prove_VVI too_RG great_JJ ._. 
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However_RRQV if_CS we_PPIS2 are_VBR to_TO understand_VVI the_AT impact_NN1 of_IO pileup_NN1 and_CC underlying-event_JJ radiation_NN1 on_II jet_NN1 finding_NN1 –_- the_AT original_JJ motivation_NN1 for_IF studying_VVG areas_NN2 –_- then_RT we_PPIS2 should_VM take_VVI into_II account_NN1 the_AT fact_NN1 that_CST these_DD2 contributions_NN2 provide_VV0 a_AT1 dense_JJ background_NN1 of_IO particles_NN2 at_II some_DD small_JJ but_CCB finite_JJ soft_JJ <Equation>_FO ._. 
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The_AT induced_JJ carrier_NN1 imbalance_NN1 and_CC exciton_NN1 quenching_VVG at_II metal_NN1 electrodes_NN2 will_VM seriously_RR affect_VVI the_AT consequent_JJ emission_NN1 efficiency_NN1 ._. 
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According_II21 to_II22 the_AT relation_NN1 (_( 60_MC )_) ,_, we_PPIS2 then_RT expect_VV0 to_TO get_VVI the_AT correlation_NN1 functions_NN2 of_IO the_AT supersymmetric_JJ theory_NN1 (_( 34_MC )_) of_IO a_AT1 free_JJ Dirac_JJ field_NN1 with_IW bosonic_JJ ghost_NN1 system_NN1 describing_VVG the_AT continuum_NN1 limit_NN1 of_IO the_AT Chalker-Coddington_NP1 network_NN1 model_NN1 without_IW disorder_NN1 (_( U_ZZ1 ≡_NULL Us_NP1 )_) ._. 
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Figure_NN1 7_MC shows_VVZ the_AT measured_JJ v2_FO coefficients_NN2 as_II a_AT1 function_NN1 of_IO pseudorapidity_NN1 for_IF high-multiplicity_NN1 d_ZZ1 +Au_FO collisions_NN2 at_II the_AT three_MC higher_JJR energies_NN2 ._. 
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To_TO illustrate_VVI this_DD1 quantitatively_RR ,_, consider_VV0 the_AT orbit-smoothed_JJ gravitational_JJ potential_NN1 of_IO the_AT giant_JJ planets_NN2 ,_, averaged_VVN over_II the_AT Keplerian_JJ trajectory_NN1 of_IO a_AT1 Kuiper_NN1 belt_NN1 object_NN1 ._. 
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This_DD1 motivates_VVZ the_AT study_NN1 of_IO nonlinear_JJ Hamiltonians_NN2 ._. 
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This_DD1 can_VM be_VBI relevant_JJ for_IF coordination_NN1 purposes_NN2 in_II neural_JJ systems_NN2 where_RRQ coherent_JJ behavior_NN1 across_II extended_JJ areas_NN2 is_VBZ observed_VVN (_( Tagliazucchi_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) in_II flocks_NN2 of_IO birds_NN2 (_( Cavagna_NP1 et_RA21 al._RA22 ,_, 2010_MC )_) and_CC in_II micro-organism_NN1 colonies_NN2 (_( De_NP1 Palo_NP1 ,_, Yi_NP1 ,_, and_CC Endres_NP1 ,_, 2017_MC )_) ._. 
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<s>
Similarly_RR ,_, the_AT emergence_NN1 of_IO very_RG large_JJ correlation_NN1 times_NNT2 and_CC a_AT1 critical_JJ slowing_VVG down_RP may_VM provide_VVI biological_JJ systems_NN2 with_IW a_AT1 useful_JJ mechanism_NN1 for_IF the_AT generation_NN1 of_IO long-lasting_JJ and/or_CC slow-decaying_JJ memories_NN2 at_II multiple_JJ time_NNT1 scales_NN2 (_( Deco_NP1 and_CC Jirsa_NP1 ,_, 2012_MC )_) ._. 
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A_AT1 relation_NN1 between_II those_DD2 would_VM be_VBI important_JJ ._. 
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The_AT solid_JJ blue_JJ and_CC dashed_JJ green_JJ lines_NN2 represent_VV0 down_RP and_CC up_RP quark_NN1 propagators_NN2 respectively_RR and_CC the_AT circles_NN2 represent_VV0 the_AT <Professional_FO Term>_FO weak_JJ vertices_NN2 ._. 
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The_AT unambiguous_JJ identification_NN1 of_IO exotic_JJ states_NN2 requires_VVZ experiments_NN2 with_IW complementary_JJ production_NN1 mechanisms_NN2 and_CC the_AT analysis_NN1 of_IO different_JJ final_JJ states_NN2 ._. 
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The_AT first_MD measurements_NN2 of_IO the_AT LIF_NN1 signal_NN1 decay_NN1 revealed_VVD that_CST the_AT effective_JJ lifetime_NNT1 of_IO the_AT excited_JJ state_NN1 is_VBZ comparable_JJ to_II the_AT laser_NN1 pulse_NN1 duration_NN1 ,_, 8ns_FO ,_, as_CSA shown_VVN in_II figure_NN1 C1_FO ._. 
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Figure_NN1 7(b)_FO shows_VVZ the_AT neutron_NN1 yields_NN2 produced_VVN by_II the_AT interaction_NN1 of_IO a_AT1 1_MC1 J_ZZ1 deuterium_NN1 beam_NN1 with_IW z-pinch_JJ plasmasor_NN1 with_IW thick_JJ targets_NN2 from_II deuterated_JJ polyethylene_NN1 and_CC lithium_NN1 fluoride_NN1 ._. 
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The_AT map_NN1 f_ZZ1 with_II31 respect_II32 to_II33 m_ZZ1 is_VBZ forward_RL quasi-invariant_JJ (_( i.e._REX ,_, for_IF each_DD1 Borel_NN1 set_VVN <Equation>_FO ,_, if_CS <Equation>_FO ,_, then_RT <Equation>_FO ,_, and_CC nonsingular_JJ (_( i.e._REX ,_, for_IF each_DD1 Borel_NN1 set_VVN A_ZZ1 S2_FO ,_, <Equation>_FO if_CS and_CC only_RR if_CS <Equation>_FO ._. 
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This_DD1 then_RT naively_RR doubles_VVZ the_AT exchange_NN1 correction_NN1 ._. 
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Current_JJ state-of-the-art_JJ developments_NN2 have_VH0 pushed_VVN the_AT achievable_JJ emission_NN1 currents_NN2 into_II the_AT 2,000-nA_FO range_NN1 (_( dashed_JJ red_JJ line_NN1 )_) ._. 
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<s>
For_IF simplicity_NN1 ,_, consider_VV0 the_AT sequential_JJ measurement_NN1 of_IO orthonormal_JJ bases_NN2 ,_, X_ZZ1 followed_VVN by_II Z_ZZ1 ,_, where_CS the_AT first_MD measurement_NN1 is_VBZ a_AT1 von_NP1 Neumann_NP1 measurement_NN1 ,_, i.e._REX ,_, it_PPH1 projects_VVZ the_AT system_NN1 onto_II an_AT1 X-basis_JJ state_NN1 ._. 
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In_II the_AT proof_NN1 of_IO the_AT previous_JJ we_PPIS2 will_VM need_VVI the_AT following_JJ lemma_NN1 ._. 
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The_AT magnetic_JJ field_NN1 of_IO the_AT Milky_JJ Way_NN1 is_VBZ concentrated_VVN in_II the_AT Galactic_JJ disk_NN1 ,_, and_CC its_APPGE regular_JJ component_NN1 approximately_RR follows_VVZ the_AT spiral_JJ arms_NN2 ._. 
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Analogous_JJ experiments_NN2 with_IW Fe_NP1 atoms_NN2 showed_VVD only_RR the_AT formation_NN1 of_IO weakly_RR bound_VVN adducts_NN2 with_IW O2_FO ,_, H2O_FO and_CC C2H2_FO that_CST were_VBDR easily_RR dissociated_VVN by_II electron_NN1 transfer_NN1 to_II He+_FO ._. 
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Super_JJ rotation_NN1 can_VM only_RR provide_VVI subcritical_JJ excitation_NN1 for_IF =_FO (_( double-diffusive_JJ instability_NN1 )_) ._. 
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The_AT results_NN2 show_VV0 that_CST the_AT protocol_NN1 is_VBZ fast_JJ and_CC robust_JJ against_II decoherence_NN1 and_CC operational_JJ imperfection_NN1 ._. 
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Though_CS backscattering-immune_JJ sound_NN1 propagation_NN1 can_VM be_VBI achieved_VVN by_II the_AT foregoing_JJ 2D_NNU EAM_NN1 ,_, challenges_NN2 in_RR21 full_RR22 acoustic_JJ field_NN1 mapping_NN1 hinder_VV0 further_RRR experimental_JJ <FIGURE>_FO exploration_NN1 ._. 
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However_RR ,_, the_AT modulation_NN1 contrast_NN1 is_VBZ only_RR 10%_NNU ,_, and_CC from_II 550_MC to_II 650_MC nm_FU the_AT intensity_NN1 of_IO transmitted_JJ light_NN1 is_VBZ equivalent_JJ to_II the_AT transmitted_JJ light_JJ intensity_NN1 at_II resonance_NN1 ._. 
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In_II the_AT above_JJ ,_, we_PPIS2 have_VH0 examined_VVN the_AT influence_NN1 of_IO CAD_NN1 noise_NN1 on_II quantum_NN1 teleportation_NN1 ._. 
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Several_DA2 other_JJ organic_JJ nanoas-semblies_NN2 have_VH0 been_VBN proposed_VVN in_II attempts_NN2 to_TO enhance_VVI ._. 
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The_AT high_JJ quality_NN1 and_CC reliability_NN1 of_IO these_DD2 large_JJ magnets_NN2 are_VBR primarily_RR due_II21 to_II22 the_AT use_NN1 of_IO a_AT1 high-purity_JJ aluminum_NN1 stabilized_VVD conductor_NN1 and_CC indirect_JJ cooling_NN1 ._. 
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Such_DA high_JJ dimensions_NN2 might_VM result_VVI in_II biased_JJ information-theoretic_JJ estimation_NN1 based_VVN on_II limited_JJ datasets_NN2 ._. 
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In_BCL21 order_BCL22 to_TO test_VVI the_AT validity_NN1 of_IO the_AT effective_JJ Hamiltonian_JJ in_II Eq_NN1 ._. 
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(_( 2_MC )_) ,_, we_PPIS2 compare_VV0 it_PPH1 to_II numerical_JJ simulations_NN2 that_CST use_VV0 the_AT original_JJ Hamiltonian_JJ in_II Eq_NN1 ._. 
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(_( 1_MC1 )_) ._. 
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An_AT1 explanation_NN1 of_IO the_AT Roper_NP1 should_VM combine_VVI an_AT1 understanding_NN1 of_IO all_DB these_DD2 things_NN2 ._. 
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The_AT density_NN1 matrix_NN1 of_IO the_AT system_NN1 is_VBZ <Equation>_FO ,_, where_CS <Professional_FO Term>_FO is_VBZ the_AT partition_NN1 function_NN1 ,_, T_ZZ1 is_VBZ the_AT spin_NN1 temperature_NN1 ,_, kB_NNU is_VBZ the_AT Boltzmann_NP1 constant_JJ ._. 
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The_AT data_NN points_NN2 are_VBR fitted_VVN by_II a_AT1 Gaussian_JJ function_NN1 to_TO obtain_VVI the_AT quoted_JJ FWHM_NP1 ._. 
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This_DD1 allows_VVZ one_PN1 to_TO classify_VVI the_AT resonant_JJ states_NN2 of_IO the_AT nanowire_NN1 into_II states_NN2 which_DDQ couple_VV0 to_II the_AT light_JJ sources_NN2 and_CC into_II states_NN2 which_DDQ have_VH0 no_AT contribution_NN1 to_II the_AT extinction_NN1 cross_NN1 section_NN1 ._. 
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It_PPH1 follows_VVZ from_II this_DD1 result_NN1 and_CC Corollary_NN1 5.5_MC that_CST the_AT distribution_NN1 <Equation>_FO belongs_VVZ to_II <Professional_FO Term>_FO ,_, for_IF any_DD <Professional_FO Term>_FO and_CC <Professional_FO Term>_FO ._. 
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In_II 2013_MC ,_, the_AT prevalence_NN1 of_IO vitamin_NN1 A_ZZ1 deficiency_NN1 was_VBDZ 29%_NNU in_II children_NN2 aged6–59_JJ months_NNT2 in_II low-_NN1 and_CC middle-income_JJ countries_NN2 &lsqb;_( 15_MC &rsqb;_) ._. 
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As_II a_AT1 comparison_NN1 of_IO ,_, e.g._REX ,_, electron_NN1 spectra_NN2 at_II different_JJ times_NNT2 in_II the_AT Solar_JJ cycle_NN1 shows_NN2 ,_, the_AT differences_NN2 above_II this_DD1 rigidity_NN1 are_VBR negligible_JJ relative_II21 to_II22 experimental_JJ uncertainties_NN2 ._. 
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The_AT algorithm_NN1 consists_VVZ in_II the_AT definition_NN1 of_IO custom_NN1 surface_NN1 at_II different_JJ distances_NN2 from_II the_AT detector_NN1 where_CS the_AT reconstructed_JJ tracks_NN2 can_VM be_VBI projected_VVN by_II backward_JJ propagation_NN1 as_CSA straight_JJ lines_NN2 ._. 
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Unlike_JJ Z1_FO ,_, q_ZZ1 ,_, this_DD1 is_VBZ not_XX a_AT1 pure-scaling_JJ variable_NN1 ._. 
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Finally_RR ,_, we_PPIS2 would_VM like_VVI to_TO bring_VVI to_II the_AT reader_NN1 '_NULL s_ZZ1 attention_NN1 that_CST the_AT molecular_JJ anisotropy_NN1 could_VM not_XX only_RR be_VBI an_AT1 intramolecular_JJ feature_NN1 influencing_VVG the_AT discrepancy_NN1 between_II γ_NULL and_CC γ_NULL EOS_NN2 ._. 
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The_AT snapshots_NN2 are_VBR taken_VVN after_II 5.0_MC ×_II 106_MC simulation_NN1 steps_NN2 ._. 
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Here_RL we_PPIS2 compare_VV0 these_DD2 results_NN2 with_IW the_AT present_JJ theory_NN1 rewriting_VVG the_AT distribution_NN1 function<Equation>_FO in_II31 terms_II32 of_II33 particle_NN1 radii<Equation>An_FO important_JJ point_NN1 is_VBZ that_CST the_AT LS_NP2 theory_NN1 takes_VVZ into_II account_NN1 the_AT mechanism_NN1 of_IO particle_NN1 coarsening_VVG when_RRQ the_AT larger_JJR crystals_NN2 evolve_VV0 at_II the_AT expense_NN1 of_IO dissolution_NN1 of_IO smaller_JJR crystals_NN2 ._. 
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Only_RR much_RR later_RRR ,_, for_IF the_AT second_MD LHC_NP1 run_NN1 starting_VVG in_II 2015_MC ,_, was_VBDZ an_AT1 additional_JJ layer_NN1 of_IO advanced_JJ pixel_NN1 technology_NN1 added_VVN to_TO further_RRR improve_VVI secondary_JJ vertexing_JJ capabilities_NN2 at_II high_JJ luminosities_NN2 ._. 
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But_CCB this_DD1 follows_VVZ from_II the_AT fact_NN1 that_CST f_ZZ1 is_VBZ Lipschitz_NP1 with_II31 respect_II32 to_II33 d_ZZ1 (_( Lemma_NN1 3.12_MC )_) and_CC <Equation>_FO ._. 
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We_PPIS2 used_VVD optimized_JJ variances_NN2 for_IF each_DD1 protocol_NN1 ,_, while_CS the_AT same_DA variances_NN2 were_VBDR used_VVN in_II &lsqb;_( 19_MC &rsqb;_) ._. 
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They_PPHS2 found_VVD that_CST the_AT variation_NN1 metric_JJ spikes_NN2 in_II most_DAT flooded_JJ areas_NN2 and_CC shows_VVZ consistence_NN1 to_II the_AT flood_NN1 impact_NN1 map_NN1 ,_, suggesting_VVG that_CST the_AT CDR-based_JJ variation_NN1 metric_JJ can_VM be_VBI used_VVN for_IF situation_NN1 awareness_NN1 ._. 
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The_AT WKB_NP1 approach_NN1 provides_VVZ an_AT1 accurate_JJ result_NN1 for_IF the_AT MTE_NN1 when_CS N_ZZ1 is_VBZ sufficiently_RR large_JJ ._. 
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However_RR ,_, a_AT1 direct_JJ observational_JJ evidence_NN1 that_CST the_AT spacetime_NNT1 geometry_NN1 around_II these_DD2 objects_NN2 is_VBZ really_RR described_VVN by_II the_AT Kerr_NP1 solution_NN1 is_VBZ still_RR lacking_VVG and_CC ,_, at_II the_AT same_DA time_NNT1 ,_, a_AT1 number_NN1 of_IO theoretical_JJ models_NN2 suggest_VV0 the_AT possibility_NN1 of_IO new_JJ physics_NN1 and_CC macroscopic_JJ deviations_NN2 from_II the_AT Kerr_NP1 background_NN1 ._. 
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Let_VV0 (_( M_ZZ1 ,_, g_ZZ1 )_) be_VBI a_AT1 compact_JJ Riemannian_JJ manifold_NN1 with_IW boundary_NN1 and_CC dimension_NN1 and_CC let_VVN be_VBI an_AT1 adjoint_JJ orbit_NN1 that_CST contains_VVZ a_AT1 basis_NN1 of_IO ._. 
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The_AT nonlinear_JJ trace_NN1 confirms_VVZ that_CST the_AT total_JJ EC-SEIRAS_NN2 peak_VV0 shift_NN1 observed_VVN during_II CV_NN1 can_VM not_XX be_VBI solely_RR explained_VVN by_II potential-induced_NN1 change_NN1 ._. 
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FTIR_NP1 device_NN1 (_( BRUKER_NN1 ALPHA_NN1 ,_, having_VHG a_AT1 resolution_NN1 of_IO 4_MC <Professional_FO Term>_FO ;_; equipped_VVN with_IW a_AT1 DTGS_NP1 detector_NN1 ,_, performing_VVG 10_MC scans_NN2 for_IF each_DD1 spectrum_NN1 )_) was_VBDZ used_VVN to_TO record_VVI WO_NP1 and_CC GO_VVI peaks_NN2 ._. 
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Different_JJ values_NN2 of_IO U_ZZ1 are_VBR appropriate_JJ for_IF the_AT 4f_RA and_CC 5d_NNU electrons_NN2 of_IO Ce_NP1 ,_, or_CC the_AT 2p_NNU electrons_NN2 of_IO oxygen_NN1 ,_, and_CC no_AT single_JJ choice_NN1 will_VM simultaneously_RR account_VVI for_IF the_AT band_NN1 gap(s)_NN2 and_CC the_AT positions_NN2 of_IO defect_NN1 levels_NN2 within_II the_AT gap_NN1 ._. 
</s>
<s>
The_AT assumption_NN1 that_CST this_DD1 number_NN1 of_IO events_NN2 is_VBZ sufficient_JJ for_IF future_JJ lepton_NN1 colliders_NN2 to_TO be_VBI sensitive_JJ to_II a_AT1 signal_NN1 is_VBZ based_VVN on_II the_AT very_RG clean_JJ final_JJ states_NN2 (_( photons_NN2 or_CC leptons_NN2 )_) and_CC the_AT strong_JJ cuts_NN2 that_CST can_VM be_VBI applied_VVN if_CS several_DA2 resonances_NN2 appear_VV0 in_II the_AT signal_NN1 ,_, e.g._REX the_AT ALP_NN1 ,_, the_AT Z_NP1 boson_NN1 and_CC the_AT Higgs_NP1 in_II the_AT process_NN1 h_ZZ1 →_NULL Z_ZZ1 a_AT1 ._. 
</s>
<s>
For_IF the_AT local_JJ observables_NN2 ,_, the_AT entanglement_NN1 spreading_NN1 implies_VVZ their_APPGE equilibration_NN1 to_II highly_RR nonthermal_JJ values_NN2 at_II long_JJ times_NNT2 set_VVN by_II initial_JJ conditions_NN2 ._. 
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<s>
Notably_RR ,_, we_PPIS2 present_VV0 modifications_NN2 to_II the_AT EI_NP1 which_DDQ are_VBR required_VVN for_IF the_AT successful_JJ application_NN1 of_IO the_AT method_NN1 to_II laser_NN1 propagation_NN1 in_II plasmas_NN2 ._. 
</s>
<s>
Downstream_RL from_II the_AT gun_NN1 box_NN1 ,_, the_AT guide_NN1 tubes_NN2 are_VBR equipped_VVN with_IW light_NN1 emitting_VVG and_CC light_JJ sensitive_JJ diodes_NN2 and_CC a_AT1 microwave_NN1 cavity_NN1 detector_NN1 (_( wC_NN1 )_) ._. 
</s>
<s>
It_PPH1 has_VHZ been_VBN recently_RR found_VVN that_CST linear_JJ stochastic_JJ equation_NN1 of_IO density_NN1 fluctuations_NN2 is_VBZ much_DA1 of_IO practical_JJ use_NN1 &lsqb;_( 37–46_MCMC &rsqb;_) :_: the_AT density_NN1 fluctuations_NN2 of_IO fluids_NN2 near_II equilibrium_NN1 are_VBR surprisingly_RR well_RR described_VVN by_II model-B_NP1 dynamics_NN of_IO a_AT1 Gaussian_JJ field_NN1 theory_NN1 whose_DDQGE effective_JJ quadratic_JJ Hamiltonian_JJ for_IF the_AT density_NN1 fluctuation_NN1 field_NN1 is_VBZ constructed_VVN to_TO yield_VVI the_AT exact_JJ form_NN1 of_IO the_AT static_JJ density-density_JJ correlation_NN1 function_NN1 &lsqb;_( 37_MC ,_, 38_MC &rsqb;_) ._. 
</s>
<s>
Then_RT by_II Theorem_NN1 5.16_MC and_CC Proposition_NN1 5.17_MC ,_, we_PPIS2 have_VH0 <Equation>_FO ._. 
</s>
<s>
They_PPHS2 found_VVD that_CST the_AT PBE0_FO functional_JJ enhances_VVZ the_AT critical_JJ temperature_NN1 by_II up_RG21 to_RG22 25%_NNU as_CSA compared_VVN to_II PBE_NP1 ,_, bringing_VVG Tc_NP1 from_II 201–217_MCMC K_NP1 to_II 253–270_MCMC K_NP1 (_( the_AT spread_NN1 invalues_NN2 is_VBZ related_VVN to_II the_AT choice_NN1 of_IO the_AT parameter_NN1 <Equation>_FO )_) ._. 
</s>
<s>
By_II the_AT canonical_JJ bracket_NN1 relations_NN2 (_( 100_MC )_) ,_, these_DD2 quadratic_JJ expressions_NN2 realize_VV0 the_AT (_( co-adjoint_JJ representation_NN1 of_IO the_AT )_) Lie_VV0 superalgebra_NN1 gl_NNU (_( 2_VV0 |_NULL 2_MC )_) at_II the_AT given_JJ link_NN1 ,_, with_IW the_AT matrix_NN1 position_NN1 of_IO each_DD1 operator_NN1 encoding_VVG its_APPGE behavior_NN1 w.r.t_NNU ._. 
</s>
<s>
Integration_NN1 is_VBZ then_RT carried_VVN along_RP a_AT1 straight_JJ line_NN1 of_IO slope_NN1 a_AT1 <Professional_FO Terms>_FO to_II so_RR ._. <Equation>with_FO A00_FO the_AT initial_JJ ray_NN1 amplitude_NN1 at_II <Professional_FO Terms>_FO ._. 
</s>
<s>
Additionally_RR ,_, a_AT1 fraction_NN1 of_IO contacts_NN2 with_IW pYAAAA_NN1 in_II 1_MC1 and_CC 4_MC involved_VVD the_AT Ala2_FO and_CC Ala5_FO residues_NN2 ._. 
</s>
<s>
In_II the_AT second_MD weight_NN1 assignment_NN1 scheme_NN1 ,_, wij_VV0 =_FO 1/_FO (_( kikj_NN1 )_) ._. 
</s>
<s>
In_II most_DAT of_IO the_AT cases_NN2 ,_, the_AT beam_NN1 was_VBDZ made_VVN of_IO a_AT1 single_JJ bunch_NN1 with_IW few_DA2 109_MC up_RG21 to_RG22 1011_MC protons_NN2 and_CC the_AT diffusion_NN1 speed_NN1 was_VBDZ governed_VVN by_II the_AT multiple_JJ scattering_NN1 of_IO circulating_VVG protons_NN2 with_IW the_AT residual_JJ gas_NN1 in_II the_AT beam_NN1 pipe_NN1 ._. 
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<s>
Scientists_NN2 have_VH0 revealed_VVN the_AT role_NN1 of_IO geographic_JJ neighbors_NN2 and_CC highlighted_VVD it_PPH1 as_II an_AT1 alternative_JJ channel_NN1 for_IF development_NN1 ._. 
</s>
<s>
Here_RL we_PPIS2 focus_VV0 on_II cognitive_JJ control_NN1 because_CS it_PPH1 is_VBZ conceptually_RR akin_JJ to_II the_AT idea_NN1 of_IO extrinsic_JJ control_NN1 :_: driving_JJ dynamics_NN from_II one_MC1 type_NN1 to_II another_DD1 ._. 
</s>
<s>
In_II what_DDQ follows_VVZ we_PPIS2 use_VV0 networks_NN2 produced_VVN by_II the_AT algorithm_NN1 as_CSA contact_NN1 patterns_NN2 for_IF the_AT cooperative_JJ SIR_NN1 dynamics_NN ._. 
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<s>
MicroBooNE_VV0 and_CC ICARUS_NP1 can_VM also_RR study_VVI neutrino–argon_NN1 cross_NN1 sections_NN2 by_II exploiting_VVG the_AT NuMI_JJ beam_NN1 ._. 
</s>
<s>
Schematic_JJ of_IO a_AT1 spherical_JJ particle_NN1 (_( a_ZZ1 )_) immersed_VVD in_II vapor_NN1 phase_NN1 and_CC (_( b_ZZ1 )_) becoming_VVG adsorbed_VVD to_II a_AT1 liquid–vapor_NN1 interface_NN1 ._. 
</s>
<s>
In_II our_APPGE case_NN1 ,_, there_EX is_VBZ no_AT region_NN1 with_IW constant_JJ activation_NN1 energy_NN1 in_II temperature_NN1 dependence_NN1 of_IO conductivity_NN1 at_II high_JJ temperatures_NN2 ._. 
</s>
<s>
Also_RR simplified_JJ ion_NN1 distributions_NN2 ,_, namely_REX ,_, the_AT uniform_JJ jellium_NN1 in_II the_AT dielectric_JJ in_II the_AT spirit_NN1 of_IO SJM33_FO and_CC Gaussian_JJ charge_NN1 sheets_NN2 as_CSA performed_VVN in_II Ref._NN1 86_MC ,_, were_VBDR tested_VVN ._. 
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<s>
It_PPH1 is_VBZ known_VVN to_TO be_VBI NP-hard_JJ &lsqb;_( 8_MC &rsqb;_) ._. 
</s>
<s>
Notice_VV0 how_RRQ the_AT final_JJ states_NN2 T_ZZ1 T_ZZ1 and_CC BB_NP1 are_VBR mainly_RR produced_VVN via_II proton-proton_JJ collision_NN1 in_II M4+14_FO as_II the_AT involved_JJ quark_NN1 partner_NN1 masses_NN2 are_VBR smaller_JJR than_CSN the_AT corresponding_JJ ones_NN2 at_II M4+5_FO (_( see(B.8)-(B.12)_NNU and_CC Fig._NN1 9_MC )_) ._. 
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<s>
The_AT rotational_JJ suppression_NN1 of_IO TI_NN2 in_II this_DD1 representation_NN1 is_VBZ strongest_JJT for_IF Pm_NP1 =_FO 1_MC1 ._. 
</s>
<s>
They_PPHS2 found_VVD that_CST the_AT length_NN1 of_IO subway_NN1 networks_NN2 scales_NN2 super_JJ linearly_RR (_( <Equation>_FO )_) while_CS the_AT yearly_JJ ridership_NN1 of_IO railway_NN1 networks_NN2 scales_NN2 linearly_RR with_IW the_AT number_NN1 of_IO stations_NN2 ._. 
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<s>
The_AT assumptions_NN2 of_IO this_DD1 theorem_NN1 are_VBR indeed_RR stronger_JJR than_CSN those_DD2 of_IO theorem_NN1 1_MC1 because_CS probabilities_NN2 are_VBR assigned_VVN to_II all_DB effects_NN2 in_II the_AT space_NN1 <Professional_FO Term>_FO ,_, not_XX just_RR collections_NN2 of_IO mutually_RR orthogonal_JJ projections_NN2 ._. 
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<s>
Similar_JJ to_II the_AT unconstrained_JJ case_NN1 ,_, we_PPIS2 have_VH0 <Equation>_FO ,_, however_RR ,_, since_CS the_AT binding_JJ rate_NN1 depends_VVZ on_II the_AT particle_NN1 occupation_NN1 ,_, the_AT mean_JJ field_NN1 equilibrium_NN1 defect_NN1 density_NN1 is_VBZ <Equation>_FO ,_, i.e._REX it_PPH1 depends_VVZ on_II the_AT particle_NN1 density8_FO ._. 
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<s>
There_EX are_VBR also_RR a_AT1 number_NN1 of_IO calculations_NN2 trying_VVG to_TO interpret_VVI <EQUATION>_FO as_II an_AT1 ordinal_JJ charmed_JJ baryon_NN1 ._. 
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<s>
Fig._NN1 7_MC :_: Schematic_JJ layout_NN1 of_IO FLASH_NN1 with_IW seven_MC TESLA_NP1 accelerator_NN1 modules_NN2 installed_VVD ._. 
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<s>
Thus_RR ,_, the_AT most_RGT trusted_JJ bounds_NN2 for_IF the_AT graviton_NN1 mass_NN1 from_II the_AT Yukawa_NP1 potential_NN1 will_VM come_VVI from_II systems_NN2 firmly_RR in_II this_DD1 regime_NN1 such_II21 as_II22 the_AT Solar_JJ System_NN1 ._. 
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<s>
For_REX21 example_REX22 ,_, urban_JJ landscape_NN1 becomes_VVZ more_RGR fragmented_JJ ,_, diverse_JJ and_CC complex_JJ in_II the_AT urbanization_NN1 process_NN1 ._. 
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<s>
However_RR ,_, most_DAT of_IO these_DD2 studies_NN2 are_VBR only_RR performed_VVN on_II the_AT mean_JJ field_NN1 level_NN1 ._. 
</s>
<s>
There_EX is_VBZ currently_RR an_AT1 increasing_JJ interest_NN1 in_II the_AT electrical_JJ manipulation_NN1 of_IO such_DA objects_NN2 as_CSA they_PPHS2 could_VM serve_VVI as_RG fundamental_JJ building_NN1 blocks_NN2 for_IF data_NN storage_NN1 and_CC logic_NN1 devices_NN2 (_( Fert_NP1 ,_, Cros_NP1 ,_, and_CC Sampaio_NP1 ,_, 2013_MC ;_; Tomasello_NP1 et_RA21 al._RA22 ,_, 2014_MC ;_; Zhang_NP1 ,_, Ezawa_NP1 ,_, and_CC Zhou_NP1 ,_, 2015_MC )_) ._. 
</s>
<s>
After_II having_VHG explored_VVN the_AT general_JJ feasibility_NN1 of_IO these_DD2 two-color_JJ experiments_NN2 ,_, attention_NN1 was_VBDZ given_VVN to_II details_NN2 of_IO the_AT photoionization_NN1 process_NN1 ._. 
</s>
<s>
Observed_JJ abundances_NN2 of_IO H+_FO (_( H2_FO O_ZZ1 )_) m_ZZ1 (_( CH3_FO OH_UH )_) n_ZZ1 clusters_NN2 for_IF m_ZZ1 =_FO 1-4_MCMC ._. 
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<s>
The_AT influence_NN1 of_IO the_AT density_NN1 gradient_NN1 in_II the_AT sheath_NN1 on_II the_AT LIF_NN1 data_NN treatment_NN1 and_CC interpretation_NN1 is_VBZ also_RR discussed_VVN ._. 
</s>
<s>
A_AT1 second_MD consequence_NN1 is_VBZ that_CST every_AT1 replacement_NN1 channel_NN1 <Equation>_FO of_IO the_AT form_NN1 <Equation>_FO ,_, with_IW a_AT1 fixed_JJ <Equation>_FO ,_, is_VBZ free_JJ &lsqb;_( i.e._REX ,_, belonging_VVG to_II OeA_NP1 →_NULL BT_NP1 &rsqb;_) ._. 
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<s>
This_DD1 can_VM be_VBI seen_VVN by_II combining_VVG the_AT partial_JJ trace_NN1 with_IW the_AT second_MD property_NN1 in_II Definition_NN1 2_MC ._. 
</s>
<s>
For_IF simplicity_NN1 ,_, we_PPIS2 show_VV0 the_AT dynamics_NN of_IO the_AT uncertainty_NN1 with_IW the_AT coupling_NN1 strength_NN1 J_ZZ1 and_CC the_AT magnetic_JJ field_NN1 B_ZZ1 with_IW T_ZZ1 =_FO 0.6_MC in_II Figs._NN2 9_MC and_CC 10_MC ._. 
</s>
<s>
GO-CoPc_NP1 and_CC GO-NiPc_NP1 have_VH0 a_AT1 good_JJ degree_NN1 of_IO charge_NN1 transfer_NN1 to_TO improve_VVI performance_NN1 in_II energy_NN1 storage_NN1 ,_, organic_JJ electronics_NN1 ,_, and_CC sensor_NN1 applications_NN2 ,_, as_II31 well_II32 as_II33 improving_JJ adhesion_NN1 and_CC improving_JJ electrical_JJ conductivity_NN1 on_II any_DD substrate_NN1 ._. 
</s>
<s>
We_PPIS2 will_VM probe_VVI this_DD1 method_NN1 for_IF increasing_VVG the_AT yield_NN1 in_II more_DAR detail_NN1 in_II future_JJ studies_NN2 ._. 
</s>
<s>
The_AT Hartmann_NP1 number_NN1 is_VBZ defined_VVN by_II Eq_NN1 ._. 
</s>
<s>
(_( 45_MC )_) ._. 
</s>
<s>
Much_DA1 of_IO this_DD1 was_VBDZ done_VDN in_II the_AT very_RG exciting_JJ early_JJ days_NNT2 of_IO FEL_NP1 science_NN1 when_CS it_PPH1 was_VBDZ even_RR not_XX clear_RR if_CS the_AT FEL_NN1 concept_NN1 could_VM be_VBI realized_VVN for_IF X-rays_NN2 ._. 
</s>
<s>
Part_NN1 of_IO the_AT work_NN1 of_IO JP_NN1 was_VBDZ done_VDN at_II the_AT Mitchell_NP1 Institute_NN1 for_IF Fundamental_JJ Physics_NN1 and_CC Astronomy_NN1 at_II Texas_NP1 A_ZZ1 &M;_NULL University_NN1 ,_, and_CC supported_VVD in_RR21 part_RR22 by_II NSF_NP1 grant_NN1 PHY_NN1 1214344_MC ._. 
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<s>
Consequently_RR ,_, we_PPIS2 naturally_RR conclude_VV0 that_CST the_AT purified_JJ maximally_RR entangled_JJ state_NN1 is_VBZ more_RGR suitable_JJ to_II the_AT Gaussian_JJ maximally_RR entangled_JJ state_NN1 than_CSN the_AT two-mode_JJ squeezed_JJ vacuum_NN1 state_NN1 ,_, in_II a_AT1 sense_NN1 that_CST it_PPH1 might_VM be_VBI useful_JJ for_IF continuous-variable_JJ quantum_NN1 information_NN1 tasks_NN2 in_II which_DDQ entangled_JJ states_NN2 are_VBR needed_VVN ._. 
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<s>
Completions_NN2 of_IO this_DD1 pre-Hilbert_JJ module_NN1 (_( see_VV0 Fomenko_NN1 and_CC Mishchenko_NP1 &lsqb;_( 14_MC &rsqb;_) )_) with_II31 respect_II32 to_II33 the_AT induced_JJ norm_NN1 make_VV0 it_PPH1 a_AT1 Hilbert_NP1 C_NP1 -module_NN1 ._. 
</s>
<s>
For_REX21 example_REX22 ,_, <Equation>_FO Note_VV0 that_CST <Equation>_FO ._. 
</s>
<s>
This_DD1 excluded-volume_JJ effect_NN1 leads_VVZ to_II particles_NN2 colliding_VVG with_IW each_PPX221 other_PPX222 ,_, causing_VVG congestion_NN1 when_CS the_AT particle_NN1 density_NN1 is_VBZ sufficiently_RR high_JJ ._. 
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<s>
The_AT DCE_NP1 has_VHZ been_VBN experimentally_RR observed_VVN in_II Josephson_NP1 meta-materials_NN2 embedded_VVN in_II a_AT1 microwave_NN1 cavity_NN1 ._. 
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<s>
No_UH HXR_NP1 signal_NN1 spikes_NN2 are_VBR observed_VVN ._. 
</s>
<s>
We_PPIS2 follow_VV0 the_AT proof_NN1 of_IO &lsqb;_( 16_MC ,_, Lemma_NN1 11_MC &rsqb;_) ._. 
</s>
<s>
In_RR21 addition_RR22 ,_, trapped_VVN and_CC untrapped_JJ electrons_NN2 widen_VV0 the_AT parametric_JJ regime_NN1 PQ_NP1 >_FO 0_MC ;_; hence_RR favoring_VVG the_AT evolution_NN1 of_IO MI_NP1 and_CC unstable_JJ excitations_NN2 ._. 
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<s>
There_EX are_VBR still_RR a_AT1 lot_NN1 of_IO problems_NN2 rendering_VVG OSCS-based_JJ devices_NN2 impractical_JJ for_IF applications_NN2 ._. 
</s>
<s>
Since_CS graphene_NN1 was_VBDZ successfully_RR achieved_VVN by_II mechanical_JJ exfoliation_NN1 technique_NN1 ,_, it_PPH1 seems_VVZ the_AT key_NN1 for_IF scientists_NN2 to_TO explore_VVI the_AT two-dimensional_JJ (_( 2D_NNU )_) materials_NN2 ._. 
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<s>
We_PPIS2 shall_VM say_VVI that_CST a_AT1 finite_JJ subset_NN1 X_ZZ1 is_VBZ in_RR21 general_RR22 position_VV0 if_CSW each_DD1 subset_NN1 YX_NN1 of_IO k_ZZ1 ≤_FO g_ZZ1 1_MC1 points_NN2 spans_VVZ a_AT1 k_ZZ1 1-dimensional_JJ projective_JJ subspace_NN1 which_DDQ contains_VVZ no_AT more_DAR points_NN2 of_IO X_ZZ1 ._. 
</s>
<s>
In_RR21 addition_RR22 ,_, the_AT FIB_NN1 etching_NN1 would_VM result_VVI in_II unparalleled_JJ slit_NN1 sides_NN2 ._. 
</s>
<s>
Finally_RR ,_, comparisons_NN2 of_IO a_AT1 N_ZZ1 seeded_JJ H-mode_NN1 with_IW high_JJ pedestal_NN1 top_NN1 pressure_NN1 and_CC an_AT1 I-mode_JJ plasma_NN1 with_IW an_AT1 L-mode_JJ reference_NN1 are_VBR both_RR found_VVN to_TO break_VVI the_AT generally_RR observed_VVN correlation_NN1 between_II the_AT Te_FW SOL_NP1 decay_NN1 length_NN1 and_CC the_AT pedestal_NN1 top_NN1 pressure_NN1 ._. 
</s>
<s>
In_II the_AT context_NN1 of_IO CHS_NN2 events_NN2 ,_, we_PPIS2 can_VM also_RR slightly_RR improve_VVI our_APPGE positivity_NN1 constraints_NN2 for_IF the_AT final_JJ jet_NN1 transverse_NN1 momentum_NN1 and_CC mass_NN1 ._. 
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<s>
Since_CS the_AT Brillouin_NP1 conversion_NN1 efficiency_NN1 is_VBZ relatively_RR low_JJ ,_, the_AT direct_JJ detection_NN1 method_NN1 exhibits_VVZ a_AT1 lower_JJR sensing_NN1 range_NN1 and_CC accuracy_NN1 ._. 
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<s>
The_AT diameters_NN2 of_IO the_AT fitted_JJ semicircles_NN2 regard_VV0 as_II Rf_NP1 (_( interface_VV0 film_NN1 resistance_NN1 )_) for_IF Li_NP1 ions_NN2 passing_VVG through_II interface_NN1 film_NN1 at_II high_JJ frequency_NN1 and_CC Rct_NP1 (_( charge_NN1 transfer_NN1 resistance_NN1 )_) for_IF the_AT charge_NN1 transfer_NN1 on_II electrode_NN1 interface_NN1 at_II medial_JJ frequency_NN1 ,_, accompanied_VVN with_IW the_AT slope_NN1 line_NN1 for_IF Wo_NP1 (_( Warburg_NP1 impedance_NN1 )_) at_II low_JJ frequency&lsqb;50&rsqb;_FO ._. 
</s>
<s>
Equality<Equation>_FO (_( 237_MC )_) employed_VVD in_II &lsqb;_( 53_MC &rsqb;_) being_VBG applied_VVN to_II the_AT first_MD resonant_JJ term_NN1 yields_VVZ the_AT positive_JJ contribution_NN1 while_CS for_IF the_AT second_MD resonant_JJ it_PPH1 gives_VVZ negative_JJ contribution_NN1 ._. 
</s>
<s>
The_AT electronic_JJ band_NN1 structure_NN1 of_IO charge_NN1 carriers_NN2 in_II g-SiC7_NN1 ,_, shown_VVN by_II Fig._NN1 2_MC ,_, tells_VVZ us_PPIO2 that_CST the_AT low-energy_JJ lying_NN1 dispersion_NN1 of_IO the_AT system_NN1 consists_VVZ of_IO two_MC separated_JJ bands_NN2 with_IW a_AT1 strain-dependent_JJ band_NN1 gap_NN1 ._. 
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<s>
This_DD1 is_VBZ no_RR21 longer_RR22 true_JJ for_IF finite_JJ β_NULL ._. 
</s>
<s>
We_PPIS2 also_RR report_VV0 a_AT1 best_JJT value_NN1 of_IO <Equation>_FO consistent_JJ at_II 3_MC with_IW the_AT one_MC1 reported_VVN by_II Planck_NP1 Collaboration_NN1 ._. 
</s>
<s>
A._NP1 H._NP1 Zewail_NP1 ,_, "_" Four-dimensional_JJ electron_NN1 microscopy_NN1 ,_, "_" Science_NN1 328_MC ,_, 187_MC (_( 2010_MC )_) ._. 
</s>
<s>
This_DD1 radical_JJ new_JJ strategy_NN1 can_VM also_RR be_VBI applicable_JJ in_II other_JJ color_NN1 converters_NN2 for_IF high-luminance_NN1 and_CC high-directionality_JJ laser-driven_JJ lighting_NN1 and_CC projection_NN1 applications_NN2 ._. 
</s>
<s>
Th_NP1 chosen_VVN (_( T_ZZ1 ,_, T_ZZ1 )_) pairs_NN2 were_VBDR <equation>_FO ._. 
</s>
<s>
From_II Merklein_NP1 et_RA21 al._RA22 ,_, 2016._MC mass_JJ production_NN1 leading_VVG to_II a_AT1 scale_NN1 reduction_NN1 of_IO cost_NN1 and_CC improved_JJ reliability_NN1 Research_NN1 on_II the_AT topic_NN1 of_IO optoelectronic_JJ oscillators_NN2 with_IW time-delayed_JJ feedback_NN1 has_VHZ already_RR been_VBN very_RG fruitful_JJ ._. 
</s>
<s>
The_AT formed_JJ gel_NN1 precursors_NN2 were_VBDR decomposed_VVN in_II the_AT furnace_NN1 (_( 400_MC °C_NNU for_IF 1_MC1 h_ZZ1 )_) ,_, preparation_NN1 details_NN2 are_VBR schematically_RR showed_VVN in_II Fig._NN1 1_MC1 and_CC more_DAR details_NN2 can_VM be_VBI found_VVN in_II &lsqb;_( 6_MC &rsqb;_) ._. 
</s>
<s>
Optical_JJ fibers_NN2 have_VH0 attracted_VVN tremendous_JJ attention_NN1 ever_RR since_CS the_AT first_MD successful_JJ fiber_NN1 manufacturing_NN1 process_NN1 was_VBDZ demonstrated_VVN in_II the_AT 1970s_MC2 ,_, which_DDQ reduced_VVD the_AT attenuation_NN1 in_II optical_JJ fibers_NN2 to_II an_AT1 acceptable_JJ level_NN1 below_RG 20_MC dB/km.1_FU During_II the_AT past_JJ few_DA2 decades_NNT2 ,_, optical_JJ fibers_NN2 have_VH0 been_VBN widely_RR deployed_VVN to_TO implement_VVI various_JJ applications_NN2 in_II high_JJ speed_NN1 long-distance_JJ telecommunication_NN1 ,_, imaging_VVG optics_NN1 ,_, laser_NN1 gain_NN1 media_NN ,_, and_CC illumination_NN1 applications_NN2 ._. 
</s>
<s>
In_II this_DD1 section_NN1 we_PPIS2 formulate_VV0 the_AT problem_NN1 of_IO the_AT computation_NN1 of_IO the_AT ground_NN1 state_NN1 degeneracy_NN1 generating_VVG functions_NN2 for_IF the_AT one_MC1 dimensional_JJ Nicolai_NN1 and_CC Z2_FO Nicolai_JJ models_NN2 in_II formal_JJ purely_RR mathematical_JJ terms_NN2 and_CC derive_VV0 recursions_NN2 for_IF these_DD2 functions_NN2 ._. 
</s>
<s>
In_II a_AT1 limit_NN1 of_IO an_AT1 infinite_JJ ghost_NN1 density_NN1 ,_, the_AT boundary_NN1 would_VM become_VVI independent_JJ of_IO the_AT set_NN1 of_IO ghost_NN1 ._. 
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<s>
This_DD1 work_NN1 was_VBDZ supported_VVN by_II the_AT National_JJ Natural_JJ Science_NN1 Foundation_NN1 of_IO China_NP1 (_( Grant_NP1 Nos_NP1 ._. 
</s>
<s>
Assuming_VVG that_CST scattering_VVG at_RR21 large_RR22 s_ZZ1 proceeds_VVZ via_II the_AT exchange_NN1 of_IO a_AT1 single_JJ resonance_NN1 of_IO spin_NN1 J_ZZ1 in_II the_AT t-channel_NN1 (_( as_CSA in_II the_AT one-pion-exchange_JJ approximation_NN1 )_) ,_, only_RR one_MC1 partial_JJ wave_NN1 of_IO Eq_NN1 ._. 
</s>
<s>
(_( 121_MC )_) will_VM contribute_VVI :_: <EQUATION>where_FO we_PPIS2 have_VH0 skipped_VVN the_AT channel_NN1 indices_NN2 on_II the_AT right-hand_JJ side_NN1 for_IF clarity_NN1 ._. 
</s>
<s>
We_PPIS2 estimate_VV0 the_AT flux_NN1 from_II dynamical_JJ ejecta_NN1 by_II modeling_VVG it_PPH1 as_II a_AT1 spherical_JJ expanding_JJ shell_NN1 with_IW a_AT1 single_JJ velocity_NN1 and_CC neglecting_VVG relativistic_JJ corrections_NN2 ._. 
</s>
<s>
Furthermore_RR ,_, if_CS avalanches_NN2 in_II the_AT model_NN1 of_IO Millman_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
are_VBR measured_VVN as_CSA in_II experiments_NN2 (_( employing_VVG a_AT1 time_NNT1 binning_NN1 )_) they_PPHS2 are_VBR not_XX scale_VV0 free_JJ (_( Martinello_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
</s>
<s>
This_DD1 yields_VVZ a_AT1 representation_NN1 of_IO the_AT data_NN in_II31 terms_II32 of_II33 intensities_NN2 and_CC relative_JJ phases_NN2 of_IO transition_NN1 amplitudes_NN2 that_CST allows_VVZ for_IF a_AT1 direct_JJ interpretation_NN1 in_II31 terms_II32 of_II33 resonances_NN2 ._. 
</s>
<s>
The_AT grey_JJ planes_NN2 indicate_VV0 the_AT top_NN1 and_CC bottom_JJ surfaces_NN2 of_IO the_AT slice_NN1 ._. 
</s>
<s>
Table_NN1 IV_MC shows_VVZ the_AT performance_NN1 of_IO mode-locked_JJ fiber_NN1 laser_NN1 based_VVN on_II 2D_NNU materials_NN2 as_II an_AT1 SA_NP1 in_II the_AT 3_MC lm_NNU region_NN1 ._. 
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<s>
Unfortunately_RR ,_, in_II the_AT case_NN1 of_IO DFIB_NP1 ,_, the_AT 12.5-ns_NN2 time_VV0 resolution_NN1 of_IO the_AT PImMS_NP2 camera_NN1 was_VBDZ not_XX sufficient_JJ to_TO distinguish_VVI the_AT I_MC1 fragment_NN1 from_II the_AT nearby_JJ CF_VV0 ,_, which_DDQ has_VHZ a_AT1 mass-to-charge_JJ ratio_NN1 that_CST differs_VVZ by_II less_DAR than_CSN one_MC1 unit_NN1 and_CC therefore_RR has_VHZ a_AT1 very_RG similar_JJ time_NNT1 of_IO flight_NN1 ._. 
</s>
<s>
In_RR21 particular_RR22 ,_, we_PPIS2 isolate_VV0 the_AT emission_NN1 spectra_NN2 of_IO N-V_NP1 and_CC N-V_NP1 ,_, allowing_VVG arbitrary_JJ diamond_NN1 spectra_NN2 to_TO be_VBI decomposed_VVN into_II a_AT1 linear_JJ combination_NN1 of_IO the_AT N-V_NP1 and_CC N-V_NP1 spectral_JJ contributions_NN2 ._. 
</s>
<s>
Consequently_RR the_AT existence_NN1 of_IO dilute_JJ rare_JJ droplets_NN2 in_II which_DDQ the_AT electronic_JJ properties_NN2 differ_VV0 from_II average_NN1 (_( e.g._REX ,_, in_II which_DDQ <Equation>_FO is_VBZ anomalously_RR large_JJ )_) can_VM have_VHI an_AT1 enormously_RR amplified_VVN effect_NN1 on_II the_AT physics_NN1 close_RR to_II the_AT QSMT_NP1 ._. 
</s>
<s>
They_PPHS2 proposed_VVD nonlinear_JJ models_NN2 that_CST can_VM predict_VVI user_NN1 income_NN1 with_IW an_AT1 accuracy_NN1 of_IO 0.633_MC using_VVG a_AT1 combination_NN1 of_IO all_DB features_NN2 ._. 
</s>
<s>
From_II Narayan_NP1 ,_, Ramaswamy_NP1 ,_, and_CC Menon_NP1 ,_, 2007_MC ._. 
</s>
<s>
More_RGR precisely_RR ,_, we_PPIS2 demonstrate_VV0 the_AT following_JJ :_: First_MD ,_, that_CST the_AT IDL_NN1 junction_NN1 conditions_NN2 both_RR for_IF timelike/spacelike_JJ as_II31 well_II32 as_II33 for_IF null_JJ hypersurfaces_NN2 are_VBR modified_VVN due_II21 to_II22 the_AT fractional_JJ generalisation_NN1 of_IO the_AT space_NN1 time_NNT1 connection_NN1 ._. 
</s>
<s>
We_PPIS2 should_VM note_VVI that_DD1 Eq_NN1 ._. 
</s>
<s>
(_( 29_MC )_) indicates_VVZ that_CST f_ZZ1 (_( R_ZZ1 )_) could_VM be_VBI negative_JJ at_II the_AT present_JJ Universe_NN1 ._. 
</s>
<s>
The_AT right_JJ part_NN1 of_IO Fig._NN1 3.4(a)_FO shows_VVZ a_AT1 skeleton_NN1 expansion_NN1 of_IO this_DD1 diagram_NN1 in_II31 terms_II32 of_II33 Bethe–Salpeter_NP1 vertices_NN2 and_CC propagators_NN2 of_IO mesons_NN2 as_II31 well_II32 as_II33 Faddeev-type_JJ vertices_NN2 for_IF baryons_NN2 ._. 
</s>
<s>
In_II &lsqb;_( 6_MC &rsqb;_) frame_NN1 functions_NN2 respecting_II the_AT single_JJ measurement_NN1 (_( 20_MC )_) have_VH0 been_VBN shown_VVN to_TO admit_VVI an_AT1 expression_NN1 as_CSA in_II equation_NN1 (_( 5_MC )_) ,_, but_CCB the_AT result_NN1 depends_VVZ the_AT assumption_NN1 that_CST the_AT frame_NN1 functions_NN2 be_VBI continuous_JJ on_II the_AT set_NN1 of_IO all_DB effects_NN2 in_II <Professional_FO Term>_FO ._. 
</s>
<s>
Once_CS the_AT betatron_NN1 oscillation_NN1 frequency_NN1 ,_, xb_NNU xp=2c1=2_FO ,_, coincides_VVZ with_IW the_AT laser_NN1 frequency_NN1 observed_VVN by_II the_AT relativistic_JJ electron_NN1 ,_, resonance_NN1 occurs_VVZ and_CC FIG_NN1 ._. 
</s>
<s>
At_II the_AT same_DA time_NNT1 ,_, the_AT value_NN1 of_IO can_VM not_XX be_VBI increased_VVN due_II21 to_II22 PNS_NP1 (_( photon_NN1 number_NN1 splitting_NN1 )_) attack_VV0 ._. 
</s>
<s>
Since_CS quark-loop_JJ effects_NN2 alone_RR determine_VV0 the_AT number_NN1 of_IO quark-flavours_NN2 ,_, Nf_NP1 is_VBZ not_XX a_AT1 well_NN1 defined_VVD quantity_NN1 in_II these_DD2 truncation_NN1 schemes_NN2 ._. 
</s>
<s>
The_AT experimental_JJ investigation_NN1 is_VBZ complemented_VVN by_II computations_NN2 aiming_VVG to_TO establish_VVI their_APPGE usefulness_NN1 for_IF spectroscopic_JJ investigations_NN2 of_IO the_AT somewhat_RR larger_JJR molecules_NN2 than_CSN have_VH0 been_VBN hitherto_RT studied_VVN in_II the_AT same_DA context_NN1 ._. 
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<s>
Spatial_JJ scale_NN1 is_VBZ normalized_VVN by_II the_AT laser_NN1 wavelength_NN1 ._. 
</s>
<s>
Spin-charge_JJ conversion_NN1 has_VHZ been_VBN reported_VVN by_II spin_NN1 pumping_VVG for_IF bismuth_NN1 and_CC antimony_NN1 chalcogenide_NN1 layers_NN2 adjacent_II21 to_II22 metallic_JJ ferromagnets_NN2 (_( Deorani_NP1 et_RA21 al._RA22 ,_, 2014_MC ;_; Shiomi_NP1 et_RA21 al._RA22 ,_, 2014_MC ;_; Jamali_NP1 et_RA21 al._RA22 ,_, 2015_MC ;_; Kondou_NP1 et_RA21 al._RA22 ,_, 2016_MC ;_; Mendes_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) and_CC insulating_JJ ferrimagnets_NN2 (_( Hailong_NP1 Wang_NP1 et_RA21 al._RA22 ,_, 2016_MC ;_; Tang_NN1 et_RA21 al._RA22 ,_, 2018_MC )_) as_II31 well_II32 as_II33 by_II magnetoresistance_NN1 measurements_NN2 (_( Ando_NP1 ,_, 2014_MC ;_; Li_NP1 ,_, Vincent_NP1 Liu_NP1 ,_, and_CC Balents_NP1 ,_, 2014_MC ;_; Yasuda_NP1 et_RA21 al._RA22 ,_, 2016_MC )_) ._. 
</s>
<s>
By_II31 way_II32 of_II33 an_AT1 example_NN1 ,_, we_PPIS2 obtain_VV0 new_JJ classes_NN2 of_IO flat_JJ band_NN1 lattice_NN1 geometries_NN2 by_II solving_VVG the_AT conditions_NN2 for_IF the_AT lattice_NN1 parameters_NN2 in_II special_JJ cases_NN2 ._. 
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<s>
However_RRQV we_PPIS2 have_VH0 not_XX yet_RR shown_VVN that_CST this_DD1 metric_JJ G_ZZ1 governs_VVZ all_DB of_IO the_AT low-energy_JJ physics_NN1 ,_, and_CC that_CST there_EX are_VBR no_AT tachyonic_JJ or_CC ghost_NN1 modes_NN2 ._. 
</s>
<s>
In_II this_DD1 case_NN1 ,_, the_AT initial_JJ relaxation_NN1 time_NNT1 is_VBZ given_VVN by_II <Professional_FO Term>_FO and_CC the_AT timescale_NN1 of_IO the_AT second_MD relaxation_NN1 is_VBZ given_VVN by_II <Professional_FO Term>_FO ._. 
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<s>
Unlike_II the_AT case_NN1 of_IO 1012_MC Wcm2_FO (_( see_VV0 figure_NN1 3(a)_FO )_) ,_, the_AT thinner_JJR foil_NN1 target_NN1 shows_VVZ the_AT larger_JJR increase_NN1 rate_NN1 of_IO Lpr_NP1 as_CSA seen_VVN in_II figure_NN1 4(a)_FO ._. 
</s>
<s>
However_RR ,_, they_PPHS2 have_VH0 shown_VVN that_CST reconstructing_VVG BDs_NP1 from_II time-series_JJ data_NN with_IW transients_NN2 leads_VVZ to_II better_JJR results_NN2 than_CSN without_IW transients_NN2 ._. 
</s>
<s>
The_AT full_JJ system_NN1 is_VBZ based_VVN on_II a_AT1 channel_NN1 geometry_NN1 with_IW box_NN1 lengths_NN2 Lx_MC =_FO 200_MC in_II the_AT x_ZZ1 direction_NN1 and_CC Ly_NP1 =_FO 40_MC in_II the_AT y_ZZ1 direction_NN1 ._. 
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<s>
V._II R._NP1 Morrison_NP1 ,_, R._NP1 P._NP1 Chatelain_NN1 ,_, K._NP1 L._NP1 Tiwari_NP1 ,_, A._NP1 Hendaoui_NP1 ,_, A._NP1 Bruhacs_NP2 ,_, M._NN1 Chaker_NN1 ,_, and_CC B._NP1 J._NP1 Siwick_NP1 ,_, "_" A_ZZ1 photoinduced_JJ metal-like_JJ phase_NN1 of_IO monoclinic_JJ VO2_FO revealed_VVN by_II ultrafast_NN1 electron_NN1 diffraction_NN1 ,_, "_" Science_NN1 346_MC ,_, 445_MC (_( 2014_MC )_) ._. 
</s>
<s>
After_CS electron_NN1 injection_NN1 from_II a_AT1 Ag(111)_FO surface_NN1 into_II one_MC1 and_CC two_MC layers_NN2 of_IO DMSO_NP1 ,_, image_NN1 potential_NN1 states_NN2 (_( IPSs_NP1 )_) of_IO Ag_FO modified_VVN by_II the_AT layers_NN2 of_IO DMSO_NP1 are_VBR initially_RR formed_VVN ._. 
</s>
<s>
To_TO find_VVI the_AT sums_NN2 we_PPIS2 perform_VV0 the_AT same_DA procedure_NN1 at_II cubic_JJ order_NN1 ._. 
</s>
<s>
But_CCB as_CSA we_PPIS2 note_VV0 the_AT conversion_NN1 devices_NN2 of_IO life_NN1 have_VH0 invariably_RR been_VBN found_VVN to_TO embody_VVI elaborations_NN2 on_II this_DD1 design_NN1 ._. 
</s>
<s>
Each_DD1 slab_NN1 is_VBZ read_VVN out_RP from_II both_DB2 sides_NN2 by_II photomultiplier_JJR tubes_NN2 ,_, providing_VVG position_NN1 resolutions_NN2 along_II z_ZZ1 of_IO <EQUATION>_FO and_CC 5.0_MC cm_NNU for_IF the_AT inner_JJ and_CC outer_JJ ring_NN1 slabs_NN2 ,_, respectively_RR ._. 
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<s>
Studies_NN2 by_II Berger_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
on_II the_AT dendritic_JJ growth_NN1 of_IO lithium_NN1 on_II Au(111)_FO revealed_VVD a_AT1 one-dimensional_JJ strand-like_JJ growth_NN1 on_II terraces_NN2 ._. 
</s>
<s>
Local_JJ Gibbs_NP1 states_NN2 are_VBR obtained_VVN by_II replacing_VVG the_AT constant_JJ parameters_NN2 <Equation>_FO <Professional_FO terms>_FO by_II functionsand_NN1 by_II considering_VVG the_AT measure_NN1 with_IW density_NN1 <Professional_FO terms>_FO <Professional_FO terms>_FO :_: <Equation>_FO is_VBZ a_AT1 normalizing_JJ constant_JJ ._. 
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<s>
In_II fact_NN1 ,_, this_DD1 asymptotic_JJ still_RR holds_VVZ for_IF <EQUATION>_FO and_CC odd_JJ positive_JJ integers_NN2 n_ZZ1 ._. 
</s>
<s>
The_AT intersection_NN1 of_IO the_AT orthonormal_JJ basis_NN1 of_IO eigenfunctions_NN2 <EQUATION>_FO with_IW <Professional_FO Term>_FO gives_VVZ us_PPIO2 an_AT1 orthonormal_JJ basis_NN1 of_IO eigenfunctions_NN2 for_IF <Professional_FO Term>_FO ._. 
</s>
<s>
Sodium_NN1 ion_NN1 batteries_NN2 are_VBR attractive_JJ alternative_JJ energy_NN1 storage_NN1 systems_NN2 for_IF replacing_VVG lithium_NN1 ion_NN1 energy_NN1 storage_NN1 systems_NN2 since_CS sodium_NN1 is_VBZ much_RR more_RGR abundant_JJ and_CC thus_RR inexpensive_JJ element_NN1 in_II nature_NN1 ._. 
</s>
<s>
In_II both_DB2 these_DD2 scenarios_NN2 ,_, the_AT initial_JJ singularity_NN1 is_VBZ absent_JJ ,_, so_RR these_DD2 are_VBR quite_RG appealing_JJ alternative_JJ scenarios_NN2 to_II the_AT standard_JJ Big_JJ Bang_NN1 cosmology_NN1 ._. 
</s>
<s>
This_DD1 represented_VVD considerable_JJ progress_NN1 in_II the_AT development_NN1 of_IO mode-locked_JJ all-solid-state_JJ lasers_NN2 in_II the_AT 2.0_MC lm_NNU spectral_JJ region.122_FO After_II that_DD1 ,_, passive_JJ mode_NN1 locking_NN1 was_VBDZ achieved_VVN in_II various_JJ Tm3t-_NN1 ,_, Ho3t-_NN1 ,_, and_CC Tm3t/Ho3t-doped_NP1 bulk_NN1 laser_NN1 materials_NN2 with_IW SESAM_NP1 and_CC semiconductor_NN1 saturable_JJ absorbers_NN2 as_CSA mode_NN1 lockers_NN2 ._. 
</s>
<s>
Accordingly_RR ,_, a_AT1 fit_NN1 of_IO I(T)_NN1 for_IF T_ZZ1 >135_FO K_ZZ1 (_( solid_JJ black_JJ line_NN1 )_) yields_VVZ a_AT1 surface_NN1 Debye-temperature_NN1 of_IO hD_NNU ?_FO 86611K_FO ,_, where_CS m_ZZ1 denotes_VVZ the_AT mass_NN1 of_IO the_AT In_II atoms_NN2 and_CC kB_NNU the_AT Boltzmann_NP1 constant_JJ ._. 
</s>
<s>
Several_DA2 other_JJ peaks_NN2 related_VVN to_II alcohols_NN2 have_VH0 been_VBN detected_VVN in_II biogas_NN2 ,_, such_II21 as_II22 2-butanol_NN1 ,_, isobutanol_NN1 and_CC 2-propanol_NN1 &lsqb;_( 45,62_MC &rsqb;_) ._. 
</s>
<s>
It_PPH1 remains_VVZ important_JJ however_RR for_IF the_AT purpose_NN1 of_IO electric_JJ field_NN1 computation_NN1 ._. 
</s>
<s>
Shimizu_NN1 and_CC Miyadera_NP1 (_( 2002_MC )_) ,_, Frwis_NP1 and_CC Dur_NP1 (_( 2012b_FO )_) ,_, and_CC Park_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2016_MC )_) optimized_VVD the_AT variance_NN1 of_IO the_AT state_NN1 over_II all_DB local_JJ operators.10_FO This_DD1 means_VVZ that_CST Frwis_NP1 and_CC Dur_NP1 (_( 2012b_FO )_) and_CC Park_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2016_MC )_) will_VM result_VVI in_II the_AT same_DA values_NN2 <Equation>_FO ._. 
</s>
<s>
Based_VVN on_II various_JJ radiation_NN1 components_NN2 in_II the_AT spectra_NN2 of_IO lightning_NN1 return_NN1 stroke_NN1 processes_NN2 ,_, the_AT temperature_NN1 of_IO the_AT lightning_NN1 channel_NN1 is_VBZ diagnosed_VVN by_II different_JJ methods_NN2 ._. 
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<s>
The_AT calculated_JJ PXR_NP1 yields_VVZ for_IF different_JJ diffraction_NN1 orders_NN2 as_II31 well_II32 as_II33 the_AT ratios_NN2 I_ZZ1 γ_NULL 1/I_MC1 γ_NULL i_ZZ1 are_VBR presented_VVN in_II Tables_NN2 2_MC ._. 
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<s>
Signals_NN2 for_IF this_DD1 transition_NN1 have_VH0 again_RT been_VBN observed_VVN in_II an_AT1 effective_JJ lattice_NN1 theory_NN1 &lsqb;_( 43_MC &rsqb;_) and_CC are_VBR also_RR visible_JJ in_II contemporary_JJ chiral_JJ mirror_NN1 meson–baryon_NN1 models_NN2 &lsqb;_( 44_MC &rsqb;_) ._. 
</s>
<s>
This_DD1 says_VVZ that_CST the_AT regularized_JJ version_NN1 of_IO all_DB asymptotically_RR continuous_JJ resource_NN1 measures_NN2 is_VBZ equivalent_JJ up_II21 to_II22 an_AT1 overall_JJ proportionality_NN1 factor_NN1 ._. 
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<s>
The_AT use_NN1 of_IO the_AT CIRD_NN1 index_NN1 allows_VVZ to_TO study_VVI development_NN1 as_II a_AT1 monodimensional_JJ process_NN1 ._. 
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<s>
Thus_RR the_AT free_JJ parameter_NN1 e_ZZ1 ,_, whose_DDQGE existence_NN1 had_VHD no_AT good_JJ explanation_NN1 in_II Sect._NP1 4.8_MC ,_, acquires_VVZ a_AT1 palpable_JJ meaning_NN1 here_RL :_: in_BCL21 order_BCL22 to_TO express_VVI the_AT physical_JJ observables_NN2 (_( conductivities_NN2 ,_, wave-function_JJ moments_NN2 and_CC correlators_NN2 ,_, etc._RA )_) of_IO the_AT network_NN1 model_NN1 in_II the_AT SUSY_JJ vertex_NN1 model_NN1 and_CC ultimately_RR in_II the_AT effective_JJ continuum_NN1 field_NN1 theory_NN1 ,_, we_PPIS2 must_VM choose_VVI some_DD arbitrary_JJ but_CCB fixed_JJ value_NN1 of_IO e_ZZ1 in_II (_( 98_MC )_) ._. 
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<s>
The_AT COMPASS_NN1 experiment_NN1 at_II the_AT CERN_NP1 SPS_NN2 is_VBZ studying_VVG the_AT excitation_NN1 spectrum_NN1 of_IO light_JJ mesons_NN2 ,_, which_DDQ are_VBR composed_VVN of_IO up_VV0 ,_, down_RP ,_, and_CC strange_JJ quarks_NN2 ._. 
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<s>
There_EX are_VBR two_MC important_JJ Raman_NN1 scattering_VVG effects_NN2 ._. 
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<s>
The_AT electrothermal_JJ activation_NN1 melts_VVZ the_AT metallic_JJ cap_NN1 of_IO the_AT reservoirs_NN2 that_CST enables_VVZ drug_NN1 release_NN1 from_II the_AT chip_NN1 ._. 
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<s>
If_CS the_AT current_JJ quench_VV0 time_NNT1 is_VBZ 50ms_FO ,_, the_AT loop_NN1 voltage_NN1 is_VBZ V?=1500V_FO ,_, and_CC the_AT density_NN1 must_VM be_VBI increased_VVN approximately_RR five_MC hundred_NNO times_NNT2 ._. 
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<s>
In_II this_DD1 reply_NN1 ,_, we_PPIS2 respond_VV0 to_II the_AT comments_NN2 of_IO Mustafaev_NP1 et_RA21 al_RA22 to_II our_APPGE paper_NN1 '_NULL Information_NN1 hidden_VVN in_II the_AT velocity_NN1 distribution_NN1 of_IO ions_NN2 and_CC the_AT exact_JJ kinetic_JJ Bohm_NP1 criterion_NN1 '_NULL (_( Plasma_NP1 Sources_NN2 Science_NN1 and_CC Technology_NN1 26_MC 055003_MC )_) ._. 
</s>
<s>
An_AT1 important_JJ implication_NN1 is_VBZ that_DD1 improved_JJ performance_NN1 following_VVG the_AT addition_NN1 of_IO other_JJ "_" catalysts_NN2 "_" may_VM not_XX be_VBI due_II21 to_II22 better_JJR surface_NN1 composition_NN1 but_CCB rather_RR to_II increases_NN2 in_II the_AT number_NN1 of_IO TPB_NP1 sites_NN2 &lsqb;_( 7_MC &rsqb;_) ._. 
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<s>
This_DD1 alternate_JJ orientation_NN1 of_IO the_AT water_NN1 molecules_NN2 is_VBZ probably_RR due_II21 to_II22 the_AT hydrogen_NN1 bond_NN1 network_NN1 formed_VVN (_( and_CC continuously_RR changing_VVG )_) between_II them_PPHO2 ._. 
</s>
<s>
Spin-orbit_JJ coupling_NN1 (_( SOC_NP1 )_) reduces_VVZ this_DD1 degeneracy_NN1 in_II a_AT1 different_JJ way_NN1 by_II providing_VVG a_AT1 spin-_JJ orbital-entangled_JJ ground_NN1 state_NN1 ._. 
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<s>
Still_RR ,_, an_AT1 accurate_JJ modelling_NN1 with_IW errors_NN2 smaller_JJR than_CSN ,_, e.g._REX ,_, 3%_NNU of_IO the_AT lithium_NN1 flux_NN1 requires_VVZ the_AT knowledge_NN1 of_IO twelve_MC cross_JJ sections_NN2 with_IW much_DA1 improved_JJ accuracy_NN1 compared_VVN to_II current_JJ knowledge_NN1 &lsqb;_( 118_MC &rsqb;_) ._. 
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<s>
For_IF a_AT1 pedagogical_JJ derivation_NN1 of_IO these_DD2 results_NN2 see_VV0 section_NN1 3.4_MC and_CC 4.2_MC of_IO Ref_NN1 ._. 
</s>
<s>
Most_DAT of_IO the_AT self-assembly_JJ protocols_NN2 use_VV0 gelation_NN1 for_IF forming_VVG graphene_NN1 3D_NNU structures_NN2 ._. 
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<s>
But_CCB a_AT1 long_JJ integration_NN1 time_NNT1 may_VM increase_VVI the_AT long-term_JJ instabilities_NN2 due_II21 to_II22 the_AT frequency_NN1 drift_NN1 from_II the_AT environmental_JJ temperature_NN1 changes_NN2 and_CC device_NN1 aging_VVG and_RR31 so_RR32 on_RR33 ._. 
</s>
<s>
By_II substituting_VVG it_PPH1 into_II equation_NN1 (_( 25_MC )_) ,_, we_PPIS2 obtain_VV0 equation_NN1 (_( 23_MC )_) ._. 
</s>
<s>
The_AT BH_NP1 is_VBZ surrounded_VVN by_II a_AT1 geometrically_RR thin_JJ and_CC optically_RR thick_JJ accretion_NN1 disk_NN1 ._. 
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<s>
Then_RT we_PPIS2 demonstrate_VV0 that_CST the_AT measure<Equation>_FO is_VBZ an_AT1 f_ZZ1 -_- invariant_JJ Gibbs_NP1 measure_NN1 ._. 
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<s>
D.E.C._NPM1 and_CC H.J.K._NP1 acknowledge_VV0 support_NN1 from_II the_AT AFOSRMURIPhotonic_JJ Quantum_NN1 Mitterrand_NP1 the_AT ONR_NP1 MURI_NP1 Quantum_NN1 Op_NN1 to-Mechanics_NN2 with_IW Atoms_NN2 and_CC Nanostructured_JJ Diamond_NN1 (_( QOMAND_NP1 )_) ._. 
</s>
<s>
In_II experiment_NN1 (_( Schreiber_NP1 et_RA21 al._RA22 ,_, 2015_MC )_) ,_, the_AT system_NN1 is_VBZ initially_RR prepared_VVN in_II a_AT1 density-wave_JJ state_NN1 ,_, with_IW particles_NN2 predominantly_RR occupying_VVG even_RR sites_NN2 ._. 
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<s>
Between_II 8_MC and_CC 16_MC Fourier_NP1 modes_NN2 are_VBR used_VVN ._. 
</s>
<s>
This_DD1 is_VBZ basically_RR optimal_JJ ,_, since_CS no_AT protocol_NN1 can_VM be_VBI secure_JJ if_CS <Equation>_FO ._. 
</s>
<s>
As_II the_AT detuning_NN1 decreases_VVZ ,_, Mode_NN1 I_ZZ1 is_VBZ excited_JJ fifirst_NN1 ._. 
</s>
<s>
While_CS the_AT analysis_NN1 of_IO the_AT isotopic_JJ composition_NN1 of_IO material_NN1 samples_NN2 in_II the_AT laboratory_NN1 clearly_RR obtains_VVZ the_AT most_RGT precise_JJ values_NN2 for_IF abundances_NN2 among_II different_JJ elements_NN2 and_CC isotopes_NN2 ,_, the_AT path_NN1 from_II cosmic_JJ interstellar_JJ gas_NN1 to_II the_AT terrestrial_JJ laboratory_NN1 includes_VVZ numerous_JJ possibilities_NN2 to_TO affect_VVI the_AT composition_NN1 ._. 
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<s>
In_BCL21 order_BCL22 for_IF the_AT full_JJ scattering_NN1 amplitude_NN1 Eq_NN1 ._. 
</s>
<s>
(_( 71_MC )_) to_TO remain_VVI finite_JJ ,_, this_DD1 divergence_NN1 must_VM be_VBI cancelled_VVN by_II the_AT appropriate_JJ behavior_NN1 of_IO the_AT partial-wave_JJ amplitudes_NN2 as_CSA <PROFESSIONAL_FO TERM>_FO ._. 
</s>
<s>
This_DD1 targeted_VVD drug_NN1 delivery_NN1 technique_NN1 can_VM also_RR effectively_RR release_VVI pharmaceutical_JJ agents_NN2 at_II deep_JJ intricate_JJ pathological_JJ sites_NN2 that_CST are_VBR not_XX directly_RR accessible_JJ with_IW systemic_JJ administration_NN1 ._. 
</s>
<s>
However_RR ,_, randomizing_VVG the_AT local_JJ oscillator_NN1 signal_NN1 '_NULL s_ZZ1 polarization_NN1 state_NN1 requires_VVZ a_AT1 repeatable_JJ and_CC accurate_JJ polarization_NN1 controller_NN1 ._. 
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<s>
The_AT subscript_NN1 "_" <Equation>_FO "_" indicates_VVZ that_CST the_AT integral_JJ is_VBZ over_II one_MC1 unit_NN1 cell_NN1 ._. 
</s>
<s>
For_IF each_DD1 sequence_NN1 <Equation>_FO of_IO points_NN2 in_II S2_FO ,_, we_PPIS2 define_VV0 the_AT Borel_NN1 probability_NN1 measures_NN2 ,_, for_IF each_DD1 <Equation>_FO ,_, where_CS <Equation>_FO ,_, for_IF <Equation>_FO ._. 
</s>
<s>
We_PPIS2 propose_VV0 that_CST the_AT degree_NN1 of_IO quantum_NN1 walk_NN1 simulation_NN1 accuracy_NN1 can_VM be_VBI treated_VVN as_II an_AT1 additional_JJ optimisation_NN1 parameter_NN1 ._. 
</s>
<s>
The_AT interaction_NN1 may_VM potentially_RR lead_VVI to_II aggregation_NN1 of_IO peptides_NN2 as_II the_AT electrostatic_JJ energy_NN1 would_VM be_VBI minimal_JJ when_CS the_AT antiparallel_NN1 peptides_NN2 are_VBR situated_VVN as_RG close_RR to_II each_PPX221 other_PPX222 as_CSA possible_JJ ._. 
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<s>
So_RR the_AT FeO-SiNT_NP1 (_( 9_MC ,_, 0_MC )_) ,_, PbO-SiNT_NP1 (_( 9_MC ,_, 0_MC )_) ,_, NbO2-_JJ SiNT_NN1 (_( 9_MC ,_, 0_MC )_) and_CC TeO2-SiNT_NP1 (_( 9_MC ,_, 0_MC )_) on_II top_JJ atom_NN1 positions_NN2 have_VH0 lower_JJR EBG_NN1 values_NN2 than_CSN bridge_NN1 bonding_NN1 positions_NN2 ._. 
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<s>
The_AT former_DA accounts_VVZ for_IF the_AT spin_NN1 current_JJ backflow_NN1 in_II the_AT nonmagnetic_JJ metal_NN1 (_( the_AT larger_JJR the_AT backflow_NN1 ,_, the_AT smaller_JJR the_AT spin_NN1 current_JJ transmission_NN1 into_II the_AT ferromag-_JJ net_NN1 )_) ,_, while_CS the_AT latter_DA opens_VVZ an_AT1 additional_JJ spin_NN1 dissipation_NN1 channel_NN1 at_II the_AT interface_NN1 (_( see_VV0 Sec_NNU ._. 
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<s>
III.C_NP1 )_) ._. 
</s>
<s>
From_II the_AT above_JJ SAs_NP1 and_CC their_APPGE deficiencies_NN2 ,_, novel_JJ materials_NN2 are_VBR introduced_VVN that_CST overcome_VV0 all_DB these_DD2 drawbacks_NN2 ._. 
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<s>
While_CS commercial_JJ machines_NN2 can_VM now_RT operate_VVI at_II 1000_MC frames_NN2 per_II second_NNT1 ,_, higher_JJR speeds_NN2 are_VBR often_RR necessary_JJ to_TO capture_VVI fast_JJ dynamics_NN ._. 
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<s>
The_AT other_JJ channel_NN1 that_CST presents_VVZ anomalous_JJ signals_NN2 is_VBZ <Professional_FO Term>_FO disappearance_NN1 ._. 
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<s>
Recently_RR ,_, several_DA2 works_NN available_JJ in_II the_AT literature_NN1 have_VH0 proven_VVN the_AT versatility_NN1 of_IO the_AT method_NN1 ,_, using_VVG it_PPH1 in_II different_JJ contexts_NN2 such_II21 as_II22 extending_VVG solutions_NN2 of_IO Einstein_NP1 field_NN1 equations_NN2 described_VVN by_II perfect_JJ fluid_NN1 to_II anisotropic_JJ domains_NN2 &lsqb;_( 13–17_MCMC &rsqb;_) ,_, Einstein–Maxwell_NP1 equations_NN2 &lsqb;_( 18_MC ,_, 19_MC &rsqb;_) ,_, black_JJ holes_NN2 &lsqb;_( 20–22_MCMC &rsqb;_) ,_, cloud_NN1 of_IO strings_NN2 &lsqb;_( 23_MC &rsqb;_) ,_, Einstein–_NP1 Klein–Gordon_NP1 equations_NN2 &lsqb;_( 24_MC &rsqb;_) and_CC within_II the_AT framework_NN1 of_IO theories_NN2 in_II higher_JJR dimensions_NN2 &lsqb;_( 25_MC &rsqb;_) ._. 
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<s>
Building_NN1 on_II the_AT ideas_NN2 sketched_VVD at_II the_AT beginning_NN1 of_IO the_AT previous_JJ section_NN1 (_( see_VV0 also_RR &lsqb;_( Hai13_FO ,_, GP17_FO &rsqb;_) )_) ,_, let_VV0 ε_FO be_VBI given_VVN as_CSA before_RT and_CC uε_FO be_VBI the_AT solution_NN1 of_IO (_( 1.2_MC )_) with_IW ε_FO replacing_VVG ._. 
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<s>
Around_II a_AT1 photon_NN1 energy_NN1 of_IO 280_MC eV_NN1 ,_, both_DB2 the_AT refractive_JJ index_NN1 and_CC the_AT opacity_NN1 are_VBR discontinuous_JJ because_II21 of_II22 the_AT K_NP1 edge_NN1 of_IO carbon_NN1 in_II CH_NN1 when_CS the_AT 1s-core_JJ electrons_NN2 become_VV0 accessible_JJ ,_, which_DDQ increases_VVZ the_AT electrical_JJ conductivity.32_FO It_PPH1 should_VM be_VBI noted_VVN that_CST the_AT discontinuity_NN1 in_II the_AT Re(n)_NN1 around_II the_AT photon_NN1 energy_NN1 of_IO 280_MC eVdoes_NN2 not_XX coincide_VV0 exactly_RR between_II the_AT FPOTs_NP2 and_CC the_AT Henke_NP1 tables_NN2 ._. 
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<s>
The_AT goal_NN1 is_VBZ to_TO recover_VVI Born_JJ '_NULL s_ZZ1 rule_NN1 and_CC the_AT representation_NN1 of_IO quant_NN1 um_UH states_NN2 as_CSA density_NN1 operators_NN2 from_II consistent_JJ probability_NN1 assignments_NN2 to_II measurement_NN1 outcomes_NN2 ._. 
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<s>
This_DD1 system_NN1 is_VBZ similar_JJ in_II setup_NN1 and_CC configuration_NN1 to_II the_AT AIDA/EURICA_NP1 experiment_NN1 at_II the_AT RIBF_NN1 in_II that_DD1 it_PPH1 utilizes_VVZ an_AT1 implantation_NN1 target_NN1 surrounded_VVN by_II HPGE_NP1 detectors_NN2 ._. 
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<s>
In_II this_DD1 subsection_NN1 ,_, the_AT quantum_NN1 circuit_NN1 realization_NN1 of_IO quantum_NN1 image_NN1 edge_NN1 extraction_NN1 is_VBZ constructed_VVN based_VVN on_II the_AT X_ZZ1 -Shift_JJ transformation_NN1 ,_, Y_ZZ1 -Shift_JJ transformation_NN1 ,_, quantum_NN1 unitary_JJ operation_NN1 US_NP1 ,_, quantum_NN1 black_JJ box_NN1 UG_NN1 and_CC threshold_NN1 operation_NN1 UT_NN1 ._. 
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<s>
Our_APPGE focus_NN1 is_VBZ to_TO study_VVI the_AT collective_JJ dynamics_NN in_II a_AT1 colony_NN1 of_IO tumor_NN1 cells_NN2 in_II both_DB2 the_AT intermediate-_NN1 and_CC long-time_JJ limits_NN2 ._. 
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<s>
They_PPHS2 were_VBDR installed_VVN in_II a_AT1 tank_NN1 on_II two_MC in-vacuum_JJ goniometers_NN2 ._. 
</s>
<s>
Culture_NN1 is_VBZ the_AT essential_JJ character_NN1 of_IO human_JJ society_NN1 ,_, and_CC it_PPH1 serves_VVZ as_II a_AT1 driving_JJ force_NN1 for_IF human_JJ development_NN1 ._. 
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<s>
In_II the_AT case_NN1 of_IO adamantane_NN1 clusters_NN2 ,_, (_( C10H16_FO )_) n_ZZ1 ,_, from_II doped_JJ HND_NP1 we_PPIS2 observed_VVD pronounced_JJ magic_JJ numbers_NN2 for_IF singly_RR ,_, doubly_RR and_CC triply_RR charged_VVN clusters_NN2 that_CST reveal_VV0 a_AT1 transition_NN1 from_II icosahedral_JJ packing_NN1 to_II fcc_NNU packing_NN1 between_II n_ZZ1 =_FO 19_MC and_CC n_ZZ1 =_FO 38_MC ._. 
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<s>
Such_DA a_AT1 structure_NN1 can_VM be_VBI realized_VVN by_II introducing_VVG a_AT1 local_JJ defect_NN1 into_II a_AT1 PCW_NP1 ,_, for_REX21 example_REX22 ,_, by_II locally_RR altering_VVG the_AT size_NN1 of_IO the_AT periodic_JJ modulation_NN1 of_IO the_AT waveguide_NN1 as_CSA seen_VVN in_II Fig._NN1 5(b)_FO ._. 
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<s>
Therefore_RR ,_, in_BCL21 order_BCL22 to_TO obtain_VVI full_JJ information_NN1 ,_, Eve_NP1 must_VM carry_VVI out_RP an_AT1 IRUD_NN1 attack_NN1 (_( intercept-resend_NN1 with_IW Unambiguous_JJ Discrimination_NN1 )_) ._. 
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<s>
Femtosecond_VV0 diffractive_JJ imaging_NN1 was_VBDZ first_MD demonstrated_VVN in_II an_AT1 experiment_NN1 at_II FLASH_NN1 using_VVG an_AT1 intense_JJ 25_MC fs_FO ,_, 4×1013_FO Wcm2_FO pulse_NN1 ,_, containing_VVG 1012_MC photons_NN2 at_II 32nm_FO wavelength_NN1 ,_, which_DDQ produced_VVD a_AT1 coherent_JJ diffraction_NN1 pattern_NN1 from_II a_AT1 nanostructured_JJ non-periodic_JJ object_NN1 ,_, before_II destroying_VVG it_PPH1 at_II 60,000_MC K_ZZ1 (_( Chapman_NP1 et_RA21 al._RA22 ,_, 2006_MC )_) ._. 
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<s>
An_AT1 entangled_JJ state_NN1 with_IW one_MC1 excitation_NN1 jointly_RR stored_VVN in_II the_AT two_MC ensembles_NN2 was_VBDZ deterministically_RR created_VVN by_II fractional_JJ STIRAP_NN1 ._. 
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<s>
This_DD1 central_JJ module_NN1 is_VBZ embedded_VVN into_II a_AT1 2_MC ×_II 39-winding_JJ coil_NN1 for_IF the_AT production_NN1 of_IO a_AT1 vertical_JJ field_NN1 (_( which_DDQ only_RR becomes_VVZ relevant_JJ when_CS discussing_VVG the_AT helical_JJ MRI_NN2 in_II Section_NN1 7_MC )_) ._. 
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<s>
The_AT data_NN are_VBR measured_VVN using_VVG the_AT harmonic_JJ Hall_NN1 voltage_NN1 analysis_NN1 method_NN1 ._. 
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<s>
In_II fact_NN1 ,_, hydrogen-like_JJ atoms_NN2 or_CC ions_NN2 formed_VVN by_II electron_NN1 capture_NN1 are_VBR nearly_RR instantaneously_RR ionized_VVN through_II electron_NN1 loss_NN1 ._. 
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<s>
Since_CS RWD_NP1 decreases_VVZ with_IW increasing_JJ MWD_NP1 ,_, recurrent_JJ novae_NN2 that_CST exhibit_VV0 very_RG short_JJ recurrence_NN1 times_NNT2 (_( a_AT1 few_DA2 years_NNT2 to_II a_AT1 few_DA2 decades_NNT2 )_) are_VBR expected_VVN to_TO be_VBI characterized_VVN by_II massive_JJ WDs_NP1 and_CC high_JJ accretion_NN1 rates_NN2 ._. 
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<s>
Most_DAT of_IO modern_JJ cryptography_NN1 follows_VVZ Kerckhoffs_NP1 '_NULL s_ZZ1 principle_NN1 (_( Kerckhoffs_NP1 ,_, 1883_MC )_) and_CC assumes_VVZ any_DD cryptographic_JJ system_NN1 can_VM fall_VVI into_II the_AT hands_NN2 of_IO the_AT adversary_NN1 and_CC that_CST all_DB the_AT details_NN2 of_IO the_AT system_NN1 are_VBR perfectly_RR known_VVN ._. 
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<s>
Figure_NN1 17_MC demonstrates_VVZ the_AT free_JJ energy_NN1 curves_NN2 of_IO crystallization_NN1 in_II two_MC series_NN of_IO single_JJ linear_JJ and_CC cyclic_JJ copolymers_NN2 with_IW each_DD1 series_NN under_II the_AT same_DA crystallization_NN1 temperatures_NN2 &lsqb;_( 154_MC &rsqb;_) ._. 
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<s>
The_AT PXR_NP1 generated_VVD by_II channeled_JJ particles_NN2 in_II bent_JJ crystals_NN2 has_VHZ been_VBN considered_VVN in_II &lsqb;_( 84_MC &rsqb;_) where_RRQ the_AT possibility_NN1 of_IO the_AT PXR_NP1 focusing_VVG was_VBDZ discussed_VVN ._. 
</s>
<s>
Alternatively_RR ,_, transient_JJ regimes_NN2 toward_II synchrony_NN1 and_CC perturbative_JJ methods_NN2 on_II synchronizability_NN1 can_VM be_VBI used_VVN to_TO describe_VVI more_RGR realistic_JJ regimes_NN2 ._. 
</s>
<s>
Electronic_JJ structures_NN2 of_IO the_AT valence_NN1 and_CC coreexcited_VVD states_NN2 are_VBR analyzed_VVN ,_, after_II which_DDQ the_AT core-to-valence_JJ absorption_NN1 strengths_NN2 relevant_JJ to_II the_AT UV_JJ photolysis_NN1 are_VBR discussed_VVN ._. 
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<s>
It_PPH1 can_VM also_RR be_VBI shown_VVN directly_RR by_II using_VVG the_AT erasure_NN1 channels<Equation>_FO (_( see_VV0 the_AT proof_NN1 of_IO theorem_NN1 2_MC in_II section_NN1 8_MC )_) ._. 
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<s>
The_AT study_NN1 also_RR shows_VVZ that_CST the_AT effect_NN1 of_IO the_AT atomic_JJ composition_NN1 of_IO the_AT rock_NN1 on_II the_AT variation_NN1 of_IO the_AT muon_NN1 flux_NN1 is_VBZ negligible_JJ with_II31 respect_II32 to_II33 the_AT density_NN1 variation_NN1 at_RR21 least_RR22 for_IF classical_JJ rocks_NN2 without_IW high_JJ Z_ZZ1 elements_NN2 ._. 
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<s>
To_TO arrive_VVI at_II this_DD1 conclusion_NN1 ,_, the_AT authors_NN2 observed_VVD that_CST the_AT decay_NN1 of_IO the_AT amplitude_NN1 of_IO the_AT pulse_NN1 for_IF chains_NN2 with_IW mass_JJ ratio_NN1 0.98_MC and_CC 0.55_MC is_VBZ almost_RR the_AT same_DA (_( numerical_JJ simulations_NN2 also_RR confirmed_VVN this_DD1 observation_NN1 )_) ._. 
</s>
<s>
The_AT residues_NN2 at_II the_AT two_MC anchors_NN2 of_IO the_AT loop_NN1 show_NN1 densities_NN2 that_CST resemble_VV0 different_JJ end_NN1 states_NN2 tetrahydrofolate_VV0 and_CC dihydro-folate_JJ complexes_NN2 ,_, respectively_RR ._. 
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<s>
Let_VV0 <EQUATION>_FO be_VBI the_AT set_NN1 of_IO RTT_NP1 generators_NN2 for_IF Uq_NP1 (_( g_ZZ1 )_) ._. 
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<s>
In_II summary_NN1 of_IO this_DD1 section_NN1 ,_, the_AT limited_JJ lamellar_JJ thickness_NN1 can_VM be_VBI quantitatively_RR explained_VVN by_II the_AT joint_JJ contributions_NN2 of_IO secondary_JJ crystal_NN1 nucleation_NN1 and_CC instant_JJ thickening_NN1 at_II the_AT wedge-shaped_JJ growth_NN1 front_NN1 in_II the_AT linear_JJ crystal_NN1 growth_NN1 rates_NN2 ,_, as_CSA described_VVN in_II Eqn_NN1 ._. 
</s>
<s>
The_AT total_JJ interaction_NN1 energies_NN2 for_IF isomers_NN2 I_PPIS1 ,_, II_MC ,_, and_CC III_MC of_IO <Equation>_FO <Equation>_FO <Equation>are_FO between_II the_AT total_JJ interaction_NN1 energies_NN2 of<Equation>_FO and_CC <Equation>_FO For_IF all_DB the_AT three_MC observed_JJ isomers_NN2 ,_, electrostatic_JJ and_CC dispersion_NN1 interactions_NN2 are_VBR the_AT dominant_JJ attractive_JJ terms_NN2 whereas_CS electrostatic_JJ ,_, induction_NN1 and_CC dispersion_NN1 interactions_NN2 primarily_RR contribute_VV0 to_II the_AT interaction_NN1 energies_NN2 of<Equation>_FO in_II which_DDQ the<Equation>_FO hydrogen_NN1 bond_NN1 is_VBZ formed_VVN ._. 
</s>
<s>
Without_IW the_AT circuit_NN1 model_NN1 ,_, one_PN1 needs_VVZ to_TO rely_VVI on_II fluid_NN1 simulations_NN2 or_CC build_VV0 RF_NP1 systems_NN2 by_II trial_NN1 and_CC error_NN1 ._. 
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<s>
In_II the_AT majority_NN1 of_IO instances_NN2 ,_, this_DD1 has_VHZ been_VBN viewed_VVN as_II a_AT1 negative_JJ strike_NN1 against_II the_AT habitability_NN1 of_IO M-dwarf_JJ exoplanets_NN2 ,_, despite_II the_AT fact_NN1 that_CST many_DA2 UV_JJ shielding_JJ mechanisms_NN2 are_VBR feasible_JJ ,_, as_CSA described_VVN in_II Sec_NNU ._. 
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<s>
III.C.1_FO ._. 
</s>
<s>
However_RR in_II practice_NN1 ,_, the_AT hard_JJ component_NN1 is_VBZ usually_RR collimated_VVN ,_, whilst_CS ,_, to_II a_AT1 first_MD approximation_NN1 ,_, the_AT pileup_NN1 component_NN1 is_VBZ uniformly_RR distributed_VVN across_II the_AT jet_NN1 ._. 
</s>
<s>
A_AT1 chain_NN1 of_IO grains_NN2 interacting_VVG only_RR under_II compression_NN1 with_IW a_AT1 harmonic_JJ force_NN1 (_( n_ZZ1 =_FO 2_MC )_) was_VBDZ considered_VVN ,_, but_CCB the_AT leftmost_JJ grain_NN1 was_VBDZ kept_VVN fixed_JJ instead_II21 of_II22 being_VBG backscattered_VVN as_CSA in_II Hinch_NP1 and_CC Saint-Jean_NP1 &lsqb;_( 15_MC &rsqb;_) ._. 
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<s>
In_RR21 addition_RR22 ,_, to_TO study_VVI the_AT effect_NN1 of_IO preplasma_NN1 on_II the_AT rear_JJ surface_NN1 ,_, a_AT1 metal_NN1 coating_NN1 on_II the_AT rear_JJ surface_NN1 would_VM also_RR be_VBI interesting_JJ and_CC helpful_JJ in_II understanding_NN1 physics_NN1 issues_NN2 related_VVN to_II sheath_NN1 field_NN1 formation_NN1 along_II21 with_II22 the_AT improvement_NN1 in_II escaping_JJ electron_NN1 flux_NN1 ._. 
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<s>
The_AT solid_JJ lines_NN2 show_VV0 the_AT phase_NN1 boundaries_NN2 as_CSA reported_VVN by_II Yen_NN and_CC Nicol_NP1 Ref_NN1 ._. 
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<s>
Nevertheless_RR ,_, the_AT non-observation_NN1 of_IO an_AT1 offset_NN1 between_II the_AT mass_JJ distribution_NN1 of_IO DM_NNU and_CC galaxies_NN2 in_II the_AT Bullet_NN1 Cluster_NN1 constrains_VVZ such_DA self-interacting_JJ cross_NN1 section_NN1 ,_, concretely/m_FU s<_FO 1.25_MC cm_NNU /g_FU at_II 68%_NNU CL_NP1 &lsqb;_( 131–133_MCMC &rsqb;_) ._. 
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<s>
The_AT introduced_JJ changes_NN2 make_VV0 that_CST partial_JJ information_NN1 gained_VVN in_II some_DD authentication_NN1 attempt_NN1 gives_VVZ the_AT eaves-droppers_NN2 no_AT advantage_NN1 in_II breaking_VVG the_AT next_MD ones_NN2 ._. 
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<s>
In_II this_DD1 appendix_NN1 ,_, we_PPIS2 give_VV0 a_AT1 brief_JJ description_NN1 of_IO the_AT global_JJ workflow_NN1 of_IO IFRIIT_NP1 and_CC discuss_VV0 the_AT current_JJ numerical_JJ cost_NN1 of_IO GO_VV0 versus_II CGO_NP1 ._. 
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<s>
For_IF this_DD1 reason_NN1 ,_, the_AT observed_JJ deflection_NN1 efficiency_NN1 is_VBZ close_JJ to_II its_APPGE maximum_JJ value_NN1 for_IF a_AT1 parallel_JJ beam_NN1 ._. 
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<s>
However_RR ,_, the_AT electrical_JJ conductivity_NN1 is_VBZ the_AT same_DA for_IF both_DB2 of_IO the_AT nonextensive_JJ and_CC Maxwellian_JJ particles_NN2 ._. 
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<s>
In_II dedicated_JJ studies_NN2 it_PPH1 was_VBDZ determined_VVN that_CST the_AT mean_JJ energy_NN1 of_IO such_DA fast_JJ electrons_NN2 generated_VVN in_II TJ-II_MC is_VBZ correlated_VVN ,_, but_CCB not_XX linear_JJ ,_, with_IW density_NN1 ,_, e.g._REX ,_, for_IF line-averaged_JJ electron_NN1 densities_NN2 ,_, ?e_FW ,_, 5×1018_FO m3_FO their_APPGE mean_JJ energy_NN1 was_VBDZ 30–50keV_JJ with_IW a_AT1 tail_NN1 up_II21 to_II22 several_DA2 100_MC '_NULL s_ZZ1 keV_NN1 ._. 
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<s>
It_PPH1 can_VM be_VBI simply_RR calculated_VVN as<Equation>where_FO T_ZZ1 is_VBZ the_AT threshold_NN1 ._. 
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<s>
The_AT Volkov_NP1 force_NN1 (_( Volkov_NP1 ,_, 1965_MC )_) was_VBDZ employed_VVN by_II KanadaEn_NN1 '_NULL yo_UH (_( 1998_MC ,_, 2007_MC )_) ._. 
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<s>
Suppose_VV0 for_IF the_AT sake_NN1 of_IO the_AT argument_NN1 that_CST the_AT sketch_NN1 of_IO Fig._NN1 2.1_MC represents_VVZ the_AT qualitative_JJ aspects_NN2 of_IO the_AT QCD_NP1 phase_NN1 diagram_NN1 accurately_RR and_CC the_AT chiral_JJ transition_NN1 line_NN1 is_VBZ not_XX affected_VVN by_II additional_JJ physics_NN1 in_II the_AT low-temperature_NN1 and_CC high_JJ chemical_JJ potential_JJ region_NN1 such_II21 as_II22 inhomogeneous_JJ condensates_NN2 or_CC other_JJ phenomena_NN2 ._. 
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Often_RR ,_, one_PN1 works_VVZ with_IW collective_JJ degrees_NN2 of_IO freedom_NN1 such_II21 as_II22 the_AT total_JJ flux_NN1 of_IO the_AT system_NN1 ._. 
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<s>
mathematically_RR ,_, this_DD1 is_VBZ equivalent_JJ to_II a_AT1 massive_JJ particle_NN1 moving_VVG in_II a_AT1 one-dimensional_JJ potential_NN1 ._. 
</s>
<s>
Through_II the_AT above_JJ result_NN1 ,_, the_AT maximum_JJ sensitivity_NN1 and_CC FoM_NN1 of_IO the_AT biosensor_NN1 are_VBR respectively_RR 333.3_MC nm/RIU_FU and_CC 16.665_MC RIU_NP1 ._. 
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<s>
It_PPH1 is_VBZ the_AT purpose_NN1 of_IO this_DD1 review_NN1 to_TO present_VVI the_AT various_JJ control_NN1 phenomena_NN2 ,_, which_DDQ all_DB rely_VV0 on_II the_AT same_DA underlying_JJ physics_NN1 ,_, within_II a_AT1 unified_JJ framework_NN1 ._. 
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<s>
We_PPIS2 do_VD0 not_XX see_VVI evidence_NN1 of_IO simultaneous_JJ delocalized_JJ and_CC localized_JJ electronic_JJ states_NN2 ,_, as_CSA suggested_VVN in_II Strader_NP1 et_RA21 al._RA22 ,_, even_RR in_II photoemission_NN1 spectra_NN2 with_IW high_JJ k_ZZ1 |_NULL |_NULL ,_, as_CSA shown_VVN in_II the_AT supplementary_JJ material_NN1 ._. 
</s>
<s>
The_AT tensile_JJ strength_NN1 was_VBDZ measured_VVN immediately_RR by_II uniaxial_JJ tensile_JJ assessment_NN1 using_VVG an_AT1 Exceed_VV0 E42_FO Universal_JJ Testing_NN1 Machine_NN1 (_( Insight_NN1 ,_, MTS_NP2 Systems_NN2 )_) equipped_VVN with_IW a_AT1 5.0_MC N_NNU load_NN1 cell_NN1 ._. 
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We_PPIS2 acknowledge_VV0 the_AT kind_NN1 support_NN1 and_CC hospitality_NN1 of_IO 426Proust_FO ?_? 
</s>
<s>
Along_II the_AT strong-field_JJ branch_NN1 of_IO the_AT instability_NN1 cone_NN1 the_AT wave_NN1 numbers_NN2 exceed_VV0 those_DD2 at_II the_AT weak-field_JJ branch_NN1 where_CS the_AT cells_NN2 are_VBR almost_RR circular_JJ in_II the_AT meridional_JJ plane_NN1 ._. 
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<s>
The_AT transverse_JJ spatial_JJ bandwidth_NN1 of_IO the_AT Gaussian_JJ pump_NN1 beam_NN1 determines_VVZ the_AT strength_NN1 of_IO transverse_JJ correlation_NN1 ,_, and_CC the_AT phase-matching_JJ bandwidth_NN1 determines_VVZ the_AT singlephoton_NN1 bandwidth_NN1 of_IO the_AT SPDC_NP1 emission_NN1 ,_, which_DDQ is_VBZ generally_RR is_VBZ significantly_RR larger_JJR than_CSN that_DD1 of_IO the_AT pump_NN1 field_NN1 ._. 
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A_AT1 quantitative_JJ understanding_NN1 of_IO epidemic_NN1 spreading_NN1 is_VBZ necessary_JJ for_IF improving_VVG public_JJ health_NN1 surveillance_NN1 ._. 
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<s>
We_PPIS2 shall_VM denote_VVI the_AT operator_NN1 <Professional_FO terms>_FO by_II and_CC the_AT operator_NN1 <Professional_FO terms>_FO by_II <Professional_FO terms>.Let_FO us_PPIO2 consider_VV0 the_AT map_NN1 <Professional_FO terms>_FO <Equation>_FO dened_VVD by_II where_RRQ <Professional_FO terms>_FO ._. 
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<s>
._. Thus_RR we_PPIS2 presented_VVD the_AT various_JJ models_NN2 in_II which_DDQ inflation_NN1 can_VM be_VBI realized_VVN in_II the_AT context_NN1 of_IO modified_JJ gravity_NN1 ._. 
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<s>
Here_RL ,_, δ_FO is_VBZ an_AT1 interpreter_NN1 in_II Definition_NN1 2_MC ,_, and_CC <Equation>_FO ._. 
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<s>
We_PPIS2 then_RT tested_VVD doubling_VVG the_AT lateral_JJ extent_NN1 ,_, and_CC this_DD1 yields_VVZ 8.4_MC ?Fcm2_FO ._. 
</s>
<s>
So_RR <Equation>_FO ,_, and_CC by_II (_( 8.5_MC )_) and_CC (_( 8.3_MC )_) ,_, we_PPIS2 have_VH0 <Equation>_FO ._. 
</s>
<s>
Extensive_JJ field_NN1 analyses_NN2 of_IO insect_NN1 (_( midge_NN1 )_) swarms_VVZ ,_, which_DDQ unlike_JJ birds_NN2 traveling_VVG in_II a_AT1 flock_NN1 hover_VV0 around_RP a_AT1 spot_NN1 on_II the_AT ground_NN1 ,_, have_VH0 also_RR been_VBN performed_VVN (_( Attanasi_NP1 et_RA21 al._RA22 ,_, 2014b_FO )_) ._. 
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These_DD2 often_RR rely_VV0 on_II a_AT1 Gaussian_JJ approximation_NN1 for_IF the_AT pileup_NN1 <Equation>_FO distribution_NN1 ,_, simplified_JJ distributions_NN2 for_IF the_AT underlying_JJ hard_JJ processes_NN2 and_CC basic_JJ understanding_NN1 of_IO jet_NN1 areas_NN2 ._. 
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<s>
The_AT two-loop_JJ Feynman_NP1 graph_NN1 (_( loop_NN1 after_II loop_NN1 )_) ._. 
</s>
<s>
The_AT electrochemical_JJ theoretical_JJ community_NN1 is_VBZ dominated_VVN by_II the_AT approach_NN1 initiated_VVN by_II Rossmeisl_NP1 ,_, Norskov_NP1 ,_, Jonsson_NP1 ,_, and_CC others_NN2 ,_, based_VVN on_II the_AT surface_NN1 science_NN1 static_JJ density_NN1 functional_JJ theory_NN1 (_( DFT_NP1 )_) calculations_NN2 of_IO the_AT thermodynamics_NN1 of_IO surface_NN1 reaction_NN1 While_CS this_DD1 approach_NN1 is_VBZ successfully_RR providing_VVG a_AT1 wealth_NN1 of_IO information_NN1 into_II the_AT screening_NN1 of_IO the_AT most_RGT promising_JJ catalysts_NN2 ,_, it_PPH1 however_RR lacks_VVZ some_DD crucial_JJ modelling_NN1 elements_NN2 in_BCL21 order_BCL22 to_TO get_VVI a_AT1 more_RGR detailed_JJ atomistic_JJ understanding_NN1 of_IO the_AT electrochemical_JJ catalysis_NN1 processes_NN2 and_CC hence_RR advance_VV0 further_RRR the_AT catalyst-material_NN1 rational_JJ design_NN1 of_IO the_AT OER_NN1 in_II electrochemical_JJ conditions_NN2 ._. 
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<s>
On_II the_AT other_JJ hand_NN1 ,_, in_II nonuniform_JJ crossed-field_JJ configurations_NN2 such_II21 as_II22 a_AT1 radial_JJ electric_JJ field_NN1 E_ZZ1 <equation>_FO in_II a_AT1 cylindrical_JJ plasma_NN1 column_NN1 permeated_VVD by_II a_AT1 uniform_JJ axial_JJ magnetic_JJ field_NN1 B_ZZ1 <equation>_FO ,_, inertial_JJ terms_NN2 introduce_VV0 charge_NN1 and_CC mass_JJ asymmetries_NN2 ._. 
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<s>
For_IF the_AT etching_NN1 experiments_NN2 ,_, these_DD2 wafers_NN2 are_VBR placed_VVN onto_II the_AT lower_JJR electrode_NN1 to_TO study_VVI the_AT etch_NN1 rate_NN1 ._. 
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<s>
In_II this_DD1 work_NN1 ,_, a_AT1 method_NN1 was_VBDZ introduced_VVN to_TO transform_VVI the_AT uncertainty_NN1 relations_NN2 in_II the_AT absence_NN1 of_IO quantum_NN1 memory_NN1 into_II those_DD2 in_II the_AT presence_NN1 of_IO it_PPH1 ._. 
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<s>
Emori_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2014_MC )_) carried_VVD out_RP measurements_NN2 on_II gated_JJ Pt=Co=GdOx_FO ,_, showing_VVG that_DD1 oxidation_NN1 of_IO the_AT top_JJ Co_NN1 interface_NN1 leads_VVZ to_II a_AT1 10-fold_JJ increase_NN1 of_IO the_AT dampinglike_JJ torque_NN1 due_II21 to_II22 oxygen_NN1 ion_NN1 migration_NN1 ,_, which_DDQ also_RR affects_VVZ the_AT magnetic_JJ anisotropy_NN1 ._. 
</s>
<s>
This_DD1 is_VBZ the_AT reason_NN1 why_RRQ the_AT standard_JJ MRI_NN1 has_VHZ not_XX yet_RR been_VBN unambiguously_RR observed_VVN experimentally_RR in_II the_AT laboratory_NN1 &lsqb;_( 47,48_MC &rsqb;_) ._. 
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<s>
The_AT white_JJ region_NN1 in_II the_AT phase_NN1 diagram_NN1 (_( fig._NN1 3_MC )_) indicate_VV0 the_AT topologically_RR trivial_JJ phase_NN1 with_IW zero_NN1 Chern_NN1 number_NN1 ;_; topologically_RR protected_JJ edge_NN1 states_NN2 are_VBR absent_JJ in_II this_DD1 phase_NN1 under_II OBC_NP1 in_II either_DD1 direction_NN1 ._. 
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<s>
Thus_RR ,_, the_AT problem_NN1 of_IO the_AT Eq_NN1 ._. 
</s>
<s>
(_( 5_MC )_) energy_NN1 functional_JJ minimization_NN1 reduces_VVZ to_II the_AT problem_NN1 of_IO finding_VVG the_AT minimum_NN1 of_IO the_AT quadratic_JJ form_NN1 built_VVN on_II the_AT triangular_JJ lattice_NN1 ,_, where_CS unknown_JJ variables_NN2 are_VBR the_AT values_NN2 of_IO the_AT functions_NN2 nu_NN1 ,_, nd2_FO ,_, Hu2_FO ,_, Hd2_FO ,_, and_CC M_ZZ1 at_II the_AT lattice_NN1 points_NN2 ._. 
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<s>
At_II first_MD glance_NN1 ,_, the_AT mathematical_JJ structure_NN1 of_IO quantum_NN1 channels_NN2 appears_VVZ to_TO be_VBI more_RGR complex_JJ than_CSN that_DD1 of_IO density_NN1 matrices_NN2 ._. 
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<s>
Often_RR the_AT price_NN1 for_IF the_AT precision_NN1 of_IO such_DA studies_NN2 is_VBZ the_AT increased_JJ distinction_NN1 of_IO the_AT studied_JJ system_NN1 from_II real-world_JJ catalytic_JJ material_NN1 ._. 
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<s>
Fibers_NN2 benefit_VV0 from_II efficient_JJ heat_NN1 removal_NN1 due_II21 to_II22 the_AT advantageous_JJ volume_NN1 to_II lateral_JJ surface_NN1 area_NN1 ._. 
</s>
<s>
Xa_NP1 (_( S_ZZ1 f_ZZ1 )_) +_FO 2i&lsqb;Xd_FO M_ZZ1 ,_, f_ZZ1 &rsqb;_) 2i&lsqb;Xd_FO ,_, f_ZZ1 &rsqb;_) M_ZZ1 2iMca&lsqb;X_FO ,_, f_ZZ1 &rsqb;_) and_CC adding_VVG them_PPHO2 yields_NN2 (_( 3.46_MC )_) ._. 
</s>
<s>
Simone_NP1 Montesano_NP1 and_CC later_RRR Marco_NP1 Gratin_NP1 secured_VVD the_AT technical_JJ coherence_NN1 of_IO the_AT UA9_FO setups_NN2 ,_, guaranteeing_VVG their_APPGE adequacy_NN1 for_IF the_AT experimental_JJ runs_NN2 ._. 
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<s>
After_CS complete_JJ addition_NN1 ,_, the_AT reaction_NN1 maintained_VVN for_IF 12_MC h_ZZ1 and_CC then_RT aged_VVN without_IW any_DD interruption_NN1 for_IF 12_MC h_ZZ1 ._. 
</s>
<s>
Finally_RR ,_, the_AT obtained_VVN white_JJ sample_NN1 was_VBDZ centrifuged_VVN ,_, washed_VVD three_MC times_NNT2 by_II ethanol/water_NN1 ,_, and_CC then_RT vacuum_NN1 dried_VVN at_II 80_MC °C_NNU for_IF 24_MC h_ZZ1 ._. 
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<s>
Additionally_RR ,_, to_TO better_RRR explore_VVI the_AT influence_NN1 of_IO morphology_NN1 on_II electrochemical_JJ properties_NN2 of_IO Na2-xMnHFC_JJ cathodes_NN2 ,_, R-Na2-_NP1 xMnHFC_NNU was_VBDZ prepared_VVN using_VVG the_AT same_DA procedure_NN1 with_IW C-Na2-xMnHFC_NP1 except_II21 for_II22 the_AT addition_NN1 of_IO trisodium_NN1 citrate_NN1 ._. 
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<s>
This_DD1 sits_VVZ at_II the_AT upper-wavelength_JJ edge_NN1 of_IO the_AT far-infrared_JJ laser_NN1 spectrum_NN1 ._. 
</s>
<s>
Thus_RR ,_, the_AT large_JJ number_NN1 of_IO the_AT relatively_RR high-energy_JJ fast_JJ ions_NN2 can_VM reach_VVI the_AT plasma_NN1 edge_NN1 ._. 
</s>
<s>
The_AT procedure_NN1 of_IO constructing_VVG such_DA a_AT1 hypermultiplet_NN1 completion_NN1 is_VBZ quite_RG analogous_JJ to_II the_AT one_MC1 developed_VVN in_II &lsqb;_( 2_MC &rsqb;_) for_IF finding_VVG the_AT N_ZZ1 =_FO 4_MC hypermultiplet_NN1 extension_NN1 of_IO the_AT 4D_NNU ,_, N_ZZ1 =_FO 2_MC SYM_NP1 effective_JJ action_NN1 ._. 
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<s>
The_AT formal_JJ framework_NN1 required_VVN to_TO incorporate_VVI retardation_NN1 in_II the_AT study_NN1 of_IO EPIs_NN1 is_VBZ presented_VVN in_II Sec_NNU ._. 
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<s>
IV_MC ._. 
</s>
<s>
On_II each_DD1 side_NN1 of_IO the_AT hypersurface_NN1 ,_, one_PN1 may_VM construct_VVI the_AT tangents_NN2 to_II the_AT generators_NN2 of_IO the_AT null_JJ hypersurface_NN1 (_( )_) and_CC the_AT transverse_JJ spacelike_JJ vectors_NN2 (_( e_ZZ1 )_) ,_, which_DDQ are_VBR tangents_NN2 to_II the_AT cross-sections_NN2 (_( taken_VVN to_TO be_VBI compact_JJ )_) of_IO the_AT hypersurface_NN1 ._. 
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<s>
Through_II its_APPGE interaction_NN1 with_IW gas_NN1 ,_, plasma_NN1 ,_, and_CC solids_NN2 ,_, CPA_NP1 can_VM become_VVI a_AT1 universal_JJ source_NN1 of_IO high-energy_JJ radiations_NN2 and_CC particles_NN2 ._. 
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<s>
In_II astrophysical_JJ ap-plications_NN2 ,_, progress_NN1 in_II the_AT identification_NN1 of_IO spectral_JJ lines_NN2 and_CC information_NN1 about_II the_AT transition_NN1 probabilities_NN2 and_CC lifetimes_NNT2 for_IF species_NN such_II21 as_II22 Pb_FO V_ZZ1 provides_VVZ new_JJ tools_NN2 that_CST may_VM allow_VVI study_NN1 within_II many_DA2 different_JJ spectral_JJ windows_NN2 for_IF space_NN1 observations_NN2 ._. 
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<s>
The_AT influence_NN1 of_IO temperature_NN1 on_II capacities_NN2 for_IF the_AT PVDF_NP1 binder_NN1 exhibited_VVD the_AT same_DA tendency_NN1 as_CSA of_IO CMC_NP1 binder_NN1 resulting_VVG 322_MC ,_, 372_MC and_CC 334_MC mAh/g_FU discharge_NN1 capacities_NN2 at_II 500_MC ,_, 750_MC and_CC 1000_MC °C_NNU during_II the_AT 1st_MD cycle_NN1 ,_, respectively_RR (_( Fig._NN1 5d_NNU )_) ._. 
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<s>
Here_RL ,_, the_AT characteristic_JJ synchrotron_NN1 frequency_NN1 and_CC the_AT cooling_JJ frequency_NN1 are_VBR given_VVN ,_, respectively_RR ,_, by_II <Equation>_FO ,_, <Equation>_FO ,_, and_CC the_AT self-absorption_JJ frequency_NN1 at_II tdec_NN1 is_VBZ estimated_VVN to_TO be_VBI <Equation>_FO ._. 
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<s>
In_II this_DD1 analysis_NN1 ,_, we_PPIS2 set_VV0 ks_FO ?_FO 1_MC1 ,_, corresponding_VVG to_II a_AT1 typical_JJ dull_JJ surface_NN1 ._. 
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<s>
Reproduced_VVN with_IW permission_NN1 from_II Qin_NP1 et_RA21 al._RA22 ,_, Opt_VV0 ._. 
</s>
<s>
A_AT1 magnetic_JJ field_NN1 is_VBZ generated_VVN by_II an_AT1 electric_JJ current_JJ ,_, which_DDQ causes_VVZ strain_NN1 in_II the_AT magnetostrictive_JJ film_NN1 ._. 
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<s>
The_AT anisotropy_NN1 constant_NN1 K1_FO has_VHZ been_VBN determined_VVN from_II the_AT efective_JJ magnetocrystalline_NN1 anisotropy_NN1 and_CC the_AT shape_NN1 anisotropy_NN1 KShape_NN1 ,_, <Equation>_FO ._. 
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<s>
Whereas_CS macroscopic_JJ state_NN1 transformations_NN2 via_II heat_NN1 exchange_NN1 are_VBR essentially_RR governed_VVN by_II a_AT1 decrease_NN1 in_II free_JJ energy_NN1 ,_, in_II the_AT quantum_NN1 regime_NN1 ,_, more_DAR constraints_NN2 dictate_VV0 whether_CSW a_AT1 given_JJ transformation_NN1 is_VBZ possible_JJ ._. 
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<s>
By_II using_VVG these_DD2 Brownian_JJ dynamics_NN integrators_NN2 ,_, the_AT system_NN1 of_IO spheres_NN2 and_CC spherocylinders_NN2 corresponds_VVZ to_II a_AT1 binary_JJ colloid_JJ mixture_NN1 in_II an_AT1 external_JJ bath_NN1 given_VVN by_II a_AT1 liquid_NN1 ._. 
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<s>
As_CSA seen_VVN in_II the_AT XRD_NP1 pattern_NN1 (_( Fig._NN1 2_MC )_) ,_, at_II CA_NP1 concentration_NN1 of_IO 0.5_MC ,_, 2.5_MC ,_, 4.5_MC and_CC 6.5_MC mmol_NN1 ,_, all_DB main_JJ peaks_NN2 are_VBR related_VVN to_II cobalt_NN1 ferrite_NN1 with_IW some_DD low-intensity_JJ peaks_NN2 of_IO hematite_NN1 ._. 
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<s>
It_PPH1 shows_VVZ also_RR that_CST a_AT1 femtosecond_NN1 laser_NN1 can_VM make_VVI a_AT1 lamellar_JJ slicepossible_JJ ._. 
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<s>
In_RR21 addition_RR22 ,_, these_DD2 methods_NN2 can_VM not_XX separate_VVI equivalent_JJ subspaces_NN2 in_II the_AT parameter_NN1 spaces_NN2 of_IO the_AT same_DA dynamical_JJ systems_NN2 ._. 
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<s>
The_AT starting_NN1 points_NN2 should_VM be_VBI on_II a_AT1 surface_NN1 that_CST is_VBZ nowhere_RL tangential_JJ to_II B_ZZ1 ._. 
</s>
<s>
The_AT dangerous_JJ flux_NN1 ,_, dang_NN1 is_VBZ less_DAR than_CSN the_AT 75_MC Vs_II of_IO poloidal_JJ flux_NN1 in_II ITER_NP1 when_RRQ the_AT number_NN1 density_NN1 of_IO seed_NN1 electrons_NN2 satisfies_VVZ ns_FO 300_MC m3_FO or_CC equivalently_RR 105_MC seed_NN1 electrons_NN2 in_II the_AT entire_JJ plasma_NN1 ._. 
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<s>
As_CSA another_DD1 example_NN1 of_IO a_AT1 theory_NN1 belonging_VVG to_II the_AT general_JJ class_NN1 of_IO models_NN2 of_IO Eq_NN1 ._. 
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<s>
(_( 269_MC )_) ,_, we_PPIS2 shall_VM consider_VVI F_ZZ1 (_( R_ZZ1 )_) theories_NN2 of_IO gravity_NN1 ._. 
</s>
<s>
Furthermore_RR ,_, to_TO prevent_VVI the_AT Ga_NP1 primary_JJ ions_NN2 splitting_VVG into_II two_MC probes_NN2 (_( Ga_NP1 and_CC Ga_NP1 )_) under_II the_AT residual_JJ magnetic_JJ ?_? eld_NN1 of_IO the_AT objective_JJ lens_NN1 ,_, a_AT1 monoisotopic_JJ Ga_NP1 ion_NN1 source_NN1 was_VBDZ chosen_VVN ._. 
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<s>
It_PPH1 was_VBDZ investigated_VVN that_CST the_AT EC_NP1 performance_NN1 of_IO the_AT all-solid-state_JJ device_NN1 were_VBDR significantly_RR improved_VVN with_IW this_DD1 additional_JJ process_NN1 ._. 
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<s>
Altogether_RR ,_, the_AT Borel-hypergeometric_JJ resummation_NN1 provides_VVZ a_AT1 continuation_NN1 from_II perturbative_JJ to_II non-perturbative_JJ physics_NN1 (_( see_VV0 also_RR Refs_NN2 ._. 
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<s>
Refraction-enhanced_JJ x-ray_JJ radiography_NN1 (_( REXR_NP1 )_) is_VBZ used_VVN to_TO infer_VVI shock-wave_JJ positions_NN2 of_IO more_DAR than_CSN one_MC1 shock_NN1 wave_NN1 ,_, launched_VVN by_II a_AT1 multiplepicket_NN1 pulse_NN1 in_II a_AT1 planar_JJ plastic_NN1 foil_NN1 ._. 
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<s>
This_DD1 simulation_NN1 study_NN1 presents_VVZ the_AT detailed_JJ investigation_NN1 of_IO the_AT evolution_NN1 of_IO EASWs_NP2 and_CC IASWs_NN2 generated_VVN in_II plasmas_NN2 having_VHG Ti_NP1 >_FO Te_FW ,_, which_DDQ will_VM have_VHI implications_NN2 in_II modeling_VVG such_DA waves_NN2 in_II space_NN1 and_CC laboratory_NN1 plasmas_NN2 ._. 
</s>
<s>
In_II contrast_NN1 ,_, <equation>is_FO far_RR above_II marginal_JJ stability_NN1 ,_, with_IW relatively_RR large_JJ growth_NN1 rates_NN2 across_II the_AT entire_JJ spectrum_NN1 and_CC no_AT finite_JJ cutoff_NN1 at_II long_JJ wavelengths_NN2 ._. 
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<s>
A_AT1 point_NN1 y_ZZ1 S2_FO is_VBZ a_AT1 postcritical_JJ point_NN1 off_II <Equation>_FO for_IF some_DD x_ZZ1 crit_NN1 f_ZZ1 and_CC n_ZZ1 N._NNU The_AT set_NN1 of_IO postcritical_JJ points_NN2 off_RP is_VBZ denoted_VVN by_II post_NN1 f_ZZ1 ._. 
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<s>
Note_VV0 that_DD1 post_NN1 <Equation>_FO for_IF all_DB n_ZZ1 N._NNU Since_CS the_AT orientations_NN2 of_IO polymer_NN1 fold-ends_NN2 align_VV0 in_II parallel_NN1 to_II the_AT lateral_JJ growth_NN1 front_NN1 of_IO lamellar_JJ single_JJ crystals_NN2 ,_, they_PPHS2 exhibit_VV0 four_MC sectors_NN2 of_IO preferred_JJ fold-end_JJ orientations_NN2 &lsqb;_( 33_MC &rsqb;_) ,_, as_CSA revealed_VVN by_II the_AT surface_NN1 decoration_NN1 experiments_NN2 in_II Fig._NN1 3_MC &lsqb;_( 34_MC &rsqb;_) ,_, which_DDQ have_VH0 also_RR been_VBN confirmed_VVN by_II the_AT atomic_JJ force_NN1 microscopy_NN1 &lsqb;_( 35_MC &rsqb;_) as_II31 well_II32 as_II33 molecular_JJ simulations_NN2 &lsqb;_( 36_MC &rsqb;_) ._. 
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<s>
Within_II the_AT broad_JJ range_NN1 of_IO parameter_NN1 regimes_NN2 found_VVD ,_, we_PPIS2 identify_VV0 the_AT ones_NN2 accessible_JJ in_II triple_JJ quantum_NN1 dot_NN1 and_CC triangular_JJ optical_JJ lattice_NN1 ,_, thus_RR opening_VVG a_AT1 way_NN1 toward_II simple_JJ implementation_NN1 of_IO maximally_RR entangled_JJ states_NN2 with_IW different_JJ types_NN2 of_IO three-spin_JJ interactions_NN2 ._. 
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<s>
FIB_VV0 machining_VVG is_VBZ also_RR a_AT1 simple_JJ approach_NN1 for_IF fabrication_NN1 of_IO microstructures_NN2 from_II crystalline_JJ material_NN1 for_IF electric_JJ and_CC magnetic_JJ measurements_NN2 ._. 
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<s>
In_II summary_NN1 ,_, Hauser_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
showed_VVD that_CST the_AT dimer_NN1 binding_JJ energy_NN1 has_VHZ only_RR a_AT1 minor_JJ influence_NN1 on_II the_AT collision_NN1 times_NNT2 ,_, whereas_CS a_AT1 strong_JJ mass_JJ dependence_NN1 was_VBDZ predicted_VVN for_IF small_JJ HNDs_NP1 ._. 
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<s>
Crystals_NN2 for_IF room_NN1 temperature_NN1 data_NN collection_NN1 were_VBDR soaked_VVN in_II a_AT1 solution_NN1 of_IO ligand_NN1 in_II crystallization_NN1 buffer_NN1 and_CC mounted_VVN as_CSA below_RL ._. 
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<s>
We_PPIS2 start_VV0 this_DD1 section_NN1 with_IW a_AT1 brief_JJ review_NN1 of_IO some_DD necessary_JJ concepts_NN2 from_II the_AT ergodic_JJ theory_NN1 and_CC dynamical_JJ systems_NN2 ._. 
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<s>
It_PPH1 is_VBZ a_RR21 priori_RR22 not_XX clear_RR what_DDQ happens_VVZ if_CS ,_, in_II a_AT1 bipartite_JJ scenario_NN1 ,_, the_AT system_NN1 size_NN1 of_IO one_MC1 party_NN1 is_VBZ increased_VVN ._. 
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<s>
The_AT indicated_JJ electron-ion_JJ equilibration_NN1 time_NNT1 is_VBZ (_( 0.9±0.2_FO )_) ps_NN2 ._. 
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<s>
The_AT small_JJ sub-core_JJ cluster_NN1 developed_VVN into_II an_AT1 important_JJ and_CC dense_JJ core_NN1 of_IO the_AT production_NN1 space_NN1 in_II 2007_MC ._. 
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<s>
Absolute_JJ band_NN1 intensities_NN2 in_II the_AT FTIR_NN1 internal_JJ reflection_NN1 mode_NN1 depend_VV0 strongly_RR on_II the_AT thin_JJ gap_NN1 distance_NN1 between_II the_AT electrode_NN1 and_CC prism_NN1 ,_, and_CC for_IF this_DD1 reason_NN1 ,_, they_PPHS2 can_VM not_XX be_VBI used_VVN for_IF comparison_NN1 between_II different_JJ experiments_NN2 ._. 
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<s>
In_II this_DD1 case_NN1 we_PPIS2 must_VM compute_VVI :_: leads_VVZ to_II the_AT optimal_JJ value_NN1 for_IF the_AT angle_NN1 that_CST is_VBZ reported_VVN in_II the_AT second_MD row_NN1 of_IO Table_NN1 3_MC ._. 
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<s>
On_II the_AT contrary_NN1 in_II the_AT low_JJ and_CC high_JJ temperatures_NN2 N_ZZ1 decrease_VV0 with_IW N_ZZ1 and_CC saturate_VV0 to_II its_APPGE respective_JJ thermodynamic_JJ limits_NN2 independent_JJ of_IO the_AT extent_NN1 of_IO asymmetryin_NN1 the_AT interaction_NN1 potential_NN1 ._. 
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However_RR ,_, there_EX is_VBZ a_AT1 significant_JJ difference_NN1 ._. 
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<s>
In_II this_DD1 case_NN1 ,_, significant_JJ coherence_NN1 is_VBZ indicated_VVN by_II all_DB surrogates_NN2 after_CS =_FO 0.2_MC ,_, and_CC less_RGR overall_RR before_CS this_DD1 threshold_NN1 ._. 
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<s>
This_DD1 observation_NN1 was_VBDZ recently_RR explained_VVN through_II analytical_JJ models_NN2 for_IF electron_NN1 and_CC ion_NN1 flows_VVZ in_II the_AT azimuthator_NN1 ._. 
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<s>
In_II fact_NN1 ,_, we_PPIS2 can_VM try_VVI to_TO provide_VVI a_AT1 simple_JJ argument_NN1 ._. 
</s>
<s>
Additionally_RR ,_, the_AT laser_NN1 configuration_NN1 used_VVN in_II these_DD2 experiments_NN2 is_VBZ strongly_RR susceptible_JJ to_II laser_NN1 plasma_NN1 instabilities_NN2 ,_, such_II21 as_II22 strong_JJ filamentation_NN1 and_CC scattering_VVG ._. 
</s>
<s>
In_RR21 short_RR22 ,_, they_PPHS2 are_VBR as_CSA follows_VVZ ._. 
</s>
<s>
If_CS N_ZZ1 M_ZZ1 is_VBZ an_AT1 invariant_JJ complex_NN1 totally_RR geodesic_JJ submanifold_JJ then_RT the_AT K?hler_NN1 quotient_NN1 of_IO N_ZZ1 is_VBZ totally_RR geodesic_JJ in_II the_AT K?hler_NN1 quotient_NN1 of_IO M._NN1 Single_JJ ionization_NN1 Beginning_VVG with_IW SI_FW ,_, Figs_NN2 ._. 
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<s>
A.1_FO and_CC A.2_FO show_VV0 examples_NN2 of_IO thuds_NN2 for_IF <equation>_FO and_CC <equation>_FO ._. 
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<s>
The_AT 18G/14G/10G_NNU ,_, 15G/12G/9G_NNU ,_, and_CC 12G/9G/7G_NNU nozzles_NN2 produced_VVD dual-layered_JJ conduits_NN2 with_IW similar_JJ WT_NN1 (_( 600–800_MCMC lm_NNU )_) but_CCB varied_JJ ID_NN1 (_( approximately_RR 900_MC lm_NNU ,_, 1500_MC lm_NNU ,_, and_CC 2000_MC lm_NNU ,_, respectively_RR )_) ._. 
</s>
<s>
Therefore_RR ,_, the_AT CO_NP1 molecule_NN1 has_VHZ a_AT1 very_RG weak_JJ physical_JJ adsorption_NN1 on_II the_AT pristine_JJ phagraphene_NN1 which_DDQ means_VVZ that_CST pristine_JJ phagraphene_NN1 has_VHZ a_AT1 finite_JJ capacity_NN1 for_IF adsorption_NN1 of_IO CO_NP1 molecule_NN1 ._. 
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<s>
Finally_RR ,_, we_PPIS2 sorted_VVD all_DB individual_JJ data_NN points_NN2 according_II21 to_II22 their_APPGE delay_NN1 time_NNT1 and_CC then_RT averaged_VVD neighboring_VVG data_NN points_NN2 within_II a_AT1 250_MC to_II 400_MC fs_FO interval_NN1 of_IO delay_NN1 times_NNT2 ._. 
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<s>
The_AT relation_NN1 Eq_NN1 ._. 
</s>
<s>
(_( 37_MC )_) provides_VVZ the_AT general_JJ expression_NN1 of_IO the_AT Ohmic_JJ nonlinear_JJ current_JJ short_JJ circuiting_NN1 G-J_NP1 charges_NN2 ,_, Eq_NN1 ._. 
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<s>
(_( 26_MC )_) ,_, in_II an_AT1 axisymmetric_JJ rotating_JJ plasma_NN1 described_VVN by_II the_AT magnetic_JJ flux_NN1 <Professional_FO Term>_FO and_CC electric_JJ potential_NN1 <Professional_FO Term>_FO ._. 
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<s>
The_AT radial_JJ velocity_NN1 vx?vR_FO (_( in_II cs0_FO units_NN2 )_) is_VBZ computed_VVN by_II tracking_VVG the_AT radial_JJ center_NN1 of_IO the_AT mass_JJ location_NN1 RCM_FO during_II a_AT1 blob_NN1 lifetime_NNT1 <EQUATION>_FO where_RRQ ti_NN2 is_VBZ the_AT snapshot_NN1 time_NNT1 (_( in_II the_AT present_JJ study_NN1 ,_, <EQUATION>_FO )_) ._. 
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<s>
The_AT large_JJ surface_NN1 area_NN1 of_IO graphene_NN1 oxide_NN1 plays_VVZ a_AT1 significant_JJ role_NN1 in_II these_DD2 outcomes_NN2 ._. 
</s>
<s>
As_CSA these_DD2 are_VBR consider_VV0 ably_RR higher_JJR than_CSN the_AT previous_JJ value_NN1 &lsqb;_( 8_MC &rsqb;_) ,_, it_PPH1 warrants_VVZ are_VBR examination_NN1 of_IO the_AT comparison_NN1 with_IW the_AT theoretical_JJ calculations_NN2 ._. 
</s>
<s>
We_PPIS2 combined_VVD a_AT1 model_NN1 for_IF heat_NN1 flux_NN1 onto_II the_AT diverter_NN1 target_NN1 plates_NN2 (_( based_VVN on_II field_NN1 line_NN1 diffusion_NN1 )_) ,_, a_AT1 model_NN1 calculating_VVG the_AT resulting_JJ heat_NN1 flux_NN1 to_II a_AT1 leading_JJ edge_NN1 (_( depending_II21 on_II22 the_AT local_JJ angle_NN1 of_IO incidence_NN1 of_IO the_AT magnetic_JJ field_NN1 )_) ,_, a_AT1 thermal_JJ model_NN1 of_IO time-dependent_JJ heat_NN1 conduction_NN1 into_II the_AT target_NN1 surface_NN1 ,_, and_CC a_AT1 model_NN1 for_IF the_AT carbon_NN1 sublimation_NN1 rate_NN1 (_( depending_II21 on_II22 the_AT surface_NN1 temperature_NN1 )_) with_IW the_AT measurement_NN1 of_IO the_AT as-built_JJ step_NN1 height_NN1 between_II adjacent_JJ parts_NN2 of_IO the_AT target_NN1 surface_NN1 ._. 
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<s>
Second_MD ,_, without_IW the_AT flatness_NN1 requirements_NN2 of_IO resist_VV0 spincoating_VVG ,_, corrugated_JJ and_CC high-aspect-ratio_JJ samples_NN2 can_VM be_VBI contacted_VVN ._. 
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<s>
In_RR21 general_RR22 ,_, the_AT generated_JJ hybrid_JJ states_NN2 are_VBR unbalanced_JJ (_( i.e._REX ,_, their_APPGE component_NN1 terms_NN2 are_VBR unequally_RR weighted_VVN )_) ,_, but_CCB the_AT initial_JJ parameters_NN2 of_IO the_AT generation_NN1 scheme_NN1 can_VM be_VBI chosen_VVN so_BCL21 as_BCL22 to_TO equalize_VVI the_AT weights_NN2 of_IO the_AT hybrid_JJ states_NN2 making_VVG them_PPHO2 balanced_VVN ._. 
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<s>
It_PPH1 is_VBZ indeed_RR known_VVN from_II early_JJ experiments_NN2 &lsqb;_( 52,53_MC &rsqb;_) and_CC theoretical_JJ studies_NN2 &lsqb;_( 54–57_MCMC &rsqb;_) that_CST the_AT correlation_NN1 lengths_NN2 in_II MHD_NP1 turbulence_NN1 become_VV0 longer_RRR in_II the_AT field_NN1 direction_NN1 the_AT stronger_JJR the_AT applied_JJ background_NN1 field_NN1 is_VBZ ._. 
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<s>
If_CS BH_NP1 candidates_NN2 were_VBDR not_XX Kerr_NP1 BHs_NP1 ,_, the_AT spin_NN1 measurements_NN2 would_VM be_VBI different_JJ and_CC we_PPIS2 would_VM lose_VVI the_AT correlation_NN1 between_II BH_NP1 spin_NN1 and_CC jet_NN1 power_NN1 ;_; see_VV0 Bambi_NP1 (_( 2012b_FO )_) ._. 
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<s>
The_AT expected_JJ number_NN1 of_IO consecutive_JJ successful_JJ protocol_NN1 cycles_NN2 followed_VVN by_II a_AT1 detection_NN1 event_NN1 depends_VVZ on_II induced_JJ error_NN1 rate<EQUATION>_FO so_CS she_PPHS1 learns_VVZ two_MC classic_JJ bits_NN2 independent_JJ on_II induced_JJ error_NN1 rate_NN1 ._. 
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<s>
Even_RR with_IW fixed_JJ global_JJ plasma_NN1 parameters_NN2 and_CC the_AT same_DA power_NN1 entering_VVG the_AT SOL_NP1 ,_, the_AT profile_NN1 in_II the_AT near_JJ SOL_NP1 region_NN1 is_VBZ broader_JJR after_II the_AT transition_NN1 to_II L-mode_NN1 ,_, with_IW <equation>_FO ,_, Analysis_NN1 shows_VVZ that_CST the_AT broadening_NN1 is_VBZ mainly_RR due_II21 to_II22 audden_NN1 increase_NN1 of_IO perpendicular_JJ transport_NN1 ._. 
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<s>
Through_II power_NN1 balance_NN1 and_CC the_AT Spitzer–Harm_NN1 condution_NN1 ,_, the_AT SOL_NP1 perpendicular_JJ transport_NN1 can_VM be_VBI derived_VVN as_CSA ._. 
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<s>
The_AT electron_NN1 temperature_NN1 at_II the_AT time_NNT1 when_RRQ the_AT microstrip_NN1 passes_VVZ through_II the_AT quarter-critical_JJ surface_NN1 ,_, the_AT key_JJ location_NN1 for_IF LPI_NN2 and_CC hot_JJ electron_NN1 generation_NN1 ,_, was_VBDZ around_II 2.460.4keV_FO according_II21 to_II22 the_AT spectral_JJ fitting_JJ method_NN1 ,_, with_IW a_AT1 similar_JJ result_NN1 when_CS only_RR isoelectronic_JJ Mn_FO and_CC CoHea_NP1 lines_NN2 are_VBR considered_VVN ._. 
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<s>
Inset_VVN in_II (_( a_ZZ1 )_) is_VBZ a_AT1 digital_JJ image_NN1 of_IO rGO_NN1 film.ammonia_NNU water_NN1 ,_, then_RT ,_, the_AT solution_NN1 is_VBZ poured_VVN into_II a_AT1 150_MC ml_NNU sealed_JJ nylon_NN1 container_NN1 ._. 
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<s>
All_DB article_NN1 content_NN1 ,_, except_CS where_CS otherwise_RR noted_VVN ,_, is_VBZ licensed_VVN under_II a_AT1 Creative_JJ Commons_NP Attribution_NN1 (_( CC_NNU BY_II )_) license_NN1 (_( http_NNU :_: )_) ._. 
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<s>
As_CSA clearly_RR seen_VVN in_II the_AT figure_NN1 ,_, the_AT simulated_JJ oxide_NN1 thickness_NN1 with_IW parameter_NN1 set_VVD 2_MC for_IF oxygen_NN1 is_VBZ larger_JJR than_CSN that_DD1 with_IW parameter_NN1 set_VVD 1_MC1 for_IF oxygen_NN1 ._. 
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<s>
This_DD1 section_NN1 is_VBZ divided_VVN in_II two_MC subsections_NN2 ._. 
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<s>
Borexino_NN1 has_VHZ now_RT measured_VVN the_AT rate_NN1 of_IO elastic_JJ neutrino–electron_NN1 interactions_NN2 from_II the_AT <equation>_FO line_NN1 to_II "_" 3%_NNU ._. 
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<s>
However_RR ,_, its_APPGE potential_NN1 for_IF constructing_VVG small-diameter_JJ vascular_JJ substitutes_NN2 with_IW both_DB2 endothelial_JJ and_CC muscular_JJ tissues_NN2 has_VHZ not_XX yet_RR been_VBN demonstrated_VVN ._. 
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<s>
Neutrino_NN1 interactions_NN2 in_II the_AT medium-energy_NN1 (_( 0.1–10_MCMC GeV_NP1 )_) range_NN1 are_VBR of_IO great_JJ interest_NN1 to_II a_AT1 variety_NN1 of_IO physics_NN1 programs.1_FO In_RR21 particular_RR22 ,_, accelerator_NN1 neutrino_NN1 oscillation_NN1 experiments_NN2 use_VV0 intense_JJ beams_NN2 of_IO predominantly_RR muon_NN1 neutrinos_NN2 or_CC antineutrinos_NN2 ,_, sent_VVN over_II short_JJ (_( kilometer_NNU1 )_) or_CC long_JJ (_( hundreds_NNO2 of_IO kilometers_NNU2 )_) distances_NN2 in_BCL21 order_BCL22 to_TO measure_VVI nonstandard_NN1 or_CC three-flavor_JJ oscillations_NN2 (_( 2_MC )_) ._. 
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<s>
The_AT emergence_NN1 and_CC widespread_JJ use_NN1 of_IO high-speed_JJ confocal_JJ microscopes_NN2 allows_VVZ precise_JJ depth_NN1 resolution_NN1 of_IO structure_NN1 and_CC the_AT tracking_NN1 of_IO individual_JJ particle_NN1 positions_NN2 in_II both_DB2 soft_JJ and_CC biological_JJ matter_NN1 ._. 
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<s>
In_II summary_NN1 ,_, the_AT assortative_JJ coefficient_NN1 presenting_VVG degree–degree_NN1 correlation_NN1 significantly_RR influences_VVZ the_AT accuracy_NN1 of_IO centrality_NN1 ._. 
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<s>
Spatially_RR ,_, the_AT temperature_NN1 and_CC electron_NN1 number_NN1 density_NN1 were_VBDR uniform_JJ across_II the_AT length_NN1 of_IO the_AT plasma_NN1 ._. 
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<s>
High-resolution_JJ data_NN and_CC improved_JJ methods_NN2 allow_VV0 us_PPIO2 to_TO reveal_VVI economic_JJ activity_NN1 and_CC socioeconomic_JJ status_NN1 in_II subnational_JJ ,_, regional_JJ and_CC urban_JJ scales_NN2 ._. 
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<s>
As_II the_AT required_JJ experimental_JJ precision_NN1 increases_NN2 ,_, QCDinduced_JJ form_NN1 factors_NN2 have_VH0 to_TO be_VBI taken_VVN into_II account_NN1 in_BCL21 order_BCL22 not_XX to_TO limit_VVI the_AT sensitivity_NN1 to_II BSM_NP1 physics_NN1 (_( Pitcairn_NP1 et_RA21 al._RA22 ,_, 2009_MC ;_; Wauters_NP1 et_RA21 al._RA22 ,_, 2009_MC ,_, 2010_MC ;_; Severijns_NP1 and_CC Naviliat-Cuncic_NN1 ,_, 2013_MC ;_; Soti_NP1 et_RA21 al._RA22 ,_, 2014_MC ;_; Sternberg_NP1 et_RA21 al._RA22 ,_, 2015_MC ;_; Fenker_NP1 ,_, 2016_MC )_) ._. 
</s>
<s>
Source_NN1 :_: Adapted_VVN with_IW permissions_NN2 from_II Pawlak_NP1 et_RA21 al_RA22 ._. 
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<s>
Probing_JJ atomic_JJ structure_NN1 and_CC Majorana_NP1 wavefunctions_NN2 in_II mono-atomic_JJ Fe_NP1 chains_NN2 on_II superconducting_JJ Pb_FO surface_NN1 ._. 
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<s>
Magnetic_JJ resonance_NN1 imaging_NN1 (_( Nakagawa_NP1 et_RA21 al._RA22 ,_, 1993_MC )_) or_CC x-ray_JJ tomography_NN1 has_VHZ severe_JJ limitations_NN2 in_II31 terms_II32 of_II33 resolution_NN1 ,_, speed_NN1 ,_, and_CC size_NN1 ._. 
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<s>
When_CS sensitized_VVN with_IW nine_MC SILAR_JJ cycles_NN2 of_IO <Equation>_FO ,_, <Equation>_FO based_VVN on_II <Equation>_FO exhibited_VVD a_AT1 PCE_NN1 of_IO 2.85%_FO and_CC FF_NNU of_IO 47%_NNU ._. 
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<s>
It_PPH1 is_VBZ possible_JJ ,_, however_RR ,_, to_TO also_RR measure_VVI high_JJ quantum_NN1 number_NN1 transitions_NN2 in_II the_AT cm-wave_JJ region_NN1 ._. 
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<s>
Their_APPGE dynamical_JJ model_NN1 can_VM accurately_RR reproduce_VVI the_AT main_JJ features_NN2 observed_VVN in_II the_AT evolution_NN1 of_IO the_AT "_" country-product_JJ "_" bipartite_JJ network_NN1 ._. 
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<s>
For_IF (_( 5.30_MC )_) ,_, let_VV0 us_PPIO2 assume_VVI first_MD <Professional_FO Term>_FO ._. 
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<s>
Consider_VV0 one_MC1 element_NN1 of_IO the_AT hadronisation_NN1 process_NN1 ,_, namely_REX resonance_NN1 decay_NN1 ,_, specifically_RR <Equation>_FO :_: if_CS the_AT has_VHZ a_AT1 pt_NNU of_IO order_NN1 2_MC GeV_NP1 ,_, the_AT rapidity–azimuth_NN1 separation_NN1 of_IO the_AT two_MC pions_NN2 is_VBZ of_IO the_AT order_NN1 of_IO 0.7_MC 1_MC1 (_( see_VV0 e.g._REX Section_NN1 11.2.1_MC )_) ._. 
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<s>
The_AT harvested_JJ TEBVs_NN2 were_VBDR stained_VVN via_II immunohistochemistry_NN1 to_TO evaluate_VVI their_APPGE in_JJ21 vivo_JJ22 maturation_NN1 ._. 
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<s>
For_REX21 example_REX22 ,_, it_PPH1 takes_VVZ 566_MC s_ZZ1 of_IO hydrogenation_NN1 to_TO erase_VVI the_AT image_NN1 in_II Fig._NN1 9(b)_FO and_CC 2224_MC s_ZZ1 to_TO fully_RR restore_VVI it_PPH1 ._. 
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<s>
Affected_VVN by_II location_NN1 and_CC neighborhood_NN1 in_II regional_JJ and_CC urban_JJ areas_NN2 ,_, house_NN1 price_NN1 is_VBZ a_AT1 sensitive_JJ and_CC important_JJ signal_NN1 in_II real_JJ estate_NN1 market_NN1 and_CC even_RR regional_JJ economic_JJ development_NN1 ._. 
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<s>
The_AT fuel_NN1 radius_NN1 then_RT varied_VVN between_II 20_MC and_CC 70_MC lm_NNU ._. 
</s>
<s>
The_AT transparency_NN1 coefficient_NN1 gr_NNU =gr_FO t_ZZ1 N_ZZ1 tanhetN=sf_FO T=sf_FO &rsqb;_) accounts_VVZ for_IF the_AT spin_NN1 current_JJ transmission_NN1 through_II the_AT interface_NN1 ,_, with_IW →_NULL 1_MC1 when_CS <Equation>_FO ._. 
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<s>
However_RR ,_, to_II the_AT best_JJT of_IO our_APPGE knowledge_NN1 ,_, the_AT pharmacokinetics_NN1 parameters_NN2 of_IO CA_NP1 have_VHI not_XX been_VBN reported_VVN to_II date_NN1 ._. 
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<s>
In_II studying_VVG the_AT mechanics_NN2 of_IO a_AT1 dry_JJ (_( or_CC indeed_RR ,_, even_RR a_AT1 wet_JJ )_) granular_JJ medium_NN1 ,_, one_PN1 can_VM ask_VVI how_RRQ microstructure_NN1 ,_, e.g._REX ,_, particle_NN1 shape_NN1 or_CC roughness_NN1 ,_, affects_VVZ the_AT dynamics_NN of_IO flow_NN1 or_CC the_AT force_NN1 transmission_NN1 through_II a_AT1 static_JJ pile_NN1 ._. 
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<s>
Keywords_NN2 :_: laser-induced_JJ breakdown_NN1 ,_, optical_JJ emission_NN1 spectroscopy_NN1 ,_, dual-pulsed_JJ laser_NN1 ,_, discharge_VV0 imaging_NN1 ._. 
</s>
<s>
The_AT de_NP1 Sitter_NN1 instabilities_NN2 generate_VV0 uncontrollable_JJ curvature_NN1 perturbations_NN2 which_DDQ cease_VV0 the_AT inflationary_JJ era_NN1 ._. 
</s>
<s>
We_PPIS2 illustrate_VV0 our_APPGE approach_NN1 for_IF :_: (_( 1_MC1 )_) characterizing_VVG memory_NN1 dependency_NN1 by_II analyzing_VVG a_AT1 synthetic_JJ system_NN1 with_IW short_JJ memory_NN1 ;_; (_( 2_MC )_) distinguishing_VVG from_II traditional_JJ methods_NN2 such_II21 as_II22 lagged_JJ mutual_JJ information_NN1 using_VVG the_AT Lorenz_NP1 chaotic_JJ model_NN1 ;_; (_( 3_MC )_) comparing_VVG the_AT memory_NN1 dependencies_NN2 of_IO two_MC long-memory_JJ processes_NN2 with_IW and_CC without_IW the_AT strange_JJ attractor_NN1 using_VVG the_AT Lorenz_NP1 model_NN1 and_CC a_AT1 linear_JJ Ornstein-Uhlenbeck_NP1 process_NN1 ;_; and_CC (_( 4_MC )_) illustrating_VVG how_RRQ dynamics_NN in_II a_AT1 complex_JJ system_NN1 is_VBZ sustained_VVN through_II the_AT interactive_JJ contribution_NN1 of_IO self-_NN1 and_CC cross-dependencies_NN2 in_II both_DB2 immediate_JJ and_CC distant_JJ causal_JJ histories_NN2 ,_, using_VVG the_AT Lorenz_NP1 model_NN1 and_CC observed_JJ stream_NN1 chemistry_NN1 data_NN known_VVN to_TO exhibit_VVI 1/f_FU long_JJ memory_NN1 ._. 
</s>
<s>
Appendix_NN1 A_ZZ1 shows_VVZ the_AT importance_NN1 of_IO exponentiation_NN1 more_RGR directly_RR ._. 
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<s>
See_VV0 supplementary_JJ material_NN1 for_IF additional_JJ XPS_NP1 spectra_NN2 ,_, SEM_NP1 images_NN2 of_IO the_AT photoanode_NN1 after_II PEC_NP1 reaction_NN1 ,_, optical_JJ properties_NN2 of_IO the_AT chelating_JJ resin_NN1 and_CC the_AT ionomer_NN1 ,_, potential-_JJ time_NNT1 curves_NN2 and_CC quantification_NN1 of_IO evolved_JJ gases_NN2 ._. 
</s>
<s>
In_RR21 addition_RR22 ,_, polymer_NN1 chain-folding_NN1 serves_VVZ as_II a_AT1 prototype_NN1 model_NN1 for_IF the_AT problems_NN2 of_IO protein_NN1 folding_NN1 ,_, misfiling_VVG and_CC unfolding_VVG ._. 
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<s>
The_AT rays_NN2 in_II regions_NN2 I_ZZ1 and_CC III_MC do_VD0 not_XX get_VVI deflected_JJ ,_, while_CS the_AT rays_NN2 in_II region_NN1 II_MC get_VV0 refracted_VVN by_II an_AT1 angle_NN1 of_IO p/3_FU at_II the_AT medium_JJ interface_NN1 and_CC get_VV0 deflected_VVN from_II their_APPGE path_NN1 ._. 
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<s>
The_AT Blandford-Znajek_NP1 mechanism_NN1 is_VBZ usually_RR considered_VVN for_IF the_AT formation_NN1 of_IO steady_JJ jets_NN2 ._. 
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<s>
Applications_NN2 of_IO the_AT EI_NP1 for_IF GO_VV0 show_VV0 that_CST the_AT reconstructed_JJ field_NN1 diverges_VVZ near_II the_AT caustic_JJ in_II a_AT1 region_NN1 much_RR larger_JJR than_CSN one_PN1 defined_VVD by_II the_AT simple_JJ Terms>_FO ,_, as_CSA shown_VVN in_II Fig._NN1 9_MC ._. 
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<s>
Thus_RR ,_, now_RT we_PPIS2 have_VH0 a_AT1 recipe_NN1 to_TO explicitly_RR construct_VVI new_JJ solutions_NN2 for_IF Einstein_NP1 '_NULL s_ZZ1 vacuum_NN1 equation_NN1 in_II arbitrary_JJ dimensions_NN2 ._. 
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<s>
The_AT lightest_JJT member_NN1 of_IO the_AT meson_NN1 family_NN1 is_VBZ the_AT pion_NN1 ,_, which_DDQ was_VBDZ discovered_VVN by_II Powell_NP1 in_II 1947_MC ._. 
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<s>
HiPIMS_NN2 with_IW a_AT1 positive_JJ voltage_NN1 pulse_NN1 after_II the_AT main_JJ negative_JJ one_PN1 is_VBZ a_AT1 potential_JJ alternative_NN1 to_TO be_VBI still_RR fully_RR investigated_VVN ._. 
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<s>
As_CSA illustrated_VVN by_II the_AT corresponding_JJ insets_NN2 in_II Fig._NN1 1_MC1 ,_, the_AT estimated_JJ characteristic_JJ lengths_NN2 0_MC for_IF CRSOS_NN2 and_CC CV_NN1 correspond_VV0 to_II 0_MC ≈_NULL 433_MC and_CC 0_MC ≈_NULL 74_MC ,_, respectively_RR ._. 
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<s>
The_AT rapid_JJ cooling_NN1 and_CC low_JJ temperature_NN1 attained_VVN in_II HNDs_NP1 also_RR offers_NN2 promise_VV0 for_IF the_AT study_NN1 of_IO pre-reaction_JJ complexes_NN2 ._. 
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<s>
Based_VVN on_II call_NN1 detail_NN1 records_NN2 (_( CDRs_NP1 )_) in_II two_MC European_JJ countries_NN2 ,_, Toole_NP1 et_RA21 al_RA22 ._. 
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<s>
&lsqb;_( 545_MC &rsqb;_) developed_VVD a_AT1 methodology_NN1 to_TO track_VVI employment_NN1 shocks_VVZ in_RP nearly_RR real_JJ time_NNT1 ._. 
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<s>
The_AT novel_JJ fiber_NN1 optics_NN1 technology_NN1 currently_RR being_VBG developed_VVN for_IF microendoscopic_JJ phototherapies_NN2 ,_, e.g._REX ,_, PDT/PTT_NP1 ,_, advancing_VVG the_AT nanotheranostic_JJ approach_NN1 in_II clinics_NN2 with_IW interstitial_JJ ,_, endoscopic_JJ ,_, intraoperative_JJ or_CC laparoscopic_JJ light_JJ delivery_NN1 into_II tumors_NN2 ._. 
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<s>
Knowing_VVG the_AT coefficients_NN2 D(1)_FO and_CC D(2)_FO ,_, the_AT cPD<equation>can_FO be_VBI calculated_VVN by_II the_AT short_JJ time_NNT1 propagator_NN1 (_( 31_MC ,_, 37_MC )_) ,_, As_CSA an_AT1 example_NN1 the_AT process_NN1 of_IO ultrafast_NN1 isomerization_NN1 of_IO acetylene_NN1 molecules_NN2 C2H2_FO triggered_VVD by_II single_JJ photon_NN1 excitation_NN1 has_VHZ been_VBN studied_VVN ._. 
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<s>
A_AT1 sintering_NN1 or_CC calcination_NN1 step_NN1 at_II high_JJ temperature_NN1 is_VBZ needed_VVN in_BCL21 order_BCL22 to_TO obtain_VVI good_JJ adhesion_NN1 andgood_VV0 mechanical_JJ properties_NN2 of_IO the_AT deposited_VVN inorganic_JJ ceramics_NN2 on_II the_AT substrate_NN1 ,_, a_AT1 process_NN1 that_CST may_VM cause_VVI some_DD cracks_NN2 on_II the_AT deposited_VVN material_NN1 ._. 
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<s>
The_AT gravitational_JJ field_NN1 around_II a_AT1 binary_JJ pulsar_NN1 is_VBZ relatively_RR strong_JJ ,_, so_CS its_APPGE gravitational_JJ wave_NN1 emission_NN1 can_VM induce_VVI sizable_JJ changes_NN2 for_IF the_AT period_NN1 of_IO the_AT binary_JJ pulsar_NN1 ._. 
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<s>
This_DD1 solution_NN1 ,_, though_CS non-intuitive_JJ ,_, is_VBZ perfectly_RR self-consistent_JJ ._. 
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<s>
Indeed_RR ,_, almost-single-spike_JJ FEL_NN1 pulses_NN2 could_VM be_VBI demonstrated_VVN at_II FLASH_NN1 ,_, see_VV0 Fig._NN1 16_MC (_( R?nsch-Schulenburg_NP1 et_RA21 al._RA22 ,_, 2014_MC )_) ._. 
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<s>
BLM_NP1 ,_, BLM1_FO and_CC BLM2_FO are_VBR the_AT beam_NN1 loss_NN1 monitors_NN2 ._. 
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<s>
The_AT caustic_JJ field_NN1 is_VBZ diagnosed_VVN by_II inserting_VVG observation_NN1 points_VVZ along_II the<Professional_FO Terms>_FO density_NN1 contour_NN1 ._. 
</s>
<s>
They_PPHS2 explored_VVD how_RRQ the_AT rate_NN1 of_IO regularization_NN1 depends_VVZ on_II the_AT frequency_NN1 of_IO word_NN1 usage_NN1 and_CC found_VVD that_CST the_AT half-life_NN1 of_IO irregular_JJ verbs_NN2 is_VBZ proportional_JJ to_II the_AT square_JJ root_NN1 of_IO their_APPGE frequency_NN1 ._. 
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<s>
The_AT primary_JJ nanoparticles_NN2 possess_VV0 diameters_NN2 ranging_VVG in_II 30–50_MCMC nm_FU ._. 
</s>
<s>
As_CSA also_RR noted_VVN by_II Sundararaman_NP1 et_RA21 al._RA22 ,_, 16_MC the_AT good_JJ description_NN1 of_IO the_AT Ag(100)_FO DC_NP1 might_VM be_VBI thus_RR inferred_VVN to_II the_AT Ag_FO UFF_VV0 ionic_JJ radius_NN1 being_VBG fortuitously_RR suitable_JJ to_TO describe_VVI the_AT cavity_NN1 size_NN1 for_IF this_DD1 system_NN1 ._. 
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<s>
We_PPIS2 introduce_VV0 a_AT1 target_NN1 system_NN1 model_NN1 in_II Sect._NP1 2_MC ._. 
</s>
<s>
Finally_RR ,_, Cozzo_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 12_MC )_) show_VV0 that_CST as_II a_AT1 function_NN1 of_IO the_AT coupling_NN1 between_II layers_NN2 ,_, different_JJ multiplexity_NN1 regimes_NN2 can_VM be_VBI identified_VVN from_II the_AT spectral_JJ properties_NN2 of_IO the_AT graph_NN1 ._. 
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<s>
For_IF the_AT vast_JJ majority_NN1 of_IO the_AT results_NN2 discussed_VVN here_RL ,_, several_DA2 simplifications_NN2 can_VM be_VBI made_VVN ._. 
</s>
<s>
One_PN1 should_VM note_VVI that_DD1 photon_NN1 and_CC carrier_NN1 lifetimes_NNT2 are_VBR typically_RR in_II the_AT ps_NN2 and_CC ns_FO ranges_VVZ ,_, respectively_RR ,_, so_CS21 that_CS22 even_RR a_AT1 delay_NN1 of_IO a_AT1 few_DA2 ns_FO is_VBZ already_RR relevant_JJ ._. 
</s>
<s>
Recent_JJ availability_NN1 of_IO high-brightness_JJ ion_NN1 sources_NN2 based_VVN on_II gas_NN1 ?_? eld_NN1 ionization_NN1 technology_NN1 has_VHZ allowed_VVN the_AT focusing_NN1 of_IO ion_NN1 beams_VVZ down_RP to_II sub-nanometer_JJ probe_NN1 sizes_NN2 ._. 
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<s>
As_II a_AT1 result_NN1 ,_, LSPR-based_JJ color_NN1 ?_? 
</s>
<s>
The_AT static_JJ structure_NN1 factor_NN1 is_VBZ a_AT1 nonlinear_JJ function_NN1 of_IO n0_FO of_IO the_AT target_NN1 material_NN1 ,_, and_CC may_VM be_VBI calculated_VVN from_II molecular_JJ simulations_NN2 ,_, measured_VVN via_II experiments_NN2 &lsqb;_( 23_MC ,_, 25_MC ,_, 26_MC &rsqb;_) ,_, or_CC derived_VVD analytically_RR through_II solutions_NN2 of_IO pair-correlation_JJ functions_NN2 as_CSA per_II the_AT Verlet–Weis_NN1 structure_NN1 factor_NN1 &lsqb;_( 27_MC &rsqb;_) ._. 
</s>
<s>
A_AT1 metallic_JJ state_NN1 is_VBZ defined_VVN as_II a_AT1 state_NN1 in_II which_DDQ the_AT conductivity_NN1 <Equation>remains_FO finite_JJ as_CSA <Equation>_FO ._. 
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<s>
Our_APPGE computational_JJ work_NN1 has_VHZ produced_VVN &lsqb;_( 1_MC1 &rsqb;_) a_AT1 value_NN1 of_IO 3002.8_MC cm_NNU ._. 
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<s>
We_PPIS2 have_VH0 examined_VVN the_AT onset_NN1 of_IO modulational_JJ instability_NN1 (_( MI_NP1 )_) and_CC ion-acoustic_NN1 (_( IA_NP1 )_) rogons_NN2 in_II dense_JJ plasma_NN1 with_IW degenerate_JJ trapped_JJ and_CC untrapped_JJ electrons_NN2 ._. 
</s>
<s>
The_AT over-_NN1 all_DB dissociation_NN1 leading_VVG to_II the_AT formation_NN1 of_IO U_JJ fragment_NN1 ions_NN2 can_VM be_VBI tentatively_RR explained_VVN as_CSA proceeding_VVG with_IW backbone_NN1 cleavage_NN1 next_II21 to_II22 the_AT Ala-2_MC residue_NN1 in_II the_AT rearranged_JJ phosphopeptide_NN1 ._. 
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The_AT mathematical_JJ approach_NN1 is_VBZ very_RG similar_JJ in_II the_AT studies_NN2 of_IO both_RR Davis_NP1 and_CC Nishiyama_NP1 ._. 
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In_II such_DA a_AT1 limit_NN1 ,_, Knudsen_NP1 layer_NN1 losses_NN2 can_VM be_VBI anticipated_VVN to_TO be_VBI strongly_RR mitigated_VVN ._. 
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The_AT identification_NN1 of_IO the_AT water_NN1 interfacial_JJ layers_NN2 at_II charged_JJ (_( and_CC non-charged_NN1 )_) interfaces_NN2 ,_, namely_REX ,_, BIL_NNO (_( Binding_VVG Interfacial_JJ Layer_NN1 )_) ,_, DL_MC (_( Diffuse_JJ Layer_NN1 )_) ,_, and_CC bulk_VV0 liquid_NN1 <chart>_FO water_NN1 ,_, has_VHZ been_VBN done_VDN following_II our_APPGE methodology_NN1 derived_VVN and_CC fully_RR described_VVN in_II Ref_NN1 ._. 
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They_PPHS2 found_VVD that_CST private_JJ enterprises_NN2 rely_VV0 more_RRR on_II market-oriented_JJ institutions_NN2 ,_, while_CS firms_NN2 with_IW local_JJ governmental_JJ supports_NN2 and_CC industrial_JJ linkages_NN2 are_VBR more_RGR likely_JJ to_TO sustain_VVI ._. 
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Schematic_JJ of_IO an_AT1 experiment_NN1 consisting_VVG of_IO three_MC coupled_VVD optoelectronic_JJ oscillators_NN2 ._. 
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Importantly_RR ,_, the_AT above_JJ general_JJ operational_JJ requirements_NN2 are_VBR differently_RR realized_VVN depending_II21 on_II22 whether_CSW the_AT engine_NN1 is_VBZ operating_VVG in_II the_AT macroscopic_JJ or_CC molecular_JJ realms_NN2 ._. 
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Fig._NN1 100b_FO shows_VVZ the_AT beam_NN1 loss_NN1 dependence_NN1 on_II the_AT crystal_NN1 orientation_NN1 observed_VVN in_II the_AT new_JJ position_NN1 with_IW monitor_NN1 BLM3_FO ._. 
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The_AT formation_NN1 of_IO CO2_FO can_VM be_VBI followed_VVN because_CS its_APPGE frequency_NN1 appears_VVZ in_II a_AT1 separate_JJ region_NN1 from_II the_AT rest_NN1 of_IO the_AT incomplete_JJ oxidation_NN1 products_NN2 ,_, and_CC thus_RR it_PPH1 can_VM be_VBI compared_VVN with_IW the_AT formation_NN1 of_IO all_DB other_JJ possible_JJ intermediate_JJ products_NN2 containing_VVG one_MC1 ,_, two_MC ,_, or_CC three_MC carbons_NN2 ._. 
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In_II electrical_JJ double-layer_JJ capacitors_NN2 ,_, energy_NN1 is_VBZ based_VVN on_II the_AT electrostatic_JJ storage_NN1 of_IO charges_NN2 at_II the_AT interface_NN1 between_II the_AT electrode_NN1 and_CC the_AT electrolyte_NN1 &lsqb;_( 5_MC &rsqb;_) ._. 
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This_DD1 is_VBZ called_VVN a_AT1 Santha-Vazirani_JJ source_NN1 and_CC was_VBDZ described_VVN as_II a_AT1 model_NN1 for_IF weak_JJ randomness_NN1 sources_NN2 by_II Santha_NP1 and_CC Vazirani_NP1 (_( 1986_MC )_) together_RL with_IW an_AT1 impossibility_NN1 proof_NN1 for_IF a_AT1 deterministic_JJ extractor_NN1 ._. 
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In_II practice_NN1 ,_, there_EX is_VBZ always_RR a_AT1 value_NN1 of_IO for_IF which_DDQ the_AT (_( 56_MC '_NULL ,_, 0+_FO )_) (_( Roper_NP1 )_) state_NN1 is_VBZ shifted_VVN below_II the_AT N_ZZ1 (_( 1535_MC )_) 1/2_MF ._. 
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Typically_RR ,_, however_RR ,_, the_AT value_NN1 is_VBZ so_RG large_JJ that_CST one_PN1 must_VM question_VVI the_AT validity_NN1 of_IO first-order_JJ perturbation_NN1 theory_NN1 (_( Isgur_NP1 and_CC Karl_NP1 ,_, 1979_MC )_) ._. 
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This_DD1 list_NN1 can_VM be_VBI extended_VVN to_II a_AT1 long_JJ series_NN of_IO people_NN I_PPIS1 have_VH0 interacted_VVN with_IW and_CC talked_VVN to_II over_II the_AT same_DA period_NN1 ._. 
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<s>
Hence_RR ,_, electrostatic_JJ ion_NN1 acoustic_NN1 waves_NN2 are_VBR excluded_VVN and_CC our_APPGE main_JJ focus_NN1 is_VBZ to_TO study_VVI the_AT resonant_JJ instability_NN1 of_IO KAWs_NP2 ._. 
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<s>
The_AT electrochemical_JJ measurements_NN2 indicated_VVD improved_JJ performance_NN1 ;_; Mg-de_NP1 ficiency_NN1 yields_VVZ better_JJR cyclic_JJ performance_NN1 during_II the_AT first_MD 50_MC cycles_NN2 ,_, however_RR ,_, the_AT specific_JJ discharge_NN1 capacity_NN1 of_IO Mg0.5Fe2O4_FO cell_NN1 is_VBZ dramatically_RR decreased_VVN during_II the_AT subsequent_JJ 50_MC cycles_NN2 ._. 
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See_VV0 supplementary_JJ material_NN1 for_IF the_AT dependence_NN1 of_IO the_AT bandgap_NN1 energy_NN1 on_II the_AT U_JJ parameter_NN1 for_IF the_AT case_NN1 of_IO 1ML_NNU of_IO water_NN1 absorbed_VVN on_II the_AT pristine_JJ TiO2_FO (_( 001_MC )_) nanotube_VV0 slab_NN1 model_NN1 ._. 
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Two_MC phases_NN2 of_IO expansion_NN1 are_VBR shown_VVN in_II the_AT profiles_NN2 ._. 
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In_II both_DB2 cases_NN2 ,_, we_PPIS2 show_VV0 the_AT average_JJ shift_NN1 and_CC the_AT corresponding_JJ dispersion_NN1 for_IF the_AT different_JJ grooming_JJ techniques_NN2 under_II scrutiny_NN1 ,_, varying_VVG their_APPGE free_JJ parameter_NN1 ._. 
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Zttl_NP1 et_RA21 al_RA22 ._. 
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have_VH0 investigated_VVN neutral_JJ C60(C2H4)n_FO by_II simulated_JJ annealing_NN1 &lsqb;_( 587_MC &rsqb;_) ._. 
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<s>
This_DD1 mismatch_NN1 results_NN2 from_II the_AT fact_NN1 that_CST other_JJ authors_NN2 have_VH0 introduced_VVN different_JJ non-experimental_JJ level_JJ energy_NN1 values_NN2 in_II their_APPGE calculation_NN1 procedure_NN1 to_TO find_VVI a_AT1 better_JJR fit_NN1 in_II the_AT energies_NN2 of_IO the_AT levels_NN2 ._. 
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From_II the_AT slope_NN1 and_CC the_AT concentration_NN1 of_IO the_AT reagent_NN1 ,_, the_AT overall_JJ bimolecular_JJ rate_NN1 constant_NN1 (_( kexp_NN1 )_) can_VM be_VBI obtained_VVN ._. 
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The_AT curve_NN1 is_VBZ given_VVN to_TO guide_VVI the_AT eye_NN1 ._. 
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Indeed_RR ,_, the_AT 2Ajj_FO state_NN1 is_VBZ calculated_VVN to_TO lie_VVI about_RG 8_MC kcal_JJ mol1_FO below_II the_AT 2Aj_FO state_NN1 ._. 
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<s>
However_RR ,_, duringXUNDLcompilation_NN1 ,_, basicconsistency_NN1 checks_NN2 are_VBR performed_VVN and_CC any_DD internal_JJ inconsistencies_NN2 are_VBR pointed_VVN out_RP to_II the_AT author_NN1 to_TO allow_VVI them_PPHO2 be_VBI reconciled_VVN in_II the_AT data_NN base_NN1 ._. 
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Since_CS the_AT specific_JJ capacitance_NN1 increases_VVZ as_II the_AT surface_NN1 area_NN1 increases_NN2 ,_, the_AT amount_NN1 of_IO charge_NN1 accumulated_VVN on_II the_AT electrode_NN1 surface_NN1 increases_NN2 ._. 
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<s>
Qualitatively_RR ,_, therefore_RR ,_, despite_II fundamental_JJ differences_NN2 in_II formulation_NN1 ,_, both_DB2 the_AT DSE_NN1 and_CC LF_NP1 CQM_NP1 approaches_NN2 arrive_VV0 at_II the_AT same_DA conclusion_NN1 regarding_II the_AT nature_NN1 of_IO the_AT proton-Roper_JJ transition_NN1 form_NN1 factors_NN2 :_: while_CS MB_NNU FSIs_NN1 contribute_VV0 materially_RR on_II x_ZZ1 2_MC ,_, a_AT1 dressed-quark_JJ core_NN1 is_VBZ exposed_VVN and_CC probed_VVN on_II x_ZZ1 2_MC ._. 
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<s>
This_DD1 study_NN1 was_VBDZ carefully_RR planned_VVN to_TO eliminate_VVI potential_JJ structural_JJ impacts_NN2 that_CST might_VM arise_VVI from_II differences_NN2 in_II crystallization_NN1 conditions_NN2 ,_, crystal_NN1 packing_NN1 ,_, diffraction_NN1 source_NN1 ,_, or_CC data_NN collection/refinement_NN1 protocols_NN2 ._. 
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<s>
The_AT price_NN1 to_TO pay_VVI is_VBZ some_DD loss_NN1 of_IO robustness_NN1 :_: the_AT relative_JJ intensity_NN1 on_II the_AT trailing_JJ slopes_NN2 of_IO the_AT pulses_NN2 needs_VVZ to_TO be_VBI controlled_VVN ._. 
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<s>
U_ZZ1 in_II this_DD1 case_NN1 significantly_RR depends_VVZ on_II z_ZZ1 and_CC that_CST two_MC strong_JJ Ekman_NN1 vortices_NN2 fill_VV0 the_AT whole_JJ container_NN1 ._. 
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<s>
Emission_NN1 spectra_NN2 of_IO optimized_JJ KLM_NP1 lasers_NN2 presented_VVN in_II logarithmic_JJ scale_NN1 at_II (_( d_ZZ1 )_) 300_MC MHz_NNU and_CC (_( e_ZZ1 )_) 100_MC MHz_NNU repetition_NN1 rates_NN2 :_: (_( i_ZZ1 )_) fundamental_JJ mid-IR_NN1 band_NN1 ,_, (_( ii_MC )_) second_MD harmonic_JJ generation_NN1 band_NN1 ,_, (_( iii_MC )_) third_MD optical_JJ harmonic_JJ ,_, (_( iv_MC )_) fourth_MD optical_JJ harmonic_JJ ,_, (_( v_ZZ1 )_) sum_NN1 frequency_NN1 generation_NN1 between_II femto-second_MD mid-IR_NN1 pulses_NN2 and_CC CW_NP1 pump_NN1 radiation_NN1 ,_, (_( vi_MC )_) residual_JJ pumping_NN1 at_II 1567nm_FO ._. 
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<s>
The_AT SISCone_NN1 jet_NN1 algorithm_NN1 is_VBZ an_AT1 infrared-_NN1 and_CC collinear-safe_JJ implementation_NN1 of_IO a_AT1 modern_JJ cone_NN1 algorithm_NN1 ._. 
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<s>
Throughout_II this_DD1 article_NN1 it_PPH1 is_VBZ assumed_VVN that_CST these_DD2 modes_NN2 are_VBR skipped_VVN in_II summations_NN2 containing_VVG zero-point_JJ amplitudes_NN2 ._. 
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<s>
Nuclear_JJ physics_NN1 input_NN1 into_II the_AT network_NN1 calculations_NN2 include_VV0 nuclear_JJ masses_NN2 ,_, β_NULL -decay_JJ properties_NN2 ,_, as_II31 well_II32 as_II33 neutron_NN1 capture_NN1 and_CC fission_NN1 rates_NN2 ._. 
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Fig._NN1 1a_FO )_) shows_VVZ schematics_NN1 of_IO exchange-spring_JJ magnet_NN1 nanopatterns_NN2 ._. 
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<s>
Evidently_RR ,_, even_RR without_IW assuming_VVG a_AT1 model_NN1 ,_, one_PN1 can_VM find_VVI interesting_JJ qualitative_JJ results_NN2 with_II31 regard_II32 to_II33 complexity_NN1 and_CC universality_NN1 in_II computation_NN1 by_II incorporating_VVG elements_NN2 of_IO time_NNT1 travel_NN1 involved_VVD ,_, as_CSA has_VHZ been_VBN done_VDN by_II &lsqb;_( 47,48_MC &rsqb;_) ._. 
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<s>
We_PPIS2 acknowledge_VV0 funding_NN1 by_II the_AT Deutsche_NP1 Forschungsgemeinschaft_NP1 under_II Germany_NP1 '_NULL s_ZZ1 Excellence_NN1 Strategy_NN1 -_- The_AT Berlin_NP1 Mathematics_NN1 Research_NN1 Center_NN1 MATH+_FO (_( EXC-2046/1_FU ,_, Project_NN1 No._NN1 390685689_MC ,_, AA4-6_MC )_) ._. 
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<s>
The_AT connection_NN1 to_II multipartite_JJ entanglement_NN1 (_( in_RR21 particular_RR22 ,_, for_IF the_AT quantum_NN1 Fisher_NP1 information_NN1 ,_, see_VV0 Sec_NNU ._. 
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<s>
II.F_NP1 )_) further_RRR supports_VVZ the_AT use_NN1 of_IO the_AT variance_NN1 to_TO measure_VVI macroscopic_JJ quantumness_NN1 of_IO pure_JJ spin-ensemble_JJ states_NN2 ._. 
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The_AT average_JJ energy_NN1 loss_NN1 ,_, a_AT1 quantity_NN1 useful_JJ in_II computing_VVG the_AT stopping_VVG power_NN1 ,_, for_REX21 example_REX22 ,_, is_VBZ therefore_RR given_VVN as_CSA <equation>_FO is_VBZ the_AT average_JJ energy_NN1 of_IO an_AT1 electron_NN1 ejected_VVN in_II single_JJ ionization_NN1 at_II a_AT1 given_JJ impact_NN1 energy_NN1 ._. 
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Ritter_VV0 et_RA21 al_RA22 ._. 
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(_( 2012_MC )_) proposed_VVD a_AT1 quantum_NN1 network_NN1 architecture_NN1 based_VVN on_II single_JJ atoms_NN2 embedded_VVN in_II optical_JJ cavities_NN2 ._. 
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<s>
With_IW the_AT definition_NN1 of_IO free_JJ operations_NN2 ,_, the_AT QRT_NP1 of_IO incompatibility_NN1 of_IO quantum_NN1 instruments_NN2 is_VBZ well_RR defined_VVN ._. 
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<s>
First_MD ,_, in_II Bell_NP1 tests_VVZ we_PPIS2 assume_VV0 we_PPIS2 have_VH0 uniform_JJ random_JJ bits_NN2 to_TO choose_VVI the_AT measurement_NN1 settings_NN2 ._. 
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Recently_RR ,_, an_AT1 explicit_JJ relation_NN1 between_II a_AT1 measure_NN1 of_IO entanglement_NN1 and_CC a_AT1 geometric_JJ entity_NN1 has_VHZ been_VBN reported_VVN in_II Deb_NP1 (_( Quantum_NN1 Inf_NN1 Process_NN1 15:1629–1638_MCMC ,_, 2016_MC )_) ._. 
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They_PPHS2 developed_VVD a_AT1 time-series_JJ causality_NN1 approach_NN1 to_TO regress_VVI monthly_JJ unemployment_NN1 rate_NN1 against_II search_NN1 activity_NN1 ._. 
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Further_JJR information_NN1 on_II the_AT structure_NN1 and_CC experimental_JJ data_NN ,_, and_CC relative_JJ interpretation_NN1 ,_, used_VMK to_TO study_VVI <Professional_FO Term>_FO can_VM be_VBI found_VVN in_II Ref_NN1 ._. 
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<s>
In_II this_DD1 work_NN1 ,_, three_MC isomers_NN2 with_IW different_JJ degrees_NN2 of_IO steric_JJ hindrance_NN1 against_II the_AT rotation_NN1 around_II the_AT donor-acceptor_JJ connection_NN1 are_VBR investigated_VVN ._. 
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The_AT flat_JJ bands_NN2 turn_VV0 to_TO disperse_VVI when_RRQ tTNN_NNU xzxz_NNU increases_NN2 ._. 
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These_DD2 findings_NN2 open_VV0 up_RP new_JJ possibilities_NN2 for_IF applications_NN2 inspired_VVN by_II either_DD1 "_" ordinary_JJ "_" (_( low_JJ field_NN1 )_) plasmonics_NN2 or_CC high_JJ intensity_NN1 laser-plasma_NN1 physics_NN1 ._. 
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More_RGR generally_RR ,_, suppose_VV0 the_AT photon_NN1 interacts_VVZ with_IW some_DD environment_NN1 system_NN1 E_ZZ1 inside_II the_AT interferometer_NN1 ._. 
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The_AT coefficient_NN1 of_IO maximum_JJ acceleration_NN1 k_ZZ1 demonstrated_VVD the_AT same_DA dependence_NN1 :_: its_APPGE values_NN2 are_VBR follows_VVZ :_: 60_MC ,_, 30_MC ,_, 150_MC ,_, and_CC 250_MC (_( scenarios_NN2 A_ZZ1 ,_, B_ZZ1 ,_, C_ZZ1 ,_, and_CC D_ZZ1 )_) ._. 
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<s>
In_II operation_NN1 ,_, the_AT completion_NN1 of_IO the_AT task_NN1 of_IO each_DD1 of_IO these_DD2 alternative_JJ enzyme_NN1 forms_NN2 triggers_VVZ the_AT transition_NN1 to_II the_AT next_MD one_PN1 in_II the_AT cycle_NN1 ._. 
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As_II a_AT1 result_NN1 ,_, analysis_NN1 of_IO the_AT unknown_JJ signal_NN1 contribution_NN1 is_VBZ highly_RR facilitated.spectral_NNU modes_NN2 in_II SVD_NP1 analysis_NN1 ,_, the_AT weight_NN1 of_IO a_AT1 spectral_JJ component_NN1 ,_, <Professional_FO term>can_FO be_VBI easily_RR calculated_VVN using_VVG vector_NN1 projection_NN1 (_( see_VV0 supplementary_JJ material_NN1 for_IF details_NN2 )_) ._. 
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Thus_RR if_CS <Professional_FO Term>_FO ,_, the_AT word_NN1 <Professional_FO Term>_FO contains_VVZ more_DAR orders_NN2 than_CSN burgers_NN2 ._. 
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Suppose_VV0 that_CST <Equation>_FO and_CC <Equation>_FO is_VBZ the_AT random_JJ walk_NN1 determined_VVN by_II <Equation>_FO described_VVN above_RL ._. 
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So_RR for_IF a_AT1 hyperk?hler_NN1 submanifold_RR <Equation>_FO <Equation>_FO <Equation>_FO and_CC so_CS S_ZZ1 vanishes_VVZ ._. 
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These_DD2 nucleate_VV0 larger_JJR Kagome_NN1 sheets_NN2 ,_, which_DDQ grow_VV0 radially_RR outward_RL in_II the_AT x-y_FO plane_NN1 until_CS they_PPHS2 collide_VV0 ._. 
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In_II principle_NN1 ,_, however_RR ,_, any_DD means_NN of_IO pinning_VVG or_CC distorting_VVG the_AT interface_NN1 far_RR from_II the_AT particle_NN1 can_VM create_VVI a_AT1 curvature_NN1 field_NN1 ._. 
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In_II this_DD1 case_NN1 ,_, for_IF an_AT1 unpolarized_JJ tissue_NN1 (_( a_AT1 >_FO 0_MC in_II Equation_NN1 11_MC )_) ,_, the_AT polarity_NN1 decays_VVZ from_II the_AT boundary_NN1 with_IW the_AT characteristic_JJ length_NN1 <Equation>_FO ,_, which_DDQ defines_VVZ the_AT width_NN1 of_IO the_AT polarized_JJ boundary_NN1 layer_NN1 observed_VVN in_II <Picture>_FO Continuum_NN1 models_NN2 ._. 
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BLM3_FO was_VBDZ used_VVN allowed_VVN observing_VVG the_AT collimation_NN1 leakage_NN1 reduction_NN1 which_DDQ was_VBDZ larger_JJR than_CSN the_AT beam_NN1 loss_NN1 reduction_NN1 in_II the_AT crystal_NN1 ._. 
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We_PPIS2 discuss_VV0 mechanism_NN1 of_IO the_AT phase_NN1 transition_NN1 and_CC the_AT evolution_NN1 of_IO the_AT phase_NN1 with_IW pressure_NN1 ._. 
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We_PPIS2 have_VH0 measured_VVN the_AT fractal_JJ dimension_NN1 for_IF the_AT <Equation>_FO and_CC Cambridge/Aachen_NP1 algorithms_NN2 and_CC find_VV0 <Equation>_FO 99_MC ._. 
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Twelve_MC models_NN2 of_IO various_JJ kinds_NN2 are_VBR considered_VVN ,_, from_II relatively_RR old_JJ ones_NN2 up_II21 to_II22 very_RG recent_JJ ._. 
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Mathematically_RR ,_, the_AT prediction_NN1 of_IO the_AT popularity_NN1 of_IO a_AT1 given_JJ target_NN1 item_NN1 ,_, In_II uplink_NN1 ,_, attenuation_NN1 is_VBZ more_RRR because_II21 of_II22 turbulence_NN1 effects_NN2 ._. 
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A_AT1 simple_JJ estimate_NN1 can_VM be_VBI made_VVN to_TO compare_VVI the_AT energies_NN2 fluxes_NN2 deposited_VVN in_II the_AT pellet_NN1 cloud_NN1 and_CC ice_NN1 volumes_NN2 by_II thermal_JJ and_CC fast_JJ electrons_NN2 ._. 
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The_AT point_NN1 is_VBZ that_DD1 coherent_JJ states_NN2 |_NULL m_ZZ1 are_VBR holomorphic_JJ in_II m_ZZ1 ._. 
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On_II the_AT contrary_NN1 ,_, there_EX may_VM be_VBI an_AT1 accumulation_NN1 of_IO gas_NN1 between_II the_AT ISCO_NN1 and_CC the_AT compact_JJ object_NN1 ,_, and_CC the_AT gas_NN1 has_VHZ to_TO lose_VVI additional_JJ energy_NN1 and_CC angular_JJ momentum_NN1 before_II plunging_VVG to_II the_AT central_JJ body_NN1 ._. 
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For_REX21 example_REX22 ,_, pointer_NN1 marks_NN2 could_VM be_VBI inscribed_VVN using_VVG a_AT1 FIB_NN1 prior_II21 to_II22 PIES_NN2 analysis_NN1 ._. 
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Two_MC pieces_NN2 of_IO information_NN1 can_VM be_VBI extracted_VVN from_II these_DD2 results_NN2 ._. 
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If_CS the_AT phase_NN1 states_NN2 are_VBR around_RG opposite_JJ values_NN2 ,_, there_EX is_VBZ a_AT1 destructive_JJ interference_NN1 and_CC the_AT output_NN1 power_NN1 is_VBZ close_JJ to_II 0_MC ._. 
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Interestingly_RR ,_, the_AT average_JJ density_NN1 of_IO water-solid_JJ HBs_NP1 is_VBZ higher_JJR at_II the_AT aqueous_JJ A-surface_NN1 than_CSN at_II the_AT aqueous_JJ B-surface_NN1 ,_, showing_VVG that_CST ,_, despite_II both_DB2 interfaces_NN2 being_VBG strongly_RR hydrophilic_JJ (_( the_AT number_NN1 of_IO HBs/nm2_FU is_VBZ larger_JJR than_CSN that_DD1 at_II the_AT most_RGT hydrophilic_JJ amorphous_JJ silica_NN1 that_CST we_PPIS2 have_VH0 investigated_VVN in_II the_AT past34,67_FO )_) ,_, the_AT aqueous_JJ A-surface_NN1 is_VBZ the_AT most_RGT hydrophilic_JJ one_PN1 with_IW 8.7_MC water-solid_JJ HBs/nm2_FU ,_, close_RR to_II the_AT value_NN1 of_IO aqueous_JJ quartz.31,32,35_FO At_II both_DB2 interfaces_NN2 ,_, the_AT inner_JJ sites_NN2 (_( ?3_FO -OH_UH for_IF the_AT A-surface_NN1 and_CC ?2_FO -OH_UH for_IF the_AT B-surface_NN1 )_) do_VD0 not_XX interact_VVI with_IW water_NN1 ._. 
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<s>
The_AT length_NN1 of_IO a_AT1 cycle_NN1 l_ZZ1 ,_, denoted_VVN by_II |_NULL l_ZZ1 |_NULL ,_, is_VBZ defined_VVN to_TO be_VBI equal_JJ to_II the_AT length_NN1 of_IO any_DD of_IO the_AT closed_JJ paths_NN2 in_II l_ZZ1 ._. 
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Actually_RR each_DD1 electron_NN1 propagator_NN1 in_II the_AT two-photon_JJ decay_NN1 rate_NN1 amplitude_NN1 has_VHZ different_JJ parameter_NN1 ε_FO and_CC the_AT limits_NN2 with_II31 respect_II32 to_II33 these_DD2 parameters_NN2 should_VM be_VBI taken_VVN independently_RR ._. 
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The_AT RQM_NP1 spectrum_NN1 is_VBZ displayed_VVN by_II horizontal_JJ lines_NN2 ._. 
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Differently_RR from_II the_AT commonly_RR studied_VVN polycrystalline_JJ NM/FM_FU samples_NN2 ,_, where_CS the_AT iSGE-based_NN1 and_CC the_AT SHE-based_JJ mechanisms_NN2 are_VBR indistinguishable_JJ in_II the_AT lowest_JJT order_NN1 terms_NN2 (_( Garello_NP1 et_RA21 al._RA22 ,_, 2013_MC )_) ,_, the_AT dependence_NN1 of_IO the_AT torques_NN2 on_II the_AT angle_NN1 of_IO the_AT current_JJ relative_II21 to_II22 the_AT high_JJ symmetry_NN1 directions_NN2 of_IO the_AT semi-conductor_NN1 crystal_NN1 provides_VVZ a_AT1 direct_JJ means_NN to_TO disentangle_VVI the_AT SHE_PPHS1 and_CC iSGE_VVI contributions_NN2 ._. 
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The_AT calculations_NN2 of_IO the_AT nuclear_JJ matrix_NN1 elements_NN2 ,_, while_CS still_RR evaluated_VVN in_II an_AT1 extreme_JJ single-particle_JJ fashion_NN1 ,_, are_VBR now_RT not_XX any_DD more_RGR analytically_RR available_JJ ._. 
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<s>
Phonon_NN1 dispersion_NN1 relations_NN2 of_IO CaC6_FO calculated_VVN using_VVG Wannier_JJR interpolation_NN1 ._. 
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In_RR21 addition_RR22 ,_, we_PPIS2 present_VV0 three_MC high_JJ resolution_NN1 structures_NN2 of_IO XcPGM_NP1 from_II X-ray_NN1 data_NN collected_VVN at_II room_NN1 temperature_NN1 (_( RT_NP1 )_) ._. 
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The_AT -like_JJ correlations_NN2 and_CC formation_NN1 is_VBZ also_RR of_IO importance_NN1 for_IF nuclei_NN2 with_IW decay_NN1 such_II21 as_II22 212Po_FO (_( R?pke_NP1 et_RA21 al._RA22 ,_, 2014_MC )_) and_CC superheavy_JJ nuclei_NN2 ._. 
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<s>
Irfan_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
have_VH0 investigated_VVN the_AT properties_NN2 of_IO dust-ion-acoustic_JJ rogons_NN2 in_II a_AT1 degenerate_JJ relativistic_JJ dusty_JJ plasma_NN1 and_CC explained_VVD the_AT restoration_NN1 of_IO modulational_JJ stability_NN1 at_II relatively_RR large_JJ wavenumbers_NN2 by_II the_AT ionic_JJ degeneracy_NN1 which_DDQ otherwise_RR become_VV0 unstable_JJ without_IW the_AT ionic_JJ pressure_NN1 effect_NN1 ._. 
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<s>
This_DD1 function_NN1 is_VBZ 1_MC1 if_CS x_ZZ1 and_CC its_APPGE ith_MD neighbour_NN1 are_VBR both_RR feasible_JJ ,_, and_CC it_PPH1 is_VBZ easily_RR checked_VVN that_CST B_ZZ1 maintains_VVZ hermiticity_NN1 with_IW this_DD1 modification_NN1 ._. 
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<s>
This_DD1 energy_NN1 transfer_NN1 process_NN1 forms_VVZ a_AT1 radical_JJ anion_NN1 or_CC cation_NN1 ,_, which_DDQ then_RT reacts_VVZ with_IW oxygen_NN1 to_TO produce_VVI oxygenated_JJ products_NN2 such_II21 as_II22 superoxide_NN1 anion_NN1 radicals_NN2 (_( O_ZZ1 )_) ,_, hydroxyl_NN1 radicals_NN2 (_( OH_UH )_) ,_, or_CC hydrogen_NN1 peroxides_NN2 (_( HO_NP1 )_) (_( type_NN1 I_MC1 reaction_NN1 )_) ._. 
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<s>
For_IF these_DD2 systems_NN2 ,_, the_AT polarity_NN1 not_XX only_JJ reorients_NN2 in_II flow_NN1 gradients_NN2 but_CCB also_RR in_II uniform_JJ flows_NN2 ,_, like_II a_AT1 weathercock_NN1 in_II the_AT wind_NN1 ._. 
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<s>
Schematic_JJ representation_NN1 of_IO synthesis_NN1 of_IO graphene_NN1 sheets_NN2 by_II oxidation_NN1 of_IO graphite_NN1 ?_? 
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<s>
Reaching_VVG to_II momentum_NN1 transfer_NN1 Q2_FO ≈_NULL 4.5_MC GeV2_FO ,_, the_AT data_NN probe_VV0 a_AT1 domain_NN1 within_II which_DDQ hard_JJ valence-quark_JJ degrees_NN2 of_IO freedom_NN1 could_VM be_VBI expected_VVN to_TO determine_VVI form_NN1 factor_NN1 behavior_NN1 ._. 
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<s>
Thus_RR ,_, the_AT bulk_NN1 lifetime_NNT1 is_VBZ more_RGR or_CC less_RGR unaffected_JJ by_II the_AT annealing_NN1 ._. 
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As_CSA already_RR discussed_VVN ,_, the_AT idea_NN1 of_IO the_AT method_NN1 is_VBZ to_TO measure_VVI changes_NN2 in_II the_AT relative_JJ position_NN1 between_II the_AT two_MC detectors_NN2 ,_, by_II31 means_II32 of_II33 reconstructed_JJ cosmic_JJ muons_NN2 ._. 
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<s>
To_TO conclude_VVI ,_, we_PPIS2 have_VH0 examined_VVN the_AT dynamics_NN of_IO the_AT entropic_JJ uncertainty_NN1 relating_VVG to_II different_JJ types_NN2 of_IO measurements_NN2 in_II the_AT spin-1_MC1 Heisenberg_NP1 chain_NN1 with_IW external_JJ magnetic_JJ fields_NN2 ._. 
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The_AT low-energy_JJ facility_NN1 currently_RR exists_VVZ and_CC is_VBZ being_VBG used_VVN coupled_VVN to_II the_AT existing_JJ facility_NN1 ._. 
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Because_CS for_IF most_DAT of_IO the_AT time_NNT1 only_RR one_MC1 pulse_NN1 is_VBZ present_JJ ,_, the_AT mixing_NN1 angle_NN1 t_ZZ1 stays_VVZ nearly_RR constant_JJ for_IF most_DAT of_IO the_AT excitation_NN1 :_: <Equation>_FO early_JJ and_CC <Equation>_FO late_RR ._. 
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<s>
The_AT first_MD implementations_NN2 of_IO the_AT OEO_NP1 reservoir_NN1 computer_NN1 were_VBDR based_VVN on_II the_AT low-pass_NN1 configuration_NN1 ,_, and_CC they_PPHS2 were_VBDR published_VVN almost_RR simultaneously_RR by_II two_MC independent_JJ research_NN1 groups_NN2 ._. 
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Typical_JJ tasks_NN2 for_IF two-party_JJ cryptography_NN1 are_VBR bit_NN1 commitment_NN1 ,_, oblivious_JJ transfer_NN1 ,_, or_CC secure_JJ identification_NN1 ._. 
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<s>
Renewed_JJ interest_NN1 in_II the_AT computation_NN1 of_IO terms_NN2 in_II the_AT expansion_NN1 ,_, used_VMK to_TO calculate_VVI critical_JJ exponents_NN2 ,_, has_VHZ been_VBN frustrated_VVN by_II the_AT differing_JJ and_CC incompatible_JJ results_NN2 for_IF the_AT high-order_JJ behaviour_NN1 of_IO the_AT perturbation_NN1 expansion_NN1 reported_VVN in_II the_AT literature_NN1 ._. 
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The_AT quantities_NN2 D_ZZ1 ,_, E_ZZ1 ,_, and_CC P_ZZ1 in_II Eq_NN1 ._. 
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<s>
(_( 2_MC )_) are_VBR a_AT1 short_JJ hand_NN1 notation_NN1 for_IF the_AT component_NN1 of_IO the_AT corresponding_JJ vector_NN1 fields_NN2 perpendicular_NN1 to_II the_AT slab_NN1 (_( see_VV0 Fig._NN1 1_MC1 )_) ._. 
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Mn_FO is_VBZ the_AT slowest_JJT reacting_JJ atomic_JJ transition_NN1 metal_NN1 cation_NN1 in_II this_DD1 study_NN1 with<Equation>_FO is_VBZ the_AT exception_NN1 asit_NN1 does_VDZ not_XX have_VHI a_AT1 half_DB filled_VVD ,_, orbital_JJ configuration_NN1 ._. 
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<s>
By_II (_( 5.16_MC )_) and_CC the_AT equation_NN1 <Equation>_FO ,_, which_DDQ comes_VVZ from_II (_( 5.43_MC )_) ,_, we_PPIS2 get_VV0 that_DD1 <Equation>_FO for_IF all_DB <Equation>_FO ._. 
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<s>
Recently_RR ,_, exploring_VVG such_DA properties_NN2 of_IO classical_JJ electromagnetic_JJ field_NN1 the_AT sequential_JJ quantum_NN1 duel_NN1 was_VBDZ performed_VVN &lsqb;_( 17_MC &rsqb;_) ._. 
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<s>
The_AT RCA_NN1 value_NN1 is_VBZ defined_VVN as_II the_AT share_NN1 of_IO product_NN1 p_ZZ1 in_II the_AT export_NN1 basket_NN1 of_IO country_NN1 c_ZZ1 to_II the_AT share_NN1 of_IO product_NN1 p_ZZ1 in_II the_AT world_NN1 trade_NN1 ._. 
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<s>
The_AT third_MD subclass_NN1 ,_, SNe_NP1 Ia-CSM_NP1 ,_, exhibit_VV0 strong_JJ Balmer_NP1 lines_NN2 in_II emission_NN1 ,_, most_RGT likely_RR obtained_VVN as_II the_AT SN_NN1 ejecta_NN1 ram_NN1 into_II a_AT1 dense_JJ CSM_NP1 (_( e.g._REX ,_, Hamuy_NP1 et_RA21 al._RA22 ,_, 2003_MC ;_; Aldering_NP1 et_RA21 al._RA22 ,_, 2006_MC ;_; Silverman_NP1 et_RA21 al._RA22 ,_, 2013_MC ;_; Leloudas_NN2 et_RA21 al._RA22 ,_, 2015_MC )_) ._. 
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<s>
Remarkably_RR ,_, quantization_NN1 of_IO molecular_JJ rotation_NN1 governs_VVZ reaction_NN1 dynamics_NN not_XX only_RR at_II low_JJ temperatures_NN2 ,_, but_CCB determines_VVZ the_AT rate_NN1 even_RR for_IF reactions_NN2 that_CST can_VM otherwise_RR be_VBI described_VVN by_II a_AT1 classical_JJ theory_NN1 ._. 
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Here_RL the_AT symbol_NN1 <Professional_FO Term>_FO indicates_VVZ convergence_NN1 in_II the_AT weak_JJ topology_NN1 ,_, deg_NNU <Equation>_FO denotes_VVZ the_AT local_JJ degree_NN1 of_IO the_AT map_NN1 and_CC is_VBZ a_AT1 potential_NN1 related_VVN to_II defined_JJ in_II (_( 6.5_MC )_) ._. 
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The_AT high_JJ experiments_NN2 on_II hydrogen_NN1 and_CC nitrogen_NN1 &lsqb;_( 124,125_MC &rsqb;_) have_VH0 shown_VVN that_CST the_AT use_NN1 of_IO pure_JJ Re_NP1 as_II the_AT gasket_NN1 material_NN1 and_CC very_RG careful_JJ execution_NN1 of_IO the_AT experiment_NN1 allow_VV0 to_TO overcome_VVI these_DD2 problems_NN2 ._. 
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<s>
In_II previous_JJ work_NN1 on_II surface_NN1 modification_NN1 of_IO cathodes_NN2 from_II our_APPGE laboratory_NN1 ,_, the_AT efiects_NN2 of_IO submonolayer_NN1 films_NN2 were_VBDR stable_JJ for_IF periods_NN2 of_IO at_RR21 least_RR22 a_AT1 day_NNT1 at_II 873_MC K_ZZ1 ;_; however_RR ,_, the_AT efiects_NN2 disappeared_VVD upon_II brief_JJ heating_NN1 to_II 1073_MC K_ZZ1 ,_, suggesting_VVG rapid_JJ difiusion_NN1 from_II the_AT surface_NN1 at_II the_AT higher_JJR temperatures_NN2 ._. 
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<s>
The_AT formation_NN1 process_NN1 of_IO the_AT dopant_JJ cluster_NN1 in_II HNDs_NP1 can_VM be_VBI understood_VVN as_CSA sequential_JJ monomer_NN1 addition_NN1 to_II the_AT growing_JJ clusters_NN2 ._. 
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<s>
For_IF O-like_JJ Cu_FO ,_, in_II our_APPGE MCDF_NP1 calculations_NN2 ,_, we_PPIS2 have_VH0 included_VVN 54_MC configurations_NN2 ,_, 2s_MC2 2_MC 2p_NNU 4_MC ,_, 2s2p_FO 5_MC ,_, 2p_NNU 6_MC ,_, 2s_MC2 2_MC 2p_NNU 3_MC 3l_NNU (_( <Equation>_FO )_) ,_, 2s2p_FO 4_MC 3l_NNU (_( <Equation>_FO )_) ,_, 2p_NNU 5_MC 3l_NNU (_( <Equation>_FO )_) ,_, 2s_MC2 2_MC 2p_NNU 3_MC 4l_NNU (_( <Equation>_FO )_) ,_, 2s2p_FO 4_MC 4l_NNU (_( <Equation>_FO )_) ,_, 2p_NNU 5_MC 4l_NNU (_( <Equation>_FO )_) ,_, 2s_MC2 2_MC 2p_NNU 3_MC 5l_NNU (_( <Equation>_FO )_) ,_, 2s2p_FO 4_MC 5l_NNU (_( <Equation>_FO )_) ,_, 2p_NNU 5_MC 5l_NNU (_( <Equation>_FO )_) ,_, 2s_MC2 2_MC 2p_NNU 3_MC 6l_NNU (_( <Equation>_FO )_) ,_, 2s2p_FO 4_MC 6l_NNU (_( <Equation>_FO )_) ,_, and_CC 2p_NNU 5_MC 6l_NNU (_( <Equation>_FO )_) ,_, which_DDQ give_VV0 rise_NN1 to_II 1434_MC fine_JJ structural_JJ levels_NN2 ._. 
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<s>
Concurrence_NN1 is_VBZ then_RT defined_VVN as<Equation>_FO &lsqb;_( 47_MC &rsqb;_) ,_, where_CS <Professional_FO Term>_FO are_VBR the_AT eigenvalues_NN2 ,_, in_II Decreasing_JJ order_NN1 ,_, of_IO the_AT non-Hermitian_JJ matrix_NN1 <Professional_FO Term>_FO ,_, with_IW <Equation>_FO ._. 
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<s>
Based_VVN on_II earlier_JJR simulations_NN2 ,_, 9_MC this_DD1 white_JJ neutron_NN1 source_NN1 also_RR exhibits_VVZ a_AT1 stable_JJ spectrum_NN1 ranging_VVG from_II keV_NN1 to_II MeV_NNU independent_NN1 of_IO the_AT c-ray_JJ spectrum_NN1 ,_, while_CS the_AT shape_NN1 and_CC the_AT stable_JJ range_NN1 of_IO the_AT photoneutron_NN1 spectra_NN2 are_VBR determined_VVN by_II the_AT material_NN1 ._. 
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<s>
We_PPIS2 model_VV0 the_AT TGQD_NP1 with_IW two_MC electrons_NN2 ?_? lled_VVD in_II the_AT degenerate_JJ shell_NN1 by_II the_AT Hamiltonian_JJ <Equation>_FO where_RRQ H1_FO (_( H2_FO )_) is_VBZ the_AT single-electron_JJ Hamiltonian_JJ with_IW the_AT formalism_NN1 of_IO Eq_NN1 ._. 
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(_( 1_MC1 )_) and_CC Vint_NP1 (_( |_NULL r2_FO ?_? 
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<s>
Thus_RR ,_, the_AT probability_NN1 density_NN1 p_ZZ1 (_( i_ZZ1 )_) is_VBZ approximated_VVN by_II dividing_VVG the_AT particular_JJ values_NN2 through_II the_AT total_JJ number_NN1 of_IO counts_NN2 and_CC the_AT bin_NN1 size_NN1 ._. 
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<s>
One_MC1 property_NN1 of_IO paramount_JJ importance_NN1 for_IF many_DA2 applications_NN2 is_VBZ the_AT threshold_NN1 to_II material_NN1 failure_NN1 from_II different_JJ applied_JJ stresses_NN2 ._. 
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<s>
Under_II the_AT scattering_NN1 coordinates_NN2 <Equation>_FO with_IW <Equation>_FO <Equation>_FO ._. 
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<s>
The_AT shifts_NN2 in_II the_AT plasmon_NN1 resonances_NN2 with_IW coupling_NN1 have_VH0 been_VBN observed_VVN experimentally_RR ,_, with_IW redshifts_NN2 observed_VVN for_IF end-to-end_JJ coupling_NN1 (_( Haynes_NP1 and_CC Van_NP1 Duyne_NP1 ,_, 2001_MC ,_, Rechberger_NP1 et_RA21 al._RA22 ,_, 2003_MC ,_, Su_NP1 et_RA21 al._RA22 ,_, 2003_MC ,_, Thaxton_NP1 and_CC Mirkin_NP1 ,_, 2005_MC ,_, Jain_NP1 ,_, Eustis_NP1 ,_, and_CC El-Sayed_JJ ,_, 2006_MC ,_, Funston_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) and_CC blueshifts_NN2 for_IF side-by-side_RR coupling_NN1 (_( Rechberger_NP1 et_RA21 al._RA22 ,_, 2003_MC ,_, Jain_NP1 ,_, Eustis_NP1 ,_, and_CC El-Sayed_JJ ,_, 2006_MC ,_, Funston_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) consistent_JJ with_IW our_APPGE previous_JJ analysis_NN1 ._. 
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<s>
Following_VVG Shannon_NP1 (_( 1948_MC )_) ,_, we_PPIS2 first_MD define_VV0 the_AT surprisal_NN1 of_IO the_AT event_NN1 <Equation>_FO distributed_VVN according_II21 to_II22 <Equation>_FO as_CSA <Equation>_FO ,_, often_RR also_RR referred_VVN to_II as_CSA information_NN1 content_NN1 ._. 
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<s>
In_II the_AT outline_NN1 of_IO the_AT pixel-plane_NN1 scrambler_NN1 depicted_VVN in_II Fig._NN1 5_MC ,_, m_ZZ1 is_VBZ 2_MC and_CC it_PPH1 is_VBZ just_RR designed_VVN for_IF one_MC1 channel_NN1 ._. 
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<s>
The_AT idea_NN1 is_VBZ the_AT measurement_NN1 of_IO the_AT time_NNT1 variation_NN1 of_IO the_AT motion_NN1 of_IO the_AT underground_JJ water_NN1 table_NN1 installing_VVG a_AT1 detector_NN1 in_II a_AT1 drainage_NN1 tunnel_NN1 drilled_VVN underneath_II an_AT1 estimated_JJ fault_NN1 plane_NN1 ._. 
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<s>
As_II a_AT1 result_NN1 ,_, the_AT angular_JJ velocity_NN1 profile_NN1 of_IO the_AT MNS_NP1 is_VBZ rearranged_VVN into_II a_AT1 rigidly_RR rotating_VVG state_NN1 ._. 
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The_AT black_JJ (_( red_NN1 )_) line_NN1 is_VBZ the_AT real_JJ (_( imaginary_JJ )_) part_NN1 of_IO band_NN1 energy_NN1 ._. 
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<s>
It_PPH1 relies_VVZ on_II powerful_JJ and_CC cheap_JJ photolithography_NN1 techniques_NN2 to_TO cast_VVI devices_NN2 that_CST control_VV0 the_AT flow_NN1 of_IO material_NN1 ._. 
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Fortran_NP1 programs_NN2 that_CST compute_VV0 polarizabilities_NN2 are_VBR available_JJ on_II a_AT1 web-site_NN1 maintained_VVN by_II the_AT authors_NN2 &lsqb;_( 80_MC &rsqb;_) ._. 
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<s>
Laser_NN1 '_NULL s_ZZ1 normalized_JJ peak_NN1 vector_NN1 Term>_FO versus_II accelerating_JJ time_NNT1 evolution_NN1 during_II laser_NN1 interaction_NN1 with_IW the_AT plasma_NN1 sheath_NN1 ._. 
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<s>
SYM_NP1 low-energy_JJ effective_JJ action_NN1 by_II invoking_VVG the_AT second_MD implicit_JJ on-shell_NN1 N_ZZ1 =_FO 1_MC1 supersymmetry_NN1 ._. 
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<s>
The_AT delay_NN1 time_NNT1 till_II the_AT mergers_NN2 of_IO such_DA double_JJ WD_FU systems_NN2 is_VBZ determined_VVN primarily_RR (_( except_II21 for_II22 delays_NN2 shorter_JJR than_CSN about_II 1_MC1 Gyr_NN1 ,_, see_VV0 below_RL )_) by_II the_AT timescale_NN1 of_IO the_AT orbit_NN1 '_NULL s_ZZ1 decay_VV0 due_II21 to_II22 gravitational_JJ radiation_NN1 ,_, t_ZZ1 ?_FO a4_FO ._. 
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<s>
The_AT written_JJ patterns_NN2 exhibited_VVD better_RRR ordered_VVN structure_NN1 with_IW less_DAR defects_NN2 and_CC a_AT1 crack-free_JJ morphology_NN1 ._. 
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<s>
The_AT functions_NN2 aab_VV0 are_VBR obtained_VVN in_II the_AT electronic_JJ structure_NN1 calculations_NN2 and_CC represented_VVN by_II polynomials_NN2 of_IO internal_JJ molecular_JJ coordinates_NN2 ,_, as_CSA explained_VVN above_RL in_II the_AT Section_NN1 2.2_MC ,_, and_CC the_AT vibrational_JJ matrix_NN1 elements_NN2 are_VBR calculated_VVN similarly_RR to_II those_DD2 of_IO the_AT vibrational_JJ Hamiltonian_JJ and_CC the_AT dipole_NN1 moment_NN1 ._. 
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<s>
In_II this_DD1 paper_NN1 ,_, we_PPIS2 use_VV0 new_JJ model_NN1 molecules_NN2 of_IO simple_JJ but_CCB anisotropic_JJ architecture_NN1 to_TO study_VVI the_AT effect_NN1 of_IO molecular_JJ anisotropy_NN1 on_II the_AT dynamic_JJ and_CC thermodynamic_JJ properties_NN2 of_IO the_AT system_NN1 ._. 
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<s>
Their_APPGE core_NN1 localization_NN1 is_VBZ confirmed_VVN by_II the_AT presence_NN1 of_IO an_AT1 electrostatic_JJ mode_NN1 between_II 25_MC and_CC 30kHz_FO in_II the_AT power_NN1 spectra_NN2 distribution_NN1 of_IO the_AT total_JJ secondary_JJ current_JJ ,_, Itotal_NP1 ,_, recorded_VVN by_II a_AT1 scanning_NN1 HIBP_NN1 &lsqb;_( 37_MC &rsqb;_) ._. 
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<s>
The_AT measurement_NN1 outcome_NN1 is_VBZ a_RR21 bit_RR22 denoted_VVN as_CSA K_ZZ1 ,_, and_CC Bob_NP1 '_NULL s_ZZ1 task_NN1 is_VBZ to_TO guess_VVI K_ZZ1 ,_, given_CS21 that_CS22 he_PPHS1 received_VVD the_AT basis_NN1 choice_NN1 denoted_VVN by_II <Equation>_FO from_II Alice_NP1 ._. 
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<s>
In_II contrast_NN1 ,_, site-selective_JJ absorption_NN1 at_II only_RR one_MC1 fragment_NN1 ,_, as_CSA is_VBZ the_AT case_NN1 in_II CH3I_FO ,_, leaves_VVZ the_AT second_MD partner_NN1 undetected_JJ ._. 
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<s>
For_IF B_ZZ1 we_PPIS2 obtain_VV0 similarly_RR EQUATION>_FO (_( 372_MC )_) and_CC finally_RR for_IF B_ZZ1 EQUATION>_FO (_( 373_MC )_) ._. 
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<s>
This_DD1 combinatorial_JJ problem_NN1 can_VM be_VBI resolved_VVN in_II polynomial_NN1 time_NNT1 with_IW the_AT maximum_JJ matching_JJ algorithm_NN1 (_( see_VV0 Fig._NN1 2_MC )_) ._. 
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If_CS both_DB2 conditions_NN2 are_VBR satisfied_VVN the_AT last_MD term_NN1 in_II Eq_NN1 ._. 
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(_( 22_MC )_) is_VBZ not_XX zero_NN1 ._. 
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<s>
As_II a_AT1 consequence_NN1 ,_, QCD_NP1 is_VBZ a_AT1 strongly_RR coupled_VVN theory_NN1 in_II the_AT regime_NN1 of_IO hadrons_NN2 ,_, which_DDQ can_VM not_XX be_VBI solved_VVN perturbatively_RR ._. 
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<s>
Unless_CS otherwise_RR stated_VVN ,_, the_AT data_NN shown_VVN in_II the_AT figures_NN2 and_CC discussed_VVN in_II the_AT text_NN1 are_VBR taken_VVN in_II magnetic_JJ fields_NN2 sufficiently_RR highto_NN1 suppress_VV0 superconductivity_NN1 ._. 
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<s>
The_AT above_JJ estimate_NN1 is_VBZ valid_JJ if_CS the_AT following_JJ three_MC conditions_NN2 are_VBR satisfied_JJ :_: <Picture>_FO The_AT self-absorption_NN1 is_VBZ negligible_JJ (_( <Equation>_FO )_) ,_, <Picture>_FO the_AT observed_JJ frequency_NN1 is_VBZ above_II the_AT characteristic_JJ synchrotron_NN1 frequency_NN1 <Equation>_FO ,_, and_CC <Picture>_FO the_AT observed_JJ frequency_NN1 is_VBZ below_II the_AT synchrotron_NN1 cooling_VVG frequency_NN1 <Equation>_FO ._. 
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The_AT algorithm_NN1 for_IF the_AT reconstruction_NN1 of_IO BDs_NP1 can_VM be_VBI simply_RR expressed_VVN as_CSA follows_VVZ ._. 
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The_AT P_ZZ1 and_CC S_ZZ1 pulses_NN2 were_VBDR provided_VVN by_II lasers_NN2 with_IW wavelengths_NN2 of_IO 850_MC and_CC 854_MC nm_FU ,_, respectively_RR ,_, while_CS the_AT other_JJ lasers_NN2 indicated_VVN in_II Fig._NN1 39_MC were_VBDR used_VVN for_IF preparation_NN1 and_CC detection_NN1 ._. 
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<s>
The_AT potential_JJ barrier_NN1 calculated_VVN from_II ab_JJ21 initio_JJ22 methods_NN2 was_VBDZ helpful_JJ in_II identifying_VVG and_CC assigning_VVG the_AT E_ND1 symmetry_NN1 species_NN of_IO the_AT parent_NN1 molecule_NN1 and_CC of_IO its_APPGE isotopologues_NN2 ._. 
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A_AT1 detailed_JJ catalog_NN1 of_IO Hadamard_NP1 matrices_NN2 can_VM be_VBI found_VVN online_RR (_( Bruzda_NP1 ,_, Tadej_NP1 ,_, and_CC yczkowski_NN2 ,_, 2015_MC )_) ._. 
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Recently_RR a_AT1 low-energy_JJ effective_JJ model_NN1 has_VHZ been_VBN used_VVN to_II found_VVD the_AT formation_NN1 of_IO bounded_JJ excitonic_JJ states_NN2 with_IW the_AT significant_JJ binding_JJ energy_NN1 of_IO the_AT order_NN1 of_IO 0.5_MC eV_NN1 in_II tBLG_NNU ,_, which_DDQ is_VBZ an_AT1 order_NN1 of_IO magnitude_NN1 larger_JJR than_CSN that_DD1 found_VVD in_II metallic_JJ carbon_NN1 nanotubes_NN2 and_CC which_DDQ is_VBZ explained_VVN by_II the_AT formation_NN1 of_IO ghost_NN1 Fano_NN1 resonance_NN1 peaks_NN2 ._. 
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<s>
The_AT above_JJ equation_NN1 assumes_VVZ that_DD1 detector_NN1 resolution_NN1 effects_NN2 that_CST lead_VV0 to_II a_AT1 smearing_NN1 of_IO the_AT variables_NN2 %_NNU are_VBR negligible_JJ ._. 
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After_CS some_DD algebraic_JJ transformation_NN1 we_PPIS2 finally_RR arrive_VV0 at_II any_DD explicit_JJ dependence_NN1 on_II the_AT states_NN2 a1_FO ,_, ._. 
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<s>
._. By_II Lunar_JJ Laser_NN1 Ranging_VVG experiment_NN1 &lsqb;_( 41_MC &rsqb;_) ,_, we_PPIS2 find_VV0 a_AT1 bound_NN1 for_IF δG_FO :_: Furthermore_RR the_AT effective_JJ variations_NN2 of_IO the_AT gravitational_JJ constant_NN1 should_VM not_XX spoil_VVI the_AT big-bang_JJ nucleosynthesis_NN1 which_DDQ gives_VVZ therefore_RR an_AT1 even_RR stringent_JJ constraint_NN1 on_II the_AT variation_NN1 of_IO the_AT gravitational_JJ constant_NN1 which_DDQ translates_VVZ for_IF our_APPGE parameters_NN2 into_II :_: expending_VVG on_II the_AT model_NN1 used_VVN for_IF nucleosynthesis_NN1 &lsqb;_( 42_MC &rsqb;_) ._. 
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<s>
The_AT typical_JJ phenomenon_NN1 of_IO electrolysis_NN1 is_VBZ the_AT production_NN1 of_IO H2_FO and_CC O2_FO bubbles_NN2 ._. 
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<s>
This_DD1 research_NN1 was_VBDZ financially_RR supported_VVN by_II the_AT National_JJ Natural_JJ Science_NN1 Foundation_NN1 of_IO China_NP1 (_( Grant_NP1 No._NN1 51602352_MC )_) ._. 
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We_PPIS2 shall_VM see_VVI below_RL that_CST its_APPGE performance_NN1 is_VBZ usually_RR marginally_RR better_RRR than_CSN the_AT much_RR simpler_JJR linear_JJ cleansing_NN1 ._. 
</s>
<s>
To_II date_NN1 ,_, the_AT widest_JJT delocalization_NN1 has_VHZ been_VBN obtained_VVN by_II launching_VVG a_AT1 Bose-Einstein_NP1 condensate_NN1 made_VVN with_IW about_RG 105_MC rubidium_NN1 atoms_NN2 in_II a_AT1 10_MC m_NNO high_JJ atomic_JJ fountain_NN1 ;_; see_VV0 Fig._NN1 17_MC ._. 
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<s>
Although_CS the_AT goal_NN1 of_IO this_DD1 section_NN1 is_VBZ to_TO give_VVI a_AT1 summary_NN1 of_IO the_AT relevant_JJ literature_NN1 as_RG neutral_JJ and_CC objective_JJ as_CSA possible_JJ ,_, we_PPIS2 draw_VV0 the_AT reader_NN1 '_NULL s_ZZ1 attention_NN1 to_II some_DD basic_JJ observations_NN2 ._. 
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<s>
Since_CS we_PPIS2 have_VH0 argued_VVN in_II Section_NN1 11_MC and_CC Appendix_NN1 C_NP1 that_DD1 correlation_NN1 coefficients_NN2 are_VBR more_RGR delicate_JJ to_TO interpret_VVI ,_, we_PPIS2 will_VM not_XX use_VVI them_PPHO2 in_II the_AT results_NN2 presented_VVN here_RL ._. 
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<s>
For_IF each_DD1 <Equation>_FO and_CC each_DD1 Borel_NN1 probability_NN1 measure_NN1 <Equation>_FO ,_, if_CS <Equation>_FO for_IF some_DD constant_JJ c_ZZ1 >_FO 0_MC ,_, then_RT a_AT1 Jacobian_JJ J_ZZ1 for_IF f_ZZ1 with_II31 respect_II32 to_II33 is_VBZ given_VVN by_II <Equation>_FO ._. 
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<s>
Anyway_RR ,_, the_AT linear_JJ composition_NN1 dependence_NN1 implies_VVZ that_CST the_AT crystal_NN1 growth_NN1 kinetics_NN1 is_VBZ dominated_VVN by_II intermolecular_JJ secondary_JJ crystal_NN1 nucleation_NN1 of_IO individual_JJ polymers_NN2 ,_, like_II the_AT colligative_JJ properties_NN2 in_II ideal_JJ solutions_NN2 ._. 
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<s>
This_DD1 product_NN1 is_VBZ precisely_RR the_AT probability_NN1 amplitude_NN1 for_IF finding_VVG an_AT1 electron_NN1 in_II the_AT position_NN1 <Equation>_FO at_II the_AT time_NNT1 t_ZZ1 ,_, after_II having_VHG in_RP traduced_VVD an_AT1 electron_NN1 in_II <Equation>_FO at_II an_AT1 earlier_JJR time_NNT1 <Equation>_FO ._. 
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<s>
Soft_JJ matter_NN1 addresses_VVZ issues_NN2 that_CST are_VBR broadly_RR relevant_JJ to_II many_DA2 areas_NN2 of_IO science_NN1 ._. 
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<s>
Unlike_JJ (_( Ga_NP1 ,_, Mn_FO )_) As_CSA ,_, the_AT damping-_NN1 like_II SOT_NN1 was_VBDZ not_XX identified_VVN in_II NiMnSb_NP1 ;_; see_VV0 Figs_NN2 ._. 
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<s>
Bending_VVG can_VM be_VBI introduced_VVN in_II the_AT field_NN1 installation_NN1 process_NN1 ,_, and_CC sharp_JJ bends_NN2 especially_RR can_VM be_VBI det-_JJ rimental_JJ to_II Rayleigh_NP1 scattering-based_JJ system_NN1 performance_NN1 ._. 
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<s>
For_IF a_AT1 given_JJ ,_, the_AT upper_JJ (_( lower_RRR )_) limit_NN1 of_IO each_DD1 band_NN1 is_VBZ for_IF f_ZZ1 DM_NNU =_FO 0_MC .003_MC (_( 0.02_MC )_) ,_, respectively_RR ._. 
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<s>
Therefore_RR by_II the_AT last_MD two_MC displays_NN2 ,_, <equation>Now_FO take_VV0 any_DD non-ull_NN1 s_ZZ1 and_CC assume_VV0 that_CST the_AT identity_NN1 for_IF ak_NN1 (_( s_ZZ1 )_) β_NULL k_ZZ1 has_VHZ been_VBN proved_VVN for_IF all_DB s_ZZ1 with_IW smaller_JJR index_NN1 ._. 
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<s>
It_PPH1 is_VBZ also_RR a_AT1 starting_NN1 point_NN1 for_IF numerical_JJ simulations_NN2 of_IO the_AT integrable_JJ semi-discretizations_NN2 of_IO the_AT continuous_JJ MTM_NP1 system_NN1 (_( 1_MC1 )_) ._. 
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<s>
V.C._NN1 acknowledges_VVZ financial_JJ support_NN1 from_II the_AT INFN_NP1 HPC.HTC_NP1 and_CC NPQCD_NP1 projects_NN2 ._. 
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<s>
The_AT testing_NN1 region_NN1 of_IO a_AT1 pair_NN of_IO d-dimensional_JJ probability_NN1 vectors_NN2 p_ZZ1 and_CC q_ZZ1 (_( see_VV0 Fig._NN1 11_MC )_) ,_, is_VBZ a_AT1 region_NN1 on_II the_AT plane_NN1 that_CST is_VBZ defined_VVN by_II <Equation>_FO where_RRQ the_AT inequalities_NN2 0_MC ≤_FO t_ZZ1 ≤_FO e_ZZ1 are_VBR entry_NN1 wise_JJ ;_; i.e._REX ,_, the_AT components_NN2 of_IO t_ZZ1 are_VBR between_II 0_MC and_CC 1_MC1 ._. 
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<s>
The_AT Fig._NN1 4_MC shows_VVZ the_AT Nyquist_NP1 plot_NN1 of_IO LLTO/LFP-C_NP1 cross_NN1 section_NN1 at_II different_JJ temperatures_NN2 ._. 
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<s>
For_IF a_AT1 hexagonal_JJ lattice_NN1 ,_, the_AT reciprocal_JJ lattice_NN1 vectors_NN2 qj_NNU form_VV0 a_AT1 star_NN1 with_IW sixfold_JJ symmetry_NN1 ._. 
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<s>
The_AT strain_NN1 in_II the_AT sensing_NN1 path_NN1 is_VBZ proportional_JJ to_II the_AT frequency_NN1 shift_NN1 obtained_VVN by_II mixing_VVG the_AT light-wave_JJ signals_NN2 of_IO the_AT two_MC OEOs_NP2 ._. 
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<s>
From_II this_DD1 Corollary_NN1 follows_VVZ ,_, in_RR21 particular_RR22 ,_, that_CST the_AT r_ZZ1 -matrix_JJ implicitly_RR present_JJ in_II the_AT paper_NN1 &lsqb;_( 34_MC &rsqb;_) is_VBZ equivalent_JJ to_II the_AT rational_JJ one_PN1 and_CC the_AT corresponding_JJ Gaudin-type_JJ model_NN1 is_VBZ also_RR equivalent_JJ to_II the_AT standard_JJ rational_JJ Gaudin_NN1 model_NN1 ._. 
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<s>
They_PPHS2 showed_VVD that_CST the_AT I-process_JJ models_NN2 successfully_RR reproduced_VVD the_AT observed_JJ abundance_NN1 patterns_NN2 of_IO 20_MC CEMP-s/r_FU stars_NN2 ._. 
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<s>
Indeed_RR ,_, in_II the_AT ordinary_JJ Einstein–Hilbert_NP1 description_NN1 of_IO wormholes_NN2 ,_, an_AT1 exotic_JJ matter_NN1 component_NN1 is_VBZ needed_VVN in_II order_NN1 the_AT solution_NN1 is_VBZ consistently_RR defined_VVN ,_, and_CC this_DD1 exotic_JJ matter_NN1 is_VBZ called_VVN exotic_JJ because_CS it_PPH1 violates_VVZ the_AT null_JJ energy_NN1 condition_NN1 Tk_NP1 k_ZZ1 ≥_FO 0_MC ,_, where_CS k_ZZ1 is_VBZ an_AT1 arbitrary_JJ null_JJ vector_NN1 ._. 
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At_II the_AT first_MD glance_NN1 ,_, this_DD1 suggests_VVZ that_CST E_ZZ1 ?_NULL is_VBZ a_AT1 polarization_NN1 field_NN1 ._. 
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<s>
The_AT first_MD breakdown_NN1 emission_NN1 is_VBZ located_VVN between_II the_AT two_MC breakdown_NN1 points_NN2 of_IO the_AT second_MD pulse_NN1 ._. 
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<s>
However_RR ,_, such_DA an_AT1 approach_NN1 has_VHZ several_DA2 drawbacks_NN2 ._. 
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<s>
This_DD1 maximally_RR simple_JJ model_NN1 captures_NN2 ,_, we_PPIS2 claim_VV0 ,_, every_AT1 essential_JJ mechanistic_JJ element_NN1 of_IO disequilibria_NN1 (_( free_JJ energy_NN1 )_) conversionsave_VV0 one_MC1 :_: how_RRQ ,_, in_II the_AT molecular_JJ domain_NN1 ,_, does_VDZ the_AT escapement_NN1 mechanism_NN1 actually_RR impose_VV0 the_AT essential_JJ requirement_NN1 that_CST neither_DD1 process_NN1 is_VBZ permitted_VVN to_TO complete_VVI unless_CS both_RR do_VD0 ._. 
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<s>
In_II the_AT past_JJ years_NNT2 ,_, all_DB these_DD2 fundamental_JJ issues_NN2 stimulated_VVD a_AT1 vivid_JJ investigation_NN1 revolving_VVG around_RP a_AT1 plausible_JJ extension_NN1 of_IO Einstein_NP1 '_NULL s_ZZ1 GR_NP1 domain_NN1 ._. 
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<s>
The_AT 2_MC →_NULL 2_MC kinematics_NN2 for_IF hh_NNU production_NN1 links_VVZ the_AT two_MC sensitive_JJ phase_NN1 space_NN1 regions_NN2 mhh_NNU ?_FO 2Mh_FO ,_, mt_NNU to_II the_AT suppressed_JJ threshold_NN1 of_IO the_AT hard_JJ production_NN1 process_NN1 ._. 
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<s>
Each_DD1 pair_NN of_IO coefficients_NN2 <Professional_FO Term>_FO for_IF a_AT1 given_JJ n_ZZ1 satisfy_VV0 certain_JJ properties_NN2 (_( see_VV0 &lsqb;_( 15_MC &rsqb;_) for_IF details_NN2 )_) ._. 
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<s>
For_IF a_AT1 given_JJ Newton_NP1 step_NN1 ,_, the_AT slope_NN1 paramete_NN1 a_AT1 <Professional_FO Terms>_FO is_VBZ fixed_VVN ._. 
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<s>
The_AT fact_NN1 that_CST ,_, at_RR21 least_RR22 on_II a_AT1 very_RG short_JJ timescale_NN1 ,_, the_AT LO-phonon_JJ interaction_NN1 provides_VVZ an_AT1 effective_JJ screening_NN1 against_II blinking_JJ effects_NN2 is_VBZ highly_RR interesting_JJ but_CCB requires_VVZ additional_JJ experimental_JJ work_NN1 to_TO be_VBI performed_VVN as_II a_AT1 function_NN1 of_IO a_AT1 controlled_JJ charge_NN1 environment_NN1 by_II ,_, for_REX21 example_REX22 ,_, embedding_VVG the_AT QDs_NP1 in_II diode_NN1 structures_NN2 ._. 
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<s>
Therefore_RR ,_, only_RR very_RG small_JJ fraction_NN1 of_IO the_AT positive_JJ particles_NN2 can_VM be_VBI captured_VVN into_II the_AT bound_JJ states_NN2 ._. 
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<s>
The_AT measurements_NN2 through_II ionization_NN1 losses_NN2 &lsqb;_( 24_MC &rsqb;_) confirmed_VVD this_DD1 behavior_NN1 ;_; So_RR was_VBDZ about_RG 10_MC cm_NNU for_IF 200_MC GeV_NP1 particles_NN2 ._. 
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<s>
ZD_NP1 They_PPHS2 give_VV0 rise_NN1 to_II two_MC dimensionless_JJ parameters_NN2 for_IF the_AT problem_NN1 :_: Knudsen_NP1 number_NN1 <equation>_FO and_CC mix_VV0 ratio_NN1 of_IO the_AT fuel_NN1 and_CC pusher_NN1 R_ZZ1 ._. 
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<s>
Z_ZZ1 chunk_NN1 <equation>These_FO two_MC dimensionless_JJ parameters_NN2 can_VM be_VBI combined_VVN to_TO remove_VVI R_ZZ1 ,_, DT_NP1 which_DDQ leads_VVZ to_II the_AT dimensionless_JJ quantity_NN1 <equation>_FO ,_, related_VVN to_II (_( though_CS certainly_RR not_XX identical_JJ to_II )_) the_AT Knudsen_NP1 number_NN1 in_II the_AT pusher_NN1 material_NN1 ._. 
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<s>
The_AT effect_NN1 of_IO pileup_NN1 on_II the_AT mass_JJ scale_NN1 and_CC resolution_NN1 is_VBZ clearly_RR visible_JJ ,_, increasingly_RR shifting_VVG the_AT peak_NN1 towards_II much_RR larger_JJR jet_NN1 masses_NN2 and_CC smearing_VVG it_PPH1 ._. 
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<s>
Figure_NN1 2(c)_FO shows_VVZ the_AT spectrum_NN1 at_II a_AT1 point_NN1 in_II space_NN1 and_CC time_NNT1 that_CST was_VBDZ used_VVN to_TO compute_VVI the_AT temperature_NN1 and_CC electron_NN1 number_NN1 density_NN1 ._. 
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<s>
It_PPH1 was_VBDZ observed_VVN that_DD1 temperature_NN1 does_VDZ not_XX influence_VVI the_AT refractive_JJ indices_NN2 and_CC opacities_NN2 significantly_RR ,_, so_CS its_APPGE dependence_NN1 can_VM be_VBI neglected_VVN ._. 
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<s>
To_TO prove_VVI this_DD1 theorem_NN1 ,_, we_PPIS2 will_VM show_VVI that_CST consistently_RR assigning_VVG probabilities_NN2 to_II projective-simulable_JJ measurements_NN2 entails_VVZ a_AT1 probability_NN1 assignment_NN1 consistent_JJ with_IW all_DB POMs_NN2 ._. 
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<s>
The_AT transmission_NN1 spectrum_NN1 is_VBZ proportional_JJ to_II Imax_NP1 <EQUATION>_FO so_CS21 that_CS22 the_AT maxima_NN2 and_CC minima_NN2 in_II the_AT determinant_NN1 δ_FO control_VV0 the_AT respective_JJ minima_NN2 and_CC maxima_NN2 in_II the_AT transmission_NN1 spectrum_NN1 ._. 
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<s>
The_AT growth_NN1 time_NNT1 of_IO the_AT instability_NN1 for_IF =_FO 0.5_MC can_VM therefore_RR never_RR be_VBI shorter_JJR than_CSN one_MC1 rotation_NN1 time_NNT1 ._. 
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<s>
It_PPH1 has_VHZ been_VBN reported_VVN that_CST the_AT F-_JJ ions_NN2 are_VBR prone_JJ to_II specific_JJ adsorption_NN1 on_II the_AT goethite_NN1 surface_NN1 ,_, due_II21 to_II22 the_AT similar_JJ sizes_NN2 of_IO the_AT hydroxyl_NN1 and_CC the_AT fluoride_NN1 ion_NN1 ._. 
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<s>
The_AT planar_JJ average_NN1 of_IO the_AT potential_NN1 on_II the_AT right-hand_JJ side_NN1 of_IO the_AT above_JJ equation_NN1 can_VM then_RT be_VBI approximated_VVN by_II the_AT one-dimensional_JJ potential_NN1 of_IO a_AT1 planar-averaged_JJ charge_NN1 distribution_NN1 ,_, namely_REX ,_, <equation>_FO ,_, where_CS q_ZZ1 is_VBZ the_AT total_JJ charge_NN1 of_IO the_AT quantum-mechanical_JJ system_NN1 and_CC we_PPIS2 have_VH0 used_VVN the_AT classical_JJ electrostatics_NN2 result_VV0 for_IF the_AT potential_NN1 of_IO a_AT1 planar_JJ charge_NN1 distribution_NN1 ._. 
</s>
<s>
Our_APPGE computations_NN2 are_VBR performed_VVN using_VVG resources_NN2 of_IO the_AT National_JJ Energy_NN1 Research_NN1 Scientific_JJ Computing_NN1 Center_NN1 (_( NERSC_NP1 )_) ,_, a_AT1 US_NP1 Department_NN1 of_IO Energy_NN1 Office_NN1 of_IO Science_NN1 User_NN1 Facility_NN1 operated_VVN under_II Contract_NN1 No_UH ._. 
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<s>
DE-AC02-05CH11231_NP1 ._. 
</s>
<s>
The_AT shape_NN1 of_IO this_DD1 break_NN1 and_CC the_AT suppression_NN1 measured_VVN by_II the_AT different_JJ experiments_NN2 vary_VV0 ,_, indicating_VVG underestimated_JJ systematic_JJ errors_NN2 ._. 
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<s>
Y._NP1 Chen_NP1 ,_, C._NP1 Zhao_NP1 ,_, S._NP1 Chen_NP1 ,_, J._NP1 Du_FW ,_, P._NP1 Tang_NN1 ,_, G._NP1 Jiang_NP1 ,_, H._NP1 Zhang_NP1 ,_, S._NP1 Wen_NP1 ,_, and_CC D._NP1 Tang_NN1 ,_, IEEE_NP1 J._NP1 Sel_NP1 ._. 
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<s>
Both_DB2 cases_NN2 are_VBR excluded_VVN from_II our_APPGE analysis_NN1 ._. 
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<s>
In_RR21 general_RR22 ,_, the_AT term_NN1 quark_NN1 model_NN1 refers_VVZ to_II a_AT1 class_NN1 of_IO models_NN2 ,_, which_DDQ describe_VV0 the_AT properties_NN2 of_IO hadrons_NN2 by_II effective_JJ degrees_NN2 of_IO freedom_NN1 carried_VVN by_II valence_NN1 quarks_NN2 ._. 
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<s>
If_CS the_AT full_JJ sequence_NN1 <Professional_FO Term>_FO n_ZZ1 N_ZZ1 failed_VVD to_TO converge_VVI uniformly_RR on_II compact_JJ subsets_NN2 of_IO <Professional_FO Term>_FO to_II the_AT law_NN1 of_IO Z_ZZ1 ,_, then_RT there_EX would_VM be_VBI a_AT1 sub-sequence_NN1 bounded_VVN away_II21 from_II22 the_AT law_NN1 of_IO Z._NP1 But_CCB by_II Prokhorov_NP1 '_NULL s_ZZ1 theorem_NN1 and_CC the_AT argument_NN1 above_RL ,_, there_EX would_VM be_VBI a_AT1 subsequent_JJ converging_JJ in_II law_NN1 to_II Z_ZZ1 ,_, a_AT1 contradiction_NN1 ._. 
</s>
<s>
Our_APPGE testing_NN1 framework_NN1 goes_VVZ as_CSA follows_VVZ ._. 
</s>
<s>
S._NP1 Nie_NP1 ,_, X._NP1 Wang_NP1 ,_, H._NP1 Park_NN1 ,_, R._NP1 Clinite_NN1 ,_, and_CC J._NP1 Cao_NP1 ,_, "_" Measurement_NN1 of_IO the_AT electronic_JJ Gruneisenconstant_NN1 using_VVG femtosecond_NN1 electron_NN1 diffraction_NN1 ,_, "_" Phys_NP1 ._. 
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<s>
Many_DA2 applications_NN2 involving_VVG high_JJ peak_NN1 power_NN1 like_II high-energy_JJ particle_NN1 acceleration_NN1 or_CC transmutation_NN1 of_IO nuclear_JJ waste_NN1 crucially_RR need_VV0 average_JJ power_NN1 ._. 
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<s>
The_AT thermionic_JJ emission_NN1 provides_VVZ access_NN1 to_II absolute_JJ ionic_JJ work_NN1 functions_NN2 ._. 
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<s>
So_RR long_RR as_CSA <Equation>_FO ,_, such<Equation>_FO entirely_RR negligible_JJ ._. 
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<s>
In_II this_DD1 work_NN1 ,_, new_JJ injections_NN2 of_IO cryogenic_JJ pellets_NN2 into_II onand_NN1 off-axis_NN1 ECRH_NN1 plasmas_NN2 having_VHG line-averaged_JJ densities_NN2 between_II 3_MC and_CC 6×1018_FO m3_FO as_II31 well_II32 as_II33 of_IO 0.66_MC and_CC 0.77mm_NNU diameter_NN1 pellets_NN2 into_II NBI_JJ heated_JJ plasmas_NN2 are_VBR performed_VVN to_TO expand_VVI the_AT previous_JJ database_NN1 &lsqb;_( 17_MC &rsqb;_) ._. 
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<s>
We_PPIS2 are_VBR grateful_JJ to_II David_NP1 Branch_NN1 ,_, Avishay_NP1 Gal-Yam_NP1 ,_, Yael_NP1 Hillman_NP1 ,_, Boaz_NP1 Katz_NP1 ,_, Doron_NP1 Kushnir_NP1 ,_, Dan_NP1 Maoz_NP1 ,_, Adam_NP1 Riess_NP1 ,_, Ofer_NP1 Yaron_NP1 ,_, and_CC in_RR21 particular_RR22 to_II Noam_NP1 Soker_NP1 ,_, for_IF very_RG fruitful_JJ discussions_NN2 ._. 
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<s>
This_DD1 is_VBZ contrary_II21 to_II22 the_AT diffusion_NN1 process_NN1 of_IO Sr_FO and_CC Zr_NP1 in_II the_AT formation_NN1 of_IO SrZrO3_FO phase_NN1 ,_, which_DDQ is_VBZ considered_VVN dominated_VVN by_II grain_NN1 boundary_NN1 diffusion_NN1 processes_NN2 &lsqb;_( 37,38_MC &rsqb;_) ._. 
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<s>
Similarly_RR ,_, the_AT complex_JJ conjugate_NN1 ck_NNU (_( ri_NN2 )_) is_VBZ written_VVN as_II a_AT1 sum_NN1 over_II retarded_JJ Feynman_NP1 paths_NN2 ?_NULL starting_VVG at_II rk_NNU and_CC ending_VVG at_II ck_NNU ,_, with_IW weight_NN1 W_ZZ1 (_( )_) ._. 
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<s>
Particles_NN2 accelerated_VVD at_II the_AT termination_NN1 surface_NN1 of_IO the_AT pulsar_NN1 wind_NN1 may_VM undergo_VVI reacceleration_NN1 in_II the_AT converging_JJ flow_NN1 formed_VVN by_II the_AT outflow_NN1 from_II the_AT wind_NN1 termination_NN1 shock_NN1 and_CC the_AT inflow_NN1 from_II the_AT bow_NN1 shock_NN1 ,_, leading_VVG to_II a_AT1 very_RG hard_JJ energy_NN1 spectra_NN2 ,_, β_NULL 1_MC1 ._. 
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2_MC ._. 
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<s>
If_CS the_AT new_JJ scalar_JJ is_VBZ light_JJ ,_, mh_NNU 63_MC GeV_NP1 ,_, and_CC the_AT heavier_JJR scalar_JJ ,_, H0_FO ,_, is_VBZ the_AT observed_JJ Higgs_NP1 boson_NN1 ,_, the_AT model_NN1 predicts_VVZ Higgs-to-Higgs_NP1 decays_VVZ with_IW the_AT partial_JJ width<equation>_FO in_II31 terms_II32 of_II33 the_AT physical_JJ triple-Higgs_NP1 coupling_NN1 Hhh_NP1 ,_, which_DDQ can_VM be_VBI extracted_VVN from_II the_AT potential_NN1 &lsqb;_( 94_MC &rsqb;_) ._. 
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<s>
This_DD1 theoretical_JJ activity_NN1 encouraged_VVD experimental_JJ developments_NN2 on_II molecular_JJ alignment_NN1 for_IF which_DDQ the_AT first_MD direct_JJ evidences_NN2 were_VBDR reported_VVN in_II the_AT late_JJ 1990s_MC2 ._. 
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<s>
The_AT values_NN2 of_IO Ye_PPY within_II the_AT dynamical_JJ ejecta_NN1 vary_VV0 widely_RR ._. 
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<s>
The_AT water_NN1 oxidation_NN1 reaction_NN1 takes_VVZ place_NN1 in_II the_AT presence_NN1 of_IO the_AT electrochemical_JJ double_JJ layer_NN1 developed_VVN together_RL by_II the_AT charged_JJ surface_NN1 species_NN at_II the_AT hematite_NN1 surface_NN1 ,_, oriented_VVD dipoles_NN2 of_IO water_NN1 molecules_NN2 near_II the_AT interface_NN1 ,_, and_CC the_AT counter_NN1 and_CC co-ions_NN2 in_II the_AT water_NN1 ._. 
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<s>
Then_RT ,_, for_IF any_DD <Equation>_FO fixed_JJ ,_, and_CC j_ZZ1 ,_, k_ZZ1 and_CC m_ZZ1 N_ZZ1 such_CS21 that_CS22 <Equation>_FO ,_, there_EX exists_VVZ a_AT1 constant_JJ <Equation>_FO ,_, depending_VVG only_RR on_II j_ZZ1 ,_, k_ZZ1 and_CC m_ZZ1 ,_, such_CS21 that_CS22 the_AT following_JJ bound_NN1 ._. 
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<s>
<Equation>_FO (_( 4.25_MC )_) holds_VVZ uniformly_RR over_II <Equation>_FO such_CS21 that_CS22 <Equation>_FO ,_, where_CS <Equation>_FO ._. 
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<s>
By_II nonlinear_JJ numerical_JJ simulations_NN2 with_IW the_AT Pencil_NN1 code_NN1 the_AT mean_JJ electromotive_JJ force_NN1 in_II plane_NN1 Couette_NN1 flows_NN2 of_IO a_AT1 nonrotating_JJ conducting_NN1 fluid_NN1 under_II the_AT influence_NN1 of_IO a_AT1 large-scale_JJ magnetic_JJ field_NN1 on_II driven_JJ turbulence_NN1 has_VHZ been_VBN calculated_VVN ._. 
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<s>
The_AT coordinates_NN2 of_IO the_AT characteristic_JJ minimum_NN1 of_IO the_AT lines_NN2 of_IO neutral_JJ stability_NN1 for_IF all_DB m_ZZ1 and_CC for_IF small_JJ magnetic_JJ Prandtl_NP1 numbers_NN2 are_VBR given_VVN in_II Fig._NN1 24_MC ._. 
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<s>
Wiseman_NP1 and_CC collaborators_NN2 &lsqb;_( 298–306_MCMC &rsqb;_) have_VH0 shown_VVN that_CST by_II using_VVG an_AT1 adaptive_JJ measurement_NN1 it_PPH1 is_VBZ possible_JJ to_TO realize_VVI a_AT1 measurement_NN1 of_IO phase_NN1 that_CST is_VBZ very_RG close_JJ to_II the_AT Heisenberg_NP1 limit_NN1 &lsqb;_( 296_MC ,_, 297_MC ,_, 307_MC ,_, 308_MC &rsqb;_) ._. 
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The_AT 0–0_MCMC and_CC 1–1_MCMC bands_NN2 of_IO the_AT F_ZZ1 -X_ZZ1 transition_NN1 were_VBDR reported_VVN by_II Edvinsson_NP1 et_RA21 al_RA22 ._. 
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&lsqb;_( 9_MC &rsqb;_) The_AT assignment_NN1 of_IO these_DD2 bands_NN2 to_II a_AT1 common_JJ electronic_JJ transition_NN1 was_VBDZ tentative_JJ due_II21 to_II22 the_AT anomalously_RR small_JJ excited_JJ state_NN1 vibrational_JJ interval_NN1 implied_VVN by_II the_AT 1–1_MCMC assignment_NN1 ._. 
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<s>
Let_VV0 d_ZZ1 be_VBI a_AT1 visual_JJ metric_JJ on_II S2_FO for_IF f_ZZ1 with_IW expansion_NN1 factor_NN1 >_FO 1_MC1 ._. 
</s>
<s>
In_II many_DA2 explicit_JJ extractors_NN2 the_AT seed_NN1 has_VHZ a_AT1 length_NN1 logarithmic_JJ in_II the_AT size_NN1 of_IO the_AT input_NN1 string_NN1 ._. 
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<s>
We_PPIS2 note_VV0 that_CST we_PPIS2 have_VH0 not_XX expanded_VVN the_AT quantum_NN1 mechanical_JJ terms_NN2 expressed_VVN with_IW harmonic_JJ functions_NN2 though_CS their_APPGE coefficients_NN2 related_VVN to_II electromagnetic_JJ fields_NN2 are_VBR linearized_VVN ._. 
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<s>
Many_DA2 methods_NN2 have_VH0 been_VBN proposed_VVN to_TO analyze_VVI and_CC predict_VVI house_NN1 price_NN1 ,_, for_REX21 example_REX22 ,_, the_AT hedonic_JJ house_NN1 price_NN1 model_NN1 &lsqb;_( 396_MC &rsqb;_) ._. 
</s>
<s>
In_II the_AT atomic_JJ limit_NN1 ,_, the_AT d_ZZ1 orbital_JJ has_VHZ a_AT1 higher_JJR energy_NN1 than_CSN the_AT p_ZZ1 orbital_JJ ,_, and_CC the_AT band_NN1 structure_NN1 in_II Fig._NN1 2(c)_FO satisfies_VVZ the_AT band_NN1 inversion_NN1 pattern_NN1 required_VVN for_IF the_AT CDSM_NP1 phase_NN1 ._. 
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<s>
This_DD1 prediction_NN1 is_VBZ supported_VVN by_II all_DB transportation_NN1 systems_NN2 (_( and_CC animal_NN1 designs_NN2 )_) ,_, which_DDQ have_VH0 evolved_VVN such_CS21 that_CS22 larger_JJR fuel_NN1 loads_NN2 belong_VV0 to_II larger_JJR vehicles_NN2 ._. 
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<s>
In_RR21 general_RR22 ,_, coated_VVN and_CC non-coated_JJ particles_NN2 did_VDD not_XX change_VVI the_AT cell_NN1 growth_NN1 process_NN1 and_CC did_VDD not_XX result_VVI in_II a_AT1 significant_JJ reduction_NN1 in_II cell_NN1 viability_NN1 ._. 
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<s>
Lines_NN2 separated_VVN less_DAR than_CSN 5_MC kHz_NNU are_VBR not_XX resolved_VVN ._. 
</s>
<s>
The_AT next_MD step_NN1 is_VBZ to_TO rigorously_RR solve_VVI the_AT modified_JJ Makeenko–Migdal_JJ equations_NN2 ,_, and_CC then_RT write_VV0 the_AT solution_NN1 as_II an_AT1 absolutely_RR convergent_JJ sum_NN1 indexed_VVN by_II trajectories_NN2 of_IO strings_NN2 in_II a_AT1 discrete_JJ string_NN1 theory_NN1 ._. 
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<s>
The_AT three_MC terms_NN2 in_II Eq_NN1 ._. 
</s>
<s>
(_( 66_MC )_) for_IF B2_FO have_VH0 fundamentally_RR different_JJ time_NNT1 dependencies_NN2 as_CSA Ku_NP1 goes_VVZ to_II infinity_NN1 and_CC Ks_NP2 goes_VVZ to_TO zero_VVI exponen_JJ tially_RR ._. 
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<s>
Since_CS <Professional_FO Term>_FO ,_, g_ZZ1 is_VBZ positive_JJ on_II some_DD interval_NN1 or_CC negative_JJ for_IF all_DB <Professional_FO Term>_FO ,_, and_CC this_DD1 depends_VVZ on_II the_AT sign_NN1 of_IO its_APPGE maximum_NN1 ._. 
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<s>
Indeed_RR ,_, after_CS the_AT values_NN2 of_IO energy_NN1 levels_NN2 are_VBR optimized_VVN ,_, one_PN1 would_VM expect_VVI the_AT values_NN2 of_IO <Professional_FO Term>_FO to_TO be_VBI randomly_RR distributed_VVN in_II the_AT linelist_NN1 ._. 
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<s>
Examples_NN2 of_IO fast_JJ 3He_FO ion_NN1 guiding-center_NN1 orbits_NN2 that_CST pass_VV0 through_II the_AT midplane_NN1 edge_NN1 of_IO the_AT plasma_NN1 on_II the_AT low_JJ field_NN1 side_NN1 are_VBR also_RR shown_VVN ._. 
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<s>
Another_DD1 tempting_JJ definition_NN1 would_VM be_VBI to_TO take_VVI the_AT convex_JJ hull_NN1 of_IO all_DB the_AT particles_NN2 constituting_VVG the_AT jet_NN1 ._. 
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<s>
The_AT HFB-based_JJ configuration-mixing_JJ calculations_NN2 indicate_VV0 an_AT1 oblate_NN1 rotational_JJ ground-state_JJ band_NN1 in_II Se_NP1 &lsqb;_( 2008Lj01_FO &rsqb;_) ._. 
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<s>
In_II that_DD1 case_NN1 ,_, the_AT production_NN1 mechanism_NN1 is_VBZ dubbed_VVN as_CSA reannihilation_NN1 &lsqb;_( 74_MC ,_, 75_MC &rsqb;_) ._. 
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<s>
Equation_NN1 (_( 12_MC )_) is_VBZ more_RGR general_JJ since_CS there_EX is_VBZ no_AT assumption_NN1 about_II the_AT shape_NN1 other_II21 than_II22 it_PPH1 is_VBZ much_RR smaller_JJR than_CSN the_AT wavelength_NN1 of_IO light_NN1 ._. 
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<s>
To_TO compute_VVI more_RGR general_JJ quantities_NN2 ,_, the_AT effects_NN2 of_IO coupling_VVG the_AT background_NN1 fields_NN2 to_II the_AT sea_NN1 quarks_NN2 need_VV0 to_TO be_VBI included_VVN ._. 
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<s>
In_II &lsqb;_( 7_MC &rsqb;_) ,_, another_DD1 step_NN1 further_RRR has_VHZ been_VBN introduced_VVN that_CST could_VM be_VBI called_VVN '_NULL Level_NN1 2.5_MC in_II time_NNT1 '_NULL :_: this_DD1 name_NN1 will_VM become_VVI clear_JJ below_RL with_IW equation_NN1 (_( 5_MC )_) ,_, where_CS the_AT rate_NN1 function_NN1 contains_VVZ an_AT1 integral_JJ over_II time_NNT1 of_IO ._. 
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<s>
These_DD2 methods_NN2 have_VH0 achieved_VVN a_AT1 certain_JJ degree_NN1 of_IO dendritic_JJ inhibition_NN1 ,_, but_CCB are_VBR still_RR far_RR from_II the_AT standards_NN2 of_IO the_AT commercial_JJ applications_NN2 ._. 
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<s>
Tezuka_NN1 ,_, Kanno_NP1 ,_, and_CC Bunsen_NP1 (_( 2016_MC )_) numerically_RR analyzed_VVD the_AT performance_NN1 of_IO Ikeda-like_JJ bandpass_NN1 OEOs_NN2 with_IW mutual_JJ coupling_NN1 for_IF the_AT Santa_NP1 Fe_NP1 chaotic_JJ time-series_JJ prediction_NN1 task_NN1 ,_, and_CC they_PPHS2 showed_VVD that_CST this_DD1 mutual_JJ coupling_NN1 permitted_VVD one_PN1 to_TO slow_VVI down_RP the_AT modulation_NN1 speed_NN1 of_IO the_AT mask_NN1 signal_NN1 at_II no_AT cost_NN1 for_IF computational_JJ performance_NN1 ._. 
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<s>
At_II room_NN1 temperature_NN1 ,_, a_AT1 sharp_JJ and_CC narrow_JJ interface_NN1 region_NN1 indicates_VVZ that_CST there_EX is_VBZ no_AT accumulation_NN1 of_IO ions_NN2 in_II the_AT interface_NN1 ._. 
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<s>
As_CSA discussed_VVN in_II the_AT Introduction_NN1 ,_, the_AT structure_NN1 of_IO resource_NN1 theories_NN2 goes_VVZ far_RR beyond_II quantum_NN1 physics_NN1 ._. 
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<s>
That_REX21 is_REX22 ,_, any_DD Shannon_NP1 entropy_NN1 uncertainty_NN1 relation_NN1 of_IO the_AT form_NN1 (_( 157_MC )_) implies_VVZ a_AT1 corresponding_JJ uncertainty_NN1 relation_NN1 in_II31 terms_II32 of_II33 the_AT conditional_JJ Shannon_NP1 entropy_NN1 of_IO the_AT form_NN1 (_( 160_MC )_) ._. 
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<s>
O.P._NN1 and_CC D.W.S._NP1 are_VBR collaborators_NN2 in_II the_AT SBN_NP1 program_NN1 ._. 
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<s>
But_CCB we_PPIS2 emphasize_VV0 that_CST these_DD2 bounds_NN2 are_VBR arguably_RR less_RGR model_JJ dependent_JJ than_CSN they_PPHS2 seem_VV0 ,_, because_CS in_II models_NN2 containing_VVG the_AT helicity-0_MC mode_NN1 ,_, this_DD1 mode_NN1 is_VBZ naturally_RR Galileon_NP1 like_VV0 ,_, as_CSA in_II the_AT Stückelberg_NP1 decomposition_NN1 two_MC indices_NN2 of_IO the_AT metric_JJ become_VV0 two_MC partial_JJ derivatives_NN2 which_DDQ respect_VV0 the_AT Galileon_NN1 symmetry_NN1 &lsqb;_( see_VV0 Eq_NN1 ._. 
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<s>
(_( 19_MC )_) and_CC Sec_NNU ._. 
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<s>
II.D.3_FO &rsqb;_) ._. 
</s>
<s>
Adapted_VVN with_IW permission_NN1 from_II J._NP1 Wang_NP1 et_RA21 al._RA22 ,_, Nanoscale_NP1 9(28)_FO ,_, 9787–9791_MCMC (_( 2017_MC )_) ._. 
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<s>
Also_RR ,_, the_AT results_NN2 of_IO the_AT inductionless_JJ approximation_NN1 basically_RR differ_VV0 from_II those_DD2 of_IO the_AT inviscid_JJ approximation_NN1 ._. 
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<s>
It_PPH1 may_VM be_VBI that_CST these_DD2 bands_NN2 belonged_VVD to_II a_AT1 common_JJ reaction_NN1 intermediate_JJ with_IW a_AT1 carboxyl_NN1 (_( COOH_NP1 )_) and_CC bidentate_VV0 COO_NN1 species_NN ,_, similar_JJ to_II suggestions_NN2 in_II Ref_NN1 ._. 
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<s>
On_II the_AT other_JJ hand_NN1 ,_, no_AT radical_JJ character_NN1 was_VBDZ found_VVN in_II the_AT phenacene_NN1 series_NN they_PPHS2 studied_VVD (_( up_RG21 to_RG22 10_MC rings_NN2 )_) ._. 
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<s>
TABLE_NN1 I._NP1 International_JJ Union_NN1 of_IO Pure_JJ and_CC Applied_JJ Chemistry_NN1 name_NN1 ,_, chemical_JJ structure_NN1 ,_, and_CC abbreviation_NN1 of_IO the_AT materials_NN2 used_VVN in_II this_DD1 work_NN1 ._. 
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<s>
It_PPH1 is_VBZ now_RT a_AT1 well-established_JJ research_NN1 field_NN1 ,_, which_DDQ offers_VVZ formidable_JJ tools_NN2 for_IF the_AT investigation_NN1 of_IO fundamental_JJ electronic_JJ processes_NN2 (_( Calegari_NP1 et_RA21 al._RA22 ,_, 2016_MC )_) ._. 
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<s>
This_DD1 endoscope_NN1 is_VBZ configured_VVN with_IW transparent_JJ bioelectronics_NN2 ,_, which_DDQ provides_VVZ impedance-_JJ and_CC pH-based_JJ sensing_NN1 ,_, in_II combination_NN1 with_IW radio_NN1 frequency_NN1 (_( RF_NP1 )_) ablation_NN1 therapy_NN1 to_TO facilitate_VVI the_AT characterization_NN1 and_CC removal_NN1 of_IO colon_NN1 cancers_NN2 &lsqb;_( Fig._NN1 13(a)_FO &rsqb;_) ._. 
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<s>
As_CSA in_II (_( 1.4_MC )_) ,_, let_VV0 <Professional_FO Term>_FO be_VBI the_AT nth_MD Fourier_NP1 coefficient_NN1 of_IO the_AT Eisenstein_NP1 series_NN of_IO the_AT form_NN1 Q._NN1 However_RR ,_, even_RR a_AT1 cursory_JJ examination_NN1 suggests_VVZ that_CST there_EX are_VBR many_DA2 other_JJ properties_NN2 ,_, aside_II21 from_II22 low_JJ elastic_JJ moduli_NN2 ,_, that_CST are_VBR also_RR caused_VVN by_II the_AT large_JJ size_NN1 of_IO the_AT component_NN1 building_NN1 blocks_NN2 and_CC that_DD1 would_VM make_VVI such_DA materials_NN2 distinctive_JJ ._. 
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<s>
FTO/GO/WO3_NP1 had_VHD a_AT1 bigger_JJR value_NN1 than_CSN the_AT others_NN2 in_II the_AT visible_JJ region_NN1 ._. 
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<s>
The_AT irradiation_NN1 condition_NN1 in_II (_( a_ZZ1 )_) –_- (_( c_ZZ1 )_) correspond_VV0 to_II the_AT case_NN1 (_( b_ZZ1 )_) of_IO figure_NN1 6_MC ,_, and_CC (_( d_ZZ1 )_) ,_, (_( e_ZZ1 )_) and_CC (_( f_ZZ1 )_) correspond_VV0 to_II the_AT case_NN1 (_( d_ZZ1 )_) of_IO figure_NN1 6_MC ,_, respectively_RR ._. 
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<s>
The_AT largest_JJT term_NN1 in_II the_AT Lorentz_NP1 force_NN1 is<Equation>_FO (_( 79_MC )_) ,_, which_DDQ predicts_VVZ an_AT1 exponentially_RR large_JJ force_NN1 as_CSA t_ZZ1 !_! 
</s>
<s>
For_IF the_AT purposes_NN2 of_IO this_DD1 illustration_NN1 ,_, is_VBZ chosen_VVN so_CS21 that_CS22 the_AT proton-N_JJ (_( 1535_MC )_) 1/2_MF splitting_NN1 associates_VVZ the_AT N_ZZ1 (_( 1535_MC )_) 1/2_MF state_VV0 with_IW the_AT (_( 70_MC ,_, 1_MC1 )_) super_JJ multiple_NN1 ,_, as_CSA suggested_VVN in_II quantum_NN1 mechanics_NN2 by_II its_APPGE spin_NN1 and_CC parity_NN1 ._. 
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<s>
The_AT stability_NN1 of_IO these_DD2 trace_VV0 compounds_NN2 is_VBZ studied_VVN from_II 0_MC h_ZZ1 up_RG21 to_RG22 24_MC h_ZZ1 and_CC the_AT experiment_NN1 was_VBDZ repeated_VVN twice_RR ,_, d1_FO and_CC d2_FO are_VBR the_AT replica_NN1 names_NN2 ._. 
</s>
<s>
To_TO sustain_VVI a_AT1 rigid_JJ body_NN1 rotation_NN1 in_II an_AT1 axisymmetric_JJ configuration_NN1 such_II21 as_II22 the_AT one_PN1 depicted_VVD in_II Fig.3_FO ,_, the_AT power_NN1 deposition_NN1 profile_NN1 <Professional_FO Term>_FO must_VM follow_VVI the_AT scaling_NN1 of_IO the_AT ratio_NN1 <Professional_FO Term>_FO as_II a_AT1 function_NN1 of_IO W._NP1 Note_VV0 that_CST this_DD1 analysis_NN1 of_IO the_AT angular_JJ momentum_NN1 generation_NN1 process_NN1 is_VBZ simpler_JJR than_CSN the_AT wave_NN1 driven_VVN current_JJ generation_NN1 because_CS the_AT relaxation_NN1 does_VDZ not_XX involve_VVI a_AT1 kinetic_JJ description_NN1 of_IO the_AT re_II sonant_NN1 particles.33_FO ,_, 34_MC Here_RL ,_, the_AT short_JJ circuiting_NN1 of_IO the_AT wave_NN1 driven_JJ charge_NN1 separation_NN1 is_VBZ ensured_VVN by_II a_AT1 bulk_NN1 inertial_JJ ionic_JJ current_JJ Eq_NN1 ._. 
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<s>
(_( 37_MC )_) even_CS21 if_CS22 the_AT wave_NN1 power_NN1 is_VBZ absorbed_VVN by_II a_AT1 minority_NN1 population_NN1 ._. 
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<s>
Interactions_NN2 break_VV0 some_DD of_IO these_DD2 symmetries_NN2 ,_, and_CC depending_II21 on_II22 the_AT filling_NN1 factor_NN1 (_( defined_JJ modulo_NN1 4_MC ,_, which_DDQ corresponds_VVZ to_II the_AT filling_NN1 of_IO all_DB four_MC valleys_NN2 in_II a_AT1 given_JJ Landau_NP1 level_NN1 )_) ,_, the_AT residual_JJ symmetries_NN2 suffice_VV0 to_TO protect_VVI some_DD or_CC all_DB of_IO the_AT gapless_JJ domain_NN1 wall_NN1 modes_NN2 ._. 
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<s>
However_RR ,_, this_DD1 implies_VVZ a_AT1 strong_JJ requirement_NN1 for_IF single_JJ shot_NN1 measurements_NN2 by_II planar_JJ LIF_NN1 ._. 
</s>
<s>
The_AT simplified_JJ model_NN1 is_VBZ described_VVN in_II Sec_NNU ._. 
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<s>
I._NP1 An_AT1 example_NN1 of_IO the_AT performance_NN1 of_IO AAFT_NN1 surrogates_NN2 when_RRQ the_AT data_NN are_VBR subject_II21 to_II22 an_AT1 invertible_JJ (_( (_( sn_NNU )_) 3_MC )_) vs._II a_AT1 non-invertible_JJ (_( (_( sn_NNU )_) 2_MC )_) transformation_NN1 is_VBZ given_VVN in_II Section_NN1 9.1.1_MC ._. 
</s>
<s>
The_AT detector_NN1 efficiency_NN1 is_VBZ close_JJ to_II 100%_NNU for_IF photons_NN2 with_IW energies_NN2 (_( 4_MC ÷_NULL 8_MC )_) keV_NN1 and_CC it_PPH1 reduces_VVZ with_IW further_JJR increase_NN1 of_IO photon_NN1 energy_NN1 ._. 
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<s>
There_EX are_VBR opportunities_NN2 to_TO explore_VVI existing_JJ and_CC emerging_JJ quantum_NN1 sensing_NN1 approaches_VVZ to_TO improve_VVI distributed_JJ sensing_NN1 platforms_NN2 beyond_II existing_JJ state-of-the-art_JJ systems_NN2 ._. 
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We_PPIS2 are_VBR grateful_JJ to_II the_AT Mainz_NP1 Institute_NN1 for_IF Theoretical_JJ Physics_NN1 for_IF its_APPGE hospitality_NN1 ._. 
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<s>
Since_CS DMAC-ortho-BN_NP1 ,_, similarly_RR to_II the_AT other_JJ isomers_NN2 ,_, shows_VVZ a_AT1 redshift_NN1 of_IO the_AT emission_NN1 with_IW increasing_JJ polarity_NN1 ,_, it_PPH1 should_VM have_VHI a_AT1 smaller_JJR ST_NP1 in_II CHCl3_FO and_CC is_VBZ expected_VVN to_TO show_VVI a_AT1 more_RGR pronounced_JJ delayed_JJ ?_? uorescence_NN1 ._. 
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<s>
For_IF the_AT maps_NN2 described_VVN in_II this_DD1 paper_NN1 ,_, a_AT1 fixed-point_JJ attractor_NN1 phase_NN1 with_IW transit-time_JJ s_ZZ1 ?_FO Np_NP1 (_( Mp_NN1 )_) represents_VVZ a_AT1 two-surface_NN1 (_( single-surface_NN1 )_) single-resonance_JJ mode_NN1 ,_, as_CSA each_DD1 impact_NN1 occurs_VVZ periodically_RR at_II half_NN1 (_( full_JJ )_) integer_NN1 multiples_NN2 of_IO the_AT RF_NP1 cycle_NN1 ._. 
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It_PPH1 is_VBZ then_RT clear_VV0 that_CST the_AT set_NN1 gn_NNU (_( E_ZZ1 )_) is_VBZ also_RR Borel_NP1 ._. 
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<s>
This_DD1 section_NN1 is_VBZ divided_VVN into_II two_MC parts_NN2 :_: electronic_JJ and_CC optical_JJ properties_NN2 ._. 
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<s>
This_DD1 was_VBDZ done_VDN expanding_JJ the_AT time-dependent_JJ perturbation_NN1 theory_NN1 amplitude_NN1 Eq_NN1 ._. 
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<s>
(_( 26_MC )_) in_II powers_NN2 of_IO the_AT eikonal_JJ phase_NN1 shift_VV0 to_TO get_VVI a_AT1 series_NN of_IO partial_JJ amplitudes_NN2 ._. 
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<s>
The_AT hope_NN1 that_CST issues_NN2 involving_VVG relativistic_JJ electrons_NN2 can_VM be_VBI resolved_VVN in_II the_AT non-nuclear_JJ phase_NN1 of_IO ITER_JJR operations_NN2 has_VHZ a_AT1 fundamental_JJ flaw_NN1 ._. 
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<s>
However_RR ,_, S_ZZ1 (_( Q_ZZ1 =_FO 0_MC )_) values_NN2 are_VBR determined_VVN by_II the_AT statistical_JJ density_NN1 fluctuations_NN2 according_II21 to_II22 the_AT relation_NN1 &lsqb;_( 22_MC &rsqb;_) <equation>_FO (_( 17_MC )_) where_RRQ overbars_NN2 represent_VV0 averages_NN2 ._. 
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<s>
In_II a_AT1 two-dimensional_JJ space_NN1 ,_, the_AT requirement_NN1 of_IO consistency_NN1 places_VVZ no_AT restriction_NN1 on_II the_AT probabilities_NN2 that_CST may_VM be_VBI assigned_VVN to_II non-orthogonal_JJ projections_NN2 ._. 
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<s>
But_CCB the_AT above_JJ does_VDZ bring_VVI forward_RL the_AT important_JJ role_NN1 of_IO literal_JJ energy_NN1 in_II conversion_NN1 processes_NN2 :_: not_XX to_TO be_VBI consumed_VVN ,_, nor_CC to_TO be_VBI transferred_VVN to_II the_AT driven_JJ process_NN1 to_TO make_VVI that_DD1 process_NN1 happen_VVI ,_, but_CCB simply_RR to_TO be_VBI '_NULL divided_VVN '_NULL –_- into_II a_AT1 larger_JJR number_NN1 of_IO quanta_NN1 (_( or_CC coalesced_VVN into_II a_AT1 smaller_JJR number_NN1 )_) and_CC to_TO thereby_RR be_VBI part_NN1 –_- often_RR the_AT dominant_JJ or_CC even_RR exclusive_JJ part_NN1 ,_, of_IO the_AT medium_NN1 in_II which_DDQ is_VBZ wrought_VVN a_AT1 change_NN1 in_II the_AT number_NN1 of_IO microstatesand_NN1 with_IW that_DD1 the_AT probability_NN1 of_IO the_AT system_NN1 '_NULL s_ZZ1 macrostate_NN1 ._. 
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<s>
The_AT physics_NN1 of_IO these_DD2 techniques_NN2 is_VBZ underlined_VVN in_II recent_JJ review_NN1 articles_NN2 and_CC book_NN1 chapters_NN2 ._. 
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<s>
We_PPIS2 next_MD develop_VV0 the_AT statistical_JJ properties_NN2 of_IO transitions_NN2 between_II microstates_NN2 ,_, and_CC inferentially_RR between_II macrostates_NN2 ,_, but_CCB emphasize_VV0 again_RT that_CST ,_, for_IF simplicity_NN1 ,_, the_AT present_JJ discussion_NN1 is_VBZ confined_VVN to_II systems_NN2 that_CST are_VBR time_VV0 invariant_JJ in_II two_MC senses_NN2 ._. 
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<s>
In_II the_AT absence_NN1 of_IO approaches_NN2 with_IW a_AT1 direct_JJ QCD_NP1 connection_NN1 ,_, studies_NN2 of_IO quantum_NN1 mechanical_JJ constituent-quark_JJ models_NN2 (_( CQMs_NP1 )_) continued_VVD ._. 
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<s>
Recently_RR ,_, data_NN with_IW improved_JJ quantity_NN1 and_CC quality_NN1 have_VH0 been_VBN used_VVN to_TO map_VVI nations_NN2 '_NULL economic_JJ characteristics_NN2 such_II21 as_II22 poverty_NN1 ,_, which_DDQ comes_VVZ with_IW economic_JJ development_NN1 and_CC is_VBZ a_AT1 major_JJ cause_NN1 of_IO societal_JJ instability_NN1 ._. 
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<s>
The_AT rise_NN1 time_NNT1 of_IO the_AT PMT_NP1 was_VBDZ approximately_RR 300_MC ps_NNU2 in_II photon_NN1 counting_NN1 mode_NN1 ._. 
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<s>
Similar_JJ ideas_NN2 are_VBR presently_RR being_VBG explored_VVN for_IF the_AT design_NN1 of_IO artificial_JJ systems_NN2 ,_, i.e._REX ,_, in_II swarm_NN1 robotics_NN2 (_( Beni_NP1 ,_, 2004_MC ;_; Erskine_NP1 and_CC Herrmann_NP1 ,_, 2014_MC )_) ._. 
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<s>
Therefore_RR ,_, for_IF frequency_NN1 from_II zero_MC to_II the_AT modulation_NN1 frequency_NN1 d_ZZ1 ,_, with_IW a_AT1 general_JJ solution_NN1 formula_NN1 <Equation>_FO ,_, the_AT spectrum_NN1 of_IO output_NN1 be_VBI numerically_RR solved_VVN as_CSA <Equation>_FO with_IW averaged_JJ thermal_JJ input_NN1 photon_NN1 fifirst_VV0 two_MC terms_NN2 are_VBR of_IO classical_JJ origin_NN1 and_CC the_AT last_MD term_NN1 is_VBZ a_AT1 purely_RR quantum_NN1 mechanical_JJ effffect_NN1 which_DDQ originates_VVZ from_II the_AT vacuum_NN1 quantum_NN1 flfluctuations_NN2 ,_, or_CC in_II other_JJ words_NN2 ,_, from_II the_AT DCE_NP1 ._. 
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<s>
Even_RR the_AT exact_JJ positions_NN2 of_IO the_AT shadow_NN1 on_II the_AT image_NN1 plane_NN1 of_IO the_AT observer_NN1 can_VM not_XX be_VBI used_VVN to_TO test_VVI the_AT Kerr_NP1 metric_JJ ,_, because_CS it_PPH1 is_VBZ difficult_JJ to_TO precisely_RR identify_VVI the_AT center_NN1 of_IO the_AT source_NN1 ._. 
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<s>
Here_RL ,_, the_AT Bell_NP1 function_NN1 B_ZZ1 is_VBZ given_VVN by_II <Equation>_FO where_RRQ <Professional_FO Term>_FO is_VBZ a_AT1 certain_JJ correlation_NN1 function_NN1 between_II Alice_NP1 '_NULL s_ZZ1 and_CC Bob_NP1 '_NULL s_ZZ1 measurements_NN2 ._. 
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<s>
This_DD1 reduces_VVZ the_AT time_NNT1 complexity_NN1 for_IF prime_JJ numbers_NN2 to_II O(1)_FO ._. 
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<s>
Fields_NN2 14_MC 445_MC )_) for_IF the_AT case_NN1 of_IO N_ZZ1 independent_JJ Markov_NP1 jump_NN1 processes_NN2 ,_, are_VBR extended_VVN to_II the_AT case_NN1 of_IO open_JJ Markov_NP1 processes_NN2 with_IW reservoirs_NN2 :_: explicit_JJ formulas_NN2 are_VBR given_VVN for_IF the_AT joint_JJ probability_NN1 of_IO empirical_JJ occupation_NN1 numbers_NN2 and_CC empirical_JJ flows_NN2 ,_, both_RR for_IF discrete-time_JJ dynamics_NN and_CC for_IF continuous-time_JJ jump_NN1 dynamics_NN ,_, with_IW possibly_RR time-dependent_JJ dynamical_JJ rules_NN2 and/or_CC time-dependent_JJ driving_NN1 of_IO the_AT reservoirs_NN2 ._. 
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<s>
Second_MD one_PN1 is_VBZ the_AT non-radiative_JJ decay_NN1 ,_, in_II which_DDQ the_AT remaining_JJ part_NN1 of_IO energy_NN1 absorbed_VVN is_VBZ radiated_VVN as_CSA heat_NN1 ._. 
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<s>
From_II the_AT snapshots_NN2 at_II <professional_FO terms>_FO ,_, we_PPIS2 can_VM see_VVI how_RRQ the_AT <professional_FO terms>instability_FO forms_VVZ in_II the_AT pinch_NN1 region_NN1 ._. 
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<s>
A_AT1 multi-stage_JJ collimation_NN1 system_NN1 is_VBZ used_VVN to_TO absorb_VVI the_AT beam_NN1 halo_NN1 particles_NN2 preventing_VVG quenches_VVZ of_IO its_APPGE superconducting_JJ magnets_NN2 and_CC reducing_VVG the_AT collider_NN1 experiment_NN1 background_NN1 ._. 
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<s>
To_TO study_VVI this_DD1 effect_NN1 ,_, we_PPIS2 tried_VVD two_MC different_JJ IE_REX configurations_NN2 ,_, one_PN1 with_IW a_AT1 solid_JJ cylinder_NN1 to_TO compare_VVI with_IW previous_JJ experiments_NN2 and_CC the_AT other_JJ with_IW a_AT1 wide_JJ hollow_NN1 to_TO improve_VVI the_AT yield_NN1 of_IO the_AT reverse_JJ polarity_NN1 case_NN1 ,_, as_CSA shown_VVN in_II Figs._NN2 2(a)_FO and_CC 2(b)_FO ._. 
</s>
<s>
Molecular_JJ orientation_NN1 of_IO polar_JJ molecules_NN2 can_VM be_VBI generated_VVN only_RR in_II the_AT adiabatic_JJ regime_NN1 if_CS the_AT inversion_NN1 symmetry_NN1 of_IO the_AT alignment_NN1 process_NN1 is_VBZ broken_VVN ._. 
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<s>
The_AT role_NN1 of_IO negative_JJ ion_NN1 detachment_NN1 is_VBZ indirectly_RR inferred_VVN from_II the_AT drop-off_NN1 in_II the_AT peak_NN1 ion_NN1 density_NN1 as_II a_AT1 function_NN1 of_IO time_NNT1 delay_NN1 ._. 
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<s>
Stimulated_JJ Rayleigh_NP1 scattering_NN1 can_VM occur_VVI ,_, but_II21 for_II22 the_AT OTDR/OFDR_NN1 techniques_NN2 described_VVN herein_RR the_AT incident_NN1 light_NN1 used_VVN is_VBZ not_XX of_IO high_RR enough_DD intensity_NN1 to_TO induce_VVI stimulated_JJ effects_NN2 ._. 
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<s>
Calculation_NN1 of_IO the_AT imaginary_JJ part_NN1 of_IO vertex_NN1 functions_NN2 ._. 
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<s>
The_AT cascade_NN1 structure_NN1 of_IO ZnTi_NP1 MMO_NP1 provides_VVZ the_AT stepwise_JJ pathways_NN2 for_IF photoexcited_JJ electrons_NN2 ,_, which_DDQ is_VBZ beneficial_JJ to_II the_AT lifetime_NNT1 of_IO charge_NN1 carriers_NN2 and_CC supression_NN1 of_IO the_AT recombination_NN1 as_RR21 well_RR22 ._. 
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<s>
They_PPHS2 imply_VV0 different_JJ Higgs_NP1 interactions_NN2 with_IW SM_NP1 fermions_NN2 ,_, as_CSA tabulated_VVN in_II Table_NN1 5_MC &lsqb;_( 204_MC &rsqb;_) ._. 
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<s>
A._NP1 Martinez_NP1 and_CC S._NP1 Yamashita_NP1 ,_, Opt_VV0 ._. 
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<s>
Figure_NN1 4_MC demonstrates_VVZ how_RRQ difficult_JJ it_PPH1 is_VBZ to_TO identify_VVI the_AT cause_NN1 of_IO data–MC_NN1 disagreement_NN1 as_II a_AT1 function_NN1 of_IO interaction_NN1 kinematics_NN2 for_IF a_AT1 broadband_JJ neutrino_NN1 flux_NN1 ._. 
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<s>
This_DD1 allows_VVZ BP_NP1 to_TO fill_VVI up_RP the_AT "_" blank_JJ space_NN1 "_" between_II the_AT semime-_JJ tallic_JJ graphene_NN1 and_CC wideband_VV0 gap_NN1 TMDs_NP1 ,_, which_DDQ can_VM be_VBI used_VVN in_II ultrafast_NN1 lasers_NN2 from_II visible_JJ wavelength_NN1 to_II mid-infrared_JJ wavelength_NN1 ._. 
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In_II this_DD1 regard_NN1 ,_, 1D-hBN_JJ nano-_JJ scrolls_NN2 (_( essentially_RR inherited_VVN from_II 2D_NNU hBN_NNU )_) possess_VV0 various_JJ unique_JJ properties_NN2 ,_, including_II excellent_JJ stability_NN1 ,_, high_JJ thermal_JJ conductivity_NN1 ,_, electrical_JJ insulation_NN1 ,_, and_CC high_JJ elastic_JJ modulus_NN1 ,_, which_DDQ make_VV0 them_PPHO2 promising_JJ for_IF a_AT1 plethora_NN1 of_IO applications_NN2 ._. 
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<s>
In_II this_DD1 context_NN1 ,_, the_AT present_JJ simulations_NN2 will_VM be_VBI helpful_JJ to_TO model_VVI spacecraft_NN observations_NN2 of_IO EASWs_NP2 and_CC IASWs_VVZ in_II the_AT Earth_NN1 '_NULL s_ZZ1 magnetosphere_NN1 ._. 
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<s>
Concerning_II the_AT singlet_NN1 partner_NN1 and_CC the_AT fourplet_NN1 ones_NN2 ,_, their_APPGE single_JJ production_NN1 in_II31 association_II32 with_II33 a_AT1 SM_NP1 quark_NN1 is_VBZ partly_RR driven_VVN by_II the_AT Higgs_NP1 boson_NN1 ,_, suppressing_VVG therefore_RR the_AT single_JJ production_NN1 of_IO the_AT up_RP and_CC charm_VV0 partner_NN1 by_II the_AT square_NN1 of_IO the_AT SM-like_JJ up_RP and_CC charm_VV0 Yukawa_NP1 coupling_NN1 ,_, respectively_RR ._. 
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<s>
For_IF the_AT two-descriptor_JJ model_NN1 for_IF the_AT oxygen_NN1 evolution_NN1 reaction_NN1 ,_, we_PPIS2 define_VV0 the_AT metric_JJ for_IF predictability_NN1 with_II31 respect_II32 to_II33 identifying_VVG the_AT potential_JJ determining_JJ step_NN1 (_( PDS_NP2 )_) as_CSA <equation>_FO ._. 
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<s>
For_IF simplicity_NN1 ,_, we_PPIS2 concentrate_VV0 on_II the_AT case_NN1 of_IO the_AT gauge_NN1 group_NN1 SU_NN1 (_( 2_MC )_) and_CC only_RR briefly_RR discuss_VV0 (_( in_II subsect._NNU 2.3_MC )_) the_AT case_NN1 of_IO SU_NP1 (_( N_ZZ1 )_) gauge_NN1 symmetry_NN1 ._. 
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<s>
For_IF this_DD1 reason_NN1 ,_, all_DB measures_NN2 discussed_VVN in_II Sec_NNU ._. 
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II.A_NP1 consider_VV0 this_DD1 state_NN1 not_XX as_RG macroscopically_RR quantum_NN1 even_RR under_RG otherwise_RR ideal_JJ circumstances_NN2 ._. 
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<s>
The_AT whole_JJ resistance_NN1 is_VBZ more_RGR stable_JJ in_II the_AT high_JJ concentration_NN1 electrolyte_NN1 ,_, which_DDQ can_VM well_RR explain_VVI its_APPGE better_JJR capacity_NN1 retention_NN1 ability_NN1 ._. 
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<s>
According_II21 to_II22 our_APPGE estimations_NN2 ,_, density_NN1 of_IO C2_FO molecules_NN2 is_VBZ roughly_RR equal_JJ to_II ?_FO of_IO C_ZZ1 atoms_NN2 density_NN1 in_II the_AT temperature_NN1 range_NN1 corresponding_VVG to_II high_JJ concentration_NN1 of_IO C2_FO molecules_NN2 (_( see_VV0 appendix_NN1 E_ZZ1 )_) ._. 
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<s>
Hence_RR ,_, a_AT1 large_JJ variance_NN1 as_II a_AT1 measure_NN1 for_IF macroscopic_JJ quantumness_NN1 proposed_VVN by_II Shimizu_NP1 and_CC Miyadera_NP1 (_( 2002_MC )_) ,_, Lee_NP1 and_CC Jeong_NP1 (_( 2011_MC )_) ,_, and_CC Frwis_NP1 and_CC Dur_NP1 (_( 2012b_FO )_) is_VBZ necessary_JJ for_IF large_JJ values_NN2 of_IO <Equation>_FO in_II the_AT case_NN1 of_IO <Equation>_FO ._. 
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<s>
Section_NN1 4_MC describes_VVZ details_NN2 of_IO the_AT classification_NN1 scheme_NN1 by_II HQSS_NP1 ._. 
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However_RR ,_, the_AT height_NN1 of_IO the_AT profile_NN1 remains_VVZ largely_RR unchanged_JJ ,_, actually_RR decreasing_VVG slightly_RR ._. 
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<s>
To_TO compare_VVI results_NN2 from_II the_AT MCRS_NP1 measurements_NN2 to_II simulations_NN2 ,_, the_AT discharges_NN2 are_VBR modelled_VVN using_VVG a_AT1 global_JJ model_NN1 in_II PLASIMO_NP1 &lsqb;_( 43_MC ,_, 44_MC &rsqb;_) ._. 
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<s>
An_AT1 in-plane_NN1 external_JJ field_NN1 of_IO 3.5_MC mT_NNU is_VBZ applied_VVN to_TO set_VVI the_AT device_NN1 at_II the_AT center_NN1 of_IO the_AT minor_JJ loop_NN1 ,_, although_CS this_DD1 is_VBZ not_XX required_VVN for_IF switching_VVG the_AT in-plane_NN1 magnetized_VVD free_JJ layer_NN1 ._. 
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<s>
The_AT temporal_JJ evolution_NN1 of_IO the_AT recorded_JJ brightness_NN1 of_IO selected_JJ impurity_NN1 emission_NN1 lines_NN2 gives_VVZ rise_NN1 to_II impurity_NN1 transport_NN1 times_NNT2 τ_NULL I_PPIS1 ,_, being_VBG a_AT1 direct_JJ measure_NN1 of_IO global_JJ impurity_NN1 transport_NN1 properties_NN2 &lsqb;_( 10_MC &rsqb;_) ._. 
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<s>
Although_CS this_DD1 is_VBZ the_AT situation_NN1 in_II which_DDQ we_PPIS2 are_VBR interested_JJ ,_, we_PPIS2 state_VV0 the_AT results_NN2 in_II this_DD1 section_NN1 for_IF general_JJ closed_JJ 1–forms_NN2 ._. 
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<s>
In_II the_AT public_JJ channel_NN1 ,_, the_AT operator_NN1 A_ZZ1 represents_VVZ the_AT correlation_NN1 which_DDQ does_VDZ not_XX decay_VVI over_II the_AT time_NNT1 scale_NN1 of_IO consecutive_JJ channel_NN1 uses_NN2 ,_, while_CS Ei_NP1 ,_, (_( i_ZZ1 =_FO 0_MC ,_, 1_MC1 )_) are_VBR the_AT Kraus_NP1 operators_NN2 of_IO AD_NN1 noise_NN1 ._. 
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<s>
Since_CS <Professional_FO Term>_FO is_VBZ nonzero_NN1 when_CS <Professional_FO Term>_FO in_II the_AT ABBA_NN1 system_NN1 ,_, only_RR the_AT mode_NN1 pairs_NN2 satisfying_VVG <Equation>_FO can_VM couple_VVI to_II each_PPX221 other_PPX222 ._. 
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<s>
The_AT next_MD step_NN1 toward_II treating_VVG an_AT1 electrolyte_NN1 in_II31 contact_II32 with_II33 a_AT1 surface_NN1 is_VBZ to_TO add_VVI the_AT ions_NN2 to_II the_AT solution_NN1 ._. 
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<s>
First_MD ,_, orbital_JJ hybridization_NN1 between_II the_AT transition_NN1 metal_NN1 and_CC the_AT topological_JJ insulator_NN1 substantially_RR alters_VVZ the_AT surface_NN1 states_VVZ at_II Fermi_NP1 energy_NN1 ._. 
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<s>
The_AT purpose_NN1 of_IO this_DD1 proposed_JJ experiment_NN1 is_VBZ to_TO see_VVI whether_CSW and_CC how_RRQ the_AT Hawking_JJ particles_NN2 and_CC their_APPGE partners_NN2 are_VBR entangled_VVN and_CC therefore_RR how_RRQ the_AT information_NN1 would_VM be_VBI preserved_VVN ._. 
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An_AT1 interesting_JJ feature_NN1 can_VM be_VBI seen_VVN in_II this_DD1 figure_NN1 ._. 
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<s>
This_DD1 work_NN1 is_VBZ supported_VVN by_II the_AT National_JJ Natural_JJ Science_NN1 Foundation_NN1 of_IO China_NP1 (_( GrantNos_NP1 ._. 
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<s>
These_DD2 are_VBR called_VVN Lagrangian_JJ coherent_JJ structures_NN2 ._. 
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<s>
Although_CS it_PPH1 has_VHZ the_AT advantage_NN1 of_IO simplicity_NN1 ,_, the_AT sign_NN1 reconciliation_NN1 scheme_NN1 is_VBZ only_RR efficient_JJ in_II the_AT case_NN1 of_IO high_JJ signal-to-noise_JJ ratio_NN1 (_( SNR_NP1 )_) ._. 
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<s>
According_II21 to_II22 the_AT authors_NN2 ,_, for_IF sufficiently_RR long_JJ chains_NN2 (_( at_RR21 least_RR22 7_MC grains_NN2 )_) ,_, the_AT evolution_NN1 of_IO the_AT initial_JJ pulse_NN1 is_VBZ not_XX affected_VVN by_II the_AT length_NN1 of_IO the_AT chain_NN1 ._. 
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<s>
On_II an_AT1 even_RR grander_JJR scale_NN1 ,_, one_PN1 can_VM conceive_VVI of_IO active_JJ matter_NN1 forming_VVG the_AT entities_NN2 that_CST comprise_VV0 a_AT1 metamaterial_JJ ._. 
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Hence_RR ,_, here_RL the_AT signal_NN1 propagates_VVZ from_II Earth_NN1 to_II space_NN1 ._. 
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<s>
A_AT1 slightly_RR high_JJ content_NN1 of_IO Ni_NP1 can_VM improve_VVI the_AT structural_JJ stability_NN1 of_IO Ni-rich_JJ cathode_NN1 materials_NN2 ._. 
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No_AT indication_NN1 of_IO ex-foliation_NN1 of_IO the_AT films_NN2 was_VBDZ found_VVN even_RR after_II electrochemical_JJ cycling_NN1 ._. 
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<s>
The_AT timeline_NN1 of_IO the_AT speed_NN1 and_CC ceiling_NN1 altitude_NN1 reached_VVN by_II commercial_JJ and_CC military_JJ aircraft.56_FO Reproduced_VVN with_IW permission_NN1 from_II Bejan_NP1 et_RA21 al._RA22 ,_, Sci_NP1 ._. 
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<s>
In_II this_DD1 section_NN1 the_AT influence_NN1 of_IO rotation_NN1 on_II the_AT Tayler_NN1 instability_NN1 will_VM be_VBI described_VVN ._. 
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<s>
Finally_RR ,_, Englert_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2008_MC )_) considered_VVD entropic_JJ measures_NN2 of_IO wave_NN1 and_CC particle_NN1 behavior_NN1 for_IF interferometers_NN2 with_IW more_DAR than_CSN two_MC paths_NN2 ._. 
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<s>
In_II this_DD1 scenario_NN1 we_PPIS2 investigate_VV0 how_RGQ many_DA2 Charlies_NP1 can_VM demonstrate_VVI standard_JJ tripartite_JJ nonlocality_NN1 as_II31 well_II32 as_II33 genuine_JJ tripartite_JJ nonlocality_NN1 through_II quantum_NN1 violations_NN2 of_IO Mermin_NP1 inequality_NN1 &lsqb;_( 25_MC &rsqb;_) and_CC Svetlichny_JJ inequality_NN1 &lsqb;_( 26_MC &rsqb;_) ,_, respectively_RR ._. 
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<s>
Overall_RR ,_, compared_VVN to_II the_AT pristine_JJ ,_, the_AT N-doping_NN1 ,_, and_CC the_AT S-doping_JJ cases_NN2 ,_, N+S-codoping_FO appears_VVZ to_TO be_VBI the_AT optimal_JJ <chart>_FO case_NN1 for_IF photocatalytic_JJ water_NN1 splitting_NN1 ._. 
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<s>
The_AT analysis_NN1 shows_VVZ that_CST the_AT quantum_NN1 Algorithm_NN1 2_MC proposed_VVD in_II this_DD1 paper_NN1 is_VBZ more_RGR efficient_JJ than_CSN any_DD classical_JJ algorithm_NN1 for_IF solving_VVG this_DD1 problem_NN1 ._. 
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<s>
The_AT general_JJ switching_JJ features_NN2 are_VBR quite_RG similar_JJ to_II the_AT ones_NN2 observed_VVN in_II CuMnAs_NP2 ,_, revealing_VVG the_AT multidomain_NN1 magnetic_JJ structure_NN1 of_IO the_AT system_NN1 ._. 
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<s>
One_PN1 should_VM be_VBI very_RG careful_JJ when_CS applying_VVG this_DD1 technique_NN1 for_IF continuous_JJ systems_NN2 ,_, since_CS goodness_NN1 of_IO fit_JJ greatly_RR increases_VVZ for_IF such_DA systems_NN2 with_IW addition_NN1 of_IO linear_JJ terms_NN2 even_CS21 when_CS22 the_AT system_NN1 is_VBZ highly_RR nonlinear_JJ ._. 
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<s>
The_AT canonical_JJ bundle_NN1 of_IO is_VBZ Kp_NP1 (_( 1_MC1 )_) and_CC has_VHZ a_AT1 basis_NN1 of_IO sections_NN2 d_ZZ1 z/w_ZZ1 ,_, zd_NNU z/w_ZZ1 ._. 
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<s>
Only_RR the_AT non-oscillatory_JJ part_NN1 of_IO the_AT correlator_NN1 is_VBZ then_RT recovered_VVN ;_; the_AT oscillatory_JJ part_NN1 is_VBZ regarded_VVN as_II the_AT result_NN1 of_IO the_AT periodic_JJ orbits_NN2 action_NN1 correlations_NN2 ._. 
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What_DDQ really_RR determines_VVZ the_AT size_NN1 of_IO the_AT beam_NN1 divergence_NN1 are_VBR the_AT optical_JJ channel_NN1 and_CC the_AT pointing_JJ jitter_NN1 ._. 
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<s>
For_IF three_MC representative_JJ cases_NN2 ,_, i.e._REX potential_JJ flow_NN1 ,_, Keplerian_JJ rotation_NN1 ,_, and_CC the_AT rigidly-rotating_JJ z-pinch_NN1 ,_, we_PPIS2 show_VV0 that_CST finite_JJ diffusivities_NN2 can_VM even_RR destabilize_VVI this_DD1 class_NN1 of_IO Chandrasekhar-type_JJ flows_NN2 ._. 
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<s>
The_AT reaction_NN1 with_IW La_NP1 is_VBZ inefficient_JJ ,_, likely_JJ again_RT due_II21 to_II22 a_AT1 curve_NN1 crossing_NN1 ,_, in_II this_DD1 case_NN1 predicted_VVN by_II theory_NN1 &lsqb;_( 14_MC &rsqb;_) ._. 
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<s>
It_PPH1 has_VHZ been_VBN reported_VVN that_CST a_AT1 coating_NN1 of_IO a_AT1 thin_JJ layer_NN1 of_IO CH_NN1 on_II the_AT front_JJ surface_NN1 of_IO the_AT metal_NN1 target_NN1 can_VM affect_VVI the_AT preplasma_NN1 before_II the_AT main_JJ pulse_NN1 interaction.17–21_NNU The_AT preplasma_NN1 formation_NN1 not_XX only_RR on_II the_AT front_JJ side_NN1 but_CCB also_RR on_II the_AT rear_JJ side_NN1 could_VM affect_VVI fast_JJ electron_NN1 and_CC proton_NN1 generation.22–25_NNU Mackinnon_NP1 et_NP1 al.22_FO has_VHZ shown_VVN that_CST the_AT proton_NN1 energy_NN1 reduced_VVD significantly_RR when_CS a_AT1 plasma_NN1 is_VBZ created_VVN at_II the_AT back_NN1 of_IO the_AT target_NN1 using_VVG another_DD1 laser_NN1 pulse_NN1 ,_, and_CC their_APPGE result_NN1 was_VBDZ supported_VVN by_II similar_JJ simulation_NN1 results.23_FO Further_RRR ,_, Yabuuchi_NP1 et_NP1 al.24_FO have_VH0 also_RR shown_VVN that_CST the_AT electron_NN1 flux_NN1 increases_VVZ nearly_RR two_MC fold_VV0 by_II creating_VVG rear_JJ plasma_NN1 by_II irradiating_VVG the_AT rear_JJ surface_NN1 with_IW a_AT1 separate_JJ laser_NN1 pulse_NN1 ._. 
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<s>
In_RR21 particular_RR22 ,_, lx_MC ,_, y_ZZ1 l_ZZ1 =_FO l_ZZ1 ._. 
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<s>
Different_JJ optimization_NN1 methods_NN2 have_VH0 been_VBN used_VVN in_II the_AT literature_NN1 for_IF maximizing_VVG molecular_JJ orientation_NN1 and_CC alignment_NN1 ._. 
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<s>
Pd_NP1 is_VBZ one_MC1 of_IO the_AT most_RGT efiective_JJ oxidation_NN1 catalysts_NN2 because_CS it_PPH1 dissociates_VVZ O2_FO readily_RR ,_, while_CS forming_VVG relatively_RR weak_JJ PdeO_NN1 bonds_NN2 that_CST facilitate_VV0 donation_NN1 of_IO that_DD1 oxygen_NN1 to_II a_AT1 reactant_NN1 ,_, an_AT1 oxygen_NN1 vacancy_NN1 site_NN1 on_II the_AT perovskite_NN1 surface_NN1 in_II this_DD1 case_NN1 ._. 
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<s>
Experiments_NN2 involving_VVG continuous_JJ coherent_JJ feedback_NN1 were_VBDR performed_VVN prior_II21 to_II22 those_DD2 realizing_VVG continuous_JJ measurement-based_JJ feedback_NN1 ,_, although_CS at_II the_AT time_NNT1 these_DD2 experiments_NN2 were_VBDR not_XX thought_VVN of_IO as_CSA involving_VVG feedback_NN1 ._. 
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<s>
In_II the_AT strong_JJ SOC_NN1 limit_NN1 or_CC small_JJ Jahn-Teller_NP1 limit_NN1 ,_, the_AT spin-orbital-_JJ entangled_JJ Jeff_NP1 =_FO 1/2_MF state_NN1 (_( =_FO 1/3_MF )_) arises_VVZ while_CS ._. 
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<s>
Since_CS the_AT neutron_NN1 yield_NN1 also_RR increases_VVZ with_IW d_ZZ1 ,_, there_EX is_VBZ an_AT1 optimal_JJ width_NN1 for_IF the_AT maximum_JJ neutron_NN1 flux_NN1 ._. 
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<s>
A_AT1 more_RGR elaborate_JJ pedagogical_JJ introduction_NN1 to_II classical_JJ and_CC quantum_NN1 parameterestimation_NN1 theory_NN1 can_VM be_VBI found_VVN in_II Fra?sse_NP1 (_( 2017_MC )_) ._. 
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<s>
The_AT gap_NN1 distance_NN1 and_CC radius_NN1 of_IO the_AT antennas_NN2 were_VBDR 20_MC and_CC 2.5mm_NNU ,_, respectively_RR ._. 
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<s>
Moreover_RR ,_, we_PPIS2 will_VM show_VVI that_CST in_II presence_NN1 of_IO the_AT external_JJ electric_JJ field_NN1 terms_NN2 linear_JJ in_II the_AT field_NN1 will_VM add_VVI to_II E1E1_FO transition_NN1 probability_NN1 ;_; these_DD2 are_VBR the_AT interference_NN1 terms_NN2 ._. 
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<s>
Let_VV0 us_PPIO2 feed_VVI the_AT interferometer_NN1 with_IW a_AT1 pure_JJ initial_NN1 state<Equation>_FO where_RRQ the_AT fermions_NN2 occupy_VV0 the_AT first_MD N_ZZ1 modes_NN2 of_IO the_AT first_MD partition_NN1 is_VBZ a_AT1 Fock_NN1 state_NN1 and_CC therefore_RR it_PPH1 is_VBZ separable_JJ ,_, as_CSA already_RR discussed_VVN ._. 
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<s>
In_BCL21 order_BCL22 to_TO distinguish_VVI the_AT order_NN1 of_IO the_AT magnetic_JJ chain_NN1 ,_, we_PPIS2 propose_VV0 applying_VVG a_AT1 magnetic_JJ field_NN1 in_II the_AT plane_NN1 of_IO the_AT superconducting_JJ substrate_NN1 ,_, forcing_VVG the_AT magnetic_JJ moments_NN2 of_IO impurities_NN2 to_TO align_VVI along_RP that_DD1 direction_NN1 ._. 
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<s>
Second_MD ,_, the_AT hierarchy_NN1 problem_NN1 can_VM be_VBI viewed_VVN as_II a_AT1 quadratic_JJ dependence_NN1 of_IO the_AT one-loop_NN1 Higgs_VVZ mass_JJ corrections_NN2 on_II the_AT exact_JJ value_NN1 of_IO the_AT matching_JJ scale_NN1 ._. 
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<s>
However_RR ,_, the_AT degradation_NN1 phenomena_NN2 along_II temperatures_NN2 in_II these_DD2 three_MC vdWHs_NNU are_VBR very_RG similar_JJ ._. 
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<s>
We_PPIS2 thank_VV0 Brian_NP1 Mooney_NP1 of_IO the_AT University_NN1 of_IO Missouri_NP1 Charles_NP1 W._NP1 Is_VBZ the_AT magnetism_NN1 principally_RR of_IO spin_NN1 or_CC orbital_JJ character_NN1 ?_? 
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<s>
This_DD1 step_NN1 can_VM be_VBI performed_VVN consistently_RR in_II the_AT strong_JJ and_CC weak_JJ sectors_NN2 of_IO the_AT theory_NN1 ,_, which_DDQ in_II the_AT case_NN1 of_IO interest_NN1 here_RL involves_VVZ <Equation>_FO transition_NN1 operators_NN2 ._. 
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<s>
Taking_VVG m_ZZ1 =_FO 10_MC and_CC m_ZZ1 =_FO 100_MC also_RR leads_VVZ to_TO produce_VVI high-quality_JJ final_JJ states_NN2 ,_, with_IW expectation_NN1 values_NN2 2.07_MC and_CC 2.11_MC ,_, respectively_RR ._. 
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<s>
We_PPIS2 further_RRR show_VV0 that_CST ,_, when_CS modeling_VVG real_JJ cases_NN2 of_IO networks_NN2 ,_, the_AT binary_NN1 and_CC weighted_JJ statistics_NN of_IO the_AT ensemble_NN1 can_VM be_VBI disentangled_VVN ,_, leading_VVG to_II a_AT1 simplified_JJ framework_NN1 for_IF a_AT1 range_NN1 of_IO practical_JJ applications_NN2 ._. 
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<s>
Collectively_RR ,_, we_PPIS2 demonstrated_VVD that_CST the_AT designed_JJ remodeling_NN1 process_VV0 not_XX only_RR improved_JJ cell_NN1 alignment_NN1 ,_, ECM_NP1 deposition_NN1 ,_, and_CC tissue_NN1 generation_NN1 but_CCB also_RR significantly_RR promoted_VVN the_AT mechanical_JJ properties_NN2 of_IO the_AT TEBVs_NP2 ._. 
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<s>
One_MC1 possibility_NN1 for_IF the_AT noise_NN1 is_VBZ <Equation>_FO where_RRQ g_ZZ1 is_VBZ the_AT Gaussian_JJ white_JJ noise_NN1 ._. 
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<s>
However_RRQV the_AT lattice_NN1 simulations_NN2 have_VH0 shown_VVN that_CST this_DD1 two-phase_JJ picture_NN1 of_IO confinement_NN1 is_VBZ misleading_JJ ._. 
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<s>
This_DD1 excitation_NN1 induces_VVZ the_AT rotation_NN1 of_IO the_AT molecules_NN2 in_II a_AT1 preferential_JJ direction_NN1 ,_, clockwise_JJ or_CC counterclockwise_RR ._. 
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<s>
Since_RR STS_NP2 measurements_NN2 with_IW SC_FO tips_NN2 provide_VV0 a_AT1 convolution_NN1 of_IO the_AT DOS_NN1 of_IO tip_NN1 and_CC sample_NN1 ,_, the_AT sample_NN1 resonances_NN2 are_VBR shifted_VVN by_II the_AT tip_NN1 SC_FO gap_NN1 such_II21 as_II22 <Equation>_FO ._. 
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<s>
The_AT location_NN1 of_IO the_AT volume_NN1 reflection_NN1 area_NN1 along_II the_AT crystal_NN1 length_NN1 will_VM be_VBI different_JJ in_II each_DD1 crystal_NN1 of_IO a_AT1 parallel_JJ sequence_NN1 ._. 
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<s>
However_RR ,_, although_CS abundant_JJ human-derived_JJ elastin_NN1 was_VBDZ found_VVN in_II the_AT explanted_JJ TEBVs_NN2 &lsqb;_( Fig._NN1 6(e-ii)_MC &rsqb;_) ,_, no_AT assembled_JJ fibrous_JJ structures_NN2 were_VBDR generated_VVN ,_, consistent_JJ with_IW the_AT results_NN2 of_IO Masson_NP1 '_NULL s_ZZ1 Trichrome_JJ staining_NN1 ._. 
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<s>
In_II the_AT following_JJ ,_, we_PPIS2 will_VM solve_VVI the_AT relevant_JJ Boltzmann_NN1 equations_NN2 analytically_RR in_II the_AT regions_NN2 of_IO interest_NN1 where_CS different_JJ processes_NN2 dominate_VV0 at_II a_AT1 time_NNT1 ._. 
</s>
<s>
There_EX are_VBR several_DA2 types_NN2 of_IO pumps_NN2 that_CST have_VH0 been_VBN studied_VVN in_II the_AT literature_NN1 for_IF drug_NN1 delivery_NN1 ,_, such_II21 as_II22 infusion_NN1 pumps_NN2 ,_, peristaltic_JJ pumps_NN2 ,_, osmotic_JJ pumps_NN2 ,_, and_CC positive_JJ displacement_NN1 pumps_NN2 ._. 
</s>
<s>
De_NP1 Stefano_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
&lsqb;_( 568_MC &rsqb;_) examined_VVD three_MC co-authorship_NN1 networks_NN2 of_IO Italian_JJ academic_JJ statisticians_NN2 ._. 
</s>
<s>
In_RR21 particular_RR22 ,_, a_AT1 second_MD peak_NN1 appears_VVZ at_II 28eV_FO with_IW a_AT1 count_NN1 rate_NN1 comparable_JJ to_II that_DD1 of_IO the_AT 2eV_FO peak_NN1 ._. 
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<s>
In_II Section_NN1 4_MC ,_, we_PPIS2 evaluated_VVD H_ZZ1 ,_, keeping_VVG e_ZZ1 (_( and_CC )_) constant_JJ (_( which_DDQ allowed_VVD us_PPIO2 to_TO project_VVI contours_NN2 of_IO H_ZZ1 onto_II plane_NN1 )_) ._. 
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<s>
As_CSA shown_VVN in_II Fig._NN1 6(c)_FO ,_, above_II 1000_MC °C_NNU ,_, small_JJ dark_JJ lines_NN2 initiated_VVN in_II the_AT YSZ_NN1 from_II the_AT YSZ/pore_NN1 interface_NN1 ._. 
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<s>
A_AT1 few_DA2 developments_NN2 in_II femtosecond_NN1 laser_NN1 technology_NN1 were_VBDR essential_JJ to_TO achieve_VVI the_AT generation_NN1 of_IO isolated_JJ attosecond_NN1 pulses_NN2 ,_, in_RR21 particular_RR22 the_AT stabilization_NN1 of_IO the_AT carrier-envelope_JJ phase_NN1 (_( CEP_NP1 )_) of_IO the_AT driving_JJ pulses_NN2 (_( Jones_NP1 et_RA21 al._RA22 ,_, 2000_MC )_) and_CC the_AT generation_NN1 of_IO high-peak-power_JJ sub-5-fs_NN2 pulses_NN2 (_( Baltuska_NP1 et_RA21 al._RA22 ,_, 2003_MC )_) ._. 
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<s>
As_CS31 far_CS32 as_CS33 radio-frequency_NN1 signal_NN1 processing_NN1 is_VBZ concerned_JJ ,_, OEOs_NN2 have_VH0 been_VBN developed_VVN for_IF signal_NN1 channelization_NN1 (_( Urick_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) ,_, low-power_JJ rf_NNU detection_NN1 (_( Devgan_NP1 et_RA21 al._RA22 ,_, 2010_MC ;_; Shao_NP1 et_RA21 al._RA22 ,_, 2018_MC ;_; Wang_NP1 et_RA21 al._RA22 ,_, 2019_MC ;_; Zhu_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) ,_, complex_JJ microwave_NN1 signal_NN1 generation_NN1 (_( Deng_NP1 et_RA21 al._RA22 ,_, 2017_MC ;_; C._NP1 Zhang_NP1 et_RA21 al._RA22 ,_, 2018_MC )_) ,_, or_CC frequency_NN1 division_NN1 (_( Liu_NP1 et_RA21 al._RA22 ,_, 2019_MC )_) ._. 
</s>
<s>
It_PPH1 was_VBDZ also_RR shown_VVN that_CST the_AT effect_NN1 of_IO multiple_JJ volume_NN1 reflections_NN2 of_IO particles_NN2 in_II one_MC1 crystal_NN1 (_( MVR_NP1 OC_NP1 )_) can_VM be_VBI realized_VVN in_II few_DA2 subsequent_JJ strips_NN2 ._. 
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<s>
Overlay_VV0 of_IO omit_VV0 electron_NN1 densities_NN2 of_IO three_MC different_JJ datasets_NN2 based_VVN on_II the_AT protein_NN1 structural_JJ alignment_NN1 ._. 
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<s>
Fig._NN1 3a_FO presents_VVZ the_AT FTIR_NN1 spectrum_NN1 ,_, which_DDQ exhibits_VVZ four_MC distinct_JJ characteristic_JJ peaks_NN2 ._. 
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<s>
A_AT1 further_JJR evidence_NN1 for_IF the_AT driving_JJ force_NN1 term_NN1 is_VBZ the_AT observation_NN1 of_IO melting_VVG rates_NN2 at_II higher_JJR temperatures_NN2 from_II the_AT lamellar_JJ crystal_NN1 at_II the_AT state_NN1 of_IO the_AT inset_NN1 snapshot_NN1 in_II Fig._NN1 34a_FO ._. 
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<s>
For_IF the_AT action_NN1 encoded_VVD in_II M_ZZ1 ,_, this_DD1 results_VVZ in_II a_AT1 fermion_NN1 determinant_NN1 DetM_NN1 in_II the_AT gauge_NN1 field_NN1 functional_JJ integral_JJ or_CC equivalently_RR an_AT1 effective_JJ action_NN1 <Equation>_FO ._. 
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<s>
This_DD1 discrepancy_NN1 may_VM be_VBI due_II21 to_II22 differences_NN2 in_II the_AT epidemic_NN1 dynamics_NN ,_, since_CS ,_, as_CSA pointed_VVN out_RP in_II Ref_NN1 ._. 
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<s>
A_ZZ1 m_ZZ1 el_VV0 e_ZZ1 ._. 
</s>
<s>
Importantly_RR ,_, in_II an_AT1 experiment_NN1 ,_, this_DD1 property_NN1 will_VM scale_VVI with_IW the_AT number_NN1 of_IO side_NN1 lobes_NN2 in_II the_AT amplitude_NN1 distribution_NN1 of_IO the_AT Bessel_NP1 beam_NN1 ._. 
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<s>
The_AT temperature_NN1 dependence_NN1 of_IO the_AT coercive_JJ field_NN1 for_IF the_AT Co/BFO_NN1 heterostructure_NN1 &lsqb;_( shown_VVN in_II Fig._NN1 &rsqb;_) clearly_RR demonstrates_VVZ the_AT significant_JJ enhancement_NN1 of_IO the_AT exchange_NN1 coupling_NN1 between_II the_AT two_MC layers_NN2 at_II low_JJ temperatures_NN2 ,_, with_IW the_AT maximum_JJ coercive_JJ field_NN1 reached_VVN at_II approximately_RR 330_MC Oe_NP1 in_II Co/BFO109_NP1 at_II 4_MC K_ZZ1 ,_, as_CSA derived_VVN from_II the_AT XMCD_NP1 intensity_NN1 at_II the_AT Co_NN1 L3_FO edge_NN1 (_( Supplemental_JJ Material_NN1 )_) ._. 
</s>
<s>
Parallel_RR SOL_NP1 transport_NN1 is_VBZ predicted_VVN to_TO be_VBI classical_JJ and_CC dominated_VVN by_II Spitzer–H?rm_NP1 conduction_NN1 ._. 
</s>
<s>
While_CS the_AT precise_JJ nature_NN1 of_IO these_DD2 (_( most_RGT likely_JJ collective_NN1 )_) excitations_NN2 and_CC the_AT origin_NN1 of_IO their_APPGE slow_JJ decay_NN1 remain_VV0 to_TO be_VBI understood_VVN ,_, it_PPH1 is_VBZ evident_JJ that_CST pump-probe_JJ experiments_NN2 with_IW disordered_JJ magnets_NN2 provide_VV0 a_AT1 promising_JJ setting_NN1 for_IF exploring_VVG the_AT breakdown_NN1 of_IO thermalization_NN1 and_CC MBL_NP1 ._. 
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<s>
Theorem_NN1 1.1_MC implies_VVZ that_DD1 convergence_NN1 holds_VVZ as_CSA <Equation>_FO with_IW a_AT1 suitable_JJ formalization_NN1 constant_NN1 ._. 
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<s>
Fig._NN1 4.19_MC also_RR shows_VVZ (_( green_JJ dashed_JJ curve_NN1 )_) the_AT jet_NN1 fragmentation_NN1 function_NN1 predicted_VVN by_II the_AT quenching_JJ model_NN1 used_VVN in_II Pyquen_NP1 ._. 
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<s>
The_AT intermediate-energy_JJ Coulomb_NN1 excitation_NN1 technique_NN1 was_VBDZ used_VVN to_TO deduce_VVI the_AT B(E2)_FO value_NN1 in_II 104_MC Sn_NN1 &lsqb;_( 2013Ba57,2014Do19_FO &rsqb;_) ._. 
</s>
<s>
For_IF each_DD1 1-tile_NN1 <Equation>_FO ,_, the_AT map_NN1 f_ZZ1 is_VBZ injective_JJ both_RR on_II <Equation>_FO and_CC on_II <Equation>_FO by_II Proposition_NN1 3.5(i)_FO ._. 
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<s>
Copyright_NN1 2009_MC American_JJ Association_NN1 for_IF the_AT Advancement_NN1 of_IO Science_NN1 ._. 
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<s>
In_II most_DAT of_IO the_AT cases_NN2 ,_, the_AT formalization_NN1 of_IO measures_NN2 for_IF macroscopic_JJ quantum_NN1 states_NN2 amounts_VVZ to_II a_AT1 study_NN1 of_IO coherences_NN2 of_IO the_AT state_NN1 in_II the_AT basis_NN1 of_IO a_AT1 given_JJ operator_NN1 A._NNU For_IF pure_JJ states_NN2 ,_, once_CS A_ZZ1 is_VBZ fixed_VVN ,_, the_AT variance_NN1 of_IO the_AT state_NN1 with_II31 respect_II32 to_II33 A_ZZ1 is_VBZ a_AT1 natural_JJ choice_NN1 that_CST allows_VVZ one_PN1 to_TO quantify_VVI the_AT coherent_JJ spread_NN1 of_IO the_AT state_NN1 ._. 
</s>
<s>
To_TO derive_VVI DQ(t)_NP1 on_II different_JJ structural_JJ units_NN2 ,_, the_AT entire_JJ unit_NN1 cell_NN1 was_VBDZ sub-divided_VVN into_II sub-volumes_NN2 containing_VVG one_MC1 atom_NN1 each_DD1 ._. 
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<s>
All_DB of_IO the_AT systems_NN2 in_II this_DD1 review_NN1 do_VD0 not_XX have_VHI back_NN1 re_II ?_? ectors_NN2 ._. 
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<s>
That_REX21 is_REX22 ,_, the_AT material_NN1 falls_VVZ out_II21 of_II22 equilibrium_NN1 when_CS the_AT thermal_JJ energy_NN1 in_II the_AT sample_NN1 is_VBZ insufficient_JJ for_IF the_AT system_NN1 to_TO explore_VVI the_AT phase_NN1 space_NN1 adequately_RR in_II the_AT accessible_JJ experimental_JJ time_NNT1 ._. 
</s>
<s>
Further_RRR ,_, the_AT width_NN1 of_IO the_AT solitary_JJ wave_NN1 does_VDZ not_XX agree_VVI quantitatively_RR with_IW values_NN2 found_VVN from_II numerical_JJ simulations_NN2 except_II21 for_II22 n_ZZ1 near_II <Equation>_FO &lsqb;_( 17_MC ,_, 18_MC &rsqb;_) ._. 
</s>
<s>
Moreover_RR ,_, the_AT antiproton_NN1 flux_NN1 is_VBZ in_II this_DD1 model_NN1 in_II tension_NN1 with_IW the_AT AMS-02_MC data_NN ,_, even_CS21 if_CS22 an_AT1 additional_JJ antiproton_NN1 component_NN1 from_II interactions_NN2 in_II CR_NP1 sources_NN2 is_VBZ included_VVN &lsqb;_( 260_MC &rsqb;_) ._. 
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<s>
The_AT integer_NN1 K_ZZ1 corresponds_VVZ to_II the_AT multipolarity_NN1 of_IO the_AT transition_NN1 and_CC must_VM form_VVI a_AT1 vector_NN1 triangle_NN1 with_IW je_FW and_CC j_ZZ1 as_II31 well_II32 as_II33 with_IW the_AT nuclear_JJ spins_NN2 Ji_NN1 and_CC Jf_NP1 ._. 
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<s>
The_AT yellow_JJ and_CC blue_JJ bands_NN2 in_II Fig._NN1 1(b)_FO correspond_VV0 to_II the_AT bipolar_JJ electric_JJ field_NN1 structures_NN2 of_IO the_AT oppositely_RR propagating_VVG solitary_JJ wave_NN1 pulses_NN2 ._. 
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<s>
Detailed_JJ analyses_NN2 of_IO the_AT Bose-Einstein_NP1 condensate_NN1 physics_NN1 beyond_II the_AT simplified_JJ single-mode_JJ treatment_NN1 here_RL are_VBR given_VVN by_II Boixo_NP1 ,_, Datta_NP1 ,_, Flammia_NP1 et_RA21 al_RA22 ._. 
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<s>
(_( 2008_MC )_) ,_, Boixo_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2009_MC )_) ,_, and_CC Tacla_NP1 and_CC Caves_NN2 (_( 2013_MC )_) ._. 
</s>
<s>
Hence_RR the_AT CAN_VM laser_NN1 could_VM provide_VVI simultaneously_RR peak_VV0 power_NN1 ,_, average_JJ power_NN1 and_CC efficiency_NN1 ._. 
</s>
<s>
In_II the_AT measurement_NN1 arm_NN1 ,_, the_AT pulse_NN1 is_VBZ focused_VVN on_II a_AT1 translation_NN1 stage_NN1 sample_NN1 ._. 
</s>
<s>
By_II Convention_NN1 ,_, We_PPIS2 Assume_VV0 That_CST Every_AT1 Boundary_NN1 Component_NN1 Of_IO (_( X_ZZ1 ,_, )_) Is_VBZ Contained_VVN In_II The_AT Set_NN1 Of_IO Slits_NN2 ._. 
</s>
<s>
In_II other_JJ words_NN2 we_PPIS2 have_VH0 ,_, for_IF any_DD k_ZZ1 ,_, m_ZZ1 N_ZZ1 such_CS21 that_CS22 m_ZZ1 <_FO c_ZZ1 ,_, there_EX exists_VVZ a_AT1 constant_JJ C_ZZ1 ,_, depending_VVG only_RR on_II k_ZZ1 and_CC m_ZZ1 ,_, for_IF which_DDQ ._. 
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<s>
Therefore_RR ,_, the_AT numerical_JJ determination_NN1 of_IO the_AT derivatives_NN2 of_IO x_ZZ1 at_II <Equation>_FO ,_, together_RL with_IW the_AT amplitude_NN1 of_IO the_AT compression_NN1 pulse_NN1 and_CC the_AT pulse_NN1 velocity_NN1 ,_, are_VBR sufficient_JJ to_TO write_VVI f_ZZ1 (_( )_) up_II21 to_II22 any_DD desired_JJ order_NN1 ._. 
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<s>
Combined_VVN with_IW the_AT Neutron_NN1 Emission_NN1 Ratio_NN1 Observer_NN1 (_( NERO_NP1 )_) &lsqb;_( 272_MC &rsqb;_) described_VVD in_II Section_NN1 3.3_MC ,_, decay_VV0 half-lives_NN2 as_II31 well_II32 as_II33 β_NULL -delayed_JJ neutron_NN1 emission_NN1 probabilities_NN2 can_VM be_VBI measured_VVN ._. 
</s>
<s>
Moreover_RR ,_, is_VBZ it_PPH1 possible_JJ to_TO overcome_VVI the_AT inherent_JJ diffraction_NN1 limit_NN1 of_IO the_AT ring-lens_NN1 using_VVG a_AT1 metamaterial_JJ hyperlens-design_NN1 ,_, &lsqb;_( 29,30_MC &rsqb;_) such_CS21 that_CS22 the_AT ring-width_NN1 reaches_VVZ the_AT sub-wavelength_JJ regime_NN1 ?_? 
</s>
<s>
The_AT X2CAMF-CCSD(T)_JJ results_NN2 for_IF the_AT ground_NN1 state_VV0 molecular_JJ constants_NN2 of_IO ThF_NP1 are_VBR summarized_VVN in_II the_AT fifth_MD column_NN1 of_IO Table_NN1 3_MC ._. 
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<s>
For_IF this_DD1 purpose_NN1 ,_, the_AT iron_NN1 yoke_NN1 ,_, and_CC hence_RR the_AT detector_NN1 ,_, is_VBZ sectioned_VVN into_II five_MC barrel_NN1 wheels_NN2 (_( each_DD1 2.5_MC m_NNO wide_JJ )_) and_CC three_MC endcap_NN1 disks_NN2 at_II each_DD1 end_NN1 ,_, for_IF a_AT1 total_JJ weight_NN1 of_IO 12,500_MC metric_JJ tons_NNU2 (_( Figure_NN1 4_MC )_) ._. 
</s>
<s>
In_II Fig._NN1 4a_FO ,_, when_CS D2_FO ?_? 0.5_MC ,_, four_MC magnetization_NN1 plateaus_NN2 can_VM be_VBI observed_VVN at_II M_NN1 ?_? 5/6_MF ,_, 7/6_MF ,_, 9/6_MF and_CC 11/6_MF ._. 
</s>
<s>
Correlative_JJ ex-situ_JJ TEM_NN1 and_CC NanoSIMS_NP1 imaging_NN1 has_VHZ found_VVN applications_NN2 in_II various_JJ ?_? elds_VVZ in_II life_NN1 sciences_NN2 ._. 
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<s>
These_DD2 results_NN2 suggest_VV0 that_CST the_AT annual_JJ expenditures_NN2 of_IO MP_NN1 users_NN2 can_VM be_VBI predicted_VVN only_RR using_VVG their_APPGE anonymous_JJ phone_NN1 usage_NN1 data_NN ._. 
</s>
<s>
However_RR ,_, in_II our_APPGE real_JJ situation_NN1 ,_, for_IF a_AT1 fixed_JJ fiber_NN1 ,_, i.e._REX ,_, a_AT1 fixed_JJ spectral_JJ curve_NN1 ,_, at_RR21 most_RR22 2k_FO of_IO our_APPGE components_NN2 can_VM intersect_VVI the_AT fiber_NN1 ._. 
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<s>
All-optical_JJ cross-correlations_NN2 of_IO the_AT pump_NN1 pulses_NN2 with_IW 800_MC nm_FU pulses_NN2 traveling_VVG along_II the_AT optical_JJ path_NN1 of_IO the_AT x-ray_JJ pulses_NN2 were_VBDR measured_VVN repeatedly_RR to_TO ensure_VVI a_AT1 proper_JJ stacking_NN1 of_IO data_NN from_II different_JJ days_NNT2 ._. 
</s>
<s>
If_CS f_ZZ1 is_VBZ a_AT1 linear_JJ function_NN1 ,_, g_ZZ1 is_VBZ a_AT1 constant_JJ ._. 
</s>
<s>
In_II the_AT low_JJ temperature_NN1 limit_NN1 ,_, where_CS the_AT electron_NN1 thermal_JJ velocity_NN1 is_VBZ much_RR lower_JJR than_CSN the_AT Fermi_NP1 velocity_NN1 (_( <Equation>_FO )_) ,_, we_PPIS2 may_VM assume_VVI <Equation>_FO for<Equation>_FO and_CC <Equation>_FO ._. 
</s>
<s>
After_CS consideration_NN1 of_IO these_DD2 three_MC points_NN2 ,_, the_AT use_NN1 of_IO two_MC rows_NN2 of_IO 6-membered_JJ rings_NN2 for_IF each_DD1 sheet_NN1 appeared_VVN to_TO be_VBI the_AT best_JJT compromise_NN1 ._. 
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<s>
The_AT ECD-1_MC1 device_NN1 with_IW a_AT1 thinner_JJR NiO_NN1 layer_NN1 showed_VVD a_AT1 high_JJ optical_JJ modulation_NN1 (_( 36.4%_FO )_) ._. 
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<s>
Similar_JJ conserved_JJ spin_NN1 quantities_NN2 in_II strained_JJ quantum_NN1 wells_NN2 were_VBDR also_RR found_VVN by_II Dollinger_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2014_MC )_) and_CC Sacksteder_NP1 and_CC Bernevig_NP1 (_( 2014_MC )_) using_VVG band_NN1 structure_NN1 models_NN2 where_RRQ the_AT linear_JJ Dresselhaus_NP1 term_NN1 plays_VVZ a_AT1 less_RGR dominant_JJ role_NN1 ._. 
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<s>
The_AT insets_NN2 show_VV0 the_AT results_NN2 for_IF some_DD particular_JJ values_NN2 of_IO g_ZZ1 ._. 
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<s>
These_DD2 humps_NN2 are_VBR associated_VVN with_IW the_AT EASW_NN1 pulses_NN2 generated_VVN in_II the_AT system_NN1 ._. 
</s>
<s>
User_NN1 operation_NN1 started_VVD in_II 2005_MC in_II the_AT FLASH1_FO experimental_JJ hall_NN1 which_DDQ after_II a_AT1 naming_NN1 ceremony_NN1 in_II 2015_MC is_VBZ now_RT the_AT "_" Albert_NP1 Einstein_NP1 Hall_NN1 "_" ._. 
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<s>
AFM_NP1 axis_NN1 is_VBZ tilted_VVN from_II the_AT surface_NN1 normal_JJ with_IW a_AT1 small_JJ angle_NN1 ,_, as_CSA observed_VVN in_II <Equation>_FO with_IW the_AT tensile_JJ strain_NN1 &lsqb;_( 44_MC &rsqb;_) ._. 
</s>
<s>
Moreover_RR ,_, the_AT intercept–resend_NN1 attack_NN1 and_CC the_AT measure–resend_NN1 attack_NN1 can_VM be_VBI found_VVN with_IW the_AT probability_NN1 of_IO 1_MC1 -_- 1/2m_FU &lsqb;_( 39_MC &rsqb;_) and_CC 1_MC1 -_- (_( 3/4_MF )_) m_ZZ1 &lsqb;_( 39_MC &rsqb;_) ,_, respectively_RR ,_, where_CS m_ZZ1 is_VBZ the_AT number_NN1 of_IO decoy_NN1 states_NN2 (_( or_CC decoy_NN1 logical_JJ qubits_NN2 )_) used_VVN to_TO detect_VVI this_DD1 attack_NN1 ._. 
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<s>
Otherwise_RR ,_, the_AT attack_NN1 will_VM disturb_VVI the_AT states_NN2 of_IO decoy_NN1 qubits_NN2 (_( or_CC decoy_NN1 logical_JJ qubits_NN2 )_) ._. 
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<s>
The_AT increase_NN1 in_II lattice_NN1 parameters_NN2 <Professional_FO Term>_FO instead_CS21 of_CS22 <Professional_FO Term>_FO ._. 
</s>
<s>
Renes_NP2 and_CC Boileau_NP1 (_( 2009_MC )_) gave_VVD the_AT first_MD quantum_NN1 memory_NN1 uncertainty_NN1 relation_NN1 in_II31 terms_II32 of_II33 the_AT quantum_NN1 state_NN1 perspective_NN1 ._. 
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<s>
More_RGR recently_RR ,_, Chen_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2019_MC )_) demonstrated_VVD a_AT1 modulatorless_JJ approach_NN1 based_VVN on_II the_AT frequency_NN1 doubling_NN1 of_IO the_AT period-one_JJ oscillation_NN1 of_IO a_AT1 distributed_JJ feedback_NN1 semiconductor_NN1 laser_NN1 with_IW optical_JJ feedback_NN1 ._. 
</s>
<s>
Application_NN1 of_IO neural_JJ networks_NN2 to_II h+jets_FO searches_NN2 ._. 
</s>
<s>
Compared_VVN to_II the_AT plain_JJ SoftKiller_NN1 ,_, this_DD1 has_VHZ three_MC extra_JJ parameters_NN2 :_: <Equation>_FO and_CC <Equation>_FO defining_VVG the_AT reference_NN1 jets_NN2 ,_, and_CC <Equation>_FO ._. 
</s>
<s>
Fusion_NN1 reactions_NN2 can_VM also_RR be_VBI initiated_VVN in_II gases_NN2 or_CC a_AT1 mist_NN1 of_IO submicron_NN1 droplets_NN2 produced_VVD using_VVG pulsed_JJ gas_NN1 jets_NN2 ._. 
</s>
<s>
Furthermore_RR ,_, while_CS the_AT radial_JJ electric_JJ field_NN1 is_VBZ time_NNT1 dependent_NN1 ,_, the_AT ion_NN1 will_VM feel_VVI an_AT1 initial_JJ force_NN1 <Equation>_FO ._. 
</s>
<s>
Masers_NN2 were_VBDR first_MD demonstrated_VVN in_II the_AT 1950s_MC2 ._. 
</s>
<s>
Therefore_RR ,_, the_AT assumption_NN1 about_II the_AT uniformity_NN1 of_IO the_AT impact_NN1 parameter_NN1 distribution_NN1 is_VBZ not_XX already_RR valid_JJ and_CC the_AT cross-section_NN1 conception_NN1 for_IF the_AT ED_NP1 processes_NN2 of_IO high_JJ energy_NN1 ions_NN2 in_II the_AT aligned_JJ crystals_NN2 is_VBZ not_XX applicable_JJ ._. 
</s>
<s>
Adiabatic_JJ alignment_NN1 is_VBZ an_AT1 alternative_NN1 to_II the_AT retrieval_NN1 of_IO the_AT molecular_JJ structure_NN1 by_II coincident_JJ ion_NN1 momentum_NN1 spectroscopy_NN1 employing_VVG delay-line_JJ anodes_NN2 ._. 
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<s>
The_AT main_JJ difference_NN1 between_II the_AT two_MC techniques_NN2 is_VBZ that_CST the_AT first_MD one_PN1 counts_VVZ the_AT number_NN1 of_IO muons_NN2 crossing_VVG a_AT1 given_JJ structure_NN1 ,_, while_CS the_AT second_MD one_PN1 relies_VVZ on_II the_AT measurement_NN1 of_IO the_AT deflection_NN1 of_IO the_AT particle_NN1 and_CC for_IF this_DD1 reason_NN1 needs_VVZ detectors_NN2 at_II two_MC sides_NN2 of_IO the_AT object_NN1 under_II study_NN1 ._. 
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<s>
It_PPH1 should_VM be_VBI pointed_VVN out_RP that_CST the_AT above_JJ calculations_NN2 are_VBR relying_VVG on_II atomic_JJ parameters_NN2 which_DDQ may_VM not_XX all_DB be_VBI very_RG precise_JJ ,_, but_CCB the_AT present_JJ calculations_NN2 suggest_VV0 that_CST the_AT primary_JJ contribution_NN1 to_II the_AT &lsqb;_( 18.3_MC &rsqb;_) 3_MC state_NN1 might_VM come_VVI from_II a_AT1 D3_FO state_VV0 which_DDQ is_VBZ probably_RR mixed_VVN with_IW some_DD U3_FO character_NN1 ._. 
</s>
<s>
In_II this_DD1 paper_NN1 ,_, the_AT exact_JJ control_NN1 of_IO the_AT scattering_NN1 ability_NN1 was_VBDZ achieved_VVN through_II elaborate_JJ microstructure_NN1 de-signs_NN2 in_II <Professional_FO Term>_FO ceramics_NN2 ._. 
</s>
<s>
We_PPIS2 also_RR thank_VV0 the_AT Cologne_NP1 laboratory_NN1 astrophysics_NN1 group_NN1 for_IF continuous_JJ support_NN1 and_CC the_AT Regional_JJ Computing_NN1 Center_NN1 of_IO the_AT Universit?t_NN1 zu_FW K?ln_NP1 (_( RRZK_NP1 )_) for_IF providing_VVG computing_JJ time_NNT1 on_II the_AT DFG-funded_JJ High_JJ Performance_NN1 Computing_NN1 (_( HPC_NP1 )_) system_NN1 CHEOPS_NN2 ._. 
</s>
<s>
The_AT line_NN1 contour_NN1 represents_VVZ the_AT density_NN1 profile_NN1 ._. 
</s>
<s>
In_BCL21 order_BCL22 to_TO relate_VVI morphology_NN1 to_II magnetism_NN1 convincingly_RR ,_, it_PPH1 would_VM be_VBI helpful_JJ to_TO be_VBI able_JK to_TO alter_VVI it_PPH1 ,_, while_CS keeping_VVG everything_PN1 else_RR the_AT same_DA ._. 
</s>
<s>
Assays_NN2 using_VVG liquid_JJ chromatography-tandem_JJ mass_JJ spectrometry_NN1 (_( LC–MS/MS_FU )_) with_IW isotope_NN1 dilution_NN1 (_( ID_NN1 )_) are_VBR more_RRR specificand_VV0 sensitive_JJ and_CC are_VBR the_AT gold_NN1 standard_NN1 for_IF many_DA2 small_JJ molecules_NN2 ,_, and_CC several_DA2 LC–MS/MS_FU methods_NN2 for_IF identifying_VVG vitamin_NN1 A_ZZ1 or_CC vita-min_NN1 E_ZZ1 metabolites_NN2 &lsqb;_( 27–30_MCMC &rsqb;_) have_VH0 been_VBN developed_VVN ._. 
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<s>
The_AT inset_NN1 shows_VVZ the_AT temperature_NN1 distribution_NN1 curve_NN1 along_II the_AT diameter_NN1 of_IO HSYAG2_FO ._. 
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<s>
Furthermore_RR ,_, because_CS they_PPHS2 depend_VV0 on_II the_AT soft_JJ matter_NN1 '_NULL s_ZZ1 configuration_NN1 ,_, which_DDQ can_VM be_VBI dynamically_RR tuned_VVN ,_, they_PPHS2 are_VBR routes_NN2 to_II reconfigurable_JJ structures_NN2 ._. 
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The_AT second_MD and_CC third_MD terms_NN2 of_IO the_AT first_MD exact_JJ sequence_NN1 appeared_VVD in_II the_AT proof_NN1 of_IO &lsqb;_( 23_MC ,_, Theorem_NN1 4.1_MC &rsqb;_) as_CSA V_ZZ1 '_NULL ,_, V_ZZ1 by_II setting_VVG <EQUATION>_FO ._. 
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If_CS the_AT input_NN1 is_VBZ a_AT1 prime_JJ number_NN1 ,_, p_ZZ1 stores_NN2 the_AT number_NN1 itself_PPX1 ._. 
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This_DD1 is_VBZ a_AT1 different_JJ result_NN1 than_CSN the_AT results_NN2 in_II &lsqb;_( 19_MC &rsqb;_) ._. 
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<s>
A_AT1 further_JJR feedback_NN1 loop_NN1 is_VBZ then_RT introduced_VVN in_II which_DDQ the_AT Hamiltonian_JJ of_IO the_AT controlled_JJ system_NN1 is_VBZ adjusted_VVN by_II the_AT quantum_NN1 nondemolition_NN1 output_NN1 of_IO x_ZZ1 to_TO increase_VVI the_AT probability_NN1 to_TO obtain_VVI a_AT1 desired_JJ superposition_NN1 state_NN1 ._. 
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In_II Taylor–Couette_NP1 flows_VVZ unbounded_JJ in_II the_AT axial_JJ direction_NN1 no_AT stratification_NN1 vector_NN1 parallel_NN1 to_II the_AT rotation_NN1 axis_NN1 exists_VVZ ._. 
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For_IF the_AT second_MD part_NN1 of_IO this_DD1 document_NN1 ,_, we_PPIS2 shall_VM switch_VVI gear_NN1 and_CC consider_VVI another_DD1 approach_NN1 that_CST can_VM be_VBI used_VVN to_TO mitigate_VVI pileup_NN1 ,_, namely_REX grooming_JJ techniques_NN2 ._. 
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<s>
For_REX21 example_REX22 ,_, random_JJ walks_NN2 give_VV0 rise_NN1 to_II power_NN1 laws_NN2 in_II the_AT distribution_NN1 of_IO return_JJ times_NNT2 and_CC "_" avalanche_NN1 "_" sizes_NN2 as_CSA illustrated_VVN in_II Fig._NN1 1_MC1 ._. 
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A_AT1 first_MD measurement_NN1 of_IO the_AT anion_NN1 yield_NN1 as_II a_AT1 function_NN1 of_IO the_AT electron_NN1 energy_NN1 was_VBDZ carried_VVN out_RP by_II Jiang_NP1 et_RA21 al_RA22 ._. 
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&lsqb;_( 207_MC &rsqb;_) ._. 
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<s>
They_PPHS2 are_VBR related_VVN to_II statistical_JJ quantities_NN2 via_II <Professional_FO Term>_FO for_IF the_AT example_NN1 of_IO baryon_NN1 number_NN1 and_CC analogous_JJ expressions_NN2 for_IF charge_NN1 and_CC strangeness_NN1 ._. 
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<s>
Thus_RR ,_, the_AT content_NN1 of_IO cobalt_NN1 ions_NN2 on_II the_AT anode_NN1 is_VBZ especially_RR important_JJ for_IF the_AT long_JJ cycle_NN1 LIBs_NN2 ._. 
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<s>
In_II the_AT second_MD application_NN1 ,_, the_AT better_JJR SNR_NP1 of_IO QGI_NN2 and_CC QGS_NP1 is_VBZ used_VVN to_TO enhance_VVI measurements_NN2 in_II environments_NN2 inducing_VVG noise_NN1 ,_, for_REX21 example_REX22 ,_, due_II21 to_II22 scattering_VVG ._. 
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For_IF the_AT SU(3)_FO case_NN1 a_AT1 fit_JJ to_II a_AT1 <Professional_FO Term>-behaviour_FO has_VHZ been_VBN given_VVN in_II &lsqb;_( 284_MC &rsqb;_) (_( a_AT1 linear_JJ fit_NN1 is_VBZ also_RR possible_JJ within_II error_NN1 bars_NN2 )_) ._. 
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<s>
To_TO arrive_VVI at_II the_AT equation_NN1 above_RL ,_, we_PPIS2 have_VH0 invoked_VVN the_AT BO_NN1 and_CC adiabatic_JJ approximations_NN2 and_CC terms_NN2 coupling_VVG the_AT nuclear_JJ motion_NN1 to_II the_AT electronic_JJ density_NN1 have_VH0 been_VBN removed_VVN and_CC the_AT equation_NN1 is_VBZ a_AT1 modified_JJ Kohn-Sham-Mermin_NP1 (_( KSM_NP1 )_) embedded_VVN in_II the_AT dielectric_JJ environment_NN1 with_IW continuum_NN1 ions_NN2 ._. 
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<s>
Many_DA2 of_IO the_AT studies_NN2 performed_VVN here_RL can_VM be_VBI repeated_VVN with_IW real_JJ data_NN rather_II21 than_II22 Monte-Carlo_NP1 simulations_NN2 ._. 
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<s>
The_AT appearance_NN1 of_IO space_NN1 time_NNT1 singularity_NN1 reveals_VVZ the_AT domain_NN1 of_IO failure_NN1 of_IO the_AT classical_JJ theory_NN1 of_IO general_JJ relativity_NN1 &lsqb;_( 40_MC &rsqb;_) ._. 
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In_BCL21 order_BCL22 to_TO investigate_VVI the_AT impact_NN1 of_IO collisionality_NN1 on_II density_NN1 fluctuations_NN2 ,_, dedicated_JJ experiments_NN2 including_II Ohmic_JJ density_NN1 scans_NN2 with_IW positive_JJ δ_FO =_FO 0.5_MC and_CC ECH_NP1 power_NN1 scans_NN2 with_IW both_DB2 positive_JJ and_CC negative_JJ δ_FO (_( +0.5_MC and_CC 0.4_MC )_) were_VBDR carried_VVN out_RP ._. 
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<s>
While_CS there_EX are_VBR clearly_RR differences_NN2 that_CST arise_VV0 from_II conceptual_JJ disagreement_NN1 ,_, 50_MC we_PPIS2 note_VV0 that_CST measures_NN2 are_VBR partially_RR defined_VVN for_IF different_JJ scales.51_FO this_DD1 further_RRR complicates_VVZ a_AT1 comparison_NN1 between_II the_AT measures_NN2 ._. 
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As_CSA shown_VVN above_RL ,_, in_II the_AT MD_NN1 case_NN1 the_AT detailed_JJ effect_NN1 of_IO non-vanishing_JJ self-interactions_NN2 can_VM easily_RR be_VBI taken_VVN into_II account_NN1 ,_, as_CSA the_AT required_JJ values_NN2 for_IF s_ZZ1 can_VM be_VBI much_RR smaller_JJR ._. 
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Photoionization_NN1 is_VBZ also_RR the_AT main_JJ process_NN1 contributing_VVG to_II plasma_NN1 opacity_NN1 and_CC radiation_NN1 transfer_NN1 inside_II plasmas_NN2 &lsqb;_( 3_MC &rsqb;_) ._. 
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In_II our_APPGE case_NN1 we_PPIS2 use_VV0 the_AT software_NN1 DERIVE_VV0 which_DDQ is_VBZ freely_RR available_JJ ._. 
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<s>
In_II this_DD1 paper_NN1 ,_, we_PPIS2 proposed_VVD a_AT1 novel_JJ initial_JJ decoding_JJ message_NN1 computation_NN1 method_NN1 for_IF multidimensional_JJ reconciliation_NN1 with_IW low_JJ density_NN1 parity_NN1 check_NN1 code_NN1 ,_, which_DDQ does_VDZ not_XX need_VVI the_AT norm_NN1 information_NN1 from_II the_AT encoder_NN1 ._. 
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This_DD1 is_VBZ shown_VVN in_II Fig._NN1 7(c)_FO where_RRQ the_AT complex_JJ trajectory_NN1 of_IO the_AT phase_NN1 difference_NN1 intersects_VVZ with_IW the_AT inapplicability_NN1 region_NN1 of_IO the_AT ray_NN1 optics_NN1 framework_NN1 for<Professional_FO Terms>_FO ._. 
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As_CSA observed_VVN ,_, the_AT initial_JJ cycling_NN1 step_NN1 delivers_VVZ a_AT1 specific_JJ discharge_NN1 capacity_NN1 of_IO 1310.1_MC mAh_NN1 g_ZZ1 and_CC specific_JJ charge_NN1 capacity_NN1 of_IO 764.5_MC mAh_NN1 g_ZZ1 ._. 
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<s>
Equation_NN1 (_( 59_MC )_) possesses_VVZ at_RR21 most_RR22 two_MC solutions_NN2 ,_, corresponding_VVG to_II the_AT overlap_NN1 of_IO incoming_JJ and_CC outgoing_JJ waves_NN2 ._. 
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Thus_RR ,_, the_AT CLs_NP1 have_VH0 the_AT bulk_NN1 resistance_NN1 of_IO the_AT polymer_NN1 and_CC polymer–LICP_VV0 interfacial_JJ resistance_NN1 ._. 
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<s>
To_TO understand_VVI the_AT reason_NN1 why_RRQ also_RR the_AT last_MD bound_NN1 holds_VVZ ,_, notice_VV0 that_CST ,_, by_II Assumption_NN1 3.12_MC ,_, there_EX exists_VVZ a_AT1 constant_JJ <Equation>_FO such_CS21 that_CS22 f_ZZ1 (_( x_ZZ1 )_) is_VBZ bounded_VVN from_II below_RL by_II c_ZZ1 f_ZZ1 for_IF all_DB <Equation>_FO ._. 
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<s>
Forces_NN2 on_II the_AT resistive_JJ wall_NN1 are_VBR consistent_JJ with_IW Pustovitov_NP1 '_NULL s_ZZ1 analysis_NN1 (_( Pustovitov_NP1 V_ZZ1 D_ZZ1 2015_MC Nucl_NP1 ._. 
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<s>
Recently_RR ,_, the_AT <Professional_FO Term>_FO composite_JJ ceramic_NN1 has_VHZ been_VBN proposed_VVN for_IF use_NN1 in_II laser_NN1 lighting_NN1 because_II21 of_II22 its_APPGE :_: i_ZZ1 )_) high_JJ thermal_JJ conductivity_NN1 and_CC ii_MC )_) high_JJ luminous_JJ efficacy_NN1 caused_VVN by_II the_AT scattering_NN1 of_IO secondary_NN1 Al2O3_FO grains_NN2 ._. 
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<s>
However_RR ,_, it_PPH1 is_VBZ only_RR that_CST :_: an_AT1 "_" irreversibility_NN1 "_" bias_NN1 that_CST can_VM be_VBI used_VVN to_TO trap_VVI useful_JJ Brownian_JJ fluctuations_NN2 ._. 
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As_CSA already_RR mentioned_VVN ,_, this_DD1 method_NN1 is_VBZ good_JJ to_TO adjust_VVI the_AT energies_NN2 but_CCB may_VM produce_VVI less_RGR accurate_JJ estimates_NN2 for_IF other_JJ parameters_NN2 ,_, such_II21 as_II22 transition_NN1 probabilities_NN2 ._. 
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<s>
Furthermore_RR <Equation>_FO does_VDZ not_XX need_VVI a_AT1 separate_JJ estimation_NN1 of_IO the_AT background_NN1 density_NN1 ,_, which_DDQ can_VM have_VHI systematics_NN2 related_VVN to_II the_AT event_NN1 structure_NN1 (_( e.g._REX <Equation>_FO events_NN2 v._II <Equation>_FO events_NN2 )_) ;_; and_CC there_EX is_VBZ no_AT need_NN1 to_TO include_VVI large_JJ numbers_NN2 of_IO ghosts_NN2 for_IF determining_JJ jet_NN1 areas_NN2 ,_, a_AT1 procedure_NN1 that_CST has_VHZ a_AT1 non-negligible_JJ computational_JJ cost_NN1 ._. 
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<s>
It_PPH1 was_VBDZ shown_VVN that_CST the_AT duration_NN1 of_IO the_AT fast_JJ stage_NN1 corresponds_VVZ to_II the_AT period_NN1 of_IO time_NNT1 when_RRQ the_AT main_JJ energy_NN1 deposition_NN1 into_II the_AT wire_NN1 occurs_VVZ ._. 
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Moreover_RR ,_, magnetization_NN1 in_II z_ZZ1 direction_NN1 can_VM be_VBI used_VVN to_TO detect_VVI W_ZZ1 type_NN1 of_IO entanglement_NN1 ._. 
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<s>
The_AT PSI_NN1 suffers_VVZ from_II the_AT same_DA problem_NN1 as_CSA the_AT synchrogram_NN1 ,_, that_CST anything_PN1 other_II21 than_II22 1:1_MC synchronization_NN1 has_VHZ to_TO be_VBI found_VVN by_II trying_VVG different_JJ combinations_NN2 of_IO n_ZZ1 and_CC m_ZZ1 to_TO eventually_RR find_VVI n_ZZ1 :_: m_ZZ1 synchronization_NN1 ._. 
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<s>
Moreover_RR ,_, our_APPGE field_NN1 theoretic_JJ treatment_NN1 newly_RR developed_VVN herein_RR leads_VVZ to_II equation_NN1 (_( 35_MC )_) ,_, revealing_VVG that_CST <Professional_FO Term>_FO can_VM be_VBI approximately_RR expressed_VVN by_II the_AT sum_NN1 of_IO the_AT equilibrium_NN1 free_JJ energy_NN1 functional_JJ HK_NP1 used_VVD in_II the_AT equilibrium_NN1 DFT_NP1 and_CC the_AT correction_NN1 term_NN1 <Professional_FO Term>_FO ._. 
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<s>
The_AT vector_NN1 <Professional_FO Term>_FO is_VBZ invariant_JJ ,_, whereas_CS the_AT scalar_JJ part_NN1 is_VBZ not_XX ._. 
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<s>
The_AT geometric_JJ study_NN1 of_IO the_AT rotation_NN1 of_IO a_AT1 rigid_JJ body_NN1 is_VBZ a_AT1 fundamental_JJ subject_NN1 in_II both_DB2 classical_JJ and_CC quantum_NN1 mechanics_NN2 ._. 
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<s>
While_CS both_DB2 modes_NN2 produce_VV0 SWCNTs_NP1 ,_, SWCNHs_NP1 ,_, and_CC amorphous_JJ carbon_NN1 ,_, the_AT ratio_NN1 of_IO SWCNTs_NP1 to_II other_JJ carbon_NN1 nanomaterials_NN2 is_VBZ higher_JJR for_IF samples_NN2 collected_VVN in_II high_JJ ablation_NN1 mode_NN1 than_CSN low_JJ ablation_NN1 mode_NN1 ._. 
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Anode_NN1 6.5_MC mm_NNU in_II diameter_NN1 ,_, cathode9.5_FO mm._NNU )_) <picture>_FO <picture>_FO <picture>_FO (_( Figure_NN1 3_MC ._. 
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<s>
They_PPHS2 also_RR study_VV0 uncertainty_NN1 relations_NN2 for_IF certain_JJ classes_NN2 of_IO MUBs_NP2 that_CST exhibit_VV0 special_JJ symmetry_NN1 properties_NN2 ._. 
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The_AT electric_JJ dipole_NN1 moment_NN1 components_NN2 of_IO the_AT molecule_NN1 were_VBDR evaluated_VVN using_VVG the_AT Stark_JJ effect_NN1 ._. 
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<s>
Behaviors_NN2 similar_JJ to_II the_AT one_PN1 of_IO vertical_JJ chains_NN2 can_VM be_VBI observed_VVN in_II (_( horizontal_JJ )_) chains_NN2 of_IO metallic_JJ grains_NN2 subject_II21 to_II22 non-uniform_JJ magnetic_JJ fields_NN2 ._. 
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It_PPH1 is_VBZ therefore_RR a_AT1 QRT_NP1 of_IO total_JJ correlations_NN2 ,_, distinguished_VVN from_II resource_NN1 theories_NN2 of_IO quantum_NN1 correlations_NN2 ,_, such_II21 as_II22 discord_NN1 ._. 
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Phonon-assisted_JJ processes_NN2 could_VM be_VBI analyzed_VVN by_II considering_VVG the_AT many-body_JJ electronic_JJ screening_NN1 function_NN1 <Equation>_FO in_II Eq_NN1 ._. 
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<s>
(_( 95_MC )_) ,_, by_II using_VVG the_AT electron_NN1 Green_JJ '_NULL s_ZZ1 function_NN1 G_ZZ1 dressed_VVN by_II the_AT electron-phonon_JJ self-energy_JJ ep_NN1 as_CSA in_II Eq_NN1 ._. 
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<s>
(_( 151_MC )_) ._. 
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<s>
We_PPIS2 see_VV0 that_CST they_PPHS2 typically_RR bring_VV0 gains_NN2 in_II resolution_NN1 but_CCB come_VV0 with_IW a_AT1 few_DA2 caveats_NN2 :_: the_AT average_JJ bias_NN1 increases_NN2 and_CC depends_VVZ on_II either_RR the_AT pileup_NN1 multiplicity_NN1 (_( for_IF cleansing_VVG )_) or_CC the_AT jet_NN1 pt_NNU (_( for_IF filtering_VVG )_) ._. 
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A_AT1 system_NN1 is_VBZ said_VVN to_TO be_VBI controllable_JJ if_CS we_PPIS2 can_VM drive_VVI it_PPH1 from_II any_DD initial_JJ state_NN1 to_II any_DD desired_JJ state_NN1 in_II finite_JJ time_NNT1 ._. 
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Standard_JJ spreading_JJ problems_NN2 are_VBR the_AT spatiotemporal_JJ evolution_NN1 of_IO a_AT1 single_JJ ,_, initially_RR localized_JJ spot_NN1 of_IO turbulence_NN1 and_CC the_AT penetration_NN1 of_IO turbulence_NN1 into_II a_AT1 linearly_RR stable_JJ region_NN1 ._. 
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This_DD1 absorbed_JJ light_NN1 will_VM be_VBI emitted_VVN from_II the_AT material_NN1 through_II two_MC processes_NN2 ._. 
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<s>
The_AT angular_JJ divergence_NN1 of_IO the_AT emitted_JJ photons_NN2 theoretically_RR scales_NN2 as<Professional_FO Terms>_FO which_DDQ could_VM be_VBI adjusted_VVN by_II changing_VVG the_AT laser_NN1 pulse_NN1 and_CC plasma_NN1 parameters_NN2 ._. 
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The_AT model_NN1 is_VBZ then_RT supplemented_VVN with_IW an_AT1 equation_NN1 describing_VVG the_AT coupling_NN1 between_II LSPs_NP1 mediated_VVD by_II their_APPGE electric_JJ near_II fields_NN2 ._. 
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Since_CS y_ZZ1 (_( t_ZZ1 )_) in_II Eq_NN1 ._. 
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(_( 1_MC1 )_) stands_VVZ for_IF the_AT ratio_NN1 of_IO CheY-P_NP1 and_CC CheY_NP1 concentration_NN1 (_( see_VV0 the_AT Appendix_NN1 )_) ,_, we_PPIS2 have_VH0 y0_FO =_FO 0.32_MC ._. 
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Kr_NP1 &lsqb;_( 2014Iw01_FO &rsqb;_) agrees_VVZ with_IW the_AT previous_JJ values_NN2 &lsqb;_( 2005Ga22,2005Go43_FO &rsqb;_) and_CC indicates_VVZ a_AT1 future_JJ potential_JJ use_NN1 of_IO this_DD1 detector_NN1 ._. 
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In_II quantum_NN1 optics_NN1 ,_, Glauber_NP1 '_NULL s_ZZ1 coherent_JJ states_NN2 and_CC their_APPGE mixtures_NN2 are_VBR regarded_VVN as_II the_AT free_JJ (_( classical_JJ )_) states_NN2 (_( Mandel_NP1 and_CC Wolf_NN1 ,_, 1965_MC )_) ,_, and_CC any_DD other_JJ state_NN1 can_VM yield_VVI a_AT1 nonclassical_JJ scaling_NN1 ._. 
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Stoichio_NP1 metric_JJ amounts_NN2 of_IO ferrous_JJ oxalate_NN1 dihydrate_NN1 (_( AR_UH 99%_NNU ,_, Aldrich_NP1 )_) (_( 17.99_MC g_NNU )_) and_CC lithium_NN1 nitrate_NN1 (_( AR_UH 99.5%_FO ,_, Aldrich_NP1 )_) (_( 6.895_MC g_NNU )_) were_VBDR dissolved_VVN in_II 1_MC1 M_ZZ1 nitric_JJ acid_NN1 solution_NN1 (_( 60_MC ml_NNU )_) (_( AR_UH 99.5%_FO ,_, Himedia_NP1 )_) ,_, into_II which_DDQ 20_MC ml_NNU citric_JJ acid_NN1 solution_NN1 (_( AR_UH 99.5%_FO ,_, Himedia_NP1 )_) (_( 66%_NNU wt_NN1 )_) was_VBDZ added_VVN drop_VV0 wise_JJ with_IW continuous_JJ stirring_JJ ._. 
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The_AT fabricated_JJ sensor_NN1 structure_NN1 has_VHZ embedded_VVN to_II the_AT waveguide_NN1 adapter_NN1 coincided_VVD with_IW the_AT sample_NN1 holder_NN1 as_CSA shown_VVN in_II Fig._NN1 7(b)_FO ._. 
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This_DD1 temperature_NN1 dependence_NN1 implies_VVZ that_CST the_AT linear_JJ crystal_NN1 growth_NN1 rates_NN2 are_VBR also_RR dominated_VVN by_II the_AT nucleation_NN1 process_NN1 ._. 
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The_AT <chart>_FO explanation_NN1 of_IO the_AT density_NN1 rise_NN1 being_VBG outside_II the_AT scope_NN1 of_IO this_DD1 paper_NN1 ,_, it_PPH1 will_VM be_VBI given_VVN in_II another_DD1 study_NN1 ._. 
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The_AT Gotthard_NP1 detector_NN1 used_VVN in_II this_DD1 experiment_NN1 will_VM soon_RR be_VBI upgraded_VVN so_CS21 that_CS22 a_AT1 full_JJ bunch_NN1 train_NN1 at_II MHz_NNU repetition_NN1 rate_NN1 can_VM be_VBI spectrally_RR monitored_VVN ._. 
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The_AT thickness_NN1 of_IO the_AT layers_NN2 is_VBZ given_VVN in_II nm_FU with_IW the_AT topmost_JJ layer_NN1 on_II the_AT right_NN1 ._. 
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Given_VVN an_AT1 appropriate_JJ mass_JJ spectrum_NN1 (_( with_IW particles_NN2 between_II the_AT MeV_NNU and_CC GeV_NP1 scales_NN2 )_) ,_, this_DD1 model_NN1 may_VM yield_VVI the_AT MiniBooNE_NN1 low-energy_JJ excess_NN1 ,_, presenting_VVG excellent_JJ agreement_NN1 with_IW angular_JJ and_CC energy_NN1 spectra_NN2 (_( 113_MC ,_, 114_MC )_) ._. 
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As_CSA example_NN1 ,_, the_AT steps_NN2 are_VBR illustrated_VVN for_IF and_CC final_JJ states_NN2 produced_VVN by_II incoming_JJ n-_NN1 scattering_VVG on_II a_AT1 proton_NN1 target_NN1 ._. 
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Using_VVG SESAM_NN1 mode-locking_NN1 ,_, 496fs_RA pulses_NN2 were_VBDR achieved_VVN in_II a_AT1 diode-_NN1 pumped_VVN Tm3t:CaYAlO4_FO laser_NN1 with_IW an_AT1 average_JJ output_NN1 power_NN1 of_IO 531_MC ._. 
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TABLE_NN1 I._NP1 Passively_RR mode-locked_JJ all-solid-state_JJ lasers_NN2 around_II the_AT 2.0lm_FO spectral_JJ region_NN1 ._. 
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This_DD1 photoluminescence_NN1 decomposition_NN1 analysis_NN1 exhibits_VVZ better_JJR reproducibility_NN1 and_CC lower_JJR noise_NN1 than_CSN the_AT Debye-Waller-factor_NP1 approach_NN1 and_CC does_VDZ not_XX require_VVI multiple_JJ excitation_NN1 wavelengths_NN2 &lsqb;_( 26_MC &rsqb;_) ._. 
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However_RR ,_, in_II this_DD1 last_MD type_NN1 of_IO system_NN1 ,_, it_PPH1 is_VBZ important_JJ to_II not_XX only_RR analyze_VV0 the_AT interplay_NN1 between_II different_JJ modes_NN2 but_CCB also_RR between_II lines_NN2 of_IO each_DD1 mode_NN1 ._. 
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The_AT incident_NN1 angle_NN1 of_IO <Professional_FO Term>_FO may_VM not_XX be_VBI regarded_VVN as_CSA appropriate_JJ points_NN2 as_CSA leads_VVZ to_II degrading_VVG one_MC1 of_IO the_AT sensing_NN1 parameters_NN2 including_II FoM_NP1 ._. 
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We_PPIS2 have_VH0 found_VVN good_JJ results_NN2 ,_, and_CC improvements_NN2 compared_VVN to_II plain_JJ zeroing_NN1 ,_, taking_VVG <Equation>_FO (_( as_CSA we_PPIS2 shall_VM use_VVI later_RRR in_II our_APPGE Monte-Carlo_NP1 studies_NN2 )_) or_CC a_AT1 fixed_JJ <Equation>_FO ._. 
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Here_RL ,_, the_AT magnitude_NN1 of_IO the_AT LF_NP1 impedance_NN1 is_VBZ used_VVN ._. 
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Once_RR21 again_RR22 we_PPIS2 have_VH0 det_NN1 <equation>_FO (_( A18_FO )_) so_CS21 that_CS22 to_II estimate_NN1 the_AT eigenvalues_NN2 of_IO J_ZZ1 we_PPIS2 also_RR meed_VV0 to_TO compute_VVI the_AT eigenvalues_NN2 of_IO the_AT matrices_NN2 Aj_VV0 ,_, evaluated_VVN on_II the_AT splay_NN1 attractor_NN1 values_NN2 j_ZZ1 and_CC j_ZZ1 obtained_VVN from_II the_AT recurrence_NN1 equations_NN2 (_( 3_MC )_) ._. 
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The_AT former_DA case_NN1 shows_VVZ small_JJ fluctuations_NN2 around_RG 1/4_MF ,_, while_CS for_IF the_AT latter_DA there_RL are_VBR large_JJ fluctuations_NN2 observed_VVN at_II 2_MC log2_FO N_ZZ1 ,_, twice_RR the_AT log_NN1 time_NNT1 ,_, and_CC possibly_RR multiples_NN2 of_IO these_DD2 with_IW decreasing_JJ amplitude_NN1 ._. 
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We_PPIS2 can_VM still_RR use_VVI a_AT1 solvable_JJ part_NN1 within_II the_AT Hamiltonian_JJ to_TO construct_VVI the_AT basis_NN1 and_CC perform_VVI an_AT1 expansion_NN1 around_II it_PPH1 ._. 
</s>
<s>
The_AT microwave_NN1 spectrum_NN1 of_IO the_AT chiral_JJ monoterpenol_NN1 molecule_NN1 ,_, (_( 1R_FO )_) -(A)-myrtenol_NN1 ,_, has_VHZ been_VBN observed_VVN using_VVG CP-FTMW_JJ spectroscopy_NN1 in_II the_AT 6-18_MCMC GHz_NNU region_NN1 of_IO the_AT electromagnetic_JJ spectrum_NN1 ._. 
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<s>
Consider_VV0 a_AT1 vertex_NN1 such_II21 as_II22 the_AT one_PN1 shown_VVN in_II the_AT first_MD diagram_NN1 in_II Fig._NN1 3_MC ._. 
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<s>
However_RR ,_, in_II the_AT alignment_NN1 limit_NN1 &lsqb;_( 41_MC &rsqb;_) ,_, the_AT heavier_JJR CP-even_JJ scalar_JJ (_( H_ZZ1 )_) can_VM serve_VVI as_II the_AT observed_JJ 125_MC GeV_NP1 Higgs_NP1 boson_NN1 while_CS the_AT other_JJ scalar_JJ h_ZZ1 can_VM be_VBI very_RG light_JJ &lsqb;_( 42,43_MC &rsqb;_) ._. 
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<s>
We_PPIS2 discuss_VV0 these_DD2 considerations_NN2 in_II detail_NN1 in_II the_AT next_MD four_MC subsections_NN2 ._. 
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<s>
This_DD1 gives_VVZ a_AT1 very_RG general_JJ result_NN1 allowing_VVG one_PN1 to_TO consider_VVI Rényi_JJ entropy_NN1 uncertainty_NN1 relations_NN2 that_CST go_VV0 beyond_II the_AT usual_JJ conjugacy_NN1 curve_NN1 ,_, defined_VVN by_II <Equation>_FO ._. 
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<s>
A_AT1 central_JJ tenet_NN1 in_II our_APPGE effort_NN1 to_TO address_VVI the_AT above_JJ questionsas_NN2 laid_VVD out_RP at_RR21 length_RR22 in_II the_AT mentioned_VVN companion_NN1 paper_NN1 &lsqb;_( 179_MC &rsqb;_) ,_, is_VBZ that_DD1 the_AT DLH_NP1 minerals_NN2 of_IO interest_NN1 are_VBR essentially_RR insulating_JJ and_CC impermeable_JJ orthogonal_JJ to_II their_APPGE layered_JJ structure_NN1 while_CS being_VBG ,_, in_II partial_JJ degrees_NN2 ,_, conducting_VVG and_CC permeable_JJ in_II the_AT parallel_JJ direction_NN1 ._. 
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<s>
In_II the_AT PMMA/GO/WO3_NN1 shown_VVN in_II Fig._NN1 1_MC1 (_( b_ZZ1 )_) ,_, GO_VV0 layers_NN2 are_VBR wrapped_VVN on_II tungsten_NN1 and_CC dense_JJ layers_NN2 were_VBDR formed_VVN sporadically_RR ._. 
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<s>
In_II most_DAT scientific_JJ works_NN ,_, as_RG well_RR as_CSA in_II this_DD1 review_NN1 ,_, the_AT term_NN1 optoelectronic_JJ oscillator_NN1 and_CC the_AT acronym_NN1 OEO_NP1 are_VBR used_VVN in_II a_AT1 broad_JJ sense_NN1 to_TO describe_VVI any_DD autonomous_JJ oscillator_NN1 that_CST concatenates_VVZ an_AT1 electronic_JJ and_CC an_AT1 optical_JJ branch_NN1 ,_, as_CSA in_II Fig._NN1 1_MC1 ._. 
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<s>
The_AT present_JJ oscillator_NN1 strength_NN1 distributions_NN2 are_VBR very_RG similar_JJ to_II those_DD2 used_VVN in_II a_AT1 previous_JJ non-relativistic_JJ investigation_NN1 of_IO the_AT dispersion_NN1 coefficients_NN2 of_IO various_JJ low-lying_JJ states_NN2 of_IO the_AT lithium_NN1 dimer_NN1 &lsqb;_( 41_MC &rsqb;_) ._. 
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<s>
This_DD1 implies_VVZ :_: <EQUATION>_FO <EQUATION>_FO <EQUATION>_FO <EQUATION>_FO <EQUATION>_FO <EQUATION>_FO <EQUATION>_FO <EQUATION>_FO leading_VVG to_II the_AT second_MD statement_NN1 ;_; here_RL the_AT <Professional_FO Term>_FO ,_, <Professional_FO Term>_FO denote_VV0 the_AT RTT_NP1 generators_NN2 and_CC Drinfeld_VV0 generators_NN2 of_IO Uq1_FO (_( g_ZZ1 )_) arising_VVG from_II &lsqb;_( 51_MC &rsqb;_) ;_; see_VV0 Remark_NN1 1.2_MC ._. 
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<s>
Consequently_RR ,_, under_II a_AT1 constant_JJ P_ZZ1 ,_, WCA_NP1 increases_VVZ with_IW increasing_JJ scanning_NN1 velocity_NN1 ._. 
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<s>
Hence_RR the_AT recent_JJ properties_NN2 of_IO the_AT CMB_NP1 are_VBR defined_VVN by_II the_AT two-photon_JJ processes_NN2 during_II the_AT cosmological_JJ recombination_NN1 epoch_NN1 ._. 
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<s>
When_CS the_AT strain_NN1 value_NN1 is_VBZ less_DAR than_CSN 6.4%_FO (_( 7%_NNU )_) with_IW the_AT biaxial_JJ (_( uniaxial_JJ )_) strain_VV0 ,_, the_AT absorption_NN1 curve_NN1 becomes_VVZ sharper_JJR ,_, and_CC the_AT absorption_NN1 range_NN1 becomes_VVZ narrower_JJR ._. 
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<s>
In_II this_DD1 context_NN1 ,_, Garmire_NP1 et_RA21 al_RA22 ._. 
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(_( 1979_MC )_) studied_VVD the_AT switching_JJ time_NNT1 of_IO a_AT1 bistable_JJ optoelectronic_JJ oscillator_NN1 with_IW a_AT1 Pockels_NP2 cell_NN1 as_CSA it_PPH1 evolved_VVD between_II two_MC stable_JJ states_NN2 ;_; Okada_NP1 and_CC Takizawa_NP1 (_( 1980_MC )_) considered_VVD the_AT dynamics_NN of_IO optical_JJ regenerative_JJ oscillation_NN1 and_CC pulse_NN1 generation_NN1 in_II an_AT1 optoelectronic_JJ oscillator_NN1 with_IW a_AT1 lithium_NN1 niobate_NN1 waveguide_NN1 modulator_NN1 ,_, and_CC Kaplan_NP1 (_( 1981_MC )_) proposed_VVD a_AT1 nonlinear_JJ analysis_NN1 of_IO an_AT1 optoelectronic_JJ oscillator_NN1 with_IW an_AT1 electro-optically_RR driven_JJ interface_NN1 ._. 
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They_PPHS2 used_VVD a_AT1 delayembedding_JJ technique_NN1 to_TO reconstruct_VVI the_AT attractor_NN1 corresponding_VVG to_II the_AT experimental_JJ time_NNT1 series_NN ._. 
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The_AT main_JJ result_NN1 and_CC some_DD corollaries_NN2 are_VBR presented_VVN in_II Sect._NP1 3_MC ._. 
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The_AT caustic_JJ region_NN1 itself_PPX1 may_VM then_RT be_VBI resolved_VVN using_VVG AMR_NP1 at_II wavelength_NN1 scales_NN2 ._. 
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The_AT energy-dependent_JJ information_NN1 of_IO the_AT theoretical_JJ spectrum_NN1 must_VM thus_RR be_VBI accurate_JJ enough_RR to_TO guarantee_VVI ll_NNU remaining_JJ slope_NN1 artifacts_NN2 to_TO be_VBI <0.1%_FO MeV1_FO ._. 
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<s>
In_RR21 addition_RR22 ,_, we_PPIS2 unveil_VV0 the_AT dynamical_JJ behaviors_NN2 of_IO the_AT uncertainty_NN1 measured_VVN on_II SU_NP1 (_( 3_MC )_) generators_NN2 ,_, and_CC it_PPH1 proves_VVZ that_CST the_AT uncertainty_NN1 '_NULL s_ZZ1 dynamics_NN are_VBR subtly_RR different_JJ from_II those_DD2 in_II the_AT former_DA ._. 
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<s>
By_II using_VVG more_DAR beam_NN1 splitters_NN2 (_( <Professional_FO Term>_FO and_CC <Professional_FO Term>_FO )_) we_PPIS2 have_VH0 four_MC <Professional_FO Term>_FO polarized_JJ beams_NN2 with_IW very_RG close_JJ powers_NN2 that_CST corresponds_VVZ to_II four_MC empty_JJ battlefields_NN2 ._. 
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However_RR ,_, till_CS date_NN1 ,_, no_AT attempt_NN1 has_VHZ been_VBN taken_VVN to_TO study_VVI quantum_NN1 entanglement_NN1 using_VVG geometry_NN1 of_IO quantum_NN1 state_NN1 space_NN1 ._. 
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<s>
Based_VVN on_II the_AT equations_NN2 from_II the_AT Spitzer–Harm_NN1 conduction_NN1 and_CC power_NN1 balance_NN1 ,_, a_AT1 simple_JJ relation_NN1 can_VM be_VBI deduced_VVN to_TO derive_VVI the_AT perpendicular_JJ heat_NN1 transport_NN1 coefficient_NN1 ,_, from_II the_AT measured_JJ parameters_NN2 ._. 
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<s>
Even_CS21 though_CS22 the_AT non-exponential_JJ behaviour_NN1 at_II large_JJ times_NNT2 was_VBDZ confirmed_VVN in_II an_AT1 experiment_NN1 measuring_VVG the_AT luminescence_NN1 decays_NN2 of_IO many_DA2 dissolved_JJ organic_JJ materials_NN2 after_II pulsed_JJ laser_NN1 excitation_NN1 &lsqb;_( 7_MC &rsqb;_) ,_, the_AT failure_NN1 of_IO the_AT nuclear_JJ and_CC particle_NN1 physics_NN1 experiments_NN2 raised_VVD questions_NN2 about_II observation_NN1 such_II21 as_II22 :_: (_( i_ZZ1 )_) how_RRQ long_RR should_VM one_PN1 wait_VVI or_CC in_II other_JJ words_NN2 ,_, what_DDQ is_VBZ the_AT critical_JJ transition_NN1 time_NNT1 from_II the_AT exponential_NN1 to_II a_AT1 power_NN1 law_NN1 behaviour_NN1 ,_, (_( ii_MC )_) does_VDZ the_AT interaction_NN1 with_IW the_AT environment_NN1 affect_VV0 the_AT measurement_NN1 and_CC (_( iii_MC )_) could_VM it_PPH1 be_VBI possible_JJ that_CST every_AT1 measurement_NN1 resets_VVZ the_AT decay_NN1 to_II an_AT1 exponential_NN1 one_MC1 ,_, thus_RR making_VVG the_AT non-exponential_JJ behaviour_NN1 not_XX observable_JJ ._. 
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<s>
If_CS this_DD1 could_VM be_VBI successfully_RR achieved_VVN ,_, then_RT one_PN1 could_VM use_VVI selected_JJ dopants_NN2 as_CSA optical_JJ probes_NN2 of_IO superfluid_JJ phenomena_NN2 ._. 
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<s>
In_II this_DD1 work_NN1 the_AT investigation_NN1 of_IO influence_NN1 of_IO the_AT beam_NN1 of_IO charged_JJ particles_NN2 on_II the_AT structural_JJ and_CC electrical_JJ properties_NN2 of_IO glassy_JJ composite_JJ AgGe1.6As0.4_NP1 (_( S_ZZ1 +CNT_FO )_) 3_MC was_VBDZ shown_VVN ._. 
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<s>
On_II the_AT contrary_NN1 ,_, if_CS the_AT Blandford-Znajek_NP1 mechanism_NN1 is_VBZ responsible_JJ for_IF the_AT formation_NN1 of_IO steady_JJ jets_NN2 ,_, the_AT absence_NN1 of_IO a_AT1 correlation_NN1 between_II BH_NP1 spin_NN1 and_CC jet_NN1 power_NN1 found_VVN by_II Fender_NN1 ,_, Gallo_NP1 ,_, and_CC Russell_NP1 (_( 2010_MC )_) can_VM be_VBI explained_VVN with_IW the_AT fact_NN1 that_CST the_AT estimate_NN1 of_IO the_AT BH_NP1 spin_NN1 is_VBZ wrong_JJ ,_, because_CS it_PPH1 was_VBDZ obtained_VVN assuming_VVG the_AT Kerr_NP1 metric_JJ ._. 
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<s>
Hence_RR ,_, we_PPIS2 include_VV0 the_AT two-reservoir_JJ setup_NN1 to_TO study_VVI the_AT quantum_NN1 coherence_NN1 by_II setting_VVG <equation>_FO ,_, shown_VVN at_II Fig._NN1 2(a)_FO ._. 
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Moreover_RR ,_, the_AT method_NN1 is_VBZ able_JK to_TO reconstruct_VVI survey-based_JJ indicators_NN2 of_IO regional_JJ poverty_NN1 with_IW high_JJ accuracy_NN1 ._. 
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<s>
For_IF the_AT field_NN1 of_IO the_AT accelerating_JJ kink_NN1 and_CC mirror_NN1 kink_VV0 we_PPIS2 can_VM choose_VVI <Equation>_FO ,_, and_CC there_RL <Equation>_FO and_CC <Equation>_FO ._. 
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<s>
Some_DD of_IO the_AT steps_NN2 in_II the_AT associative_JJ path_NN1 have_VH0 lower_JJR Tafellike_JJ barriers_NN2 ._. 
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<s>
We_PPIS2 have_VH0 demonstrated_VVN the_AT wide_JJ ranging_JJ applicability_NN1 of_IO the_AT QMC_NP1 model_NN1 in_II different_JJ areas_NN2 of_IO physics_NN1 ._. 
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<s>
Besides_II that_DD1 ,_, restriction_NN1 of_IO the_AT space_NN1 accessible_JJ to_II membrane-associated_JJ components_NN2 results_NN2 in_II increased_JJ likelihood_NN1 of_IO their_APPGE interactions_NN2 and_CC average_JJ number_NN1 of_IO collisions_NN2 per_II unit_NN1 time_NNT1 ._. 
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The_AT lithiation_NN1 mechanism_NN1 of_IO Ag2S_FO is_VBZ deduced_VVN to_TO be_VBI displacement_NN1 reaction_NN1 ._. 
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<s>
One_MC1 of_IO the_AT first_MD architectures_NN2 in_II this_DD1 category_NN1 was_VBDZ proposed_VVN by_II Yao_NP1 (_( 1997_MC )_) ,_, and_CC it_PPH1 was_VBDZ based_VVN on_II Brillouin_NP1 scattering_VVG in_II the_AT optical_JJ fiber-delay_JJ line_NN1 ._. 
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This_DD1 is_VBZ our_APPGE next_MD corollary_NN1 ,_, stated_VVN below_RL ._. 
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<s>
An_AT1 artistic_JJ view_NN1 of_IO a_AT1 fully_RR integrated_VVN OEO_NP1 based_VVN on_II stimulated_JJ Brillouin_NP1 scattering_NN1 (_( SBS_NP1 )_) ._. 
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<s>
In_II this_DD1 work_NN1 ,_, we_PPIS2 investigate_VV0 the_AT scattering_NN1 properties_NN2 and_CC non-reciprocal_JJ quantum_NN1 entanglement_NN1 in_II non-Hermitian_JJ system_NN1 of_IO SP_NN1 coupled_VVN to_II two_MC PCs_NN2 with_IW different_JJ resonance_NN1 frequencies_NN2 ._. 
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<s>
The_AT typical_JJ molecules_NN2 ,_, rubrene_NN1 and_CC pentacene_NN1 ,_, with_IW recorded_JJ mobility_NN1 in_II their_APPGE crystals_NN2 as_CSA exemplified_VVN above_RL only_RR satisfy_VV0 the_AT former_DA requirement_NN1 ._. 
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<s>
LCK-3_MC delivers_VVZ discharge_NN1 capacities_NN2 of_IO 104.4_MC ,_, 88.9_MC ,_, and_CC 73.1_MC mAh_NN1 g_ZZ1 at_II 0.5_MC ,_, 7_MC ,_, and_CC 15_MC C_NP1 ,_, respectively_RR ,_, 26.7_MC ,_, 42.9_MC ,_, and_CC 53.0_MC mAh_NN1 g_ZZ1 higher_RRR than_CSN those_DD2 of_IO LC_NP1 ._. 
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<s>
The_AT 4th_MD order_NN1 coefficient_NN1 Cxxxx_NP1 has_VHZ a_AT1 weak_JJ stabilizing_JJ contribution_NN1 up_II21 to_II22 about_II 70_MC and_CC is_VBZ destabilizing_VVG at_II larger_JJR angles_NN2 ._. 
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Then_RT the_AT color-tunable_JJ light-emission_NN1 can_VM be_VBI altered_VVN from_II yellow-green_NN1 (_( without_IW a_AT1 polarizer_NN1 )_) to_II green_NN1 (_( TE_FW mode_NN1 )_) ,_, and_CC yellow_JJ (_( TM_NP1 mode_NN1 )_) ._. 
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<s>
This_DD1 implies_VVZ that_CST the_AT '_NULL weight_NN1 '_NULL and_CC the_AT '_NULL probability_NN1 '_NULL of_IO each_DD1 macrostate_NN1 are_VBR inferentially_RR defined_VVN by_II the_AT obvious_JJ sums_NN2 :_: <Equation>where_FO w_ZZ1 is_VBZ the_AT weight_NN1 of_IO the_AT th_NNU macrostate_NN1 and_CC is_VBZ just_RR the_AT sum_NN1 of_IO the_AT weights_NN2 of_IO all_DB of_IO the_AT microstates_NN2 it_PPH1 contains_VVZ ._. 
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<s>
H_ZZ1 0_MC is_VBZ the_AT spin-independent_JJ part_NN1 ,_, <Equation>_FO is_VBZ the_AT s-d_ZZ1 exchange_NN1 ._. 
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<s>
They_PPHS2 found_VVD that_CST the_AT logistic_JJ regression_NN1 and_CC linear_JJ SVM_NP1 perform_VV0 the_AT best_JJT with_IW an_AT1 accuracy_NN1 0.814_MC ._. 
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<s>
By_II the_AT definition_NN1 of_IO F_ZZ1 ,_, and_CC the_AT fact_NN1 that_CST A2n_FO =_FO 0_MC ,_, we_PPIS2 obtain_VV0 the_AT values_NN2 of_IO <Equation>_FO Ak_NP1 (_( 0_MC )_) for_IF k_ZZ1 <_FO n_ZZ1 ._. 
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<s>
We_PPIS2 also_RR recover<Professional_FO Term_NN1 >_FO for_IF z_ZZ1 close_JJ to_II p_ZZ1 in_II a_AT1 similar_JJ way_NN1 ._. 
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<s>
It_PPH1 is_VBZ easy_JJ to_TO see_VVI that_CST X_ZZ1 is_VBZ C_ZZ1 H_ZZ1 -hermitian_JJ in_II the_AT sense_NN1 that_CST <Professional_FO terms>_FO where_RRQ <Professional_FO terms>_FO ._. 
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<s>
However_RR ,_, for_IF a_AT1 system_NN1 implemented_VVN with_IW realistic_JJ capacitors_NN2 ,_, the_AT imperfect_JJ boundaries_NN2 should_VM be_VBI modeled_VVN by_II the_AT standard_JJ input-output_NN1 formalism_NN1 discussed_VVD later_RRR ._. 
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Thus_RR ,_, the_AT calculation_NN1 of_IO Gx_NP1 and_CC G_ZZ1 y_ZZ1 is_VBZ defined_VVN in_II Eq_NN1 ._. 
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<s>
(_( 4_MC )_) <Equation>_FO ._. 
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<s>
Although_CS the_AT laser_NN1 pulse_NN1 was_VBDZ 10_MC ns_FO ,_, the_AT spatial_JJ resolution_NN1 at_II the_AT 40_MC km_NNU position_NN1 was_VBDZ several_DA2 meters_NN2 due_II21 to_II22 dispersion_NN1 in_II the_AT 50/125_MF lm_NNU graded-index_JJ multimode_JJ fiber_NN1 used_VVN for_IF this_DD1 demonstration_NN1 ._. 
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<s>
Stellar_JJ winds_NN2 are_VBR streams_NN2 of_IO plasma_NN1 that_CST originate_VV0 from_II the_AT outer_JJ regions_NN2 of_IO stellar_JJ coronae_NN2 (_( Parker_NP1 ,_, 1958_MC ;_; Priest_NN1 ,_, 2014_MC )_) ._. 
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<s>
The_AT sharp_JJ peak_NN1 in_II Cel/T_NP1 versus_II p_NNU (_( Figure_NN1 6a_FO )_) is_VBZ a_AT1 classic_JJ thermodynamic_JJ signature_NN1 of_IO a_AT1 QCP_NP1 ._. 
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Thus_RR ,_, while_CS it_PPH1 is_VBZ reasonable_JJ to_TO describe_VVI the_AT quarks_NN2 as_II ,_, on_II average_NN1 ,_, being_VBG confined_VVN in_II a_AT1 bag-like_JJ region_NN1 ,_, the_AT interior_NN1 of_IO the_AT cavity_NN1 can_VM no_RR21 longer_RR22 be_VBI regarded_VVN as_II having_VHG a_AT1 purely_RR perturbative_JJ character_NN1 and_CC the_AT boundary_NN1 surface_NN1 is_VBZ just_RR a_AT1 device_NN1 to_TO account_VVI for_IF the_AT fact_NN1 that_CST the_AT quarks_NN2 do_VD0 not_XX escape_VVI ._. 
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The_AT EIS_NN1 spectra_NN2 of_IO the_AT three_MC discharged_JJ cells_NN2 measured_VVN indicate_VV0 consistent_JJ stabilization_NN1 in_II the_AT values_NN2 of_IO charge_NN1 transfer_NN1 resistance_NN1 (_( R2_FO )_) and_CC Li_NP1 ion_NN1 difiusion_NN1 impedance_NN1 suggesting_VVG ceasing_NN1 of_IO electrolyte_NN1 and_CC electrode_VV0 oxidation_NN1 ._. 
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In_II this_DD1 approach_NN1 the_AT individual_JJ background_NN1 contributions_NN2 are_VBR floated_VVN individually_RR ,_, and_CC a_AT1 scaling_NN1 factor_NN1 is_VBZ then_RT applied_VVN under_II the_AT Higgs_NP1 pole_NN1 ._. 
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Many_DA2 real_JJ systems_NN2 display_VV0 the_AT number_NN1 of_IO links_NN2 increases_VVZ faster_JJR than_CSN the_AT number_NN1 of_IO nodes_NN2 ,_, thus_RR the_AT increase_NN1 of_IO the_AT average_JJ degree_NN1 in_II growing_JJ network_NN1 describes_VVZ the_AT corresponding_JJ scaling_NN1 relations_NN2 for_IF the_AT accelerated_JJ growth_NN1 ._. 
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Since_CS the_AT computational_JJ workload_NN1 of_IO standard_NN1 (_( not_XX linear-scaling_JJ )_) DFT_NP1 calculations_NN2 scales_NN2 as_II the_AT cube_NN1 of_IO the_AT number_NN1 of_IO electrons_NN2 ,_, the_AT saving_NN1 afforded_VVN by_II DFPT_NP1 over_II the_AT frozen-phonon_JJ method_NN1 is_VBZ proportional_JJ to_II N2_FO p_ZZ1 ,_, and_CC typically_RR corresponds_VVZ to_II a_AT1 <Equation>_FO ._. 
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In_II this_DD1 expression_NN1 ,_, the_AT Nmax-by-Nmax_NP1 diagonal_JJ matrix_NN1 the_AT cavity_NN1 susceptibility_NN1 ._. 
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We_PPIS2 estimate_VV0 density_NN1 between_II L0_FO /50_MF and_CC L0_FO /500_MF ._. 
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Using_VVG the_AT artificial_JJ neural_JJ network_NN1 we_PPIS2 have_VH0 explored_VVN the_AT interplay_NN1 between_II bunched_JJ and_CC antibunched_JJ photon_NN1 exchange_NN1 statistics_NN for_IF different_JJ engine_NN1 parameters_NN2 ._. 
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The_AT first_MD J_ZZ1 blocks_NN2 are_VBR identical_JJ to_II the_AT ones_NN2 of_IO JH_NP1 ,_, while_CS the_AT following_JJ ones_NN2 are_VBR obtained_VVN by_II evaluating_VVG the_AT linearized_JJ equation_NN1 along_II the_AT splay_NN1 state_NN1 part_NN1 of_IO the_AT attractor_NN1 ._. 
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Therefore_RR ,_, different_JJ electrolytes_NN2 do_VD0 not_XX have_VHI an_AT1 effect_NN1 on_II the_AT XRD_NP1 results_NN2 before_II cycle_NN1 ,_, which_DDQ improves_VVZ the_AT reliability_NN1 of_IO the_AT test_NN1 results_NN2 ._. 
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To_TO understand_VVI the_AT reservations_NN2 ,_, we_PPIS2 have_VH0 to_TO examine_VVI the_AT weaknesses_NN2 of_IO this_DD1 scenario_NN1 ._. 
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Matter_VV0 wave_NN1 interferometry_NN1 and_CC quantum_NN1 optomechanics_NN2 with_IW more_DAR and_CC more_RGR massive_JJ systems_NN2 are_VBR also_RR at_II the_AT core_NN1 of_IO intensive_JJ experimental_JJ efforts_NN2 ._. 
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As_II a_AT1 result_NN1 ,_, 2_MC GPa_NP1 applied_VVD to_II a_AT1 sample_NN1 with_IW <equation>_FO eliminates_VVZ the_AT upturn_NN1 completely_RR ,_, and_CC (_( T_ZZ1 )_) then_RT becomes_VVZ perfectly_RR T_ZZ1 linear_JJ (_( Figure_NN1 8b_FO )_) ._. 
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Secondly_RR ,_, and_CC more_RGR importantly_RR ,_, the_AT accuracy_NN1 in_II absolute_JJ electron_NN1 densities_NN2 has_VHZ to_TO be_VBI increased_VVN ._. 
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The_AT growth/damping_NN1 rate_NN1 of_IO KAWs_NP2 can_VM be_VBI obtained_VVN from_II Eq_NN1 ._. 
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(_( 26_MC )_) by_II assuming_VVG <Equation>_FO ,_, where_RRQ Or_CC is_VBZ the_AT real_JJ frequency_NN1 and_CC <Equation>_FO is_VBZ the_AT growth/damping_NN1 rate_NN1 of_IO the_AT wave_NN1 ._. 
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Particularly_RR ,_, the_AT effect_NN1 of_IO the_AT nonlinear_JJ behavior_NN1 on_II a_AT1 ME_NN1 antenna_NN1 '_NULL s_ZZ1 communication_NN1 distance_NN1 ,_, bandwidth_NN1 ,_, and_CC modulation_NN1 scheme_NN1 is_VBZ preliminarily_RR discussed_VVN ._. 
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In_RR21 particular_RR22 ,_, the_AT Glauber-Sudarshan_NP1 P_ZZ1 representation_NN1 is_VBZ an_AT1 expansion_NN1 of_IO the_AT state_NN1 in_II the_AT over_JJ complete_JJ basis_NN1 of_IO coherent_JJ states_NN2 <Equation>_FO ._. 
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Conventionally_RR ,_, one_PN1 calls_VVZ spallation_NN1 reactions_NN2 those_DD2 interactions_NN2 where_RRQ CR_NP1 nuclei_NN2 fragment_VV0 on_II gas_NN1 of_IO the_AT ISM_FU ,_, loosing_VVG one_MC1 or_CC more_DAR nucleons_NN2 and_CC producing_VVG thereby_RR lighter_JJR nuclei_NN2 ._. 
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They_PPHS2 ask_VV0 if_CSW for_IF any_DD bipartite_JJ quantum_NN1 state_NN1 <Equation>_FO ,_, <Equation>_FO ,_, where_CS <Equation>_FO and_CC <Equation>_FO are_VBR the_AT registers_NN2 associated_VVN with_IW measuring_VVG two_MC MUBs_NP2 <Equation>_FO and_CC <Equation>_FO on_II system_NN1 A_ZZ1 ,_, and_CC likewise_RR for_IF <Equation>_FO and_CC <Equation>_FO on_II system_NN1 B._NP1 Equation_NN1 (_( 238_MC )_) says_VVZ that_CST the_AT quantum_NN1 mutual_JJ information_NN1 is_VBZ lower_RRR bounded_VVN by_II the_AT sum_NN1 of_IO the_AT classical_JJ mutual_JJ information_NN1 in_II two_MC mutually_RR unbiased_JJ bases_NN2 ._. 
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<s>
Type_NN1 III_MC complexes_NN2 were_VBDR most_RGT frequently_RR represented_VVN among_II the_AT low-energy_JJ structures_NN2 ,_, as_CSA illustrated_VVN by_II structures_NN2 5_MC and_CC 6_MC ,_, in_II31 addition_II32 to_II33 2_MC and_CC 3_MC ._. 
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This_DD1 uniform_JJ density_NN1 is_VBZ then_RT replaced_VVN by_II that_DD1 of_IO Eq_NN1 ._. 
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(_( 37_MC )_) ,_, from_II which_DDQ we_PPIS2 can_VM calculate_VVI the_AT electric_JJ potential_NN1 at_II the_AT center_NN1 of_IO the_AT nucleus_NN1 ,_, yielding_VVG (_( Wilkinson_NP1 ,_, 1994_MC )_) <Equation>for_FO the_AT prolate_NN1 case_NN1 and<Equation>in_FO the_AT notation_NN1 of_IO Behrens_NN2 and_CC Buhring_NP1 (_( 1967_MC )_) ,_, where_RRQ are_VBR simple_JJ functions_NN2 of_IO the_AT lepton_NN1 momenta_NN1 andslowly_RR varying_JJ Coulomb_NN1 functions_NN2 ,_, proportional_JJ to_II R_ZZ1 ,_, and_CC where_CS the_AT subscript_NN1 NR_II stands_NN2 for_IF nonrelativistic_JJ ._. 
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An_AT1 example_NN1 of_IO the_AT transformations_NN2 C(x+)_FO and_CC C(y-)_NN1 for_IF an_AT1 image_NN1 with_IW size_NN1 of_IO 4_MC ×_II 4_MC also_RR is_VBZ shown_VVN in_II Fig._NN1 14_MC ,_, where_CS all_DB pixels_NN2 shift_VV0 one_MC1 unit_NN1 rightwards_RL and_CC upwards_RL ,_, respectively_RR ._. 
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It_PPH1 then_RT follows_VVZ directly_RR from_II Eq_NN1 ._. 
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(_( 71_MC )_) that_CST the_AT cross_NN1 correlation_NN1 vanishes_VVZ :_: jz_NNU (_( z_ZZ1 ,_, <EQUATION>_FO (_( 93_MC )_) and_CC that_CST the_AT diagonal_JJ correlations_NN2 are_VBR holomorphic_JJ and_CC anti-holomorphic_JJ :_: <EQUATION>_FO (_( 94_MC )_) for_IF some_DD parameter_NN1 n_ZZ1 ._. 
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In_II the_AT following_JJ we_PPIS2 focus_VV0 on_II a_AT1 selected_JJ range_NN1 of_IO Higgs-relevant_JJ processes_NN2 that_CST demonstrate_VV0 the_AT improvement_NN1 that_CST can_VM be_VBI achieved_VVN at_II such_DA machines_NN2 compared_VVN to_II the_AT LHC_NP1 ,_, and_CC how_RRQ measurements_NN2 in_II these_DD2 channels_NN2 will_VM compare_VVI against_II lepton_NN1 collider_NN1 concepts_NN2 ._. 
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This_DD1 process_NN1 was_VBDZ then_RT repeated_VVN for_IF the_AT desired_JJ number_NN1 of_IO cycles_NN2 ._. 
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It_PPH1 is_VBZ found_VVN that_CST the_AT aqueous_JJ H2O2_FO and_CC peroxynitrite_NN1 are_VBR mainly_RR dissolved_VVN from_II the_AT gas_NN1 phase_NN1 ,_, the_AT aqueous_JJ O2-_NN1 is_VBZ mainly_RR generated_VVN by_II the_AT electron_NN1 absorption_NN1 by_II dissolved_JJ oxygen_NN1 ,_, and_CC the_AT aqueous_JJ OH_UH is_VBZ mainly_RR generated_VVN by_II the_AT deposition_NN1 of_IO positive_JJ ions_NN2 ._. 
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The_AT term_NN1 E_ZZ1 (_( ,_, 0_MC )_) is_VBZ the_AT energy_NN1 of_IO neutron–_JJ proton_NN1 symmetric_JJ nuclear_JJ matter_NN1 ._. 
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It_PPH1 was_VBDZ reported_VVN that_DD1 chitosan_NN1 was_VBDZ used_VVN as_II a_AT1 dispersing_NN1 and_CC charging_JJ agent_NN1 for_IF both_RR HNT_NP1 and_CC HAP_NP1 ._. 
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Many_DA2 of_IO these_DD2 challenges_NN2 are_VBR related_VVN to_II the_AT relatively_RR slow_JJ kinetics_NN1 of_IO the_AT oxygen_NN1 reduction_NN1 reaction_NN1 (_( ORR_NP1 )_) at_II the_AT cathode_NN1 ;_; 5–7_MCMC this_DD1 necessitates_VVZ the_AT use_NN1 of_IO a_AT1 high_JJ overpotential_JJ and_CC directly_RR lowers_VVZ the_AT efficiency_NN1 of_IO the_AT fuel_NN1 cell_NN1 ._. 
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On_II the_AT other_JJ hand_NN1 ,_, the_AT additional_JJ CP-even_JJ and_CC CP-odd_JJ singlet_NN1 field_NN1 can_VM be_VBI light_JJ with_IW sizeable_JJ couplings_NN2 to_II the_AT singlino_NN1 and_CC reduced_VVD couplings_NN2 to_II the_AT Standard_JJ Model_NN1 ._. 
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In_II the_AT TROVE_NN1 approach_NN1 &lsqb;_( 24,25_MC &rsqb;_) ,_, the_AT wave_NN1 functions_NN2 Urv_NN1 and_CC Urv_NP1 are_VBR expressed_VVN as_CSA linear_JJ combinations_NN2 of_IO basic_JJ functions_NN2 ,_, i.e._REX ,_, <equation>with_FO an_AT1 analogous_JJ expression_NN1 for_IF Urv_NN1 ._. 
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In_II semiconductor_NN1 materials_NN2 where_RRQ the_AT iSGE_NN1 and_CC SHE_PPHS1 were_VBDR initially_RR discovered_VVN ,_, and_CC even_RR more_RRR in_II metal_NN1 structures_NN2 ,_, multiple_JJ bands_NN2 cross_VV0 the_AT Fermi_NP1 level_NN1 and_CC their_APPGE respective_JJ contributions_NN2 to_II the_AT current-induced_JJ spin_NN1 density_NN1 tend_VV0 to_TO compensate_VVI each_PPX221 other_PPX222 ._. 
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Hence_RR the_AT right-hand_JJ side_NN1 of_IO (_( 6.21_MC )_) amounts_VVZ to_II some_DD field_NN1 redefinition_NN1 ._. 
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For_REX21 example_REX22 ,_, signatures_NN2 of_IO criticality_NN1 have_VH0 been_VBN reported_VVN to_TO fade_VVI away_RL during_II epileptic_JJ seizures_NN2 (_( Hobbs_NP1 ,_, Smith_NP1 ,_, and_CC Beggs_NP1 ,_, 2010_MC ;_; Meisel_NP1 et_RA21 al._RA22 ,_, 2012_MC )_) as_II31 well_II32 as_II33 during_II anomalously_RR large_JJ periods_NN2 of_IO wakefulness_NN1 (_( Meisel_NP1 et_RA21 al._RA22 ,_, 2013_MC )_) or_CC while_CS performing_VVG simple_JJ tasks_NN2 (_( Tomen_NP1 ,_, Rotermund_NP1 ,_, and_CC Ernst_NP1 ,_, 2014_MC ;_; Hahn_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
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Spectra_NN2 showing_VVG 2_MC extra_JJ lines_NN2 at_II <Equation>_FO ,_, accompanying_VVG the_AT <Professional_FO Term>_FO and_CC P_ZZ1 (_( 15_MC )_) lines_NN2 ,_, are_VBR shown_VVN in_II Fig._NN1 6_MC ._. 
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As_II an_AT1 important_JJ consequence_NN1 ,_, the_AT present_JJ results_NN2 show_VV0 that_CST the_AT acoustic_JJ absorption_NN1 at_II low_JJ temperatures_NN2 is_VBZ limited_VVN by_II extrinsic_JJ (_( rather_CS21 than_CS22 by_II intrinsic_JJ )_) mechanisms_NN2 ,_, which_DDQ can_VM be_VBI minimized_VVN by_II improving_VVG the_AT quality_NN1 of_IO the_AT surfaces_NN2 and_CC interfaces_NN2 ._. 
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In_II the_AT <Equation>_FO of_IO this_DD1 equation_NN1 ,_, the_AT second_MD term_NN1 (_( the_AT term_NN1 )_) is_VBZ the_AT average_JJ shift_NN1 ,_, the_AT third_MD term_NN1 (_( the_AT <Equation>_FO term_NN1 )_) is_VBZ the_AT pileup_NN1 fluctuations_NN2 ,_, responsible_JJ for_IF degrading_VVG the_AT jet_NN1 energy_NN1 resolution_NN1 ,_, and_CC the_AT fourth_MD is_VBZ the_AT back-reaction_JJ effects_NN2 ,_, all_RR introduced_VVN above_RL ._. 
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The_AT independence_NN1 on_II representatives_NN2 of_IO the_AT second_MD argument_NN1 of_IO (_( ,_, )_) CH_NN1 follows_VVZ from_II the_AT hermitian_JJ symmetry_NN1 of_IO <Professional_FO terms>_FO ._. 
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This_DD1 probe_NN1 allows_VVZ absolute_JJ electron_NN1 density_NN1 measurements_NN2 ,_, while_CS due_II21 to_II22 its_APPGE small_JJ size_NN1 ,_, the_AT plasma_NN1 density_NN1 depletion_NN1 caused_VVN by_II its_APPGE presence_NN1 in_II the_AT plasma_NN1 is_VBZ low_JJ ._. 
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Wess-Zumino_JJ model_NN1 )_) can_VM be_VBI a_AT1 counterexample_NN1 for_IF the_AT "_" CT_NN1 "_" theorem_NN1 ._. 
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For_IF detection_NN1 ,_, a_AT1 frequency_NN1 mixing_NN1 effect_NN1 based_VVN on_II the_AT AMR_NP1 was_VBDZ used_VVN ._. 
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By_II the_AT use_NN1 of_IO suitable_JJ coordinate_NN1 transformations_NN2 ,_, this_DD1 exponential_NN1 can_VM be_VBI explicitly_RR computed_VVN and_CC the_AT attained_JJ line_NN1 element_NN1 can_VM have_VHI different_JJ algebraic_JJ structures_NN2 depending_II21 on_II22 the_AT canonical_JJ form_NN1 of_IO Q_ZZ1 0_MC ._. 
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In_II both_DB2 the_AT projectile_NN1 fragmentation_NN1 or_CC the_AT transfer_NN1 method_NN1 ,_, the_AT neutron–core_NN1 interaction_NN1 that_CST one_PN1 is_VBZ trying_VVG to_TO determine_VVI appears_VVZ in_II the_AT reaction_NN1 as_II a_AT1 "_" final_JJ state_NN1 "_" interaction_NN1 and_CC therefore_RR reliable_JJ information_NN1 on_II its_APPGE form_NN1 and_CC on_II the_AT values_NN2 of_IO its_APPGE parameters_NN2 can_VM be_VBI extracted_VVN only_RR if_CS the_AT primary_JJ reaction_NN1 is_VBZ well_JJ under_II control_NN1 from_II the_AT point_NN1 of_IO view_NN1 of_IO the_AT reaction_NN1 theory_NN1 ._. 
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Small_JJ stellar_JJ systems_NN2 ,_, dwarf_VV0 spheroidal_JJ galaxies_NN2 ,_, are_VBR found_VVN near_II the_AT Milky_JJ Way_NN1 Galaxy_NN1 ,_, sufficiently_RR close_VV0 so_CS21 that_CS22 interactions_NN2 with_IW the_AT Galaxy_NN1 are_VBR plausible_JJ ._. 
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The_AT recent_JJ advancements_NN2 in_II MEMS_NP2 technology_NN1 have_VH0 played_VVN a_AT1 pivotal_JJ role_NN1 in_II miniaturizing_VVG the_AT size_NN1 of_IO a_AT1 drug_NN1 delivery_NN1 device_NN1 by_II integrating_VVG components_NN2 ,_, such_II21 as_II22 batteries_NN2 ,_, electronics_NN1 ,_, processing_VVG unit_NN1 ,_, and_CC tiny_JJ reservoirs_NN2 within_II a_AT1 compact_JJ space_NN1 ._. 
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A_AT1 clear_JJ oscillation_NN1 is_VBZ identified_VVN after_II the_AT pump_NN1 with_IW the_AT oscillation_NN1 frequency_NN1 given_VVN by_II the_AT asymptotic_JJ value_NN1 of_IO the_AT superconducting_JJ gap_NN1 <Equation>_FO caused_VVN by_II the_AT quasiparticle_NN1 injection_NN1 ._. 
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Being_VBG a_AT1 Hermitian_JJ operator_NN1 ,_, the_AT spectral_JJ theorem_NN1 implies_VVZ that_CST the_AT effect_NN1 e_ZZ1 can_VM be_VBI written_VVN as_II a_AT1 linear_JJ combination_NN1 <Equation>_FO (_( 14_MC )_) ,_, where_CS <Professional_FO Term>_FO are_VBR rank-1_MC1 projections_NN2 onto_II mutually_RR orthogonal_JJ subspaces_NN2 of_IO H._NP1 Defining_VVG the_AT projectors_NN2 <Equation>_FO and_CC letting_VVG <Equation>_FO ,_, where_CS <Equation>_FO ,_, we_PPIS2 may_VM rewrite_VVI equation_NN1 (_( 14_MC )_) as_CSA <Equation>_FO ._. 
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Furthermore_RR ,_, it_PPH1 can_VM be_VBI clearly_RR seen_VVN in_II Fig._NN1 4_MC that_CST the_AT DCNC_NP1 field_NN1 ensemble_NN1 achieves_VVZ a_AT1 much_RR faster_JJR convergence_NN1 of_IO the_AT polarization_NN1 over_II its_APPGE thermodynamic_JJ conjugate_NN1 condition_NN1 ECNC_NN1 ._. 
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Yet_RR ,_, these_DD2 results_NN2 are_VBR affected_VVN by_II age_NN1 and_CC gender_NN1 ._. 
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By_II irradiation_NN1 of_IO this_DD1 pulse_NN1 on_II a_AT1 precompressed_JJ cylindrical_JJ fuel_NN1 with_IW a_AT1 length_NN1 of_IO 1.2_MC mm_NNU ,_, an_AT1 initial_JJ temperature_NN1 of_IO 0.25_MC keV_NN1 ,_, and_CC an_AT1 areal_JJ density_NN1 of_IO <Equation>_FO ,_, the_AT target_NN1 behavior_NN1 has_VHZ been_VBN investigated_VVN in_II the_AT ignition_NN1 phase_NN1 ._. 
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For_IF stability_NN1 b_ZZ1 =_FO 0_MC and_CC so_RR <Equation>_FO ._. 
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In_BCL21 order_BCL22 to_TO be_VBI valid_JJ it_PPH1 requires_VVZ that_CST ,_, besides_II the_AT semiclassical_JJ condition_NN1 ka_NN1 >_FO 1_MC1 be_VBI valid_JJ ,_, with_IW a_AT1 a_AT1 typical_JJ distance_NN1 over_II which_DDQ the_AT nuclear_JJ potential_NN1 varies_VVZ appreciably_RR ,_, and_CC k_ZZ1 is_VBZ the_AT asymptotic_JJ momentum_NN1 of_IO relative_JJ motion_NN1 ,_, also_RR the_AT condition_NN1 of_IO scattering_VVG at_II very_RG small_JJ angles_NN2 be_VBI satisfied_VVN ._. 
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<s>
For_IF each_DD1 M_ZZ1 >_FO 0_MC ,_, two_MC states_NN2 with_IW E_ZZ1 =_FO ±1_FO exist_VV0 ,_, so_CS21 that_CS22 in_II total_NN1 the_AT multiplicity_NN1 of_IO the_AT spin_NN1 state_NN1 is_VBZ 2_MC J_ZZ1 +1_MC ,_, as_CSA in_II the_AT canonical_JJ basis_NN1 ._. 
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The_AT red_JJ curve_NN1 is_VBZ for_IF the_AT bundle_NN1 of_IO lines_NN2 of_IO sight_NN1 covering_VVG the_AT seismic_JJ source_NN1 zone_NN1 and_CC corresponding_VVG to_II the_AT direction_NN1 of_IO the_AT hydrothermal_JJ source_NN1 ._. 
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In_II the_AT free-space_JJ configuration_NN1 of_IO the_AT discussed_JJ generators_NN2 the_AT available_JJ lasers_NN2 limited_VVN the_AT rate_NN1 to_II the_AT range_NN1 of_IO kbps_NNU ._. 
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The_AT discharge_NN1 capacities_NN2 of_IO LTO_NP1 are_VBR 198.7_MC ,_, 164.3_MC ,_, 134.3_MC and_CC 91.6_MC mAh_NN1 g_ZZ1 at_II 1_MC1 ,_, 2_MC ,_, 5_MC and_CC 10C_FO ,_, while_CS for_IF 1YFLTO_FO are_VBR 200.5_MC ,_, 184_MC ,_, 172.7_MC and_CC 147.6_MC mAh_NN1 g_ZZ1 ,_, respectively_RR ._. 
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The_AT interaction_NN1 matrix_NN1 element_NN1 ,_, H12_FO ,_, connecting_VVG the_AT two_MC states_NN2 is_VBZ given_VVN by_II <Equation>_FO Experimentally_RR ,_, <Equation>is_FO the_AT difference_NN1 between_II the_AT observed_JJ energy_NN1 and_CC the_AT energy_NN1 calculated_VVD using_VVG the_AT constants_NN2 obtained_VVN from_II the_AT fit_JJ to_II the_AT unperturbed_JJ levels_NN2 ._. 
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The_AT probability_NN1 of_IO finding_VVG the_AT system_NN1 in_II a_AT1 given_JJ eigenstate_NN1 ji_NN2 ,_, <Equation>_FO ,_, is_VBZ set_VVN by_II the_AT choice_NN1 of_IO the_AT initial_JJ state_NN1 and_CC does_VDZ not_XX change_VVI over_II time_NNT1 ._. 
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III_MC F_ZZ1 )_) and_CC the_AT CGO_NP1 rays_NN2 are_VBR an_AT1 exponentially_RR growing_JJ solution_NN1 behind_II the_AT caustic_JJ ._. 
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However_RR ,_, this_DD1 has_VHZ been_VBN clearly_RR stated_VVN in_II the_AT paper_NN1 and_CC the_AT data_NN points_NN2 in_II all_DB plots_NN2 in_II the_AT paper_NN1 ,_, which_DDQ require_VV0 these_DD2 values_NN2 ,_, have_VH0 been_VBN consequently_RR excluded_VVN from_II the_AT graphs_NN2 and_CC the_AT analysis_NN1 ._. 
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We_PPIS2 have_VH0 compared_VVN our_APPGE results_NN2 with_IW those_DD2 obtained_VVN by_II Froese_JJ Fischer_NP1 and_CC Tachiev_NP1 &lsqb;_( 29_MC &rsqb;_) that_CST represent_VV0 ab_JJ21 initio_JJ22 calculations_NN2 without_IW fitting_NN1 ._. 
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It_PPH1 means_VVZ that_CST <Equation>_FO each_DD1 with_IW probability_NN1 1/2_MF in_II the_AT phase_NN1 space_NN1 I_ZZ1 ,_, and_CC <Equation>_FO each_DD1 with_IW probability_NN1 1/2_MF in_II the_AT phase_NN1 space_NN1 II_MC ._. 
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However_RR ,_, this_DD1 is_VBZ a_AT1 different_JJ issue_NN1 ,_, since_CS the_AT present_JJ degrees_NN2 of_IO freedom_NN1 are_VBR only_RR 4-dimensional_JJ ._. 
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By_II comparing_VVG the_AT calculated_JJ area_NN1 under_II the_AT two_MC peaks_NN2 ,_, the_AT atomic_JJ ratio_NN1 of_IO Fe_NP1 to_II Mg_NNU could_VM be_VBI determined_VVN for_IF the_AT difierent_JJ samples_NN2 &lsqb;_( 32_MC &rsqb;_) ;_; the_AT ratio_NN1 is_VBZ found_VVN to_TO be_VBI 1.95_MC for_IF x_ZZ1 =1.0_FO while_CS for_IF x_ZZ1 =0.5_FO it_PPH1 is_VBZ 3.94_MC ._. 
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In_II Section_NN1 3.5_MC ,_, the_AT smaller_JJR particles_NN2 (_( range_NN1 of_IO 20_MC m_NNO to_II 25_MC m_NNU )_) were_VBDR used_VVN to_TO decrease_VVI the_AT thickness_NN1 of_IO the_AT OPTMs_NP1 ;_; the_AT OPTMs_NP1 with_IW the_AT smaller_JJR particles_NN2 are_VBR denoted_VVN as_CSA SP-_JJ RIE-y_NP1 ._. 
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We_PPIS2 now_RT assess_VV0 the_AT possibilities_NN2 for_IF dielectric_JJ engineering_NN1 of_IO MA-tBLG_NN1 in_II experimental_JJ setups_NN2 as_CSA shown_VVN in_II Figs._NN2 1(a)_FO and_CC 1(b)_FO ._. 
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These_DD2 two_MC mechanisms_NN2 lead_VV0 to_II a_AT1 different_JJ dependence_NN1 of_IO the_AT transfer_NN1 efficiency_NN1 on_II :_: exponential_NN1 at_II small_JJ and_CC polynomial_NN1 at_RR21 large_RR22 ._. 
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With_IW similar_JJ technique_NN1 in_II the_AT proof_NN1 of_IO Lemma_NN1 1_MC1 ,_, for_IF any_DD adversary_NN1 A_ZZ1 ,_, we_PPIS2 build_VV0 a_AT1 <Professional_FO Term>which_FO works_VVZ as_CSA follows_VVZ :_: Asets_VVZ the_AT control_NN1 register_NN1 of_IO <Professional_FO Term>to_FO |_NULL 1_MC1 ,_, then_RT passes_VVZ it_PPH1 to_II A_ZZ1 and_CC finally_RR outputs_VVZ what_DDQ A_ZZ1 outputs_VVZ ._. 
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Based_VVN on_II Eq_NN1 ._. 
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(_( 57_MC )_) in_II Section_NN1 3.1.3_MC ,_, we_PPIS2 construct_VV0 a_AT1 model_NN1 for_IF the_AT cross_NN1 section_NN1 of_IO reaction_NN1 (_( 139_MC )_) by_II assuming_VVG that_CST the_AT n-body_JJ final_JJ state_NN1 is_VBZ produced_VVN via_II t-channel_JJ exchange_NN1 processes_NN2 and_CC by_II performing_VVG an_AT1 s-channel_JJ partial-wave_JJ expansion_NN1 of_IO the_AT n-body_JJ system_NN1 by_II inserting_VVG a_AT1 complete_JJ set_NN1 of_IO intermediate_JJ states_NN2 X_ZZ1 with_IW well-defined_JJ quantum_NN1 numbers_NN2 ._. 
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The_AT sputtering_JJ power_NN1 was_VBDZ maintained_VVN at_II 50_MC W._NP1 Their_APPGE sheet_NN1 resistance_NN1 was_VBDZ 125_MC /_FO ._. 
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The_AT average_JJ optical_JJ transmission_NN1 of_IO the_AT films_NN2 was_VBDZ about_RG 82%_NNU in_II the_AT visible_JJ spectrum_NN1 ._. 
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At_II the_AT same_DA time_NNT1 ,_, it_PPH1 brings_VVZ new_JJ challenges_NN2 to_II the_AT design_NN1 of_IO color_NN1 converters_NN2 to_TO accommodate_VVI the_AT distinguishing_JJ features_NN2 of_IO <Professional_FO Term>_FO Firstly_RR ,_, the_AT phosphor_NN1 materials_NN2 must_VM withstand_VVI long-term_JJ high_JJ flux_NN1 density_NN1 laser_NN1 irradiations_NN2 and_CC dissipate_VV0 the_AT generated_JJ heat_NN1 within_II the_AT small_JJ laser_NN1 spot_NN1 ._. 
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A_ZZ1 the_AT relation_NN1 to_II thermal_JJ entropy_NN1 ._. 
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Kiselev_NP1 and_CC Kim_NP1 (_( 2000b_FO )_) studied_VVD an_AT1 effective_JJ spin_NN1 model_NN1 of_IO the_AT type_NN1 (_( 9_MC )_) where_RRQ the_AT momentum_NN1 <equation>_FO is_VBZ a_AT1 classical_JJ quantity_NN1 (_( also_RR neglecting_VVG the_AT difference_NN1 between_II canonical_JJ and_CC kinetic_JJ momenta_NN1 due_II21 to_II22 spin-orbit_JJ coupling_NN1 )_) whose_DDQGE time_NNT1 dependence_NN1 is_VBZ generated_VVN by_II a_AT1 Markov_NP1 chain_NN1 modeling_VVG independent_JJ elastic_NN1 scattering_VVG events_NN2 ._. 
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The_AT setup_NN1 allows_VVZ us_PPIO2 to_TO control_VVI the_AT spot_NN1 radius_NN1 R_ZZ1 (_( up_II21 to_II22 an_AT1 uncertainty_NN1 of_IO 0.1_MC mm_NNU )_) ,_, the_AT distance_NN1 <equation>_FO between_II spot_NN1 boundaries_NN2 and_CC the_AT Ferroin_NN1 concentration_NN1 in_II the_AT spots_NN2 The_AT diffusive_JJ coupling_NN1 between_II spots_NN2 is_VBZ mediated_VVN by_II the_AT diffusion_NN1 of_IO the_AT bromide_NN1 ions_NN2 with_IW diffusion_NN1 coefficient_NN1 D_ZZ1 ,_, and_CC we_PPIS2 take_VV0 the_AT rate_NN1 <equation>_FO as_II a_AT1 measure_NN1 for_IF the_AT coupling_NN1 strength_NN1 &lsqb;_( 29_MC &rsqb;_) ._. 
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As_CSA UKL_NP1 values_NN2 are_VBR less_DAR than_CSN 1.5_MC V-RHE_NP1 ,_, NH3_FO formation_NN1 rates_NN2 on_II the_AT low_JJ index_NN1 Fe_NP1 surfaces_NN2 will_VM be_VBI very_RG low_JJ and_CC selectivity_NN1 against_II the_AT HER_PPHO1 would_VM be_VBI very_RG poor_JJ ._. 
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In_II conclusion_NN1 ,_, we_PPIS2 have_VH0 identified_VVN a_AT1 sharp_JJ peak_NN1 in_II the_AT density_NN1 of_IO states_NN2 of_IO the_AT FeRh_NN1 FM_NN1 phase_NN1 close_RR to_II the_AT Fermi_NP1 level_NN1 ,_, which_DDQ can_VM be_VBI used_VVN to_TO discriminate_VVI between_II the_AT AFM_NP1 and_CC FM_NN1 phases_NN2 ._. 
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Also_RR ,_, due_II21 to_II22 the_AT Markov_NP1 property_NN1 of_IO the_AT time-series_JJ DAG_NN1 ,_, <equation>_FO separates_VVZ <equation>_FO from_II their_APPGE nondescendants_NN2 ,_, including_II the_AT remaining_JJ nodes_NN2 in_II the_AT conditions_NN2 in_II Eq_NN1 ._. 
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(_( 7_MC )_) ,_, and_CC thus_RR gives_VVZ <equation>_FO (_( 8_MC )_) where_RRQ Gi_NN1 is_VBZ the_AT generalized_JJ version_NN1 of_IO the_AT momentary_JJ information_NN1 transfer_NN1 along_II causal_JJ paths_NN2 &lsqb;_( 12,18_MC &rsqb;_) from_II multiple_JJ source_NN1 nodes_NN2 Vti_NN1 to_II Zt_NP1 along_II the_AT multiple_JJ causal_JJ paths_NN2 CVtiZt_VV0 ._. 
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A_AT1 quantum_NN1 measurement_NN1 of_IO a_AT1 system_NN1 in_II quantum_NN1 state_VV0 that_CST depends_VVZ on_II a_AT1 classical_JJ parameter_NN1 is_VBZ performed_VVN (_( general_JJ POV_NP1 measurement_NN1 )_) and_CC produces_VVZ data_NN x1_FO ;_; ;_; xM_NNU ._. 
</s>
<s>
Also_RR the_AT mass_JJ spectrum_NN1 measured_VVN at_II an_AT1 electron_NN1 energy_NN1 of_IO 23_MC eV_NN1 (_( upper_JJ diagram_NN1 of_IO Fig._NN1 28_MC )_) reveals_VVZ a_AT1 lack_NN1 of_IO Na+_FO cluster_VV0 ions_NN2 beyond_II n_ZZ1 =_FO 21_MC ,_, as_CSA these_DD2 clusters_NN2 after_II submersion_NN1 are_VBR not_XX ionized_VVN via_II Penning_VVG ionization_NN1 ._. 
</s>
<s>
The_AT resulting_JJ number_NN1 of_IO possible_JJ transitions_NN2 is_VBZ extensive_JJ ,_, making_VVG it_PPH1 impractical_JJ to_TO include_VVI all_DB of_IO them_PPHO2 here_RL ._. 
</s>
<s>
As_II a_AT1 consequence_NN1 ,_, the_AT energy_NN1 spectra_NN2 of_IO primary_JJ cosmic_JJ rays_NN2 should_VM be_VBI also_RR universal_JJ ,_, being_VBG ,_, e.g._REX ,_, independent_JJ of_IO the_AT Galactic_JJ longitude_NN1 ._. 
</s>
<s>
The_AT measured_JJ composition_NN1 is_VBZ shown_VVN by_II the_AT squares_NN2 ;_; the_AT circles_NN2 indicate_VV0 a_AT1 reconstruction_NN1 of_IO the_AT composition_NN1 of_IO the_AT primary_JJ excited_JJ projectile-like_JJ fragment_NN1 immediately_RR following_VVG the_AT collision_NN1 ._. 
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<s>
Even_RR after_II 200_MC cycles_NN2 ,_, the_AT electrode_NN1 still_RR retains_VVZ a_AT1 specific_JJ reversible_JJ capacity_NN1 of_IO ca_VM ._. 
</s>
<s>
Source_NN1 :_: Reprinted_VVN from_II &lsqb;_( 138_MC &rsqb;_) with_IW permission_NN1 of_IO the_AT APS._NP1 <Picture>Fig._FO 42_MC ._. 
</s>
<s>
By_II infinitesimal_JJ perturbation_NN1 of_IO these_DD2 new_JJ variables_NN2 ,_, the_AT solutions_NN2 approach_VV0 the_AT same_DA state_NN1 corresponding_VVG to_II the_AT attractor_NN1 state_NN1 ._. 
</s>
<s>
Coherent_JJ phase_NN1 space_NN1 manipulation_NN1 via_II deceleration_NN1 and_CC acceleration_NN1 of_IO electrons_NN2 in_II oscillating_VVG radio-frequency_NN1 cavities_NN2 or_CC by_II using_VVG terahertz_NN1 fields_NN2 has_VHZ resulted_VVN in_II temporal_JJ pulse_NN1 durations_NN2 down_RP to_II a_AT1 few_DA2 femtoseconds_NN2 ._. 
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<s>
The_AT most_RGT prominent_JJ barrier_NN1 at_RR21 present_RR22 is_VBZ the_AT high_JJ price_NN1 point_NN1 of_IO most_DAT interrogation_NN1 systems_NN2 ,_, which_DDQ often_RR hinders_VVZ the_AT adoption_NN1 of_IO the_AT distributed_JJ optical_JJ fiber_NN1 sensor_NN1 systems_NN2 ._. 
</s>
<s>
The_AT H2_FO Q-branch_JJ detection_NN1 adds_VVZ additional_JJ benefits_NN2 including_II a_AT1 much_RR wider_JJR dynamic_JJ range_NN1 of_IO signal_NN1 gain_NN1 ,_, compared_VVN to_II the_AT pure-rotational_JJ S-branch_JJ detection_NN1 ._. 
</s>
<s>
The_AT instrumental_JJ resolution_NN1 is_VBZ better_JJR than_CSN 6_MC kHz_NNU ._. 
</s>
<s>
Thus_RR we_PPIS2 are_VBR confident_JJ volumes_NN2 are_VBR large_JJ enough_RR ,_, and_CC the_AT systematic_JJ errors_NN2 due_II21 to_II22 the_AT finite_JJ volume_NN1 are_VBR negligible_JJ ._. 
</s>
<s>
The_AT repetition_NN1 rate_NN1 of_IO the_AT laser_NN1 was_VBDZ increased_VVN to_II 230_MC kHz_NNU in_II a_AT1 26_MC km_NNU length_NN1 SMF_NP1 ._. 
</s>
<s>
The_AT parabolic_JJ form_NN1 of_IO the_AT curves_NN2 (_( so_RG prominent_JJ in_II 124T_FO )_) is_VBZ not_XX yet_RR reached_VVN at_II the_AT available_JJ J-range_NN1 ._. 
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<s>
Like_II the_AT condition_NN1 provided_VVN by_II Sayre_NP1 ,_, Spence_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
provided_CS estimates_NN2 for_IF the_AT minimum_JJ coherence_NN1 lengths_NN2 ._. 
</s>
<s>
This_DD1 strain_NN1 generates_VVZ a_AT1 RBS_NP1 spectral_JJ shift_NN1 ,_, which_DDQ is_VBZ measured_VVN in_II a_AT1 distributed_JJ fashion_NN1 ._. 
</s>
<s>
When_CS searching_VVG Web_NN1 of_IO Science_NN1 with_IW the_AT term_NN1 "_" organic_JJ single_JJ crystals_NN2 ,_, "_" more_DAR than_CSN 41_MC 000_MC publications_NN2 can_VM be_VBI found_VVN within_II the_AT last_MD half_DB century_NNT1 ._. 
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<s>
As_II a_AT1 result_NN1 ,_, for_IF the_AT ?_? rst_NNU time_NNT1 ,_, biomimetic_JJ TEBVs_NN2 consisting_VVG of_IO a_AT1 mature_JJ endothelium_NN1 and_CC dense_JJ smooth_JJ muscles_NN2 were_VBDR achieved_VVN using_VVG the_AT cell-printing_JJ technique_NN1 ._. 
</s>
<s>
Quantum_NN1 key_JJ distribution_NN1 (_( QKD_NP1 )_) enables_VVZ two_MC remote_JJ legitimate_JJ parties_NN2 ,_, commonly_RR called_VVN Alice_NP1 and_CC Bob_NP1 ,_, to_TO share_VVI secret_JJ keys_NN2 in_II the_AT presence_NN1 of_IO an_AT1 eavesdropper_NN1 (_( Eve_NP1 )_) by_II encoding_VVG information_NN1 on_II photons_NN2 ._. 
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<s>
It_PPH1 may_VM be_VBI expressed_VVN via_II the_AT non-analytic_JJ prepotential_JJ V<EQUATION>_FO which_DDQ ,_, in_II turn_NN1 ,_, is_VBZ expressed_VVN through_II V_ZZ1 by_II the_AT harmonic-flatness_JJ condition_NN1 D<EQUATION>_FO The_AT classical_JJ action_NN1 of_IO the_AT hypermultiplet_NN1 q_ZZ1 (_( a_ZZ1 =_FO 1_MC1 ,_, 2_MC )_) in_II the_AT adjoint_JJ representation_NN1 of_IO the_AT gauge_NN1 group_NN1 reads_VVZ &lsqb;_( 31–33_MCMC &rsqb;_) <EQUATION>_FO where<EQUATION>_FO is_VBZ the_AT integration_NN1 measure_NN1 on_II the_AT analytic_JJ super_JJ space_NN1 and_CC <EQUATION>_FO is_VBZ the_AT gauge-covariant_JJ harmonic_JJ derivative_NN1 ._. 
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<s>
Such_DA a_AT1 phenomenon_NN1 of_IO insulation_NN1 breakdown_NN1 of_IO the_AT vacuum_NN1 is_VBZ long_RR known_VVN as_II the_AT Schwinger_JJR Mechanism_NN1 and_CC one_MC1 of_IO the_AT modern_JJ challenges_NN2 in_II laser_NN1 physics_NN1 is_VBZ to_TO reach_VVI the_AT Schwinger_JJR limit_NN1 ._. 
</s>
<s>
This_DD1 effect_NN1 is_VBZ related_VVN to_II the_AT topology_NN1 of_IO trapped_JJ orbits_NN2 (_( figure_NN1 2_MC (_( c_ZZ1 )_) )_) ,_, where_CS ions_NN2 born_VVN outside_II the_AT separatrix_NN1 can_VM also_RR explore_VVI inner_JJ regions_NN2 of_IO the_AT plasma_NN1 on_II the_AT inner_JJ banana_NN1 orbit_NN1 leg_NN1 ._. 
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<s>
One_MC1 of_IO the_AT most_RGT authoritative_JJ reviews_NN2 on_II the_AT theory_NN1 of_IO EPIs_NN1 is_VBZ the_AT classic_JJ book_NN1 by_II Grimvall_NP1 (_( 1981_MC )_) ._. 
</s>
<s>
The_AT analogous_JJ result_NN1 holds_VVZ for_IF a_AT1 singularity_NN1 at_II <EQUATION>_FO ._. 
</s>
<s>
The_AT guessing_NN1 game_NN1 in_II the_AT presence_NN1 of_IO a_AT1 quantum_NN1 memory_NN1 system_NN1 ._. 
</s>
<s>
The_AT model_NN1 is_VBZ similar_JJ to_II that_DD1 used_VVD in_II the_AT famous_JJ paper_NN1 by_II Tajima_NP1 and_CC Dawson_NP1 on_II electron_NN1 acceleration_NN1 in_II wake_NN1 plasma_NN1 waves_NN2 ,_, the_AT main_JJ difference_NN1 being_VBG the_AT essential_JJ two-dimensional_JJ (_( 2D_NNU )_) nature_NN1 of_IO the_AT SP_NN1 ._. 
</s>
<s>
As_CSA we_PPIS2 did_VDD in_II Section_NN1 3.1.1_MC ,_, we_PPIS2 define_VV0 uk_NN1 as_II the_AT displacement_NN1 of_IO the_AT k-th_JJ grain_NN1 from_II its_APPGE equilibrium_NN1 position_NN1 ,_, so_CS21 that_CS22 the_AT equation_NN1 of_IO motion_NN1 reads_VVZ <Equation>_FO ._. 
</s>
<s>
Aligned_VVN crystalline_JJ samples_NN2 can_VM be_VBI selectively_RR carved_VVN from_II polycrystals_NN2 ,_, microcrystallites_NN2 ,_, and_CC powders_NN2 ._. 
</s>
<s>
In_II Eq_NN1 ._. 
</s>
<s>
(_( 190_MC )_) only_JJ transitions_NN2 with_IW E1_FO photons_NN2 are_VBR included_VVN ._. 
</s>
<s>
Many_DA2 different_JJ government_NN1 agencies_NN2 support_VV0 nuclear_JJ data_NN evaluation_NN1 activities_NN2 ,_, including_II several_DA2 components_NN2 of_IO the_AT US_NP1 Department_NN1 of_IO Energy_NN1 National_JJ Nuclear_JJ Security_NN1 Agency_NN1 (_( DOENNSA_NP1 )_) and_CC the_AT National_JJ Criticality_NN1 Safety_NN1 Program_NN1 (_( NCSP_NP1 )_) ._. 
</s>
<s>
Consider_VV0 a_AT1 digital_JJ image_NN1 with_IW a_AT1 size_NN1 of_IO 2n_FO ×_II 2n_FO as_II an_AT1 example_NN1 ._. 
</s>
<s>
Additionally_RR ,_, the_AT CoeO_NP1 peak_NN1 located_VVN at_II 531.5_MC eV_NN1 has_VHZ the_AT highest_JJT strength_NN1 in_II the_AT fresh_JJ cathode_NN1 ,_, while_CS the_AT metal-O_NP1 peak_NN1 in_II the_AT cycled_VVN electrode_NN1 using_VVG PE-STD_JJ and_CC GPE_NN1 can_VM not_XX be_VBI detected_VVN ,_, caused_VVN by_II the_AT thick_JJ covered_JJ product_NN1 from_II the_AT decomposition_NN1 of_IO liquid_JJ electrolyte_NN1 ._. 
</s>
<s>
Furthermore_RR ,_, they_PPHS2 can_VM possibly_RR control_VVI the_AT thickness_NN1 and_CC chemical_JJ composition_NN1 of_IO the_AT coatings_NN2 ._. 
</s>
<s>
We_PPIS2 can_VM turn_VVI this_DD1 feature_NN1 around_RP and_CC use_VVI it_PPH1 to_TO probe_VVI the_AT existence_NN1 of_IO heavy_JJ quarks_NN2 which_DDQ get_VV0 their_APPGE mass_NN1 through_II a_AT1 Yukawa_NN1 coupling_NN1 to_II the_AT Higgs_NP1 field_NN1 ._. 
</s>
<s>
In_II Monte_NP1 Carlo_NP1 simulations_NN2 ,_, this_DD1 fraction_NN1 has_VHZ to_TO be_VBI determined_VVN by_II fitting_VVG to_II experimental_JJ data_NN of_IO the_AT retained_JJ ion_NN1 fluence_NN1 ._. 
</s>
<s>
Such_DA experiments_NN2 mainly_RR highlighted_VVN a_AT1 strong_JJ feed-in_NN1 of_IO particles_NN2 into_II skew_NN1 planar_JJ channels_NN2 stretched_VVN to_II the_AT side_NN1 opposite_RL to_II that_DD1 of_IO bending_VVG ._. 
</s>
<s>
For_IF an_AT1 appropriate_JJ Rashba_NN1 coupling_NN1 tuned_VVN by_II a_AT1 gate_NN1 voltage_NN1 ,_, they_PPHS2 observed_VVD clearly_RR enhanced_JJ spin_NN1 lifetimes_NNT2 exceeding_VVG 30_MC ns_FO for_IF all_DB spin_VV0 directions_NN2 ._. 
</s>
<s>
This_DD1 is_VBZ the_AT energy_NN1 required_VVN to_TO polarize_VVI the_AT disk_NN1 ._. 
</s>
<s>
From_II Figure_NN1 2a_FO ,_, it_PPH1 is_VBZ observed_VVN that_CST the_AT silver_NN1 nanowire_NN1 placed_VVN on_II the_AT silver_NN1 substrate_NN1 (_( Figure_NN1 1b_FO )_) supports_VVZ one_MC1 SPP_NP1 waveguide_NN1 mode_NN1 ,_, and_CC its_APPGE effective_JJ refractive_JJ index_NN1 (_( neff_NN1 )_) increases_VVZ with_IW the_AT radius_NN1 of_IO the_AT silver_NN1 nanowire_NN1 (_( see_VV0 the_AT black_JJ line_NN1 with_IW rectangle_NN1 symbols_NN2 in_II Figure_NN1 2a_FO )_) ._. 
</s>
<s>
This_DD1 was_VBDZ seen_VVN ,_, for_REX21 example_REX22 ,_, for_IF coupled_JJ chemical_JJ oscillators_NN2 of_IO various_JJ sizes_NN2 and_CC coupling_NN1 mechanisms_NN2 &lsqb;_( 13–17_MCMC &rsqb;_) ._. 
</s>
<s>
Polarization_NN1 of_IO the_AT Stern_JJ layer_NN1 will_VM also_RR add_VVI to_II ,_, or_CC subtract_VV0 from_II ,_, the_AT fixed_JJ charge_NN1 ±0_FO on_II the_AT outermost_JJ crystal_NN1 planes_NN2 ._. 
</s>
<s>
In_II the_AT component_NN1 formulation_NN1 ,_, the_AT 5D_NNU ,_, N_ZZ1 =_FO 2_MC effective_JJ action_NN1 constructed_VVN displays_VVZ the_AT F_ZZ1 /_FO |_NULL X_ZZ1 |_NULL -term_JJ where_CS |_NULL X_ZZ1 |_NULL is_VBZ SO(5)-invariant_JJ bilinear_JJ combination_NN1 of_IO scalar_JJ fields_NN2 ._. 
</s>
<s>
They_PPHS2 found_VVD that_DD1 building_NN1 land_NN1 cover_NN1 and_CC calls_NN2 made_VVD out_RP at_II 10am_RA are_VBR the_AT top-two_MC predictors_NN2 that_CST are_VBR sufficient_JJ to_TO provide_VVI accurate_JJ predictions_NN2 ._. 
</s>
<s>
Naturally_RR ,_, at_II t_ZZ1 =_FO 0_MC ,_, the_AT peak_NN1 energy_NN1 of_IO the_AT time-resolved_NN1 P_ZZ1 1_MC1 is_VBZ the_AT same_DA as_CSA P_ZZ1 1_MC1 in_II the_AT static_JJ 2PPE_FO spectrum_NN1 ;_; however_RR ,_, large_JJ changes_NN2 in_II energy_NN1 and_CC intensity_NN1 of_IO P_ZZ1 1_MC1 occur_VV0 as_II a_AT1 function_NN1 of_IO pump-probe_JJ time-delay_JJ &lsqb;_( the_AT shifting_NN1 in_II energy_NN1 can_VM be_VBI clearly_RR seen_VVN in_II Fig._NN1 2(b)_FO &rsqb;_) ._. 
</s>
<s>
V_ZZ1 ,_, the_AT capabilities_NN2 of_IO this_DD1 diagnostic_JJ are_VBR summarized_VVN ._. 
</s>
<s>
Additionally_RR ,_, it_PPH1 must_VM be_VBI pointed_VVN out_RP that_DD1 ,_, unlike_JJ acoustic_JJ topological_JJ insulators_NN2 ,_, which_DDQ are_VBR robust_JJ against_II a_AT1 large_JJ class_NN1 of_IO defects_NN2 &lsqb;_( 55_MC &rsqb;_) ,_, the_AT proposed_JJ structure_NN1 works_VVZ only_RR for_IF zigzag_NN1 waveguides_NN2 ._. 
</s>
<s>
There_EX is_VBZ no_AT indication_NN1 ,_, however_RR ,_, for_IF a_AT1 different_JJ scaling_NN1 of_IO the_AT critical_JJ values_NN2 with_IW Pm_NP1 for_IF the_AT different_JJ mode_NN1 numbers_NN2 m_ZZ1 (_( as_CSA we_PPIS2 shall_VM find_VVI below_RL in_II Figs._NN2 48_MC and_CC 65_MC )_) ._. 
</s>
<s>
We_PPIS2 adopt_VV0 all_DB notations_NN2 from_II reference_NN1 &lsqb;_( 42_MC &rsqb;_) where_CS we_PPIS2 have_VH0 ,_, after_II setting_VVG p1_FO =_FO p2_FO ,_, ==2_FO p1_FO +p2_FO The_AT metric_JJ for_IF the_AT sigma_NN1 in_II this_DD1 symmetric_JJ case_NN1 to<EQUATION>Here_FO we_PPIS2 have<EQUATION>We_FO set_VV0 z_ZZ1 ≡_NULL cos_CS 2_MC θ_NULL and_CC introduce_VV0 y_ZZ1 such_CS21 that_CS22 e_ZZ1 <EQUATION>so_FO y_ZZ1 ∈_FO &lsqb;_( ∞_FO ,_, ∞_FO &rsqb;_) ._. 
</s>
<s>
Thus_RR after_II very_RG long_JJ time_NNT1 annealing_VVG ,_, the_AT conductivity_NN1 data_NN shown_VVN in_II Fig._NN1 1_MC1 b_ZZ1 )_) should_VM approach_VVI a_AT1 value_NN1 of_IO about_II 0.12mScm_FO ._. 
</s>
<s>
The_AT two-fold_JJ decrease_NN1 of_IO the_AT LiF_NN1 thick-target_NN1 yield_NN1 with_IW the_AT 20_MC m_NNO Al_NP1 foil_NN1 corresponds_VVZ to_II the_AT effective_JJ deuterium_NN1 energy_NN1 of_IO 3.5_MC MeV_NNU ._. 
</s>
<s>
In_II the_AT right_JJ panel_NN1 of_IO the_AT same_DA figure_NN1 we_PPIS2 plot_VV0 the_AT individual_JJ probability_NN1 of_IO finding_VVG the_AT random_JJ walker_NN1 in_II run_NN1 state_NN1 and_CC in_II tumble_NN1 state_NN1 for_IF a_AT1 given_JJ value_NN1 of_IO y_ZZ1 ,_, after_CS steady_JJ state_NN1 has_VHZ been_VBN reached_VVN ._. 
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<s>
The_AT log2_FO z_ZZ1 piece_NN1 of_IO this_DD1 equation_NN1 takes_VVZ the_AT form<Equation>_FO ._. 
</s>
<s>
Open_JJ circles_NN2 show_VV0 data_NN from_II halo_NN1 stars_NN2 ,_, red_JJ boxes_NN2 are_VBR data_NN from_II stars_NN2 in_II dwarf_NN1 galaxy_NN1 Ret_NN1 II_MC ._. 
</s>
<s>
Our_APPGE results_NN2 suggest_VV0 that_CST carefully_RR engineered_VVN but_CCB simple_JJ to_TO manufacture_VVI patterned_JJ substrates_NN2 could_VM yield_VVI self-assembled_JJ single_JJ crystals_NN2 of_IO sufficient_JJ quality_NN1 to_TO exhibit_VVI a_AT1 complete_JJ photonic_JJ bandgap_NN1 ._. 
</s>
<s>
If_CS <Equation>is_FO positive_JJ the_AT stateis_NN1 a_AT1 mere_JJ mixture_NN1 of_IO coherent_JJ states_NN2 and_CC is_VBZ said_VVN to_TO be_VBI classical_JJ ._. 
</s>
<s>
This_DD1 physics_NN1 is_VBZ important_JJ to_TO know_VVI because_CS the_AT emerging_JJ hierarchy_NN1 can_VM help_VVI us_PPIO2 predict_VVI how_RGQ few_DA2 the_AT even_RR bigger_JJR models_NN2 will_VM be_VBI and_CC how_RRQ more_DAR numerous_JJ the_AT smaller_JJR models_NN2 will_VM be_VBI ,_, naturally_RR ._. 
</s>
<s>
Most_DAT of_IO these_DD2 companies_NN2 address_VV0 multiple_JJ market_NN1 segments_NN2 ,_, while_CS energy_NN1 is_VBZ the_AT dominant_JJ market_NN1 overall_NN1 ._. 
</s>
<s>
Parameters_NN2 are_VBR fixed_VVN at_II <equation>_FO )_) the_AT total_JJ flux_NN1 giving_VVG low_JJ values_NN2 of_IO the_AT Fano_NN1 factors_NN2 violating_VVG the_AT mathematical_JJ uncertainty_NN1 ._. 
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<s>
Remarkably_RR ,_, collimation_NN1 in_II a_AT1 backscattering-immune_JJ zigzag_NN1 path_NN1 can_VM be_VBI observed_VVN with_IW the_AT SPS_NN2 ,_, which_DDQ is_VBZ illustrated_VVN in_II Figs_NN2 ._. 
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<s>
These_DD2 techniques_NN2 can_VM give_VVI correct_JJ predictions_NN2 but_CCB the_AT results_NN2 are_VBR difficult_JJ to_TO generalize_VVI and_CC the_AT underlying_JJ dynamics_NN are_VBR not_XX obvious_JJ ._. 
</s>
<s>
The_AT random_JJ variables_NN2 <Professional_FO Term>_FO are_VBR independent_JJ ,_, and_CC by_II translation_NN1 in_II variance_NN1 of_IO the_AT law_NN1 of_IO X_ZZ1 together_RL with_IW our_APPGE above_JJ observation_NN1 about_II <Professional_FO Term>_FO ,_, the_AT law_NN1 of_IO each_DD1 NJ_NP1 converges_VVZ as_CSA k_ZZ1 tends_VVZ to_II infinity_NN1 to_II the_AT law_NN1 of_IO <Professional_FO Term>_FO ._. 
</s>
<s>
Let_VV0 f_ZZ1 :_: <Equation>_FO be_VBI an_AT1 expanding_JJ Thurston_NN1 map_NN1 ._. 
</s>
<s>
The_AT micronanostructure_NN1 of_IO carbon_NN1 based_VVN materials_NN2 can_VM provide_VVI reversible_JJ storage_NN1 of_IO lithium_NN1 ions_NN2 ,_, which_DDQ can_VM not_XX only_RR shorten_VVI lithiumion_NN1 transmission_NN1 path_NN1 ,_, but_CCB also_RR brings_VVZ about_RP large_JJ electrode/electrolyte_NN1 interface_NN1 for_IF the_AT charge_NN1 transfer_NN1 reaction_NN1 &lsqb;_( 25,26_MC &rsqb;_) ._. 
</s>
<s>
The_AT terminology_NN1 and_CC notation_NN1 used_VVN in_II this_DD1 section_NN1 is_VBZ defined_VVN in_II Secs_NNU2 ._. 
</s>
<s>
Each_DD1 neutron_NN1 (_( macro_NN1 )_) particle_NN1 in_RP at_II the_AT simulation_NN1 was_VBDZ recorded_VVN at_II the_AT position_NN1 where_RRQ it_PPH1 was_VBDZ born_VVN ._. 
</s>
<s>
To_TO compare_VVI the_AT growth_NN1 rate_NN1 predicted_VVN by_II the_AT Warp_NN1 simulations_NN2 to_II our_APPGE theoretical_JJ model_NN1 ,_, a_AT1 bifurcation_NN1 scan_NN1 for_IF the_AT parameter_NN1 E0_FO (_( with_IW a_AT1 fixed_JJ g_ZZ1 ?_FO 0_MC )_) is_VBZ constructed_VVN according_II21 to_II22 the_AT simulation_NN1 parameters_NN2 ._. 
</s>
<s>
Interestingly_RR ,_, she_PPHS1 only_RR uses_VVZ POMs_NP2 with_IW at_RR21 most_RR22 three_MC outcomes_NN2 :_: the_AT measurement_NN1 set_NN1 is_VBZ given_VVN by_II <Equation>_FO where_RRQ any_DD <Equation>_FO (_( 9_MC )_) is_VBZ a_AT1 collection_NN1 of_IO no_AT more_DAR than_CSN three_MC effects_NN2 ._. 
</s>
<s>
According_II21 to_II22 some_DD experts_NN2 ,_, the_AT architect_NN1 Filippo_NN1 Brunelleschi_NN1 might_VM have_VHI built_VVN some_DD reinforcement_NN1 structures_NN2 in_II the_AT Cupola_NP1 including_II iron_NN1 chains_NN2 inside_II the_AT wall_NN1 ._. 
</s>
<s>
The_AT initial_JJ jet_NN1 finding_NN1 is_VBZ done_VDN with_IW the_AT anti-kt_JJ algorithm_NN1 with_IW R_ZZ1 =_FO 1_MC1 ,_, to_TO ensure_VVI that_CST most_DAT of_IO the_AT final_JJ state_NN1 W_ZZ1 and_CC top-quark_JJ decays_NN2 can_VM be_VBI collected_VVN into_II one_MC1 jet_NN1 ._. 
</s>
<s>
When_CS the_AT ?_? eld_NN1 is_VBZ purely_RR radial_JJ but_CCB its_APPGE direction_NN1 e_ZZ1 is_VBZ varied_VVN ,_, the_AT effective_JJ shielding_JJ factor_NN1 Se_NP1 ?_? is_VBZ sensitive_JJ to_II the_AT misalignment_NN1 angle_NN1 θ_NULL (_( bottom_NN1 )_) ._. 
</s>
<s>
In_RR21 particular_RR22 ,_, the_AT state_NN1 <Equation>_FO after_CS preparation_NN1 but_CCB before_CS the_AT uncertainty_NN1 principle_NN1 is_VBZ applied_VVN does_VDZ not_XX need_VVI to_TO have_VHI any_DD particular_JJ structure_NN1 and_CC is_VBZ assumed_VVN to_TO be_VBI arbitrary_JJ ._. 
</s>
<s>
Moving_VVG to_II a_AT1 proper_JJ deformed_JJ potential_NN1 alleviates_VVZ these_DD2 problems_NN2 for_IF the_AT investigated_JJ cases_NN2 ._. 
</s>
<s>
III.B_NP1 ._. 
</s>
<s>
Because_II21 of_II22 the_AT great_JJ challenge_NN1 of_IO incorporating_VVG the_AT full_JJ complexity_NN1 of_IO the_AT bilayer_NN1 systems_NN2 at_RR21 once_RR22 ,_, almost_RR all_DB theoretical_JJ studies_NN2 have_VH0 been_VBN focused_VVN either_RR on_II iSGE_NN1 in_II model_NN1 systems_NN2 or_CC on_II the_AT SHE_PPHS1 mechanism_NN1 only_RR ,_, with_IW a_AT1 handful_NN1 of_IO them_PPHO2 attempting_VVG a_AT1 comprehensive_JJ modeling_NN1 ._. 
</s>
<s>
We_PPIS2 will_VM not_XX pursue_VVI this_DD1 point_NN1 further_RRR ._. 
</s>
<s>
By_II taking_VVG quadrature_NN1 operators_NN2 <Equation>_FO ,_, as_CSA the_AT canonical_JJ choice_NN1 for_IF the_AT variance_NN1 ,_, a_AT1 large_JJ variance_NN1 necessarily_RR comes_VVZ from_II many-photon_JJ states_NN2 since_CS <Equation>_FO ._. 
</s>
<s>
These_DD2 masses_NN2 are_VBR shown_VVN as_II a_AT1 function_NN1 of_IO the_AT gap_NN1 parameter_NN1 ,_, which_DDQ enters_VVZ the_AT quark_NN1 self_NN1 energies_NN2 via_II <Professional_FO Term>_FO ._. 
</s>
<s>
We_PPIS2 would_VM like_VVI to_TO thank_VVI R._NP1 M._NN1 Bradley_NP1 for_IF extensive_JJ e-mail_NN1 exchange_NN1 ,_, in_RR21 particular_RR22 on_II the_AT topic_NN1 of_IO coefficients_NN2 for_IF the_AT non-linear_JJ terms_NN2 ._. 
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<s>
Then_RT ,_, one_PN1 writes_VVZ down_RP dynamical_JJ equations_NN2 ._. 
</s>
<s>
We_PPIS2 again_RT used_VVD 12_MC =_FO ?_? 
</s>
<s>
In_II a_AT1 PCW_NP1 ,_, the_AT shift_NN1 of_IO level_NN1 s_ZZ1 can_VM occur_VVI via_II interactions_NN2 with_IW other_JJ atoms_NN2 in_II level_NN1 s_ZZ1 ._. 
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<s>
These_DD2 interaction-induced_JJ shifts_NN2 create_VV0 new_JJ transparencies_NN2 for_IF different_JJ components_NN2 of_IO the_AT input_NN1 probe_NN1 ._. 
</s>
<s>
Notably_RR ,_, these_DD2 rich-club_JJ hubs_NN2 acting_VVG as_II control_NN1 regions_NN2 most_RGT altered_JJ energetic_JJ outcomes_NN2 when_RRQ the_AT brain_NN1 '_NULL s_ZZ1 rich-club_JJ organization_NN1 was_VBDZ destroyed_VVN by_II simulated_JJ lesioning_NN1 ,_, an_AT1 increasingly_RR common_JJ model_NN1 of_IO neurodegenerative_JJ disease_NN1 (_( Alstott_NP1 et_RA21 al._RA22 ,_, 2009_MC )_) ._. 
</s>
<s>
It_PPH1 ,_, however_RR ,_, holds_VVZ true_JJ when_CS geometric_JJ contributions_NN2 are_VBR zero_MC ._. 
</s>
<s>
These_DD2 advances_NN2 present_VV0 strong_JJ evidence_NN1 for_IF the_AT feasibility_NN1 of_IO STIRAP_NN1 in_II semiconductor_NN1 quantum_NN1 dots_NN2 ._. 
</s>
<s>
Copyright_NN1 2015_MC ,_, Royal_JJ Society_NN1 of_IO Chemistry_NN1 ._. 
</s>
<s>
<picture>_FO FIG._NN1 8_MC ._. 
</s>
<s>
Recently_RR ,_, Norbutas_NP2 and_CC Corten_NP1 &lsqb;_( 280_MC &rsqb;_) explored_VVD the_AT relations_NN2 between_II network_NN1 structure_NN1 and_CC economic_JJ prosperity_NN1 of_IO 438_MC municipalities_NN2 in_II the_AT Netherlands_NP1 by_II analyzing_VVG data_NN of_IO over_RG 10_MC million_NNO users_NN2 on_II the_AT Dutch_JJ online_JJ social_JJ network_NN1 Hyves_NN2 ._. 
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<s>
The_AT participants_NN2 and_CC discussion_NN1 leaders_NN2 are_VBR listed_VVN in_II the_AT Appendix_NN1 ._. 
</s>
<s>
W._NP1 H._NP1 Knox_NP1 ,_, IEEE_NP1 J._NP1 Sel_NP1 ._. 
</s>
<s>
They_PPHS2 have_VH0 to_TO be_VBI be_VBI perfectly_RR segregated_VVN ._. <Picture>_FO <Picture>_FO <Picture>_FO <Picture>_FO <Picture>Figure_FO 19_MC ._. 
</s>
<s>
We_PPIS2 define_VV0 a_AT1 function_NN1 v_ZZ1 on_II A_ZZ1 by_II setting_VVG <Equation>_FO ._. 
</s>
<s>
Kinetic_JJ measurements_NN2 were_VBDR performed_VVN using_VVG an_AT1 ICP/Selected_FU Ion_NP1 Flow_NN1 Tube_NN1 (_( ICP/SIFT_VV0 )_) tandem_NN1 mass_NN1 spectrometer_NN1 with_IW helium_NN1 bath_NN1 gas_NN1 at_II 0.35_MC Torr_NP1 and_CC <Equation>_FO Our_APPGE survey_NN1 showed_VVD that_CST bimolecular_JJ H2_FO elimination_NN1 to_TO produce_VVI MNH_NP1 predominated_VVD with_IW very_RG early_RR atomic_JJ transition_NN1 metal_NN1 cations_NN2 :_: <Equation>_FO in_II the_AT first_MD row<Equation>_FO in_II the_AT second_MD row_NN1 ,_, and_CC <Equation>and_FO Ir_NN1 in_II the_AT third_MD row_NN1 ._. 
</s>
<s>
While_CS this_DD1 wall-touching_JJ kink_NN1 mode_NN1 (_( WTKM_NP1 )_) is_VBZ predicted_VVN to_TO be_VBI most_RGT problematic_JJ for_IF the_AT <equation>_FO ,_, <equation>_FO mode_NN1 ,_, which_DDQ arises_VVZ with_IW sufficiently_RR small_JJ q-values_NN2 ,_, the_AT physics_NN1 of_IO reversed_JJ surface_NN1 currents_NN2 also_RR arises_VVZ with_IW other_JJ external_JJ modes_NN2 &lsqb;_( 53,54_MC &rsqb;_) ._. 
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<s>
In_II Section_NN1 3.3_MC ,_, we_PPIS2 note_VV0 the_AT existence_NN1 of_IO reversed_JJ parallel_JJ current_JJ density_NN1 at_II the_AT time_NNT1 of_IO maximum-Ip_NN1 in_II the_AT forced_JJ 3D_NNU computation_NN1 ,_, but_CCB the_AT nonlinearly_RR distorted_JJ current_JJ profile_NN1 makes_VVZ it_PPH1 difficult_JJ to_TO relate_VVI the_AT reversed_JJ parallel_JJ current_JJ density_NN1 with_IW any_DD particular_JJ kink_NN1 mode_NN1 ._. 
</s>
<s>
The_AT effect_NN1 of_IO the_AT external_JJ AC_NN1 field_NN1 is_VBZ taken_VVN into_II account_NN1 using_VVG Floquet_NP1 states_VVZ as_II the_AT basis_NN1 ._. 
</s>
<s>
A_AT1 pulsed_JJ laser_NN1 creates_VVZ an_AT1 oscillation_NN1 in_II each_DD1 OPO_NN1 in_II one_MC1 out_RP of_IO two_MC possible_JJ stable_JJ states_NN2 with_IW a_AT1 phase_NN1 centered_VVD around_RG 0_MC or_CC with_II31 respect_II32 to_II33 the_AT pump_NN1 ._. 
</s>
<s>
Note_VV0 the_AT Maxwell_NP1 time_NNT1 sM_NNU associated_VVN with_IW the_AT resistive_JJ decay_NN1 of_IO the_AT uncompensated_JJ free_JJ charges_NN2 q_ZZ1 is_VBZ no_RR21 longer_RR22 given_VVN by_II the_AT classical_JJ expression_NN1 <Professional_FO Term>_FO but_CCB is_VBZ given_VVN by_II the_AT ratio_NN1 :_: <Professional_FO Term>_FO ._. 
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<s>
It_PPH1 may_VM be_VBI possible_JJ to_TO exploit_VVI the_AT properties_NN2 of_IO BNS_NP2 much_RR like_VV0 we_PPIS2 have_VH0 begun_VVN to_TO utilise_VVI graphene_NN1 nanoplatelets_NN2 in_II antimicrobial_JJ work_NN1 ._. 
</s>
<s>
A_AT1 way_NN1 based_VVN on_II random_JJ walk_NN1 dynamics_NN can_VM be_VBI used_VVN to_TO predict_VVI and_CC identify_VVI the_AT emergence_NN1 of_IO functional_JJ modules_NN2 in_II collective_JJ phenomena_NN2 &lsqb;_( 210_MC &rsqb;_) ._. 
</s>
<s>
Another_DD1 factor_NN1 affecting_VVG the_AT long-term_JJ stability_NN1 of_IO PEC_NN1 cells_NN2 is_VBZ catalyst_NN1 poisoning_VVG on_II the_AT surfaces_NN2 of_IO the_AT photo-_JJ electrodes_NN2 ,_, especially_RR the_AT photocathodes_NN2 ._. 
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<s>
Namely_REX ,_, we_PPIS2 expect_VV0 no_AT quantized_JJ conductanceinthe_NN1 =1case_FO since_CS the_AT wall_NN1 transports_VVZ charge_NN1 between_II the_AT edge_NN1 modes_NN2 ,_, whereas_CS for_IF =2_FO we_PPIS2 expect_VV0 the_AT quantized_JJ charge_NN1 conductance_NN1 but_CCB no_AT quantized_JJ thermal_JJ conductance_NN1 ._. 
</s>
<s>
The_AT first_MD one_PN1 is_VBZ caused_VVN by_II the_AT electron_NN1 wave_NN1 function_NN1 overlaps_NN2 and_CC energy_NN1 difference_NN1 of_IO the_AT valence_NN1 band_NN1 maximum_NN1 and_CC conduction_NN1 band_NN1 minimum_NN1 ,_, which_DDQ belong_VV0 to_II different_JJ materials_NN2 ,_, whereas_CS the_AT latter_DA one_PN1 is_VBZ strongly_RR correlated_VVN to_II the_AT thermal_JJ excitations_NN2 ._. 
</s>
<s>
The_AT quantity_NN1 in_II the_AT exponential_NN1 is_VBZ the_AT '_NULL classical_JJ '_NULL result_NN1 and_CC is_VBZ essentially_RR the_AT action_NN1 of_IO the_AT instanton_NN1 ._. 
</s>
<s>
The_AT instability_NN1 of_IO the_AT theory_NN1 at_II negative_JJ coupling_NN1 means_VVZ that_CST the_AT vertex_NN1 functions_NN2 develop_VV0 an_AT1 imaginary_JJ part_NN1 ;_; this_DD1 is_VBZ what_DDQ we_PPIS2 wish_VV0 to_TO calculate_VVI ._. 
</s>
<s>
Let_VV0 us_PPIO2 take_VVI a_AT1 principal_JJ bundle_NN1 atlas_NN1 <Professional_FO terms>_FO I_ZZ1 in_II the_AT differentiable_JJ structure_NN1 of_IO the_AT principal_JJ bundle_NN1 ._. 
</s>
<s>
A_AT1 feature_NN1 that_CST arises_VVZ when_CS adding_VVG many_DA2 ghosts_NN2 to_II an_AT1 event_NN1 is_VBZ that_CST some_DD of_IO the_AT final_JJ jets_NN2 contain_VV0 nothing_PN1 but_II ghost_NN1 particles_NN2 ._. 
</s>
<s>
This_DD1 characteristic_NN1 is_VBZ used_VVN in_II this_DD1 section_NN1 to_TO introduce_VVI various_JJ plasma_NN1 filter_NN1 configurations_NN2 proposed_VVN to_II date_NN1 ._. 
</s>
<s>
Rupp_VV0 et_RA21 al_RA22 ._. 
</s>
<s>
studied_VVD the_AT nanoplasma_NN1 formation_NN1 and_CC explosion_NN1 dynamics_NN of_IO single_JJ large_JJ xenon_NN1 clusters_NN2 in_II ultrashort_NN1 ,_, intense_JJ x-ray_JJ free-electron_JJ laser_NN1 pulses_NN2 via_II ion_NN1 spectroscopy_NN1 (_( Rupp_NP1 et_RA21 al._RA22 ,_, 2016_MC )_) ._. 
</s>
<s>
Under_II the_AT phase_NN1 transition_NN1 from_II the_AT CDSM_NP1 to_II the_AT TCI_NN1 ,_, the_AT surface_NN1 states_VVZ also_RR transform_VV0 &lsqb;_( see_VV0 Figs._NN2 3(c)_FO and_CC 3(d)_FO &rsqb;_) ._. 
</s>
<s>
There_EX are_VBR opportunities_NN2 yet_RR challenges_NN2 of_IO leveraging_VVG MP_NN1 data_NN to_TO link_VVI human_JJ mobility_NN1 patterns_NN2 with_IW infectious_JJ disease_NN1 dynamics_NN ._. 
</s>
<s>
Finally_RR ,_, our_APPGE conclusions_NN2 are_VBR presented_VVN in_II Sec_NNU ._. 
</s>
<s>
V._II Then_RT the_AT recursion_NN1 for_IF the_AT Poincaré_NN1 polynomials_NN2 derived_VVN above_RL can_VM also_RR be_VBI applied_VVN in_II the_AT case_NN1 m=2_FO ._. 
</s>
<s>
At_II intermediate_JJ collision_NN1 energies_NN2 ,_, modeling_VVG using_VVG the_AT set_NN1 of_IO processes_NN2 listed_VVN above_RL has_VHZ missing_JJ energy_NN1 loss_NN1 processes_NN2 ,_, inclusion_NN1 of_IO which_DDQ results_VVZ in_II significantly_RR better_JJR agreement_NN1 with_IW the_AT recommended_JJ stopping_VVG power_NN1 ._. 
</s>
<s>
One_MC1 of_IO them_PPHO2 at_II 531.41_MC eV_NN1 belongs_VVZ to_II C_ZZ1 &rsqb;_) Obonds_NN2 and_CC 532.93_MC eV_NN1 ascribed_VVN to_II phenol_NN1 (_( COH_NP1 )_) or_CC ester_JJR (_( COC_NP1 )_) groups_NN2 ._. 
</s>
<s>
And_CC A_ZZ1 Non-Empty_JJ Set_NN1 As_CSA Defined_VVN Above_RL ._. 
</s>
<s>
Another_DD1 new_JJ physics_NN1 scenario_NN1 that_CST can_VM be_VBI probed_VVN by_II the_AT high_JJ energy_NN1 atmospheric_JJ neutrinos_NN2 observed_VVN by_II the_AT Ice_NN1 Cube_NN1 is_VBZ the_AT non-standard_JJ neutrino_NN1 interactions_NN2 ._. 
</s>
<s>
However_RR ,_, it_PPH1 is_VBZ plausible_JJ that_CST a_AT1 positive_JJ mass_JJ term_NN1 may_VM simply_RR imply_VVI an_AT1 IR_NN1 cutoff_NN1 for_IF gravity_NN1 here_RL ,_, while_CS the_AT large-scale_JJ structure_NN1 of_IO the_AT background_NN1 solution_NN1 might_VM not_XX be_VBI affected_VVN ._. 
</s>
<s>
The_AT vector_NN1 =_FO f_ZZ1 b_ZZ1 e_ZZ1 0_MC is_VBZ the_AT '_NULL toroidal_JJ '_NULL magnetic_JJ field_NN1 unit_NN1 vector_NN1 ,_, and_CC =_FO B_ZZ1 b_ZZ1 B_ZZ1 0_MC is_VBZ the_AT unit_NN1 vector_NN1 along_II the_AT total_JJ magnetic_JJ field_NN1 ,_, assuming_VVG that_CST the_AT poloidal_JJ magnetic_JJ field_NN1 is_VBZ small_JJ relative_II21 to_II22 the_AT toroidal_JJ field_NN1 ._. 
</s>
<s>
The_AT transportation_NN1 of_IO the_AT fluid_NN1 and_CC its_APPGE flow_NN1 direction_NN1 are_VBR physically_RR demonstrated_VVN &lsqb;_( Fig._NN1 8(d)_FO &rsqb;_) ._. 
</s>
<s>
The_AT algebraic_JJ method_NN1 is_VBZ derived_VVN from_II an_AT1 electrostatic_JJ formalism_NN1 ,_, appropriate_JJ for_IF near-field_JJ interactions_NN2 at_II optical_JJ frequencies_NN2 ,_, which_DDQ is_VBZ then_RT used_VVN to_TO demonstrate_VVI a_AT1 variety_NN1 of_IO optical_JJ effects_NN2 associated_VVN with_IW localized_JJ surface_NN1 plasmons_NN2 ,_, such_II21 as_II22 plasmon_NN1 hybridization_NN1 ,_, induced_VVD transparency_NN1 ,_, Fano_NP1 resonances_NN2 ,_, optical_JJ phase_NN1 detection_NN1 ,_, and_CC all-optical_JJ modulation_NN1 ,_, among_II others_NN2 ._. 
</s>
<s>
The_AT Si/Cu-RTP_FU capacity_NN1 decay_NN1 is_VBZ also_RR slower_JJR during_II the_AT overall_JJ cycles_NN2 ._. 
</s>
<s>
Subtracting_VVG the_AT background_NN1 fluorescence_NN1 intensity_NN1 ,_, no_AT desired_JJ signal_NN1 is_VBZ detected_VVN for_IF the_AT well_NN1 C_ZZ1 ,_, so_RR not_XX shown_VVN in_II figure_NN1 5(b)_FO ._. 
</s>
<s>
All_DB these_DD2 oscillations_NN2 come_VV0 from_II the_AT fact_NN1 that_CST the_AT average_JJ environment_NN1 of_IO spheres_NN2 i_ZZ1 and_CC j_ZZ1 characterized_VVN by_II Pi_NN1 and_CC Pj_NP1 differ_VV0 from_II the_AT average_JJ global_JJ environments_NN2 P_ZZ1 (_( r_ZZ1 )_) &lsqb;_( see_VV0 the_AT relation_NN1 (_( 20_MC )_) &rsqb;_) ._. 
</s>
<s>
VII.C_NP1 ,_, these_DD2 operations_NN2 have_VH0 proven_VVN to_TO be_VBI quite_RG useful_JJ in_II the_AT study_NN1 of_IO asymptotic_JJ resource_NN1 convertibility_NN1 ._. 
</s>
<s>
However_RR ,_, it_PPH1 facilitates_VVZ ,_, for_REX21 example_REX22 ,_, the_AT creation_NN1 of_IO a_AT1 localized_JJ source_NN1 of_IO charge_NN1 in_BCL21 order_BCL22 to_TO study_VVI the_AT electron_NN1 rearrangement_NN1 ._. 
</s>
<s>
It_PPH1 is_VBZ therefore_RR very_RG important_JJ to_TO ensure_VVI that_CST the_AT data_NN are_VBR indeed_RR stationary_JJ ,_, i.e._REX their_APPGE statistical_JJ properties_NN2 are_VBR invariant_JJ ,_, before_II applying_VVG any_DD surrogate_NN1 technique_NN1 with_IW this_DD1 assumption_NN1 in_II their_APPGE null_JJ hypothesis_NN1 ._. 
</s>
<s>
For_IF fiber_NN1 lasers_NN2 ,_, the_AT coupling_NN1 methods_NN2 are_VBR various_JJ ,_, which_DDQ should_VM be_VBI chosen_VVN according_II21 to_II22 practical_JJ applications_NN2 ._. <chart>_FO FIG_NN1 ._. 
</s>
<s>
What_DDQ is_VBZ known_VVN about_II how_RRQ the_AT mechanism_NN1 by_II which_DDQ hexokinases_NN2 mediate_VV0 the_AT above_JJ conversion_NN1 ?_? 
</s>
<s>
The_AT kink–antikink_NN1 force_NN1 is_VBZ attractive_JJ and_CC decays_VVZ similarly_RR ._. 
</s>
<s>
The_AT formation_NN1 of_IO lithium_NN1 dendrites_NN2 continuously_RR consumed_VVN metal_NN1 lithium_NN1 and_CC electrolytes_NN2 ,_, resulting_VVG in_II low_JJ coulombic_JJ effciency_NN1 ._. 
</s>
<s>
Due_II21 to_II22 the_AT novelty_NN1 of_IO computational_JJ study_NN1 on_II phagraphene_NN1 as_II a_AT1 sensor_NN1 surface_NN1 and_CC in_II continuing_VVG our_APPGE previous_JJ computational_JJ studies_NN2 using_VVG Density_NN1 Functional_JJ Theory_NN1 (_( DFT_NP1 )_) ,_, the_AT electronic_JJ sensitivity_NN1 of_IO pristine_JJ and_CC Al_NP1 ,_, Si_FW and_CC Ga_NP1 doped_VVD phagraphene_NN1 towards_II CO_NP1 molecule_NN1 was_VBDZ investigated_VVN via_II DFT_NP1 approach_NN1 ._. 
</s>
<s>
Even_CS21 though_CS22 in_II both_DB2 cases_NN2 luminosities_NN2 are_VBR sufficiently_RR low_JJ to_TO neglect_VVI pileup_NN1 effects_NN2 ,_, the_AT case_NN1 of_IO heavy-ion_JJ collisions_NN2 has_VHZ a_AT1 different_JJ effect_NN1 that_CST behaves_VVZ similarly_RR to_TO pileup_VVI :_: the_AT quark–gluon_NN1 plasma_NN1 created_VVN during_II a_AT1 heavy-ion_JJ collision_NN1 decays_VVZ into_II a_AT1 large_JJ number_NN1 (_( thousands_NNO2 )_) of_IO particles_NN2 in_II the_AT final-state_NN1 of_IO the_AT collision_NN1 ,_, corresponding_VVG to_II a_AT1 huge_JJ Underlying_JJ Event_NN1 activity_NN1 ._. 
</s>
<s>
The_AT impact_NN1 of_IO microporosity_NN1 on_II the_AT biocompatibility_NN1 of_IO hard_JJ implants_NN2 was_VBDZ assessed_VVN by_II Sharkawy_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
and_CC Ward_NP1 et_RA21 al._RA22 ,_, who_PNQS both_RR demonstrated_VVN implants_NN2 were_VBDR surrounded_VVN by_II a_AT1 denser_JJR fibrous_JJ capsule_NN1 than_CSN porous_JJ implants_NN2 ._. 
</s>
<s>
From_II quantum_NN1 entanglement_NN1 to_II quantum_NN1 computation_NN1 ,_, resource_VV0 theories_NN2 can_VM be_VBI used_VVN to_TO quantify_VVI a_AT1 desirable_JJ quantum_NN1 effect_NN1 ,_, develop_VV0 new_JJ protocols_NN2 for_IF its_APPGE detection_NN1 ,_, and_CC identify_VV0 processes_NN2 that_CST optimize_VV0 its_APPGE use_NN1 for_IF a_AT1 given_JJ application_NN1 ._. 
</s>
<s>
The_AT close_JJ proximity_NN1 of_IO the_AT LIF_NN1 excitation_NN1 and_CC fluorescence_NN1 wavelengths_NN2 allows_VVZ the_AT same_DA profile_NN1 to_TO be_VBI used_VVN for_IF LIF_NN1 signal_NN1 measurements_NN2 :_: <equation>_FO (_( 13_MC )_) ._. 
</s>
<s>
The_AT standard_JJ approach_NN1 to_II CR_NP1 propagation_NN1 in_II the_AT Galaxy_NN1 based_VVN on_II diffusion_NN1 models_NN2 ,_, the_AT necessary_JJ inputs_NN2 and_CC the_AT basic_JJ results_NN2 are_VBR described_VVN next_MD ._. 
</s>
<s>
This_DD1 approach_NN1 aimed_VVN at_II circumventing_VVG the_AT drawback_NN1 of_IO offline_JJ training_NN1 that_CST is_VBZ standard_JJ for_IF most_DAT OEO_NP1 reservoir_NN1 computers_NN2 ._. 
</s>
<s>
Such_DA samples_NN2 require_VV0 an_AT1 in-plane_NN1 anisotropy_NN1 that_CST is_VBZ stronger_JJR than_CSN the_AT magnetostatic_JJ energy_NN1 cost_NN1 ._. 
</s>
<s>
The_AT rotational_JJ Doppler_NP1 shift_VV0 in_II the_AT harmonics_NN2 frequency_NN1 was_VBDZ observed_VVN by_II Faucher_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2016_MC )_) and_CC Prost_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2017_MC )_) ._. 
</s>
<s>
The_AT QFC_NP1 model_NN1 of_IO &lsqb;_( 21_MC &rsqb;_) is_VBZ also_RR constrained_VVN by_II other_JJ independent_JJ experiments_NN2 which_DDQ constrains_VVZ the_AT effective_JJ variation_NN1 of_IO the_AT gravitational_JJ constant_JJ ._. 
</s>
<s>
To_TO test_VVI this_DD1 hypothesis_NN1 ,_, two_MC examples_NN2 ,_, where_CS the_AT general_JJ trend_NN1 appears_VVZ to_TO be_VBI broken_VVN were_VBDR identified_VVN and_CC studied_VVN ._. 
</s>
<s>
Devetak_VV0 and_CC winter_NNT1 (_( 2004_MC )_) introduced_VVD a_AT1 useful_JJ notation_NN1 to_TO account_VVI for_IF the_AT different_JJ types_NN2 of_IO resources_NN2 that_CST are_VBR typically_RR encountered_VVN in_II quantum_NN1 information_NN1 ._. 
</s>
<s>
Indeed_RR ,_, in_II one_MC1 of_IO the_AT first_MD in_JJ21 vivo_JJ22 demonstrations_NN2 of_IO an_AT1 MMR_NP1 ,_, Martel_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
applied_VVN these_DD2 principles_NN2 for_IF a_AT1 small_JJ sphere_NN1 in_II blood_NN1 to_TO magnetically_RR actuate_VVI a_AT1 1.5_MC mm_NNU ferromagnetic_JJ bead_NN1 through_II the_AT carotid_JJ artery_NN1 of_IO a_AT1 porcine_JJ model_NN1 ._. 
</s>
<s>
Therefore_RR ,_, there_EX are_VBR few_DA2 reports_NN2 on_II successful_JJ preparation_NN1 of_IO LiNixMnyCo1-x-yO2_NP1 single_JJ with_IW crystal_NN1 particles_NN2 ._. 
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<s>
In_II lattice_NN1 QCD_NP1 calculations_NN2 ,_, the_AT extent_NN1 of_IO the_AT space-time_JJ lattice_NN1 is_VBZ necessarily_RR finite_JJ ._. 
</s>
<s>
However_RR ,_, in_II real_JJ solid_JJ materials_NN2 ,_, like_II silica_NN1 ,_, &lsqb;_( 27_MC &rsqb;_) silicon_NN1 ,_, &lsqb;_( 28_MC &rsqb;_) or_CC silicon_NN1 carbide_NN1 ,_, &lsqb;_( 29_MC &rsqb;_) the_AT Raman_NN1 gain_NN1 profifile_NN1 is_VBZ not_XX simply_RR composed_VVN of_IO only_RR a_AT1 few_DA2 discrete_JJ peaks_NN2 ,_, but_CCB rather_RR is_VBZ a_AT1 continuum_NN1 ;_; therefore_RR ,_, it_PPH1 is_VBZ natural_JJ to_TO introduce_VVI a_AT1 coupling_NN1 term_NN1 between_II the_AT two_MC lasing_NN1 modes_NN2 (_( see_VV0 Figure_NN1 1f_RA )_) ._. 
</s>
<s>
Examples_NN2 include_VV0 Bayesian_JJ optimization_NN1 and_CC genetic_JJ algorithms_NN2 (_( 90_MC )_) ,_, as_II31 well_II32 as_II33 variational_JJ optimization_NN1 ._. 
</s>
<s>
As_CSA before_RT ,_, the_AT inversion_NN1 of_IO Eq_NN1 ._. 
</s>
<s>
(_( 44_MC )_) leads_VVZ to_II a_AT1 measure_NN1 that_CST scales_NN2 (_( at_RR21 most_RR22 )_) with_IW the_AT spectral_JJ radius_NN1 and_CC that_DD1 is_VBZ applicable_JJ to_II general_JJ quantum_NN1 states_NN2 ,_, but_CCB without_IW the_AT need_NN1 of_IO a_AT1 convex-roof_JJ construction_NN1 ._. 
</s>
<s>
Some_DD of_IO these_DD2 organisms_NN2 have_VH0 very_RG similar_JJ motility_NN1 mechanism_NN1 as_CSA E._NP1 coli_NN2 ,_, e.g._REX ,_, S._NP1 typhimurium_NN1 &lsqb;_( 1_MC1 &rsqb;_) ,_, B._NP1 subtilis_NN1 &lsqb;_( 2_MC &rsqb;_) or_CC S._NP1 marcescens_NN2 &lsqb;_( 4_MC &rsqb;_) ,_, but_CCB prokaryotes_VVZ like_II R._NP1 sphaeroides_NN2 have_VH0 a_AT1 somewhat_RR different_JJ mechanism_NN1 ._. 
</s>
<s>
In_II this_DD1 effective_JJ three-level_NN1 (_( resonant_JJ )_) scenario_NN1 though_CS ,_, the_AT outer_JJ entangling_JJ spins_NN2 are_VBR being_VBG mediated_VVN solely_RR by_II the_AT anomalous_JJ eigenstate_NN1 at_II <Equation>_FO ._. 
</s>
<s>
On_II the_AT basis_NN1 of_IO the_AT gained_VVN pinhole_NN1 images_NN2 ,_, one_PN1 could_VM conclude_VVI that_CST the_AT number_NN1 of_IO ions_NN2 actually_RR emitted_VVD right_RR from_II the_AT z-pinch_JJ center_NN1 is_VBZ not_XX significant_JJ ._. 
</s>
<s>
Conversely_RR ,_, Zuzek_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 65_MC )_) set_VVD the_AT transmission_NN1 probability_NN1 on_II interlayer_NN1 links_VVZ to_II 1_MC1 so_CS21 that_CS22 they_PPHS2 only_RR play_VV0 the_AT role_NN1 of_IO connecting_VVG the_AT layers_NN2 (_( there_EX is_VBZ no_AT actual_JJ transmission_NN1 through_II them_PPHO2 )_) ._. 
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<s>
As_CSA noted_VVN before_RT ,_, these_DD2 kinds_NN2 of_IO models_NN2 are_VBR not_XX only_RR interesting_JJ on_II their_APPGE own_DA ._. 
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<s>
To_TO conclude_VVI ,_, the_AT success_NN1 of_IO STIRAP_NN1 in_II nearly_RR degenerate_JJ systems_NN2 depends_VVZ on_II the_AT existence_NN1 of_IO an_AT1 adiabatic_JJ path_NN1 that_CST connects_VVZ the_AT initial_NN1 and_CC final_JJ states_NN2 ._. 
</s>
<s>
In_CS21 case_CS22 the_AT DM_NNU particles_NN2 interacted_VVD so_RG feebly_RR that_CST they_PPHS2 never_RR became_VVD part_NN1 of_IO the_AT SM_NP1 equilibrium_NN1 heat_NN1 bath_NN1 ,_, the_AT coupling_NN1 between_II DM_NNU and_CC the_AT visible_JJ sector_NN1 typically_RR has_VHZ to_TO be_VBI orders_NN2 of_IO magnitude_NN1 larger_JJR than_CSN in_II the_AT usual_JJ freeze-in_NN1 case_NN1 to_TO compensate_VVI the_AT larger_JJR expansion_NN1 rate_NN1 ._. 
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<s>
We_PPIS2 here_RL compare_VV0 the_AT purified_JJ continuous-variable_NN1 maximally_RR entangled_JJ state_NN1 with_IW a_AT1 two-mode_JJ squeezed_JJ vacuum_NN1 state_NN1 ,_, which_DDQ is_VBZ a_AT1 conventional_JJ entangled_JJ state_NN1 in_II Gaussian_JJ regime_NN1 ,_, by_II the_AT explicit_JJ calculation_NN1 of_IO quantum_NN1 fidelities_NN2 between_II those_DD2 states_NN2 and_CC an_AT1 -dimensional_JJ maximally_RR entangled_JJ state_NN1 in_II the_AT finite_JJ Hilbert_NP1 space_NN1 ._. 
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<s>
We_PPIS2 will_VM now_RT proceed_VVI to_TO quantify_VVI the_AT PES_NN2 between_II system_NN1 and_CC cavity_NN1 ._. 
</s>
<s>
The_AT accelerated_JJ expansion_NN1 in_II the_AT present_JJ epoch_NN1 is_VBZ usually_RR attributed_VVN to_II a_AT1 fluid_NN1 with_IW negative_JJ pressure_NN1 and_CC hence_RR ,_, it_PPH1 can_VM be_VBI thought_VVN that_CST the_AT contribution_NN1 coming_VVG from_II the_AT bulk_NN1 viscosity_NN1 is_VBZ greater_JJR than_CSN the_AT usual_JJ pressure_NN1 ._. 
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<s>
Nonetheless_RR ,_, we_PPIS2 stress_VV0 that_CST these_DD2 issues_NN2 are_VBR significant_JJ and_CC complex_JJ ._. 
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<s>
The_AT distances_NN2 labeled_VVD in_II the_AT schematic_JJ determine_VV0 the_AT magnification_NN1 of_IO the_AT imaging_NN1 system_NN1 ._. 
</s>
<s>
The_AT regularity_NN1 of_IO X_ZZ1 is_VBZ then_RT <Professional_FO Term>_FO ,_, <Professional_FO Term>_FO ,_, and_CC the_AT estimate_NN1 (_( 5.8_MC )_) holds_VVZ for_IF <Equation>_FO ._. 
</s>
<s>
The_AT mesons_NN2 carry_VV0 the_AT required_JJ quantum_NN1 numbers_NN2 ,_, but_CCB the_AT y-axis_NN1 intercept_VV0 a(0)_FO of_IO the_AT corresponding_JJ Regge_NN1 trajectory_NN1 is_VBZ too_RG low_JJ (_( see_VV0 Fig._NN1 5_MC )_) ._. 
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<s>
In_II phase_NN1 space_NN1 ,_, coherent_JJ states_NN2 are_VBR selected_VVN as_II the_AT most-classical_JJ pure_JJ states_NN2 ._. 
</s>
<s>
In_II this_DD1 case_NN1 ,_, the_AT sum_NN1 of_IO forces_NN2 on_II the_AT particles_NN2 is_VBZ zero_MC ._. 
</s>
<s>
Sacksteder_VV0 et_RA21 al_RA22 ._. 
</s>
<s>
(_( 2012_MC )_) investigated_VVD spin_NN1 conduction_NN1 in_II surface_NN1 states_NN2 of_IO three-dimensional_JJ topological_JJ insulators_NN2 with_IW anisotropic_JJ dispersion_NN1 ._. 
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<s>
In_II a_AT1 fair_JJ sense_NN1 ,_, moreover_RR ,_, all_DB of_IO thermodynamics_NN1 blossoms_NN2 out_II21 of_II22 the_AT simple_JJ matter_NN1 of_IO how_RGQ many_DA2 of_IO a_AT1 system_NN1 '_NULL s_ZZ1 microstates_NN2 lie_VV0 within_II any_DD particular_JJ macrostate_NN1 (_( or_CC ,_, in_II the_AT more_RGR common_JJ and_CC physical_JJ case_NN1 in_II which_DDQ all_DB microstates_NN2 do_VD0 not_XX have_VHI the_AT same_DA probability_NN1 ,_, what_DDQ is_VBZ the_AT total_JJ statistical_JJ weight_NN1 of_IO those_DD2 microstates_NN2 )_) ._. 
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<s>
As_CSA mentioned_VVN before_RT ,_, the_AT rotation_NN1 operated_VVN by_II the_AT beam_NN1 splitter_NN1 is_VBZ not_XX around_II the_AT z_ZZ1 axis_NN1 and_CC i_ZZ1 s_ZZ1 thus_RR nonlocal_JJ with_II31 respect_II32 to_II33 the_AT chosen_JJ bipartition_NN1 ._. 
</s>
<s>
Only_RR the_AT data_NN that_CST are_VBR adjusted_VVN by_II subtraction_NN1 of_IO the_AT weak_JJ antilocalization_NN1 contribution_NN1 display_VV0 a_AT1 plain_JJ logarithmic_JJ temperature_NN1 dependence_NN1 ._. 
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<s>
This_DD1 phase_NN1 noise_NN1 ,_, also_RR known_VVN as_II phase_NN1 diffusion_NN1 ,_, comes_VVZ from_II a_AT1 combination_NN1 of_IO different_JJ quantum_NN1 effects.6_FO Direct_JJ phase_NN1 measurement_NN1 is_VBZ not_XX technologically_RR feasible_JJ for_IF optical_JJ signals_NN2 ,_, but_CCB an_AT1 unbalanced_JJ Mach-Zehnder_NP1 interferometer_NN1 (_( MZI_NP1 )_) (_( see_VV0 Fig._NN1 9_MC )_) can_VM translate_VVI phase_NN1 differences_NN2 into_II amplitude_NN1 variations_NN2 ._. 
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<s>
Therefore_RR ,_, further_RRR experimental_JJ verification_NN1 of_IO the_AT Higgs_NP1 and_CC Leggett_NP1 modes_NN2 is_VBZ left_VVN as_II a_AT1 future_JJ problem_NN1 ._. 
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<s>
The_AT authors_NN2 have_VH0 no_AT additional_JJ financial_JJ is_VBZ closures_NN2 ._. 
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<s>
The_AT rate_NN1 at_II which_DDQ work_VV0 is_VBZ done_VDN per_II unit_NN1 volume_NN1 for_IF time-averaged_JJ quantities_NN2 is_VBZ given_VVN by_II the_AT real_JJ part_NN1 of_IO <equation>_FO in_II31 terms_II32 of_II33 the_AT induced_JJ current_JJ density_NN1 J_ZZ1 exp(it)_NN1 and_CC the_AT electric_JJ field_NN1 that_CST drives_VVZ it_PPH1 ._. 
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<s>
The_AT variance_NN1 of_IO the_AT quadrature_NN1 is_VBZ independent_JJ of_IO ._. 
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<s>
This_DD1 divergence_NN1 is_VBZ not_XX a_AT1 problem_NN1 ;_; it_PPH1 is_VBZ simply_RR a_AT1 consequence_NN1 of_IO the_AT failure_NN1 of_IO the_AT large_JJ precompression_NN1 hypothesis_NN1 ._. 
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<s>
The_AT positron_NN1 annihilation_NN1 rate_NN1 at_II defects_NN2 D_ZZ1 =1/_JJ τ_NULL 2_MC increases_VVZ slightly_RR after_II annealing_VVG ,_, but_CCB the_AT main_JJ effect_NN1 of_IO the_AT annealing_NN1 is_VBZ the_AT decrease_NN1 of_IO τ_NULL 1and_FO the_AT increase_NN1 of_IO the_AT intensity_NN1 ratio_NN1 I2/_NN1 I1_FO ._. 
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<s>
Dipole_NN1 corrections_NN2 were_VBDR also_RR added_VVN in_II the_AT direction_NN1 normal_JJ to_II the_AT surface_NN1 ._. 
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<s>
This_DD1 fixed_VVD the_AT position_NN1 of_IO the_AT *L_FO ammonium_NN1 cation_NN1 while_CS allowing_VVG access_NN1 of_IO the_AT diarizing_JJ tag_NN1 to_II a_AT1 limited_JJ conformational_JJ space_NN1 ,_, cheery_JJ including_II the_AT Ala2_FO residue_NN1 ._. 
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<s>
The_AT quantities_NN2 J_ZZ1 and_CC D_ZZ1 increases_NN2 and_CC decreases_VVZ ,_, respectively_RR ,_, with_IW increasing_JJ τ_NULL ,_, converging_VVG to_II some_DD nonzero_NN1 values_NN2 when_RRQ τ_NULL is_VBZ around_RG 500_MC ._. 
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<s>
One_MC1 of_IO the_AT most_RGT exciting_JJ things_NN2 about_II entropic_JJ uncertainty_NN1 relations_NN2 is_VBZ that_CST they_PPHS2 give_VV0 insight_NN1 into_II basic_JJ physics_NN1 ._. 
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<s>
This_DD1 formula_NN1 is_VBZ somewhat_RR lengthy_JJ but_CCB the_AT various_JJ contributions_NN2 have_VH0 a_AT1 very_RG clear_JJ physical_JJ meaning_NN1 :_: the_AT second_MD line_NN1 corresponds_VVZ to_II the_AT statistics_NN of_IO the_AT outgoing_JJ sites_NN2 x_ZZ1 of_IO the_AT system_NN1 at_II even_RR times_NNT2 ,_, the_AT third_MD line_NN1 corresponds_VVZ to_II the_AT statistics_NN of_IO the_AT outgoing_JJ flows_NN2 <Equation>_FO from_II sites_NN2 x_ZZ1 of_IO the_AT system_NN1 at_II odd_JJ times_NNT2 ,_, the_AT fourth_MD line_NN1 corresponds_VVZ to_II the_AT statistics_NN of_IO the_AT outgoing_JJ flows<Equation>_FO from_II even_RR times_NNT2 ,_, the_AT fifth_MD line_NN1 corresponds_VVZ to_II the_AT statistics_NN of_IO the_AT outgoing_JJ reservoirs_NN2 r_ZZ1 at_II odd_JJ times_NNT2 ,_, while_CS the_AT last_MD line_NN1 corresponds_VVZ to_II the_AT dynamical_JJ constraints_NN2 on_II the_AT incoming_JJ flows_NN2 towards_II sites_NN2 x_ZZ1 of_IO the_AT system_NN1 at_II even_RR and_CC odd_JJ times_NNT2 respectively_RR ._. 
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<s>
In_II the_AT time_NNT1 domain_NN1 ,_, amplitude_NN1 noise_NN1 remains_VVZ bounded_VVN owing_II21 to_II22 the_AT transverse_JJ stability_NN1 of_IO the_AT limit_NN1 cycle_NN1 and_CC is_VBZ therefore_RR inconsequential_JJ in_II most_DAT applications_NN2 ._. 
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<s>
Let_VV0 (_( M_ZZ1 ,_, g_ZZ1 )_) be_VBI an_AT1 n-dimensional_JJ compact_NN1 closed_VVD smooth_JJ Riemannian_JJ manifold_NN1 ,_, and_CC let_VV0 <Professional_FO Term>_FO be_VBI the_AT associated_JJ Laplace-Beltrami_JJ operator_NN1 ._. 
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<s>
II_MC ,_, we_PPIS2 analyze_VV0 the_AT data_NN from_II two_MC groups_NN2 of_IO experiments_NN2 to_TO determine_VVI the_AT stagnation_NN1 pressure_NN1 and_CC effective_JJ mix_NN1 fraction_NN1 ._. 
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<s>
Evidence_NN1 that_CST model_NN1 errors_NN2 contribute_VV0 significantly_RR to_II the_AT large_JJ residuals_NN2 is_VBZ shown_VVN in_II the_AT last_MD column_NN1 of_IO It_PPH1 contains_VVZ the_AT deviations_NN2 of_IO selected_JJ DR_NNB frequencies_NN2 from_II the_AT newer_JJR measurements_NN2 ,_, the_AT largest_JJT shown_VVN is_VBZ 0.13_MC MHz_NNU ,_, but_CCB the_AT residuals_NN2 of_IO the_AT DR_NNB frequencies_NN2 in_II the_AT ERHAM_NN1 fits_VVZ range_NN1 from_II 0.2_MC to_II 1.4_MC MHz_NNU ._. 
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<s>
The_AT second_MD term_NN1 accounts_VVZ for_IF the_AT spin_NN1 1_MC1 pure_JJ gauge_NN1 mode_NN1 Aa_NP1 as_CSA discussed_VVN in_II section_NN1 5.1_MC ,_, whose_DDQGE contribution_NN1 to_II the_AT graviton_NN1 hab_NN1 was_VBDZ computed_VVN in_II (_( 5.91_MC )_) ._. 
</s>
<s>
The_AT density_NN1 of_IO hit_NN1 points_VVZ on_II the_AT target_NN1 surface_NN1 is_VBZ then_RT a_AT1 measure_NN1 for_IF the_AT power_NN1 density_NN1 in_II this_DD1 location_NN1 for_IF the_AT underlying_JJ magnetic_JJ configuration_NN1 ._. 
</s>
<s>
Stark_NP1 et_RA21 al_RA22 ._. 
</s>
<s>
&lsqb;_( 275_MC &rsqb;_) investigated_VVD the_AT development_NN1 of_IO high_JJ throughput_NN1 assays_NN2 to_TO identify_VVI the_AT behavior_NN1 of_IO proteins_NN2 ,_, sugars_NN2 ,_, lipids_NN2 ,_, and_CC other_JJ metabolites_NN2 in_II cellular_JJ interactions_NN2 ._. 
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<s>
For_IF prime_JJ numbers_NN2 ,_, we_PPIS2 force_VV0 the_AT algorithm_NN1 to_TO execute_VVI the_AT main_JJ computational_JJ block_NN1 ._. 
</s>
<s>
TNPs_NP1 with_IW a_AT1 GNR_NP1 core_NN1 and_CC inorganic_JJ Gd(III)_JJ layer_NN1 that_CST retain_VV0 shape_NN1 and_CC ablative_JJ capability_NN1 over_II multiple_JJ cycles_NN2 and_CC are_VBR stable_JJ in_RR21 vivo_RR22 ,_, while_CS providing_VVG usable_JJ MR_NNB and_CC CT_NN1 contrasts_VVZ on_II clinical_JJ scanners_NN2 for_IF clearly_RR visualizing_VVG CRLM_NP1 tumors_NN2 ._. 
</s>
<s>
It_PPH1 Is_VBZ A_AT1 Properly_RR Embedded_JJ Minimal_JJ Surface_NN1 ,_, So_RR In_II Fact_NN1 Coincides_VVZ With_IW M_ZZ1 ,_, Which_DDQ Is_VBZ Thereby_RR Outer-Minimizing_JJ ._. 
</s>
<s>
It_PPH1 also_RR shows_VVZ that_CST although_CS CW_NP1 bias_NN1 of_IO E._NP1 coli_NN2 increases_VVZ really_RR sharply_RR as_CSA CheY-P_NP1 level_JJ changes_NN2 ,_, when_CS that_DD1 response_NN1 is_VBZ actually_RR replaced_VVN by_II a_AT1 jump_NN1 in_II the_AT switching_JJ probability_NN1 ,_, system_NN1 shows_VVZ qualitatively_RR different_JJ behavior_NN1 in_II many_DA2 aspects_NN2 ._. 
</s>
<s>
To_TO set_VVI the_AT time_NNT1 step_VV0 we_PPIS2 compare_VV0 this_DD1 distance_NN1 with_IW characteristic_JJ surface-to-surface_JJ distance_NN1 between_II molecules_NN2 ,_, <equation>_FO ,_, which_DDQ is_VBZ the_AT distance_NN1 between_II surfaces_NN2 of_IO neighboring_VVG molecules_NN2 arranged_VVN in_II a_AT1 cubic_JJ lattice_NN1 at_II a_AT1 given_JJ ._. 
</s>
<s>
Comparison_NN1 of_IO the_AT experimentally_RR measured_VVN line_NN1 shifts_NN2 of_IO the_AT transition_NN1 <Professional_FO term>_FO for_IF He-like_JJ Al_NP1 (_( black_NN1 scatters_VVZ )_) 35_MC with_IW the_AT present_JJ calculations_NN2 ._. 
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<s>
The_AT results_NN2 ,_, shown_VVN in_II Figure_NN1 21(C)_FO ,_, demonstrate_VV0 the_AT failure_NN1 of_IO FT_NNU surrogates_NN2 in_II this_DD1 case_NN1 ,_, with_IW them_PPHO2 incorrectly_RR identifying_VVG nonlinearity_NN1 in_II the_AT data_NN ,_, purely_RR as_II a_AT1 result_NN1 of_IO the_AT measurement_NN1 transformation_NN1 ._. 
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<s>
In_II 2017_MC ,_, he_PPHS1 joined_VVD Tsinghua_NP1 University_NN1 as_II a_AT1 professor_NN1 ._. 
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<s>
J._NP1 Sotor_NP1 ,_, I._NP1 Pasternak_NP1 ,_, A._NP1 Krajewska_NP1 ,_, W._NP1 Strupinski_NP1 ,_, and_CC G._NP1 Sobon_NP1 ,_, Opt_VV0 ._. 
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<s>
In_RR21 addition_RR22 ,_, notably_RR ,_, nonlinearity_NN1 generally_RR exists_VVZ in_II a_AT1 ME_NN1 resonator_NN1 ,_, but_CCB is_VBZ not_XX limited_VVN to_II ME_NN1 antennas_NN2 ,_, and_CC we_PPIS2 believe_VV0 this_DD1 fundamental_JJ work_NN1 will_VM open_VVI up_RP a_AT1 new_JJ dimension_NN1 for_IF the_AT design_NN1 and_CC operation_NN1 of_IO such_DA resonant_JJ ME_NN1 devices_NN2 in_II the_AT future_NN1 ._. 
</s>
<s>
The_AT first_MD significant_JJ peaks_NN2 in_II the_AT electric_JJ field_NN1 profile_NN1 are_VBR observed_VVN at_II the_AT height_NN1 of_IO the_AT surface_NN1 in_II31 contact_II32 with_II33 air_NN1 at_II the_AT bare_JJ surface_NN1 ,_, with_IW a_AT1 negative_JJ peak_NN1 located_VVD just_RR below_II the_AT surface_NN1 layer_NN1 and_CC a_AT1 more_RGR intense_JJ positive_JJ peak_NN1 located_VVN at_II the_AT surface_NN1 layer_NN1 ._. 
</s>
<s>
For_IF <Equation>_FO with_IW 71°_NNU and_CC 109°_NNU domains_NN2 ,_, much_RR weaker_JJR XLD_NP1 are_VBR observed_VVN compared_VVN to_II that_DD1 of_IO BFO/STO_NN1 due_II21 to_II22 the_AT weaker_JJR compressive_JJ strain_NN1 ._. 
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<s>
Namely_REX ,_, to_TO find_VVI the_AT first_MD ,_, we_PPIS2 substituted_VVD <Equation>_FO from_II (_( 13_MC )_) in_II the_AT right-hand_JJ side_NN1 of_IO expression_NN1 (_( 14_MC )_) at_II <Equation>_FO ._. 
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<s>
While_CS there_EX are_VBR certainly_RR a_AT1 range_NN1 of_IO interesting_JJ and_CC non-trivial_JJ questions_NN2 regarding_II such_DA feedback_NN1 ,_, such_DA as_CSA controlling_VVG thermal_JJ dynamics_NN &lsqb;_( 70–74_MCMC &rsqb;_) and_CC quantum_NN1 error_NN1 correction_NN1 &lsqb;_( 75–_VV0 81_MC &rsqb;_) ,_, the_AT mathematical_JJ machinery_NN1 required_VVN to_TO analyze_VVI it_PPH1 does_VDZ not_XX require_VVI stochastic_JJ differential_JJ equations_NN2 ._. 
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<s>
Social_JJ media_NN users_NN2 indeed_RR serve_VV0 as_RG social_JJ sensors_NN2 with_IW their_APPGE posts_NN2 being_VBG the_AT sensory_JJ information_NN1 ._. 
</s>
<s>
Applying_VVG <equation>_FO to(2)_FO and(3)_FO gives_VVZ <equation>_FO (_( 4_MC )_) and_CC <equation>_FO (_( 5_MC )_) where_RRQ ns_FO is_VBZ the_AT plasma_NN1 density_NN1 ,_, J0_FO is_VBZ a_AT1 Bessel_NN1 function_NN1 of_IO the_AT first_MD kind_NN1 ,_, <equation>_FO ,_, is_VBZ a_AT1 modified_JJ Bessel_NN1 function_NN1 of_IO the_AT first_MD kind_NN1 ,_, <equation>_FO ,_, and<equation>.If_FO the_AT confining_JJ magnetic_JJ geometry_NN1 is_VBZ up–down_NN1 symmetric_JJ ,_, the_AT gyrokinetic-Poisson_NP1 system_NN1 (_( 4_MC )_) and_CC (_( 5_MC )_) possesses_VVZ a_AT1 symmetry_NN1 that_CST inhibits_VVZ momentum_NN1 transport_NN1 :_: If_CS <equation>is_FO a_AT1 solution_NN1 with_IW associated_JJ potential_NN1 j1_FO (_( k_ZZ1 ,_, k_ZZ1 ,_, θ_NULL ,_, t_ZZ1 )_) ,_, theng<equation>is_FO also_RR a_AT1 solution_NN1 with_IW associated_JJ potential_NN1 <equation>_FO &lsqb;_( 12–15_MCMC &rsqb;_) ._. 
</s>
<s>
Therefore_RR ,_, P_ZZ1 2_MC can_VM not_XX be_VBI directly_RR populated_VVN by_II an_AT1 ultrafast_NN1 laser_NN1 excitation_NN1 from_II occupied_JJ electronic_JJ states_NN2 of_IO the_AT Cu_FO substrate_NN1 ._. 
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<s>
It_PPH1 remains_VVZ to_TO multiply_VVI the_AT result_NN1 by_II the_AT factor_NN1 (_( 2_MC )_) 3_MC (_( see_VV0 Eq_NN1 ._. 
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<s>
(_( 13_MC )_) )_) ,_, by_II the_AT factor_NN1 (_( 2_MC )_) 2_MC (_( see_VV0 Eq_NN1 ._. 
</s>
<s>
(_( 4_MC )_) )_) and_CC by_II the_AT factor_NN1 from_II Eq_NN1 ._. 
</s>
<s>
(_( 225_MC )_) and_CC after_CS the_AT integration_NN1 over_II space_NN1 variable_NN1 ,_, summation_NN1 over_II photon_NN1 polarizations_NN2 and_CC integration_NN1 over_II the_AT photon_NN1 emission_NN1 directions_NN2 ,_, we_PPIS2 again_RT arrive_VV0 at_II the_AT equation_NN1 for_IF the_AT width_NN1 of_IO state_NN1 A_ZZ1 &lsqb;_( 56_MC &rsqb;_) :_: <Equation>235_FO )_) ._. 
</s>
<s>
Non-zero_JJ defect_NN1 hopping_VVG rates_NN2 ,_, unconstrained_JJ defect_NN1 binding_VVG ._. 
</s>
<s>
This_DD1 cutoff_NN1 radius_NN1 is_VBZ taken_VVN to_TO represent_VVI the_AT radius_NN1 of_IO the_AT daughter_NN1 nucleus_NN1 ,_, although_CS it_PPH1 has_VHZ in_II fact_NN1 no_AT real_JJ physical_JJ significance_NN1 ._. 
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<s>
Then_RT ,_, the_AT complementary_JJ distant_JJ causal_JJ history_NN1 can_VM be_VBI naturally_RR expressed_VVN as_II the_AT remaining_JJ part_NN1 of_IO the_AT causal_JJ history_NN1 ,_, <equation>_FO ,_, where_CS <equation>is_FO the_AT subtraction_NN1 operator_NN1 &lsqb;_( the_AT red_JJ dashed_JJ box_NN1 in_II Fig._NN1 1(a)_FO &rsqb;_) ._. 
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<s>
Meanwhile_RR ,_, the_AT size_NN1 of_IO the_AT individual_JJ bubbles_NN2 represents_VVZ the_AT ratio_NN1 of_IO this_DD1 magnitude_NN1 to_II the_AT rms_NN1 dispersion_NN1 of_IO observable_JJ particles_NN2 ,_, /_FO ._. 
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<s>
The_AT phenomenology_NN1 entailed_VVN by_II such_DA interactions_NN2 is_VBZ thoroughly_RR analysed_VVN by_II studying_VVG heavy_JJ vector_NN1 resonances_NN2 production_NN1 and_CC decay_VV0 modes_NN2 in_II the_AT viable_JJ resonance_NN1 mass_NN1 range_NN1 ._. 
</s>
<s>
The_AT third_MD term_NN1 gives_VVZ the_AT reduction_NN1 in_II magnetic_JJ energy_NN1 due_II21 to_II22 resistive_JJ dissipation_NN1 and_CC due_II21 to_II22 the_AT relaxation_NN1 of_IO <equation>along_FO stochastic_JJ magnetic_JJ field_NN1 lines_NN2 ._. 
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<s>
Typically_RR ,_, we_PPIS2 set_VV0 the_AT displacement_NN1 energy_NN1 to_TO zero_VVI (_( since_CS it_PPH1 is_VBZ not_XX defined_VVN in_II an_AT1 amorphous_JJ solid_JJ )_) ,_, and_CC only_RR a_AT1 small_JJ cut-off_NN1 energy_NN1 (_( 1_MC1 eV_NN1 )_) limits_VVZ the_AT generated_JJ recoils_VVZ ._. 
</s>
<s>
If_CS <Equation>_FO ,_, then_RT by_II Lemma_NN1 3.12_MC ,_, (_( 3.11_MC )_) ,_, and_CC the_AT fact_NN1 that_CST K_ZZ1 >_FO l_ZZ1 f_ZZ1 ,_, ._. 
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<s>
First_MD ,_, the_AT LPS–NMC_NP1 composites_NN2 were_VBDR placed_VVN into_II a_AT1 sealed_JJ Al_NP1 pan_NN1 and_CC heated_VVN under_II atmospheric-pressure_NN1 at_II different_JJ temperatures_NN2 for_IF 1_MC1 h_ZZ1 in_II an_AT1 electric_JJ furnace_NN1 ._. 
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<s>
Here_RL ,_, <Professional_FO Term>_FO are_VBR the_AT square_JJ roots_NN2 of_IO eigenvalues_NN2 ,_, in_II descending_JJ order_NN1 ,_, of_IO the_AT following_JJ non-Hermitian_JJ matrix_NN1 :_: <Equation>_FO ._. 
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<s>
For_IF this_DD1 ,_, we_PPIS2 must_VM first_MD realize_VVI the_AT Fermi_NP1 function_NN1 comes_VVZ about_RP by_II extracting_VVG the_AT electron_NN1 amplitude_NN1 at_II either_RR the_AT origin_NN1 or_CC the_AT nuclear_JJ radius_NN1 from_II the_AT transition_NN1 amplitude_NN1 ._. 
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<s>
This_DD1 is_VBZ investigated_VVN for_IF the_AT sample_NN1 with_IW <Equation>_FO and_CC pH_NN1 of_IO 11.5_MC (_( Fig._NN1 1b_FO )_) ._. 
</s>
<s>
In_II the_AT shock_NN1 waves_NN2 ,_, kinetic_JJ energy_NN1 associated_VVN with_IW the_AT NSs_NP1 '_NULL plunging_VVG motion_NN1 is_VBZ converted_VVN to_II thermal_JJ energy_NN1 ,_, which_DDQ enhances_VVZ thermal_JJ pressure_NN1 and_CC induces_VVZ ejection_NN1 of_IO the_AT shocked_JJ matter_NN1 ._. 
</s>
<s>
In_II an_AT1 ideal_JJ noiseless_JJ oscillator_NN1 ,_, the_AT phase_NN1 would_VM remain_VVI null_JJ ,_, but_CCB in_II the_AT presence_NN1 of_IO noise_NN1 ,_, it_PPH1 randomly_RR drifts_NN2 along_II the_AT limit_NN1 cycle_NN1 ,_, with_IW variance_NN1 :_: it_PPH1 can_VM be_VBI considered_VVN in_II fact_NN1 that_CST the_AT phase_NN1 of_IO the_AT oscillator_NN1 undergoes_VVZ a_AT1 diffusion_NN1 process_NN1 ,_, in_II all_DB points_NN2 similar_JJ to_II a_AT1 one-dimensional_JJ Brownian_JJ motion_NN1 on_II a_AT1 ring_NN1 ._. 
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By_II temperature_NN1 dependent_JJ grazing_JJ incidence_NN1 X-ray_NN1 diffraction_NN1 measurements_NN2 ,_, the_AT high_JJ quality_NN1 of_IO the_AT deposited_VVN thin_JJ films_NN2 was_VBDZ shown_VVN as_II31 well_II32 as_II33 crystallization_NN1 temperatures_NN2 were_VBDR determined_VVN ._. 
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The_AT electron_NN1 number_NN1 density_NN1 for_IF SLIB_NN1 of_IO 30mJ_FO and_CC three_MC energy_NN1 combinations_NN2 of_IO DPLIB_NN1 with_IW a_AT1 time_NNT1 interval_NN1 between_II pulses_NN2 of_IO 50ns_FO is_VBZ shown_VVN in_II figure_NN1 10_MC ._. 
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The_AT conventional_JJ Landau-Ginsburg-Wilson_NP1 treatment_NN1 of_IO classical_JJ finite_JJ temperature_NN1 phase_NN1 transitions_NN2 is_VBZ an_AT1 example_NN1 of_IO a_AT1 purely_RR subsonic_JJ theory.5_FO <Equation>_FO is_VBZ "_" local_JJ "_" in_II an_AT1 interval_NN1 of_IO temperatures_NN2 near_II <Equation>_FO ,_, and_CC on_II spatial_JJ scales_NN2 larger_JJR than_CSN the_AT coherence_NN1 length_NN1 of_IO the_AT normal_JJ metal_NN1 <Equation>_FO evaluated_VVN at_II <Equation>_FO ._. 
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Fig._NN1 6_MC shows_VVZ the_AT photovoltaic_JJ performance_NN1 of_IO manufactured_JJ solar_JJ cells_NN2 ,_, and_CC some_DD relevant_JJ parameters_NN2 are_VBR summarized_VVN in_II Table_NN1 1_MC1 ._. 
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Similarly_RR the_AT entanglement_NN1 entropy_NN1 of_IO the_AT union_NN1 <Equation>_FO is_VBZ equal_JJ to_II that_DD1 of_IO the_AT boosted_JJ interval_NN1 connecting_VVG the_AT left_JJ end_NN1 point_NN1 of_IO B_ZZ1 and_CC the_AT right_JJ end_NN1 point_NN1 of_IO C_NP1 ,_, 34<Equation>_FO ._. 
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A_AT1 fast_JJ stage_NN1 is_VBZ realized_VVN due_II21 to_II22 multiple_NN1 scattering_VVG on_II the_AT crystal_NN1 nuclei_NN2 for_IF particles_NN2 with_IW large_JJ oscillation_NN1 amplitudes_NN2 in_II the_AT channels<Equation>_FO ,_, where_CS <Equation>_FO is_VBZ the_AT channel_NN1 half_NN1 width_NN1 ._. 
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<s>
Salt_NN1 concentration_NN1 in_II electrolyte_NN1 can_VM also_RR influence_VVI elec-trochemical_JJ properties_NN2 &lsqb;_( 24,25_MC &rsqb;_) ._. 
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<s>
Black_JJ circles_NN2 and_CC error_NN1 bars_NN2 correspond_VV0 to_II the_AT mean_JJ and_CC standard_JJ deviation_NN1 for_IF ten_MC equal-sized_JJ municipalities_NN2 ._. 
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It_PPH1 plays_VVZ an_AT1 important_JJ role_NN1 in_II the_AT general_JJ theory_NN1 of_IO Taylor–Couette_NP1 flows_VVZ ._. 
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<s>
A_AT1 similar_JJ approach_NN1 is_VBZ employed_VVN to_TO obtain_VVI the_AT ensemble_NN1 of_IO limiting_JJ potentials_NN2 from_II the_AT associated_JJ potential_NN1 determining_VVG elementary_JJ steps_NN2 for_IF the_AT oxygen_NN1 evolution_NN1 reaction_NN1 ._. 
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<s>
An_AT1 emerging_JJ and_CC increasingly_RR tractable_JJ avenue_NN1 for_IF understanding_VVG the_AT mechanisms_NN2 of_IO these_DD2 dynamics_NN lies_VVZ in_II the_AT notion_NN1 of_IO control_NN1 or_CC how_RRQ to_TO effectively_RR guide_VVI neural_JJ dynamics_NN ._. 
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As_II A_AT1 Result_NN1 ,_, It_PPH1 Suffices_VVZ To_II Use_NN1 R_ZZ1 D_ZZ1 S_ZZ1 For_IF The_AT Volume_NN1 Form_NN1 ._. 
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<s>
In_II the_AT language_NN1 of_IO burgers_NN2 ,_, the_AT symbol_NN1 F_ZZ1 represents_VVZ a_AT1 "_" flexible_JJ order_NN1 "_" which_DDQ requests_VVZ the_AT freshest_JJT available_JJ burger_NN1 ._. 
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<s>
Similarly_RR ,_, the_AT averaged_JJ single-neuron_JJ spectrum_NN1 <equation>_FO is_VBZ computed_VVN from_II all_DB spikes_NN2 of_IO the_AT neuron_NN1 group_NN1 ._. 
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<s>
In_II another_DD1 new_JJ paradigm_NN1 ,_, the_AT observation_NN1 of_IO the_AT Higgs_NP1 mode_NN1 would_VM pave_VVI a_AT1 new_JJ pathway_NN1 for_IF the_AT study_NN1 of_IO nonequilibrium_NN1 phenomena_NN2 ,_, particularly_RR for_IF the_AT photoinduced_JJ superconductivity_NN1 (_( 127–130_MCMC )_) ._. 
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<s>
In_II other_JJ mass_JJ measurement_NN1 techniques_NN2 ,_, such_II21 as_II22 in_II Schottky_NP1 ,_, isochronous_JJ ,_, and_CC time-of-flight_JJ mass_JJ spectrometry_NN1 ,_, calibration_NN1 is_VBZ performed_VVN in_II a_AT1 more_RGR complex_JJ way_NN1 ,_, and_CC thus_RR absolute_JJ mass_JJ values_NN2 have_VH0 been_VBN published_VVN ._. 
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<s>
By_II using_VVG the_AT explicit_JJ values_NN2 of_IO the_AT activation_NN1 barrier_NN1 for_IF all_DB the_AT steps_NN2 ,_, we_PPIS2 evaluate_VV0 the_AT validity_NN1 of_IO the_AT BEP_NN1 relationships_NN2 for_IF N–H_NN1 formation_NN1 steps_NN2 of_IO the_AT associative_JJ mechanism_NN1 on_II Fe_NP1 (_( 110_MC )_) and_CC Fe_NP1 (_( 100_MC )_) surfaces_NN2 ._. 
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This_DD1 property_NN1 is_VBZ known_VVN as_II Distributional_JJ Unique_JJ Ergodicity_NN1 ,_, see_VV0 &lsqb;_( Kar14_FO &rsqb;_) ._. 
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<s>
Moreover_RR ,_, by_II changing_VVG the_AT asymptotic_JJ behavior_NN1 at_II long_JJ distances_NN2 ,_, one_PN1 can_VM capture_VVI the_AT dielectric_JJ screening_NN1 ,_, providing_VVG an_AT1 inexpensive_JJ and_CC reliable_JJ way_NN1 to_TO predict_VVI the_AT photophysical_JJ properties_NN2 of_IO an_AT1 emitter_NN1 in_II a_AT1 specific_JJ environment_NN1 ._. 
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<s>
For_REX21 example_REX22 ,_, if_CS a_AT1 new_JJ result_NN1 forces_NN2 changes_NN2 to_II data_NN formats_NN2 (_( step_NN1 2_MC )_) or_CC processing_NN1 (_( step_NN1 3_MC )_) or_CC to_II application_NN1 codes_NN2 (_( step_NN1 4_MC and_CC the_AT eventual_JJ user_NN1 )_) ,_, this_DD1 fact_NN1 should_VM be_VBI considered_VVN when_CS developing_VVG a_AT1 new_JJ activity_NN1 ._. 
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By_II stretching_VVG the_AT incoming_JJ femtosecond_NN1 x-ray_NN1 pulse_NN1 ,_, then_RT ampleflying_VVG and_CC finally_RR compressing_VVG the_AT pulse_NN1 ,_, most_DAT of_IO the_AT stored_JJ energy_NN1 may_VM be_VBI transferred_VVN to_II the_AT x-ray_JJ pulse_NN1 ._. 
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This_DD1 is_VBZ a_AT1 barrierless_JJ reaction_NN1 with_IW a_AT1 modest_JJ exothermicity_NN1 (_( 130_MC kJ_NNU mol1_NN1 (_( 1.35_NNU eV_NN1 )_) )_) ,_, which_DDQ makes_VVZ it_PPH1 possible_JJ to_TO generate_VVI and_CC contain_VVI the_AT products_NN2 inside_II the_AT relatively_RR small_JJ HNDs_NP1 (_( <104_FO helium_NN1 atoms_NN2 )_) preferred_VVD for_IF depletion_NN1 spectroscopy_NN1 ._. 
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<s>
Considering_CS a_AT1 stretch_NN1 of_IO rock_NN1 of_IO length_NN1 L_ZZ1 with_IW mass_JJ density_NN1 ,_, the_AT opacity_NN1 X_ZZ1 is_VBZ defined_VVN as_II :_: <EQUATION>_FO (_( 6_MC )_) If_CS the_AT density_NN1 is_VBZ constant_JJ along_II the_AT equation_NN1 becomes_VVZ :_: <EQUATION>_FO (_( 7_MC )_) while_CS ,_, if_CS this_DD1 is_VBZ not_XX the_AT case_NN1 ,_, the_AT opacity_NN1 can_VM be_VBI written_VVN in_II31 terms_II32 of_II33 the_AT average_JJ density_NN1 :_: <EQUATION>_FO (_( 8_MC )_) <EQUATION>_FO (_( 9_MC )_) ._. 
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<s>
In_II this_DD1 work_NN1 ,_, we_PPIS2 report_VV0 on_II a_AT1 first-principle_JJ calculation_NN1 to_TO study_VVI the_AT PGE_NN1 of_IO monolayer_NN1 WSe2-MoS2_JJ lateral_JJ heterojunction_NN1 ._. 
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The_AT information_NN1 is_VBZ mixed_VVN to_II the_AT signal_NN1 using_VVG an_AT1 arbitrary_JJ waveform_NN1 generator_NN1 (_( AWG_NP1 )_) ._. 
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Analogous_JJ to_II the_AT defy_VV0 of_IO the_AT spin-density_JJ matrix_NN1 in_II Eq_NN1 ._. 
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(_( 170_MC )_) ,_, where_CS J_ZZ1 <_FO M_ZZ1 <_FO +J_FO ,_, we_PPIS2 can_VM write_VVI the_AT spin-density_JJ matrix_NN1 in_II the_AT reflectivity_NN1 basis_NN1 :_: <EQUATION>_FO ._. 
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<s>
Stochastic_JJ simulation_NN1 of_IO reaction_NN1 kinetics_NN1 in_II a_AT1 given_JJ time_NNT1 step_NN1 of_IO the_AT looped_JJ contacts_NN2 sequence_NN1 proceeds_VVZ as_CS31 long_CS32 as_CS33 times_NNT2 to_II a_AT1 next_MD event_NN1 lie_VV0 within_II t_ZZ1 ._. 
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Furthermore_RR ,_, AMF_NP1 can_VM also_RR be_VBI used_VVN to_TO release_VVI drugs_NN2 from_II nanocarriers_NN2 such_II21 as_II22 MNPs_NP1 ,_, liposomes_NN2 or_CC nanoemulsions_NN2 ._. 
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<s>
The_AT experiment_NN1 gave_VVD raw_JJ generation_NN1 rates_NN2 of_IO 1_MC1 Mbps_NP1 ,_, 650_MC kbps_NNU after_II postprocessing_VVG ._. 
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We_PPIS2 see_VV0 that_CST <Equation>for_FO any_DD closed_JJ loop_NN1 that_CST is_VBZ contractible_JJ to_II a_AT1 point_NN1 ._. 
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<s>
Using_VVG the_AT standard_JJ multiscale_NN1 reductive_JJ perturbation_NN1 technique_NN1 ,_, a_AT1 nonlinear_JJ Schrodinger_NP1 (_( NLS_NP1 )_) equation_NN1 is_VBZ derived_VVN ,_, admitting_VVG IA_NP1 wavepackets_NN2 ._. 
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<s>
The_AT tacit_JJ assumptions_NN2 are_VBR that_RG interplanetary_JJ dust_NN1 particles_NN2 reaching_VVG Earth_NN1 are_VBR representative_JJ of_IO the_AT current_JJ interstellar_JJ medium_NN1 composition_NN1 in_II the_AT solar_JJ vicinity_NN1 ,_, and_CC that_CST this_DD1 is_VBZ sufficiently_RR well_RR mixed_VVN to_TO represent_VVI nearby_JJ nucleosynthesis_NN1 over_II the_AT past_JJ 108_MC years_NNT2 ._. 
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<s>
Variation_NN1 of_IO the_AT non-toroidal_JJ magnetic_JJ field_NN1 at_II three_MC different_JJ toroidal_JJ locationsobtained_VVD by_II multiplying_VVG the_AT total_JJ field_NN1 by_II the_AT major_JJ radius_NN1 R_ZZ1 ,_, and_CC calculating_VVG the_AT difference_NN1 with_II31 respect_II32 to_II33 the_AT mean_JJ value._NNU )_) turbulence_NN1 simulations_NN2 in_II non-axisymmetric_JJ geometries_NN2 ._. 
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<s>
On_II the_AT other_JJ hand_NN1 conversions_NN2 of_IO this_DD1 type_NN1 may_VM well_RR have_VHI been_VBN critical_JJ in_II enabling_VVG the_AT emergence_NN1 of_IO life_NN1 as_CSA discussed_VVN in_II Section_NN1 14_MC ._. 
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<s>
The_AT solid_JJ curve_NN1 shows_VVZ the_AT singly_RR differential_JJ cross_NN1 section_NN1 as_II a_AT1 function_NN1 of_IO electron_NN1 ejection_NN1 angle_NN1 ,_, that_REX21 is_REX22 ,_, the_AT doubly_RR differential_JJ cross_NN1 section_NN1 summed_VVN over_II electron_NN1 ejection_NN1 angles_NN2 ,_, for_IF small_JJ or_CC relatively_RR large_JJ emission_NN1 angles_NN2 ,_, thispeak_NN1 shifts_VVZ to_TO lower_VVI or_CC higher_JJR energies_NN2 ,_, respectively_RR ,_, and_CC drops_VVZ in_II magnitude_NN1 compared_VVN to_II the_AT emission_NN1 at_II intermediate_JJ angles_NN2 ._. 
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<s>
Using_VVG standard_JJ DFT_NP1 techniques_NN2 it_PPH1 is_VBZ possible_JJ to_TO calculate_VVI the_AT total_JJ potential_JJ energy_NN1 of_IO electrons_NN2 and_CC nuclei_NN2 in_II the_AT <Equation>_FO supercell_NN1 ._. 
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<s>
In_RR21 addition_RR22 ,_, highly_RR reflective_JJ polymeric_JJ foils_NN2 that_CST are_VBR evaporatively_RR coated_VVN with_IW TPB_NP1 and_CC laminated_JJ to_II a_AT1 thin_JJ substrate_NN1 are_VBR sandwiched_VVN between_II the_AT layers_NN2 of_IO conductive_JJ mesh_NN1 in_II the_AT cathode_NN1 plane_NN1 ._. 
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The_AT text_NN1 above_RL has_VHZ made_VVN a_AT1 survey_NN1 on_II our_APPGE cutting-edge_JJ knowledge_NN1 about_II chain-folding_NN1 in_II polymer_NN1 crystals_NN2 ,_, from_II its_APPGE origin_NN1 ,_, further_JJR development_NN1 to_II unfolding_VVG ,_, for_IF its_APPGE roles_NN2 in_II various_JJ molecular_JJ scenarios_NN2 of_IO crystallization_NN1 and_CC melting_NN1 of_IO semi-crystalline_JJ polymers_NN2 as_II31 well_II32 as_II33 of_IO their_APPGE mechanical_JJ performances_NN2 ._. 
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<s>
With_IW this_DD1 review_NN1 we_PPIS2 aimed_VVD to_TO provide_VVI the_AT latest_JJT developments_NN2 in_II modified_JJ gravity_NN1 ,_, and_CC also_RR to_TO provide_VVI a_AT1 virtual_JJ toolbox_NN1 for_IF studying_VVG inflation_NN1 ,_, dark_JJ energy_NN1 and_CC bouncing_JJ cosmologies_NN2 in_II the_AT context_NN1 of_IO modified_JJ gravity_NN1 ._. 
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<s>
By_II Lemma_NN1 3.13_MC ,_, we_PPIS2 have_VH0 that_DD1 for_IF each<Equation>_FO ,_, each_DD1 <Equation>_FO ,_, each_DD1 <Equation>_FO ,_, and_CC for_IF <Equation>_FO ,_, ._. 
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<s>
As_II a_AT1 result_NN1 ,_, the_AT interlayer_NN1 tunneling_NN1 is_VBZ greatly_RR suppressed_VVN ,_, which_DDQ will_VM reduce_VVI the_AT on-state_JJ currents_NN2 in_II vdWH_NNU TFETs_NN2 &lsqb;_( 21–23_MCMC &rsqb;_) ._. 
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<s>
Therefore_RR ,_, a_AT1 characteristic_JJ long_JJ period_NN1 for_IF a_AT1 semi-crystalline_JJ texture_NN1 of_IO alternating_JJ crystalline_JJ and_CC amorphous_JJ layers_NN2 has_VHZ been_VBN commonly_RR observed_VVN by_II small-angle_JJ X-ray_NN1 scattering_VVG measurement_NN1 on_II polymers_NN2 filled_VVN with_IW spherules_NN2 ._. 
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<s>
The_AT magneto-acoustic_JJ cyclotron_NN1 instability_NN1 (_( MCI_MC )_) and_CC the_AT compressional_JJ Alfvén_JJ eigenmodes_NN2 (_( CAEs_NP2 )_) cyclotron_NN1 instability_NN1 are_VBR suggested_VVN as_CSA possible_JJ emission_NN1 mechanisms_NN2 for_IF the_AT ICE_NN1 &lsqb;_( 2_MC ,_, 3_MC ,_, 10_MC ,_, 15_MC ,_, 19–27_MCMC &rsqb;_) ._. 
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<s>
Then_RT ,_, scaling_VVG the_AT U_JJ -invariant_JJ metric_JJ tensor_NN1 by_II a_AT1 diverging_JJ factor_NN1 ε_FO we_PPIS2 get_VV0 <EQUATION>_FO (_( 182_MC )_) ._. 
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<s>
Specifically_RR ,_, we_PPIS2 review_VV0 methods_NN2 for_IF predicting_VVG nodes_NN2 '_NULL future_JJ popularity_NN1 in_II growing_JJ networks_NN2 ,_, as_II31 well_II32 as_II33 methods_NN2 for_IF predicting_VVG future_JJ links_NN2 in_II networks_NN2 ._. 
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<s>
The_AT discussion_NN1 from_II section_NN1 5_MC also_RR applies_VVZ to_II these_DD2 global_JJ effects_NN2 ,_, so_CS21 that_CS22 they_PPHS2 too_RR do_VD0 not_XX lead_VVI to_II momentum_NN1 transport_NN1 for_IF a_AT1 reduced_JJ system_NN1 with_IW no_AT magnetic_JJ shear_VV0 or_CC radial_JJ magnetic_JJ drifts_NN2 ._. 
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<s>
This_DD1 work_NN1 is_VBZ supported_VVN by_II the_AT NSF_NP1 of_IO China_NP1 under_II Grant_NP1 No._NN1 11675113_MC and_CC NSF_NP1 of_IO Beijing_NP1 under_II No_UH ._. 
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KZ201810028042_FO ._. 
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<s>
These_DD2 pixels_NN2 are_VBR equally_RR spaced_VVN in_II the_AT frequency_NN1 interval_NN1 defined_VVN by_II the_AT bandwidth_NN1 ._. 
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Any_DD combination_NN1 of_IO such_DA actions_NN2 leaves_VVZ the_AT set_NN1 of_IO Markov_NP1 states_VVZ invariant_JJ ._. 
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<s>
For_IF a_AT1 matched_JJ pair_NN of_IO jets_NN2 we_PPIS2 can_VM compute_VVI the_AT corresponding_JJ shift_NN1 <Equation>_FO as_CSA introduced_VVN in_II Eq_NN1 ._. 
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<s>
(_( 3.5_MC )_) ._. 
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<s>
Whereas_CS metallic_JJ features_NN2 of_IO weak_JJ antilocalization_NN1 dominate_VV0 the_AT magnetic_JJ field_NN1 dependence_NN1 ,_, insulating_JJ features_NN2 of_IO electron-electron_JJ interaction_NN1 predominate_VV0 in_II controlling_VVG the_AT temperature_NN1 dependence_NN1 of_IO the_AT resistance_NN1 ._. 
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<s>
This_DD1 allows_VVZ us_PPIO2 to_TO conclude_VVI that_DD1 ,_, different_JJ from_II QDs_NP1 featuring_VVG strong_JJ confinement_NN1 ,_, "_" p-shell_JJ "_" excitation_NN1 is_VBZ not_XX a_AT1 viable_JJ route_NN1 to_TO obtain_VVI photons_NN2 with_IW meaningful_JJ in_II distinguish_VV0 ability_NN1 from_II weakly_RR confining_JJ QDs_NP1 ._. 
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In_II this_DD1 section_NN1 ,_, comparative_JJ experiments_NN2 of_IO initial_JJ decoding_JJ message_NN1 are_VBR performed_VVN to_TO analyze_VVI the_AT performance_NN1 of_IO our_APPGE initial_JJ decoding_JJ message_NN1 computation_NN1 method_NN1 ._. 
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<s>
Some_DD call_VV0 these_DD2 generators_NN2 that_CST use_VV0 nondeterministic_JJ events_NN2 ,_, nonphysical_JJ nondeterministic_JJ RNGs_NP1 (_( Killmann_NP1 and_CC Schindler_NP1 ,_, 2008_MC )_) that_CST stand_VV0 in_II contrast_NN1 to_II physical_JJ TRNGs_NP1 based_VVD in_II nondeterministic_JJ physical_JJ effects_NN2 in_II electronic_JJ circuits_NN2 or_CC in_II the_AT result_NN1 of_IO some_DD physical_JJ experiment_NN1 ._. 
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<s>
In_II other_JJ words_NN2 ,_, <Picture>_FO if_CS we_PPIS2 desire_VV0 to_TO prepare_VVI a_AT1 Gaussian_JJ state_NN1 which_DDQ corresponds_VVZ to_II an_AT1 the_AT pMES_NN2 is_VBZ more_RGR appropriate_JJ than_CSN the_AT TMSV_NP1 state_NN1 ._. 
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Alice_NP1 then_RT sends_VVZ him_PPHO1 the_AT basis_NN1 choice_NN1 ._. 
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The_AT low-temperature_JJ plasma_NN1 community_NN1 is_VBZ nowadays_RT engaged_VVN in_II the_AT investigation_NN1 of_IO the_AT possible_JJ exploitation_NN1 of_IO plasma_NN1 technologies_NN2 for_IF the_AT efficient_JJ destruction_NN1 of_IO CO2_FO produced_VVN in_II the_AT anthropogenic_JJ activities_NN2 ._. 
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When_CS using_VVG normalized_JJ units_NN2 ,_, the_AT area_NN1 under_II the_AT ROC_NN1 curve_NN1 (_( AUC_NP1 )_) is_VBZ equal_JJ to_II the_AT probability_NN1 that_CST a_AT1 predictor_NN1 can_VM rank_VVI a_AT1 real_JJ future_JJ event_NN1 er_FU higher_JJR than_CSN a_AT1 randomly_RR chosen_VVN event_NN1 ec_NN1 that_CST will_VM not_XX happen_VVI in_II the_AT future_NN1 ._. 
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Diagram_NN1 of_IO the_AT tripartite_JJ quantum_NN1 memory_NN1 setup_NN1 ._. 
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<s>
This_DD1 result_NN1 compares_VVZ reasonably_RR well_RR with_IW traditional_JJ ATR-FTIR_JJ measurements_NN2 reported_VVD ,_, for_REX21 example_REX22 ,_, in_RP ,_, where_CS analysis_NN1 of_IO MIR_NP1 spectra_NN2 of_IO pairs_NN2 of_IO organic_JJ molecules_NN2 resulted_VVN in_II retrieval_NN1 uncertainties_NN2 between_II 1%_NNU and_CC 7%_NNU ._. 
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The_AT set_NN1 <Professional_FO Term>_FO defines_VVZ the_AT von_NP1 Neumann_NP1 measurement_NN1 scenario_NN1 ._. 
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Alice_NP1 and_CC Bob_NP1 maybe_RR working_VVG in_II their_APPGE own_DA quantum_NN1 laboratory_NN1 while_CS being_VBG separated_VVN from_II each_PPX221 other_PPX222 by_II some_DD large_JJ distance_NN1 ._. 
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<s>
For_IF the_AT first_MD instead_RR it_PPH1 suffices_VVZ to_TO notice_VVI that_CST g_ZZ1 ,_, by_II Assumption_NN1 3.13_MC is_VBZ different_JJ and_CC such_CS21 that_CS22 <Professional_FO Term>_FO ,_, which_DDQ in_RR21 particular_RR22 implies_VVZ that_DD1 g(k)/k_FU is_VBZ a_AT1 bounded_JJ continuous_JJ function_NN1 ._. 
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Double-differential_JJ cross_NN1 sections_NN2 for_IF <Professional_FO Term>_FO with_II31 respect_II32 to_II33 muon_NN1 energy_NN1 and_CC angle_NN1 ,_, <Professional_FO Term>_FO ,_, have_VH0 been_VBN published_VVN by_II T2K_FO (_( 72_MC ,_, 73_MC )_) and_CC MiniBooNE_NP1 (_( 64_MC ,_, 65_MC )_) ._. 
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However_RR ,_, the_AT direct_JJ examinations_NN2 of_IO their_APPGE impact_NN1 on_II the_AT difference_NN1 between_II γ_NULL and_CC γ_NULL EOS_NN2 as_II31 well_II32 as_II33 on_II any_DD physical_JJ characteristic_NN1 of_IO the_AT system_NN1 require_VV0 specific_JJ computational_JJ examination_NN1 ._. 
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When_CS we_PPIS2 keep_VV0 <Professional_FO Term>_FO and_CC k3_FO at_II 100_MC and_CC 100_MC ×_II 109_MC N/m3_FU ,_, respectively_RR ,_, it_PPH1 is_VBZ clearly_RR shown_VVN in_II Fig._NN1 2(b)_FO that_CST the_AT decrease_NN1 in_II the_AT driving_JJ force_NN1 F_ZZ1 will_VM weaken_VVI and_CC finally_RR eliminate_VVI the_AT nonlinear_JJ behavior_NN1 ,_, as_CSA the_AT amplitude_NN1 of_IO the_AT driving_JJ force_NN1 goes_VVZ from_II 0.5_MC N_NNU down_RP to_II 0.1_MC N._NNU Researchers_NN2 have_VH0 also_RR tried_VVN to_TO connect_VVI students_NN2 '_NULL educational_JJ achievements_NN2 with_IW their_APPGE behavioral_JJ patterns_NN2 ._. 
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Similarly_RR ,_, left-multiplication_NN1 by_RP induces_VVZ an_AT1 almost_RR complex_JJ structure_NN1 on_RP ,_, which_DDQ we_PPIS2 denote_VV0 by_II J._NP1 In_II subsequent_JJ work_NN1 ,_, Brando_NP1 and_CC Gour_NP1 (_( 2015_MC )_) explicitly_RR connected_JJ Eqs_NN2 (_( 117_MC )_) and_CC (_( 118_MC )_) to_II the_AT problem_NN1 of_IO asymptotic_JJ resource_NN1 convertibility_NN1 under_II asymptotically_RR RNG_NP1 operations_NN2 ._. 
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<s>
The_AT second_MD sum_NN1 rule_NN1 ,_, Eq._NP1 (_( 194_MC )_) ,_, suggests_VVZ to_TO express_VVI the_AT matrix_NN1 elements_NN2 of_IO the_AT second_MD derivatives_NN2 of_IO the_AT potential_NN1 in_II31 terms_II32 of_II33 first-order_JJ derivatives_NN2 ._. 
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<s>
Consider_VV0 two_MC POVMs_NN2 given_VVN by_II <Equation>_FO ._. 
</s>
<s>
Typically_RR ,_, the_AT laser_NN1 pulse_NN1 comprises_VVZ a_AT1 sequence_NN1 of_IO one_MC1 to_II three_MC low-intensity_JJ pulses_NN2 known_VVN as_II "_" pickets_NN2 ._. "_" 
</s>
<s>
While_CS it_PPH1 is_VBZ unlikely_JJ that_CST the_AT asymmetries_NN2 of_IO the_AT orbital_JJ structure_NN1 of_IO the_AT distant_JJ solar_JJ system_NN1 point_NN1 to_II fundamentally_RR new_JJ physics_NN1 (_( as_CSA in_II the_AT case_NN1 of_IO Vulcan_NP1 )_) ,_, we_PPIS2 must_VM acknowledge_VVI alternative_JJ explanations_NN2 for_IF the_AT observations_NN2 that_CST do_VD0 not_XX invoke_VVI the_AT existence_NN1 of_IO Planet_NN1 Nine_MC ._. 
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<s>
The_AT polestars/nanorods_NN2 are_VBR grown_VVN by_II a_AT1 hydrothermal_JJ synthesis_NN1 whereby_RRQ an_AT1 aqueous_JJ solution_NN1 of_IO NaOH_NN1 is_VBZ added_VVN gradually_RR to_II a_AT1 cerium_NN1 chloride_NN1 aqueous_JJ solution_NN1 after_II which_DDQ ethylenediamine_VV0 (_( which_DDQ acts_VVZ as_II a_AT1 complexion_NN1 agent_NN1 )_) is_VBZ added_VVN drop-wise_JJ ._. 
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<s>
More_DAR research_NN1 experimentally_RR and_CC theoretically_RR is_VBZ necessary_JJ to_TO achieve_VVI a_AT1 comprehensive_JJ understanding_NN1 of_IO open_JJ charm_NN1 hadrons_NN2 ._. 
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<s>
In_RR21 addition_RR22 ,_, when_CS no_AT voltage_NN1 is_VBZ applied_VVN ,_, a_AT1 lower_JJR transmission_NN1 was_VBDZ found_VVN in_II the_AT as-deposited_JJ device_NN1 with_IW a_AT1 thick_JJ NiO_NN1 layer_NN1 ._. 
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<s>
In_II He-like_JJ uranium_NN1 <Equation>_FO transition_NN1 rate_NN1 turns_VVZ to_TO zero_VVI when_RRQ the_AT frequencies_NN2 of_IO three_MC photons_NN2 are_VBR equal_JJ while_CS 21P1_FO →_NULL 11S0_FO +_FO 3_MC γ_NULL (_( E1_FO )_) transition_NN1 rate_NN1 has_VHZ the_AT maximum_NN1 in_II the_AT same_DA situation_NN1 ._. 
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<s>
The_AT most_RGT exotic_JJ nuclei_NN2 are_VBR those_DD2 just_RR beyond_II the_AT dripline_NN1 ._. 
</s>
<s>
This_DD1 hypothesis_NN1 can_VM be_VBI verified_VVN using_VVG the_AT computer_NN1 simulations_NN2 of_IO molecular_JJ dynamics_NN of_IO systems_NN2 specially_RR designed_VVN ._. 
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<s>
This_DD1 divergence_NN1 signals_VVZ the_AT conformal_JJ anomaly_NN1 in_II even_JJ dimensions_NN2 and_CC modifies_VVZ the_AT mass_JJ expansion_NN1 of_IO for_IF even_RR de_NP1 ,_, <Equation>and_FO use_NN1 Eq_NN1 ._. 
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<s>
(_( 206_MC )_) with_IW ._. 
</s>
<s>
The_AT ponderomotive_JJ approximation_NN1 ,_, when_CS valid_JJ ,_, describes_VVZ the_AT dynamics_NN in_II31 terms_II32 of_II33 time_NNT1 averaged_VVN (_( over_II high-frequencies_NN2 )_) quantities_NN2 ,_, which_DDQ leads_VVZ to_II a_AT1 simpler_JJR and_CC often_RR integrable_JJ formalism_NN1 ._. 
</s>
<s>
In_II fact_NN1 ,_, near_II band_NN1 extrema_NN1 the_AT bands_NN2 are_VBR approximately_RR parabolic_JJ ,_, and_CC the_AT integrand_NN1 in_II the_AT adiabatic_JJ Fan-Migdal_JJ self-energy_NN1 goes_VVZ as_CSA <Equation>_FO for_IF <Equation>_FO ,_, while_CS the_AT volume_NN1 element_NN1 goes_VVZ only_RR as_CSA <Equation>_FO ._. 
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<s>
BEB_NP1 cross_NN1 sections_NN2 for_IF total_JJ ionization_NN1 (_( solid_JJ lines_NN2 )_) of_IO a3_FO metastable_JJ (_( this_DD1 work_NN1 )_) and_CC of_IO <equation>_FO ground_NN1 (_( circles_NN2 )_) state_NN1 &lsqb;_( 30_MC &rsqb;_) of_IO CO_NP1 by_II electron-impact_NN1 ._. 
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<s>
Next_MD ,_, we_PPIS2 present_VV0 quantum_NN1 Algorithm_NN1 2_MC to_TO determine_VVI the_AT degree_NN1 of_IO a_AT1 perfect_JJ nonlinear_JJ Boolean_NN1 function_NN1 by_II calling_VVG quantum_NN1 Algorithm_NN1 1_MC1 repeatedly_RR ._. 
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<s>
In_II qualitative_JJ agreement_NN1 with_IW this_DD1 ,_, we_PPIS2 observe_VV0 a_AT1 correlation_NN1 of_IO the_AT etch_NN1 rate_NN1 with_IW the_AT measured_JJ optical_JJ emission_NN1 from_II an_AT1 atomic_JJ oxygen_NN1 line_NN1 and_CC the_AT computed_JJ dissociative_JJ electron_NN1 impact_NN1 excitation_NN1 rate_NN1 shown_VVN in_II Fig._NN1 2(b)_FO ,_, which_DDQ are_VBR markers_NN2 of_IO the_AT atomic_JJ oxygen_NN1 density_NN1 ,_, and_CC the_AT computed_JJ O2_FO ion_NN1 flux_NN1 shown_VVN in_II Fig._NN1 3(b)_FO ._. 
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<s>
This_DD1 results_VVZ in_II the_AT surrogates_NN2 being_VBG approximately_RR aligned_VVN with_IW the_AT data_NN ,_, and_CC should_VM significantly_RR reduce_VVI computation_NN1 time_NNT1 ._. 
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<s>
However_RR ,_, if_CS Bob_NP1 has_VHZ only_RR a_AT1 limited_JJ quantum_NN1 memory_NN1 ,_, then_RT he_PPHS1 could_VM not_XX keep_VVI a_AT1 perfect_JJ copy_NN1 of_IO the_AT n_ZZ1 qubits_VVZ he_PPHS1 gets_VVZ from_II Alice_NP1 ._. 
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<s>
However_RR ,_, there_EX exists_VVZ a_AT1 grid_NN1 spacing_NN1 ,_, in_II this_DD1 case_NN1 <Equation>_FO ,_, for_IF which_DDQ the_AT shift_NN1 is_VBZ not_XX too_RG far_RR from_II zero_MC and_CC not_XX too_RG dependent_JJ either_RR on_II the_AT hard_JJ sample_NN1 choice_NN1 or_CC on_II the_AT level_NN1 of_IO pileup_NN1 ._. 
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<s>
Thus_RR ,_, represents_VVZ a_AT1 nite_NN1 set_NN1 of_IO generators_NN2 of_IO H_ZZ1 <Equation>_FO ._. 
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<s>
This_DD1 work_NN1 represents_VVZ the_AT first_MD experimental_JJ investigation_NN1 of_IO the_AT electronic_JJ transition_NN1 spectrum_NN1 of_IO the_AT WS_NP2 molecule_NN1 ._. 
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<s>
The_AT electronic_JJ systems_NN2 in_II both_DB2 cases_NN2 are_VBR shifted_VVN by_II a_AT1 few_DA2 tens_MC2 of_IO cm1_FO relative_II21 to_II22 the_AT gas_NN1 phase_NN1 ,_, which_DDQ is_VBZ significant_JJ but_CCB not_XX huge_JJ ._. 
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<s>
The_AT presence_NN1 of_IO a_AT1 low_JJ density_NN1 region_NN1 ,_, 0.91.0_MC g/cm3_FU with_IW a_AT1 diameter_NN1 of_IO 300_MC m_NNO at_II 135_MC ÷_NULL 190_MC m_NNO from_II the_AT summit_NN1 crater_NN1 was_VBDZ ,_, anyway_RR ,_, confirmed_VVN and_CC interpreted_VVN as_II a_AT1 rhyolitic_JJ magma_NN1 with_IW a_AT1 60%_NNU vesicularity_NN1 ._. 
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<s>
Q_ZZ1 and_CC driving_JJ force_NN1 are_VBR kept_VVN as_CSA 100_MC and_CC 1_MC1 N_ZZ1 ,_, respectively_RR ._. 
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<s>
Here_RL ,_, we_PPIS2 developed_VVD and_CC validated_VVD an_AT1 accurate_JJ and_CC precise_JJ measurement_NN1 procedure_NN1 based_VVN on_II ID-LC–MS/MS_FU for_IF detecting_VVG vitamins_NN2 A_ZZ1 and_CC E_ZZ1 in_II serum_NN1 and_CC amniotic_JJ fluid_NN1 ._. 
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<s>
In_RR21 addition_RR22 ,_, interesting_JJ results_NN2 revealed_VVD the_AT importance_NN1 of_IO the_AT anisotropy_NN1 in_II the_AT mechanism_NN1 of_IO the_AT magnetization_NN1 plateaus_NN2 in_II many_DA2 low-dimensional_JJ magnetic_JJ systems_NN2 such_II21 as_II22 the_AT Ising_JJ chain_NN1 with_IW spin_NN1 S_ZZ1 ?_? 3/2_MF ,_, Bethe_NP1 lattice_NN1 and_CC ferrimagnetic_JJ core-shell_JJ nanoparticle_NN1 ._. 
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<s>
Expressions_NN2 such_II21 as_II22 τ_NULL τ_NULL should_VM hence_RR be_VBI understood_VVN modulo_NN1 β_NULL ._. 
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<s>
There_EX are_VBR many_DA2 types_NN2 of_IO surrogates_NN2 other_II21 than_II22 the_AT FT_NNU based_VVN ones_NN2 already_RR discussed_VVN ,_, and_CC the_AT most_RGT useful_JJ for_IF the_AT purpose_NN1 of_IO testing_VVG for_IF independence_NN1 between_II signals_NN2 are_VBR discussed_VVN in_II this_DD1 section_NN1 ._. 
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<s>
The_AT robustness_NN1 relies_VVZ in_RR21 part_RR22 on_II the_AT observation_NN1 that_CST the_AT phases_NN2 of_IO the_AT cooperating_JJ laser_NN1 fields_NN2 do_VD0 not_XX matter_VVI for_IF EIT_NP1 or_CC STIRAP_VV0 to_TO be_VBI successful_JJ as_CS31 long_CS32 as_CS33 they_PPHS2 are_VBR constant_JJ during_II the_AT particlefield_NN1 interaction_NN1 period_NN1 ._. 
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<s>
The_AT advantages_NN2 of_IO ELMs_NN2 are_VBR that_CST the_AT learning_NN1 algorithm_NN1 is_VBZ extremely_RR fast_JJ and_CC that_CST its_APPGE generalization_NN1 capabilities_NN2 are_VBR good_JJ in_II31 spite_II32 of_II33 its_APPGE simple_JJ structure_NN1 &lsqb;_( 11_MC &rsqb;_) ._. 
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<s>
R._NP1 I._NP1 Woodward_NP1 ,_, R._NP1 C._NP1 T._NP1 Howe_NP1 ,_, G._NP1 Hu_NP1 ,_, F._NP1 Torrisi_NP1 ,_, M._NN1 Zhang_NN1 ,_, T._NP1 Hasan_NP1 ,_, and_CC E._NP1 J._NP1 R._NP1 Kelleher_NP1 ,_, Photonics_NP1 Res._NN1 3_MC ,_, A30_FO (_( 2015_MC )_) ._. 
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<s>
The_AT connection_NN1 A_ZZ1 induces_VVZ a_AT1 covariant_JJ derivative_NN1 in_II the_AT adjoint_JJ bundle_NN1 which_DDQ we_PPIS2 denote_VV0 by_II D._NP1 Shen_FW et_RA21 al_RA22 ._. 
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<s>
&lsqb;_( 26,27_MC &rsqb;_) presented_VVD a_AT1 compositive_JJ system_NN1 that_CST a_AT1 cavity_NN1 or_CC a_AT1 whispering_JJ gallery_NN1 resonator_NN1 contains_VVZ a_AT1 two-level_JJ atom_NN1 coupled_VVN to_II a_AT1 single-mode_JJ waveguide_NN1 ._. 
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<s>
With_IW such_DA recent_JJ research_NN1 and_CC emerging_JJ trends_NN2 ,_, the_AT tantalizing_NN1 but_CCB technically_RR demanding_VVG vision_NN1 of_IO MMRs_NP1 is_VBZ coming_VVG closer_RRR ._. 
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<s>
Our_APPGE proposed_JJ wave_NN1 guiding_JJ strategy_NN1 hinges_VVZ on_II the_AT use_NN1 of_IO metamaterials_NN2 that_CST exhibit_VV0 strong_JJ anisotropy_NN1 and_CC is_VBZ numerically_RR and_CC experimentally_RR shown_VVN to_TO support_VVI robust_JJ one-way_JJ propagation_NN1 in_II zigzag_NN1 paths_NN2 ._. 
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<s>
In_II this_DD1 numerical_JJ experiment_NN1 ,_, we_PPIS2 use_VV0 the_AT SAP-ELM_NN1 with_IW the_AT numbers_NN2 of_IO input_NN1 and_CC output_NN1 neurons_NN2 both_RR set_VV0 equal_JJ to_II 1_MC1 ,_, and_CC the_AT number_NN1 of_IO hidden_JJ neurons_NN2 set_VVN to_II 4_MC after_II pruning_NN1 ._. 
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<s>
Although_CS the_AT approach_NN1 of_IO including_VVG only_JJ Neptune_NP1 and_CC Planet_NN1 Nine_MC as_CSA active_JJ perturbers_NN2 is_VBZ often_RR used_VVN ,_, the_AT extent_NN1 to_II which_DDQ this_DD1 approximation_NN1 captures_VVZ the_AT relevant_JJ physics_NN1 remains_VVZ to_TO be_VBI determined_VVN quantitatively_RR ._. 
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<s>
The_AT PY_JJ fluids_NN2 described_VVN by_II equation_NN1 (_( 46_MC )_) would_VM be_VBI available_JJ for_IF this_DD1 purpose_NN1 not_XX only_RR because_CS the_AT analytical_JJ form_NN1 of_IO the_AT direct_JJ correlation_NN1 function_NN1 is_VBZ given_VVN &lsqb;_( 47_MC &rsqb;_) ,_, but_CCB also_RR because_II21 of_II22 the_AT clear_JJ physical_JJ meaning_NN1 of_IO <Professional_FO Term>_FO in_II equation_NN1 (_( 46_MC )_) ._. 
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<s>
The_AT different_JJ chemical_JJ affinities_NN2 between_II carbon_NN1 and_CC boron_NN1 ,_, and_CC carbon_NN1 and_CC nitrogen_NN1 ,_, inparticular_JJ ,_, could_VM be_VBI incorporated_VVN to_II the_AT model_NN1 via_II these_DD2 parameters_NN2 ._. 
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<s>
In_II31 addition_II32 to_II33 these_DD2 calculations_NN2 ,_, several_DA2 studies_NN2 of_IO the_AT electron-phonon_JJ self-energy_NN1 at_II metal_NN1 surfaces_NN2 were_VBDR reported_VVN ,_, namely_REX ,_, for_IF the_AT Cu(111)_FO and_CC Ag(111)_FO surfaces_NN2 (_( Eiguren_NP1 et_RA21 al._RA22 ,_, 2002_MC )_) ,_, the_AT Al(100)_FO ,_, Ag(111)_FO ,_, Cu(111)_FO ,_, and_CC Au(111)_FO surfaces_NN2 (_( Eiguren_NP1 ,_, Hellsing_NP1 et_RA21 al._RA22 ,_, 2003_MC )_) ,_, and_CC the_AT W(110)_FO surface_NN1 (_( Eiguren_NP1 and_CC Ambrosch-Draxl_NP1 ,_, 2008a_FO )_) ._. 
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<s>
Regarding_II the_AT latter_DA ,_, solvation_NN1 in_II the_AT water_NN1 and_CC methanol_NN1 dielectrics_NN2 gave_VVD practically_RR identical_JJ results_NN2 ,_, and_CC thus_RR only_RR the_AT water_NN1 data_NN are_VBR reported_VVN ._. 
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<s>
Power_NN1 load_NN1 on_II the_AT divertor_NN1 :_: the_AT rapid_JJ cooling_NN1 during_II the_AT thermal_JJ quench_VV0 ,_, In_II fact_NN1 ,_, Sage_NN1 et_RA21 al_RA22 ._. 
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<s>
(_( 2005_MC )_) demonstrated_VVD photoassociation_NN1 of_IO ultracold_NN1 Rb_NP1 and_CC Cs_NP2 atoms_NN2 to_TO form_VVI RbCs_NP1 molecules_NN2 in_II v_ZZ1 ?_FO 0_MC of_IO the_AT electronic_JJ ground_NN1 state_NN1 using_VVG stimulated_JJ emission_NN1 pumping_NN1 ,_, an_AT1 incoherent_JJ process_NN1 (_( Kittrell_NP1 et_RA21 al._RA22 ,_, 1981_MC ;_; Bartels_NN2 et_RA21 al._RA22 ,_, 2013_MC )_) ._. 
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<s>
For_IF the_AT light_JJ SM-like_JJ Higgs_NP1 couplings_NN2 to_II fermions_NN2 there_RL exist_VV0 two_MC sources_NN2 of_IO coupling_NN1 modifications_NN2 :_: first_MD ,_, the_AT fermionic_JJ 2HDM_FO mixing_NN1 structure_NN1 includes_VVZ a_AT1 CP-odd_JJ gauge_NN1 boson_NN1 A0_FO ._. 
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<s>
These_DD2 provide_VV0 timing_NN1 signals_NN2 while_CS the_AT wC_NN1 also_RR provides_VVZ a_AT1 mass_JJ dependent_JJ signal_NN1 that_CST facilitates_VVZ particle_NN1 accountability_NN1 ._. 
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<s>
The_AT history_NN1 of_IO applied_JJ electric_JJ potentials_NN2 may_VM have_VHI affected_VVN the_AT background_NN1 by_II causing_VVG disappearance_NN1 of_IO oxide_NN1 domains_NN2 ,_, not_XX rapidly_RR reversible_JJ coverage_NN1 with_IW adsorbed_JJ molecules_NN2 ,_, and_CC irreversible_JJ modifications_NN2 of_IO the_AT surface_NN1 nanostructure_NN1 ._. 
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<s>
In_RR21 addition_RR22 ,_, lewis_NN1 acid_NN1 products_NN2 such_II21 as_II22 PF5_FO and_CC HF_NP1 ,_, originated_VVN from_II the_AT interaction_NN1 reaction_NN1 between_II lithium_NN1 salt_NN1 and_CC a_AT1 small_JJ quantity_NN1 of_IO water_NN1 in_II liquid_JJ electrolyte_NN1 ,_, can_VM be_VBI captured_VVN by_II lewis_NN1 base_NN1 ._. 
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<s>
Accounting_VVG for_IF these_DD2 processes_NN2 imposes_VVZ appropriate_JJ restrictions_NN2 on_II the_AT applicability_NN1 of_IO the_AT theory_NN1 under_II consideration_NN1 ._. 
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<s>
Momentum_NN1 distribution_NN1 for_IF various_JJ possible_JJ orderings_NN2 for_IF the_AT P_ZZ1 (_( )_) ,_, and_CC C_ZZ1 (_( )_) pulses_NN2 in_II tripod_NN1 STIRAP_NN1 ._. 
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Dressed_JJ quark_NN1 masses_NN2 function_VV0 M_ZZ1 (_( p_ZZ1 )_) in_II Eq_NN1 ._. 
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<s>
(_( 5.1_MC )_) ._. 
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<s>
This_DD1 paper_NN1 reviews_VVZ the_AT observational_JJ motivation_NN1 ,_, dynamical_JJ constraints_NN2 ,_, and_CC prospects_NN2 for_IF detection_NN1 of_IO this_DD1 proposed_JJ object_NN1 known_VVN as_II Planet_NN1 Nine_MC ._. 
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<s>
We_PPIS2 have_VH0 employed_VVN the_AT WKB_NP1 approach_NN1 to_TO find_VVI approximate_JJ expressions_NN2 for_IF the_AT MTE_NN1 ._. 
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<s>
Our_APPGE recommendation_NN1 is_VBZ to_TO adopt_VVI <Equation>_FO as_II a_AT1 default_NN1 value_NN1 for_IF the_AT split–merge_NN1 threshold_NN1 (_( together_RL with_IW the_AT use_NN1 of_IO the_AT <Equation>_FO variable_NN1 ,_, already_RR the_AT default_NN1 in_II SISCone_NP1 ,_, for_IF reasons_NN2 related_VVN to_II infrared_JJ safety_NN1 and_CC longitudinal_JJ boost_NN1 invariance_NN1 )_) ._. 
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<s>
On_II the_AT other_JJ hand_NN1 ,_, as_CSA one_MC1 takes_VVZ h_ZZ1 0_MC ,_, the_AT resulting_JJ curve_NN1 is_VBZ purely_RR downhill_RL (_( particles_NN2 are_VBR repelled_VVN from_II the_AT potential_NN1 )_) as_CSA found_VVN in_II the_AT Lagrangian_JJ theories_NN2 ._. 
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<s>
The_AT mean_JJ energy_NN1 loss_NN1 rate_NN1 in_II this_DD1 region_NN1 for_IF various_JJ materials_NN2 is_VBZ shown_VVN in_II Fig._NN1 4_MC &lsqb;_( 13_MC &rsqb;_) ._. 
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<s>
However_RR ,_, due_II21 to_II22 the_AT lack_NN1 of_IO optical_JJ fiber_NN1 components_NN2 in_II the_AT 2.0lm_FO range_NN1 ,_, there_EX were_VBDR few_DA2 mode-locked_JJ results_NN2 reported_VVN in_II the_AT following_JJ decade_NNT1 ._. 
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<s>
The_AT operation_NN1 of_IO the_AT tracking_JJ system_NN1 was_VBDZ possible_JJ with_IW up_RG21 to_RG22 3_MC kHz_NNU trigger_NN1 rate_NN1 ._. 
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<s>
The_AT two_MC flat_JJ walls_NN2 of_IO the_AT cavity_NN1 have_VH0 a_AT1 thickness_NN1 of_IO 5mm_NNU ,_, and_CC the_AT curved_JJ wall_NN1 has_VHZ a_AT1 thickness_NN1 of_IO 3mm_NNU ._. 
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<s>
While_CS theinformation_NN1 from_II the_AT immediate_JJ causal_JJ history_NN1 quantifies_VVZ the_AT impact_NN1 on_II the_AT state_NN1 of_IO a_AT1 specific_JJ variable_NN1 from_II trajectories_NN2 of_IO recent_JJ dynamics_NN ,_, its_APPGE complement_NN1 ,_, the_AT distant_JJ causal_JJ history_NN1 ,_, illustrates_VVZ such_DA impact_NN1 stemming_VVG from_II the_AT remaining_JJ older_JJR history_NN1 ._. 
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<s>
Actual_JJ data_NN may_VM be_VBI used_VVN to_TO better_RRR understand_VVI the_AT atmospheric_JJ turbulence_NN1 Banerjee_NN1 and_CC define_VV0 a_AT1 propagation_NN1 model_NN1 that_CST should_VM help_VVI the_AT receiver_NN1 and_CC transmitter_NN1 design_NN1 ._. 
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<s>
II.D_NP1 )_) ,_, whereas_CS a_AT1 simple_JJ noninteracting_NN1 Anderson_NP1 insulator_NN1 does_VDZ not_XX exhibit_VVI such_DA a_AT1 continued_JJ growth_NN1 of_IO entanglement_NN1 as_CSA a_AT1 function_NN1 of_IO time_NNT1 ._. 
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<s>
We_PPIS2 say_VV0 in_II this_DD1 case_NN1 that_CST the_AT two_MC probability_NN1 distributions_NN2 are_VBR incomparable_JJ ._. 
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<s>
An_AT1 intuitive_JJ explanation_NN1 of_IO this_DD1 behavior_NN1 is_VBZ that_CST the_AT local_JJ inversion_NN1 breaking_NN1 is_VBZ opposite_JJ for_IF the_AT two_MC sub-lattices_NN2 and_CC thus_RR the_AT induced_JJ spin_NN1 densities_NN2 are_VBR also_RR opposite_JJ ._. 
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<s>
What_DDQ is_VBZ the_AT CP_NP1 phase_NN1 in_II the_AT PMNS_NP1 matrix_NN1 ?_? 
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<s>
In_II contrast_NN1 ,_, the_AT degradation_NN1 in_II type-II-A_NN1 heterojunctions_NN2 is_VBZ alleviated_VVN because_II21 of_II22 the_AT tunneling_JJ barriers_NN2 induced_VVN by_II the_AT negative_JJ <Professional_FO Term>_FO ._. 
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<s>
Using_VVG a_AT1 rainbow-ladder_JJ framework_NN1 ,_, the_AT study_NN1 of_IO Ref_NN1 ._. 
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<s>
The_AT same_DA order_NN1 of_IO magnitude_NN1 for_IF the_AT minimum_JJ required_JJ seed_NN1 electron_NN1 density_NN1 is_VBZ reported_VVN for_IF a_AT1 pulsed_JJ plasma_NN1 jet_NN1 in_II pure_JJ He_PPHS1 &lsqb;_( 12_MC ,_, 49_MC &rsqb;_) ._. 
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<s>
Multiple_JJ oxygen_NN1 vacancies_NN2 have_VH0 a_AT1 tendency_NN1 to_TO align_VVI along_II <111>_FO directions&lsqb;35&rsqb;_FO ._. 
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<s>
Therefore_RR ,_, each_DD1 system_NN1 corresponds_VVZ to_II a_AT1 single-layer_JJ network_NN1 ,_, whose_DDQGE adjacency_NN1 matrices_NN2 are_VBR shown_VVN ._. 
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<s>
Flat_JJ surfaces_NN2 are_VBR preferred_VVN to_TO avoid_VVI topography-related_JJ artifacts_NN2 induced_VVN by_II sputtering_VVG rate_NN1 anisotropy_NN1 ._. 
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<s>
Note_VV0 that_CST we_PPIS2 have_VH0 defined_VVN a_AT1 scale_NN1 evolution_NN1 of_IO ri_NN2 running_VVG with_IW the_AT index_NN1 i_ZZ1 from_II large_JJ to_II small_JJ scale_NN1 ,_, which_DDQ can_VM be_VBI illustrated_VVN as_II a_AT1 process_NN1 in_II which_DDQ one_PN1 zooms_VVZ in_RP to_TO resolve_VVI smaller_JJR and_CC smaller_JJR structures_NN2 ._. 
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<s>
Xi_NN1 is_VBZ the_AT ith_MD number_NN1 used_VVN as_II the_AT internal_JJ state_NN1 ._. 
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<s>
Harris_NP1 had_VHD determined_VVN various_JJ transitions_NN2 in_II atoms_NN2 and_CC ions_NN2 that_CST would_VM have_VHI resonances_NN2 for_IF high_JJ order_NN1 even_RR harmonics_NN2 ._. 
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<s>
The_AT resemblance_NN1 becomes_VVZ even_RR more_RGR striking_JJ in_II regimes_NN2 of_IO low-amplitude_JJ fields_NN2 ,_, where_CS after_II a_AT1 Taylor_NP1 expansion_NN1 of_IO Hamiltonian_JJ (_( 4_MC )_) ,_, the_AT beat-wave_JJ field_NN1 takes_VVZ on_RP the_AT electrostatic-like_JJ shape_NN1 of_IO an_AT1 additive_JJ potential_NN1 ._. 
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<s>
Note_VV0 that_CST the_AT expres-_JJ sions_NN2 for_IF x_ZZ1 and_CC Dxx_MC given_VVN in_II Ref_NN1 ._. 
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<s>
The_AT Rényi_JJ entropy_NN1 of_IO order_NN1 is_VBZ defined_VVN as_CSA <Equation>_FO for_IF <Equation>_FO ,_, and_CC as_II the_AT corresponding_JJ limit_NN1 for<Equation>_FO ._. 
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<s>
By_II then_RT the_AT partner_NN1 modes_NN2 will_VM be_VBI released_VVN ._. 
</s>
<s>
The_AT WBF_NP1 version_NN1 of_IO the_AT off-shell_JJ Higgs_NP1 measurement_NN1 introduced_VVN in_II Section_NN1 1.6.1_MC is_VBZ actually_RR the_AT more_RGR robust_JJ channel_NN1 to_TO constrain_VVI the_AT Higgs_NP1 width_NN1 &lsqb;_( 246_MC &rsqb;_) when_CS we_PPIS2 fully_RR correlate_VV0 the_AT production_NN1 and_CC h_ZZ1 →_NULL VV_NP1 decay_NN1 and_CC in_II this_DD1 way_NN1 minimize_VV0 the_AT vulnerability_NN1 to_II unknown_JJ BSM_NP1 loop_NN1 contributions_NN2 &lsqb;_( 233,416_MC &rsqb;_) ._. 
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<s>
We_PPIS2 dedicate_VV0 this_DD1 paper_NN1 to_II the_AT memory_NN1 of_IO our_APPGE kind_NN1 colleague_NN1 and_CC wise_JJ friend_NN1 ._. 
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<s>
We_PPIS2 fix_VV0 a_AT1 Jordan_NP1 curve_NN1 <Equation>_FO that_DD1 satisfies_VVZ the_AT Assumptions_NN2 (_( see_VV0 Theorem_NN1 3.10_MC for_IF the_AT existence_NN1 of_IO such_DA C_ZZ1 )_) ._. 
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S.G.A._NP1 was_VBDZ supported_VVN through_II the_AT Institute_NN1 for_IF Scientific_JJ Research_NN1 of_IO Boston_NP1 College_NN1 under_II Contract_NN1 No_UH ._. 
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<s>
FA9453-10-C-0206_NP1 ._. 
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<s>
After_CS transmission_NN1 ,_, the_AT correlation_NN1 property_NN1 is_VBZ examined_VVN for_IF testing_VVG whether_CSW the_AT two_MC photons_NN2 are_VBR still_RR entangled_VVN or_CC not_XX ,_, in_BCL21 order_BCL22 to_TO confirm_VVI the_AT security_NN1 ._. 
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<s>
Even_CS21 though_CS22 further_JJR investigations_NN2 are_VBR required_VVN ,_, including_II optimization_NN1 of_IO the_AT water_NN1 splitting_NN1 reaction_NN1 conditions_NN2 and_CC the_AT materials_NN2 used_VVN as_II the_AT chelating_JJ resin_NN1 and_CC ionomer_NN1 layer_NN1 ,_, these_DD2 results_NN2 should_VM assist_VVI in_II the_AT development_NN1 of_IO highly_RR durable_JJ and_CC efficient_JJ PEC_NN1 cells_NN2 using_VVG semiconductor_NN1 photo-_NN1 electrodes_NN2 ._. 
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<s>
This_DD1 phase_NN1 diagram_NN1 illustrates_VVZ the_AT case_NN1 for_IF symmetric_JJ (_( N_ZZ1 =_FO Z_ZZ1 )_) matter_VV0 ,_, but_CCB of_RR21 course_RR22 the_AT phase_NN1 diagram_NN1 may_VM be_VBI different_JJ for_IF asymmetric_JJ nuclear_JJ matter_NN1 ._. 
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There_EX is_VBZ a_AT1 need_NN1 to_TO develop_VVI devices_NN2 that_CST operate_VV0 reliably_RR in_II inhospitable_JJ environments_NN2 ranging_VVG from_II human_JJ bodies_NN2 in_II which_DDQ the_AT devices_NN2 generate_VV0 immune_JJ response_NN1 to_II the_AT harsh_JJ conditions_NN2 presented_VVN by_II chemical_JJ synthesis_NN1 applications_NN2 involving_VVG organic_JJ solvents_NN2 ._. 
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<s>
In_RR21 addition_RR22 ,_, the_AT analysis_NN1 approach_NN1 is_VBZ applicable_JJ to_II all_DB two-_JJ electron_NN1 systems_NN2 with_IW degenerate_JJ energy_NN1 levels_NN2 ,_, not_XX just_RR the_AT TGQD_NP1 ._. 
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<s>
While_CS a_AT1 classical_JJ glass_NN1 can_VM remain_VVI in_II a_AT1 glassy_JJ phase_NN1 even_CS21 when_CS22 coupled_VVN to_II a_AT1 reservoir_NN1 ,_, the_AT MBL_NP1 phase_NN1 is_VBZ expected_VVN to_TO be_VBI destroyed_VVN (_( becoming_VVG either_RR a_AT1 thermalizing_JJ phase_NN1 or_CC a_AT1 glassy_JJ phase_NN1 ,_, in_II31 case_II32 of_II33 a_AT1 frustrated_JJ system_NN1 at_II low-energy_JJ density_NN1 )_) ._. 
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<s>
Next-generation_JJ ,_, ton-scale_JJ ,_, experiments_NN2 aim_VV0 to_TO improve_VVI sensitivity_NN1 by_II one_MC1 or_CC two_MC orders_NN2 of_IO magnitude_NN1 ._. 
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<s>
Together_RL with_IW the_AT development_NN1 of_IO the_AT theoretical_JJ works_NN ,_, many_DA2 prediction_NN1 methods_NN2 have_VH0 been_VBN used_VVN in_II practice_NN1 ._. 
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<s>
The_AT latter_DA requires_VVZ that_CST the_AT LBAW_NN1 propagates_VVZ without_IW wave-front_JJ distortions_NN2 ,_, which_DDQ can_VM arise_VVI from_II di_FW ?_? raction_NN1 or_CC re_II ?_? ections_NN2 on_II irregular_JJ surfaces_NN2 ,_, since_CS these_DD2 will_VM reduce_VVI the_AT reconversion_NN1 efficiency_NN1 to_II an_AT1 electrical_JJ signal_NN1 by_II the_AT BAWR_NN1 ._. 
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<s>
Here_RL ,_, we_PPIS2 do_VD0 not_XX specify_VVI the_AT forms_NN2 of_IO the_AT potential_NN1 V()_ZZ1 and_CC the_AT Gauss–Bonnet_NN1 coupling_NN1 (_( )_) ,_, which_DDQ could_VM be_VBI determined_VVN by_II the_AT non-perturbative_JJ effects_NN2 in_II string_NN1 theory_NN1 (_( 70_MC )_) ._. 
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The_AT most_RGT obvious_JJ are_VBR the_AT beam_NN1 voltage_NN1 and_CC current_JJ ._. 
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<s>
A_AT1 muon_NN1 in_II the_AT atmosphere_NN1 needs_VVZ to_TO have_VHI an_AT1 energy_NN1 greater_JJR than_CSN about_RG 5_MC GeV_NP1 (_( at_II sea_NN1 level_NN1 )_) in_BCL21 order_BCL22 to_TO emit_VVI Cherenkov_NP1 light_NN1 ._. 
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<s>
This_DD1 work_NN1 has_VHZ been_VBN carried_VVN out_RP within_II the_AT framework_NN1 of_IO the_AT EUROfusion_NN1 Consortium_NN1 and_CC has_VHZ received_VVN funding_NN1 from_II the_AT Euratom_NN1 research_NN1 and_CC training_NN1 programme_NN1 2014–2018_MCMC under_II grant_NN1 agreement_NN1 No_AT 633053_MC ._. 
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<s>
However_RR ,_, this_DD1 loss_NN1 can_VM be_VBI compensated_VVN ,_, at_RR21 least_RR22 partially_RR ,_, by_II increasing_VVG the_AT radius_NN1 of_IO curvature_NN1 of_IO the_AT curved_JJ sector_NN1 ._. 
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Riemannian_JJ metric_JJ corresponding_JJ to_II this_DD1 state_NN1 will_VM be_VBI <Equation>_FO where_RRQ <Professional_FO Term>_FO ._. 
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<s>
For_REX21 example_REX22 ,_, instead_II21 of_II22 leaving_VVG the_AT collision_NN1 complex_NN1 as_CSA in_II the_AT case_NN1 of_IO the_AT triradical_JJ (_( Scheme_NN1 3_MC )_) ,_, the_AT hydrogen_NN1 atom_NN1 likely_RR undergoes_VVZ barrierless_JJ ,_, exothermic_JJ radical-radical_JJ recombination_NN1 ,_, which_DDQ is_VBZ followed_VVN by_II elimination_NN1 of_IO two_MC ethylene_NN1 molecules_NN2 to_TO yield_VVI the_AT C2H4_FO abstraction_NN1 product_NN1 (_( Scheme_NN1 4_MC )_) ._. 
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These_DD2 results_NN2 are_VBR reproduced_VVN with_IW Gogny_NP1 D1S_FO force_NN1 calculations_NN2 ._. 
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This_DD1 effect_NN1 may_VM be_VBI due_II21 to_II22 the_AT action_NN1 of_IO the_AT differential_JJ rotation_NN1 ._. 
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<s>
Our_APPGE approach_NN1 to_TO model_VVI the_AT carbon_NN1 sublimation_NN1 rates_NN2 at_II leading_JJ edges_NN2 ,_, to_TO measure_VVI the_AT as-built_JJ steps_NN2 between_II different_JJ parts_NN2 of_IO the_AT targets_NN2 and_CC to_TO combine_VVI these_DD2 into_II a_AT1 prediction_NN1 of_IO carbon_NN1 sublimation_NN1 for_IF different_JJ magnetic_JJ configurations_NN2 is_VBZ described_VVN in_II section_NN1 4_MC ._. 
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<s>
The_AT energy_NN1 of_IO formation_NN1 of_IO Ce-UiO-66_NP1 (_( Mn_FO )_) is_VBZ the_AT energy_NN1 of_IO this_DD1 ,_, the_AT energy_NN1 of_IO formation_NN1 (_( Ef_NP1 )_) is_VBZ given_VVN in_II eV/_NN1 (_( metal_NN1 atom_NN1 )_) by<equation>_FO ,_, where_CS ECeUiO66_NP1 (_( Mn_FO )_) ,_, ECe_NP1 ,_, EM_FU ,_, EO2_FO ,_, EC_NP1 ,_, EH2_FO are_VBR the_AT DFT_NP1 calculated_VVN electronic_JJ energies_NN2 for_IF a_AT1 Ce-UiO-66_NP1 (_( Mn_FO )_) primitive_JJ cell_NN1 ,_, a_AT1 Ce_NN1 atom_NN1 in_II cerium_NN1 metal_NN1 ,_, a_AT1 Zr_NP1 or_CC Ti_JJ atom_NN1 in_II bulk_NN1 metal_NN1 ,_, a_AT1 gas-phase_NN1 O2_FO molecule_NN1 ,_, a_AT1 C_NP1 atom_NN1 in_II graphite_NN1 ,_, and_CC a_AT1 gas-phase_NN1 H2_FO molecule_NN1 ,_, respectively_RR ,_, and_CC the_AT denominator_NN1 is_VBZ the_AT number_NN1 of_IO metal_NN1 atoms_NN2 in_II a_AT1 Ce-UiO-66_NP1 (_( Mn_FO )_) primitive_JJ cell_NN1 ._. 
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Consider_VV0 first_MD the_AT kernel_NN1 ,_, the_AT sheaf_NN1 of_IO centralizers_NN2 of_IO ._. 
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<s>
Thus_RR W(n)_NP1 has_VHZ generators_NN2 (_( 2.32_MC )_) and_CC defining_VVG relations_NN2 (_( 3.1_MC )_) –_- (_( 3.7_MC )_) and_CC (_( 4.16_MC )_) ._. 
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<s>
The_AT output_NN1 energy_NN1 of_IO the_AT pump_NN1 laser_NN1 was_VBDZ approximately_RR 100_MC mJ_NNU and_CC the_AT dye_NN1 laser_NN1 output_NN1 energy_NN1 was_VBDZ about_RG 10_MC mJ_NNU ,_, with_IW an_AT1 estimated_JJ energy_NN1 fluctuation_NN1 of_IO 12%_NNU ._. 
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The_AT rechanneling_JJ length_NN1 decreases_VVZ approximately_RR by_II a_AT1 factor_NN1 of_IO two_MC in_II the_AT angular_JJ range_NN1 considered_VVN ._. 
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Li_NP1 diffusion_NN1 coefficient_NN1 limits_VVZ its_APPGE properties_NN2 in_II NiO_NP1 films_NN2 ._. 
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<s>
In_II communication_NN1 systems_NN2 the_AT wavelength_NN1 of_IO choice_NN1 is_VBZ 1.5_MC m_NNO ,_, a_AT1 spectral_JJ region_NN1 where_CS the_AT fiber_NN1 exhibits_VVZ negative_JJ group_NN1 velocity_NN1 dispersion_NN1 ._. 
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<s>
They_PPHS2 found_VVD that_CST at_II zero_MC environment_NN1 temperature_NN1 ,_, the_AT system-environment_JJ interaction_NN1 acts_VVZ as_II a_AT1 pump_NN1 toward_II the_AT dark_JJ state_NN1 ._. 
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<s>
In_II the_AT ATLAS_NN1 and_CC CMS_NP1 experiments_NN2 ,_, SM_NP1 physics_NN1 can_VM be_VBI studied_VVN with_IW unprecedented_JJ precision_NN1 ,_, enabling_VVG comparison_NN1 with_IW the_AT precise_JJ predictions_NN2 of_IO the_AT SM_NP1 ._. 
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<s>
These_DD2 expressions_NN2 demonstrate_VV0 that_CST a_AT1 magnetized_JJ MMR_NP1 will_VM move_VVI toward_II "_" a_AT1 local_JJ maximum_NN1 of_IO the_AT field_NN1 "_" due_II21 to_II22 the_AT magnetic_JJ force_NN1 and_CC that_CST a_AT1 magnetic_JJ MMR_NP1 will_VM rotate_VVI due_II21 to_II22 torque_NN1 ,_, because_CS torque_NN1 causes_VVZ the_AT device_NN1 to_TO align_VVI with_IW the_AT magnetic_JJ field_NN1 ,_, and_CC as_II such_DA ,_, a_AT1 rotating_JJ magnetic_JJ field_NN1 will_VM cause_VVI the_AT device_NN1 to_TO rotate_VVI ._. 
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This_DD1 builds_VVZ upon_II an_AT1 already_RR rich_JJ body_NN1 of_IO work_NN1 investigating_VVG "_" self-organization_NN1 "_" of_IO atoms_NN2 ,_, where_CS the_AT interplay_NN1 between_II the_AT scatterings_NN2 of_IO light_NN1 ,_, the_AT forces_NN2 exerted_VVD ,_, and_CC the_AT atomic_JJ positions_NN2 are_VBR treated_VVN self-consistently_RR ._. 
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<s>
In_II this_DD1 situation_NN1 ,_, v_ZZ1 could_VM not_XX be_VBI mapped_VVN to_II a_AT1 bit_NN1 string_NN1 by_II using_VVG spherical_JJ codes_NN2 ._. 
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The_AT spectrum_NN1 peaks_NN2 at_II around_RG 1_MC1 ?m_FO wavelength_NN1 ,_, which_DDQ is_VBZ thought_VVN to_TO reflect_VVI a_AT1 composition_NN1 rich_JJ in_II heavy_JJ elements_NN2 ._. 
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<s>
Comparing_VVG figures_NN2 5(a)_FO and_CC 13(a)_FO shows_VVZ that_CST the_AT largest_JJT horizontal_JJ force_NN1 on_II the_AT wall_NN1 occurs_VVZ much_RR later_RRR than_CSN the_AT peak_NN1 of_IO the_AT asymmetric_JJ magnetic_JJ fluctuations_NN2 ._. 
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Second_MD ,_, we_PPIS2 use_VV0 this_DD1 algebraic_JJ model_NN1 to_TO describe_VVI some_DD of_IO the_AT important_JJ experimental_JJ observations_NN2 that_CST arise_VV0 from_II localized_JJ surface_NN1 plasmon_NN1 resonance_NN1 phenomena_NN2 ._. 
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<s>
Hydrocarbon_NN1 anions_NN2 are_VBR more_RGR efficiently_RR formed_VVN via_II ion_NN1 pair_NN formation_NN1 ,_, where_CS the_AT production_NN1 of_IO a_AT1 negatively_RR charged_VVN fragment_NN1 and_CC its_APPGE positively_RR charged_VVN counterpart_NN1 can_VM be_VBI observed_VVN ._. 
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A_AT1 cavity_NN1 is_VBZ placed_VVN on_II each_DD1 arm_NN1 of_IO a_AT1 Michelson_NN1 interferometer_NN1 ._. 
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<s>
If_CS this_DD1 could_VM be_VBI achieved_VVN with_IW the_AT necessary_JJ stability_NN1 in_RR21 particular_RR22 the_AT high_JJ repetition_NN1 rate_NN1 FELs_NN2 would_VM be_VBI below_RG 10nm_FO very_RG competitive_JJ sources_NN2 in_II comparison_NN1 to_II lab-based_JJ laser_NN1 sources_NN2 which_DDQ rely_VV0 on_II high-harmonic_JJ generation_NN1 and_CC have_VH0 certain_JJ limits_NN2 in_II average_JJ power_NN1 (_( Heyl_NP1 et_RA21 al_RA22 ,_, 2017_MC )_) ._. 
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<s>
The_AT synergistic_JJ effect_NN1 of_IO current_JJ collector_NN1 in_II improving_VVG the_AT long-term_JJ stability_NN1 of_IO the_AT Al-TiO2_JJ cell_NN1 is_VBZ also_RR explored_VVN ._. 
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Chate_VV0 ?_? and_CC Mu_NN1 ?_? oz_NNU ,_, 2014_MC ;_; Cavagna_NP1 et_RA21 al._RA22 ,_, 2017_MC )_) ._. 
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One_MC1 example_NN1 is_VBZ the_AT Deck-background_NN1 (_( see_VV0 Fig._NN1 21d_NNU )_) ,_, which_DDQ is_VBZ further_RRR discussed_VVN in_II Section_NN1 4.1_MC ._. 
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<s>
We_PPIS2 propose_VV0 a_AT1 machine-learning_JJ approach_NN1 based_VVN on_II artificial_JJ neural_JJ network_NN1 to_TO efficiently_RR obtain_VVI new_JJ insights_NN2 on_II the_AT role_NN1 of_IO geometric_JJ contributions_NN2 to_II the_AT nonequilibrium_NN1 fluctuations_NN2 of_IO an_AT1 adiabatically_RR temperature-driven_JJ quantum_NN1 heat_NN1 engine_NN1 coupled_VVN to_II a_AT1 cavity_NN1 ._. 
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<s>
We_PPIS2 can_VM now_RT also_RR look_VVI at_II the_AT real_JJ connected_JJ components_NN2 for_IF the_AT Prym_NN1 variety_NN1 for_IF S_ZZ1 ,_, which_DDQ is_VBZ the_AT Hitchin_NP1 fiber_NN1 for_IF SL_NP1 (_( 2_VV0 ,_, C_ZZ1 )_) ,_, and_CC of_IO the_AT quotient_NN1 variety_NN1 Pic0(S)/Pic0_NP1 (_( X_ZZ1 )_) ,_, which_DDQ is_VBZ the_AT Hitchin_NP1 fiber_NN1 for_IF PGL_NP1 (_( 2_VV0 ,_, C_ZZ1 )_) ._. 
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In_II figure_NN1 15_MC ,_, we_PPIS2 plot_VV0 this_DD1 data_NN point_NN1 in_II the_AT Kikuchi_JJ diagram_NN1 &lsqb;_( 2_MC ,_, 46_MC &rsqb;_) ._. 
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We_PPIS2 can_VM eliminate_VVI time_NNT1 dependence_NN1 by_II the_AT coordinate_NN1 transformation_NN1 :_: <Equation>_FO (_( 106_MC )_) Then_RT ,_, the_AT Floquet_NN1 transformation_NN1 of_IO the_AT basis_NN1 ,_, <Equation>_FO (_( 107_MC )_) with_IW the_AT replacement_NN1 of<Profession_FO term>_FO with_IW the_AT Vierbein_NP1 reduces_VVZ the_AT problem_NN1 into_II a_AT1 static_JJ one_PN1 characterized_VVD by_II the_AT transformed_JJ Lagrangian_JJ density_NN1 :_: <Equation>_FO (_( 108_MC )_) Now_RT ,_, we_PPIS2 see_VV0 that_CST a_AT1 rotating_JJ magnetic_JJ field_NN1 is_VBZ transformed_VVN into_II a_AT1 static_JJ one_PN1 ,_, as_CSA expected_VVN from_II the_AT frame_NN1 change_NN1 ,_, and_CC the_AT effect_NN1 is_VBZ not_XX only_RR that_DD1 but_CCB also_RR the_AT transformation_NN1 gives_VVZ rise_NN1 to_II a_AT1 new_JJ term_NN1 ,_, which_DDQ can_VM be_VBI identified_VVN with_IW the_AT axial_JJ vector_NN1 potential_NN1 corresponding_VVG to_II <Profession_FO term>_FO ,_, leading_VVG to_II &lsqb;_( 78_MC &rsqb;_) <Equation>_FO (_( 109_MC )_) ._. 
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In_II the_AT present_JJ paper_NN1 ,_, the_AT isomorphic_JJ relationship_NN1 was_VBDZ first_MD established_VVN between_II a_AT1 spin_NN1 2/7_MF and_CC three_MC interacting_JJ fictitious_JJ spins_VVZ 1/2_MF ._. 
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As_II a_AT1 first_MD step_NN1 in_II this_DD1 direction_NN1 ,_, experiments_NN2 using_VVG a_AT1 highly_RR focused_VVN beam_NN1 of_IO FLASH_NN1 demonstrated_VVD that_CST pictures_NN2 of_IO 2_MC dimensional_JJ objects_NN2 could_VM be_VBI reconstructed_VVN from_II single-shot_JJ single-_JJ particle_NN1 diffraction_NN1 patterns_NN2 ._. 
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We_PPIS2 remark_VV0 here_RL that_DD1 more_RGR future_JJ effort_NN1 is_VBZ required_VVN to_TO put_VVI in_II problem_NN1 ._. 
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The_AT effects_NN2 of_IO other_JJ hopping_JJ parameters_NN2 on_II Dirac_NP1 points_NN2 and_CC band_NN1 structures_NN2 are_VBR indicated_VVN in_II Fig._NN1 4(b)_FO ,_, in_II which_DDQ the_AT arrows_NN2 represent_VV0 the_AT motion_NN1 of_IO Dirac_NP1 points_NN2 and_CC band_NN1 structures_NN2 when_RRQ the_AT corresponding_JJ hopping_JJ parameters_NN2 increase_VV0 ._. 
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XRD_NP1 pattern_NN1 of_IO the_AT synthesized_JJ SiOx/C_NP1 ._. 
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The_AT proof_NN1 of_IO (_( 3.8_MC )_) is_VBZ entirely_RR analogous_JJ ,_, with_IW now_RT <Equation>_FO instead_II21 of_II22 (_( 3.9_MC )_) ._. 
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The_AT origin_NN1 of_IO chain-folding_NN1 was_VBDZ elaborated_VVN by_II the_AT intermolecular_JJ crystal_NN1 nucleation_NN1 model_NN1 ,_, by_II31 means_II32 of_II33 free_JJ energy_NN1 calculation_NN1 of_IO single-chain_JJ crystallization_NN1 ._. 
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Such_DA a_AT1 system_NN1 then_RT effectively_RR represents_VVZ an_AT1 atomic_JJ ensemble_NN1 simultaneously_RR coupled_VVN to_II a_AT1 Nano_NN1 fiber_NN1 (_( the_AT TM_NP1 mode_NN1 )_) and_CC cavity_NN1 (_( the_AT TE_FW mode_NN1 )_) ,_, which_DDQ is_VBZ a_AT1 very_RG difficult_JJ hybrid_JJ system_NN1 to_TO create_VVI in_II conventional_JJ settings_NN2 ._. 
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In_BCL21 order_BCL22 to_TO extract_VVI a_AT1 clean_JJ signal_NN1 for_IF the_AT chiral_JJ transition_NN1 of_IO the_AT light_JJ quark_NN1 flavour_NN1 ,_, the_AT mass_NN1 of_IO the_AT heavy_JJ quark_NN1 needs_VVZ to_TO be_VBI sufficiently_RR larger_JJR than_CSN the_AT one_PN1 of_IO the_AT light_JJ quark_NN1 ._. 
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The_AT potential_NN1 in_II the_AT electrolyte_NN1 region_NN1 is_VBZ obtained_VVN by_II averaging_VVG the_AT macroscopic_JJ potential_NN1 in_II a_AT1 region_NN1 of_IO the_AT electrolyte_NN1 3_MC ?_AT1 above_RL the_AT position_NN1 of_IO the_AT first_MD water_NN1 layer_NN1 ._. 
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From_II the_AT relations_NN2 <EQUATION>_FO and_CC <EQUATION>_FO ,_, we_PPIS2 have_VH0 the_AT form_NN1 for_IF e_ZZ1 as_CSA given_VVN in_II Eq._NP1 (_( 2_MC )_) ._. 
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If_CS <Equation>_FO we_PPIS2 use_VV0 (_( 11_MC )_) for_IF <Equation>_FO and_CC (_( 12_MC )_) for_IF the_AT two_MC follows_VVZ directly_RR from_II the_AT Euler_NN1 product_NN1 of_IO ._. 
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By_II the_AT optical_JJ radiation_NN1 characteristics_NN2 of_IO the_AT return_NN1 stroke_NN1 process_NN1 and_CC combining_VVG with_IW the_AT synchronized_JJ electric_JJ field_NN1 information_NN1 ,_, the_AT core_NN1 current_JJ channel_NN1 radius_NN1 and_CC the_AT luminous_JJ channel_NN1 radius_NN1 are_VBR estimated_VVN ._. 
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It_PPH1 is_VBZ here_RL that_DD1 effective_JJ field_NN1 theories_NN2 can_VM bridge_VVI the_AT gap_NN1 ._. 
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They_PPHS2 are_VBR identified_VVN with_IW the_AT observed_JJ n_ZZ1 ,_, K_ZZ1 ,_, and_CC n_ZZ1 mesons_NN2 ,_, which_DDQ have_VH0 smaller_JJR masses_NN2 than_CSN the_AT lightest_JJT vector_NN1 meson_NN1 ,_, the_AT p(770)_FO ._. 
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Bottom_NN1 :_: Population_NN1 transfer_NN1 efficiency_NN1 vs_II peak_NN1 Rabi_NP1 frequency_NN1 ._. 
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B._NP1 C._NP1 S._NP1 was_VBDZ supported_VVN by_II the_AT National_JJ Research_NN1 Council_NN1 Research_NN1 Associateship_NN1 Program_NN1 ._. 
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Using_VVG 318,379_MC influenza-related_JJ tweets_NN2 generated_VVN by_II 101,853_MC users_NN2 ,_, Salathé_NP1 and_CC Khandelwal_NP1 &lsqb;_( 735_MC &rsqb;_) trained_VVD a_AT1 machine_NN1 learning_NN1 algorithm_NN1 to_TO automatically_RR judge_VVI sentiments_NN2 of_IO tweets_NN2 ._. 
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<s>
The_AT curl_NN1 of_IO the_AT magnetic_JJ field_NN1 ,_, when_CS calculated_VVN using_VVG Lagrangian_JJ coordinates_NN2 ,_, is<Equation>_FO (_( 67_MC )_) where_RRQ ijk_NN1 is_VBZ the_AT fully_RR antisymmetric_JJ tensor_NN1 :_: <Equation>_FO as_CSA ,_, which_DDQ are_VBR even_RR permutations_NN2 of_IO the_AT indices_NN2 ._. 
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Are_VBR the_AT flows_NN2 in_II such_DA active_JJ materials_NN2 related_VVN to_II the_AT excitations_NN2 of_IO their_APPGE static_JJ counterparts_NN2 and_CC can_VM one_PN1 gain_VVI intuition_NN1 into_II biological_JJ crowding_VVG by_II its_APPGE analogy_NN1 with_IW jammed_JJ systems_NN2 (_( Henkes_NP2 ,_, Fily_NP1 ,_, and_CC Marchetti_NP1 ,_, 2011_MC )_) ?_? 
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<s>
Therefore_RR ,_, they_PPHS2 are_VBR relatively_RR safe_JJ to_TO use_VVI ,_, as_CSA all_DB of_IO their_APPGE pitfalls_NN2 have_VH0 been_VBN studied_VVN in_II detail_NN1 ._. 
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<s>
The_AT root-mean-square_NN1 (_( rms_NN1 )_) surface_NN1 roughnesses_NN2 of_IO the_AT films_NN2 increased_VVN (_( from_II 1.43_MC nm_FU to_II 2.94_MC nm_FU )_) with_IW increased_JJ film_NN1 thickness_NN1 ._. 
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This_DD1 mathematical_JJ property_NN1 has_VHZ led_VVN to_II the_AT (_( unique_JJ )_) characterization_NN1 classification_NN1 of_IO the_AT umbral_JJ moonshine_NN1 mock_VV0 modular_JJ forms_NN2 H_ZZ1 X_ZZ1 &lsqb;_( 9,10_MC &rsqb;_) ._. 
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We_PPIS2 then_RT review_VV0 the_AT various_JJ crystal-growth_JJ strategies_NN2 to_TO prepare_VVI high-quality_JJ OSCSs_NN1 via_II solution_NN1 ,_, melting_VVG ,_, and_CC vapor_NN1 phases_NN2 ,_, which_DDQ contributes_VVZ much_RR to_II the_AT rapid_JJ development_NN1 of_IO OSCS-based_JJ light-emitting_JJ devices_NN2 ._. 
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It_PPH1 is_VBZ demonstrated_VVN that_CST with_IW the_AT proper_JJ treatment_NN1 of_IO QM_FO approach_NN1 we_PPIS2 arrive_VV0 again_RT at_II the_AT expression_NN1 Eq_NN1 ._. 
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(_( 110_MC )_) (_( and_CC not_XX Eq_NN1 ._. 
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(_( 116_MC )_) )_) for_IF the_AT cascade_NN1 contribution_NN1 in_II31 case_II32 of_II33 the_AT 3s_MC2 →_NULL 1s_MC2 +_FO 2_MC γ_NULL transition_NN1 ._. 
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We_PPIS2 optimized_VVD the_AT C34H16_FO dimer_NN1 at_II these_DD2 two_MC levels_NN2 and_CC obtained_VVD interplane_NN1 distances_NN2 of_IO 3.29_MC and_CC 3.39_MC ?_AT1 ,_, respectively_RR ._. 
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After_II passing_VVG to_II components_NN2 ,_, the_AT N_ZZ1 =_FO 2_MC effective_JJ action_NN1 constructed_VVN displays_NN2 ,_, along_II21 with_II22 other_JJ terms_NN2 ,_, the_AT SO(5)-invariant_JJ F_ZZ1 /X_FU term_NN1 ._. 
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When_CS the_AT packing_NN1 fraction_NN1 decreases_VVZ ,_, lowand_VV0 high-CCN_JJ spheres_NN2 tend_VV0 to_TO have_VHI more_DAR similar_JJ angular_JJ environments_NN2 ._. 
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The_AT well-distributed_JJ pores_NN2 ,_, acting_VVG as_RG light_JJ scattering_NN1 centers_NN2 ,_, enable_VV0 reduction_NN1 of_IO the_AT luminescent_JJ spot_NN1 size_NN1 greatly_RR but_CCB without_IW any_DD losses_NN2 in_II conversion_NN1 efficiency_NN1 ._. 
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The_AT STT_NP1 torques_NN2 ,_, Eq_NN1 ._. 
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(_( 72_MC )_) ,_, depend_VV0 on_II the_AT magnetization_NN1 gradient_NN1 along_II the_AT current_JJ direction_NN1 ,_, i.e._REX ,_, eu_NNU Tm_NP1 (_( ≡_NULL m=x_FO with_IW the_AT axes_NN2 convention_NN1 defined_VVN in_II Fig._NN1 46_MC )_) ._. 
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The_AT directions_NN2 of_IO steepest_JJT descent_NN1 are_VBR <Equation>_FO ._. 
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However_RR ,_, the_AT local_JJ roughness_NN1 distributions_NN2 &lsqb;_( 23_MC &rsqb;_) suggest_VV0 that_CST the_AT one-dimensional_JJ DT_NP1 model_NN1 has_VHZ normal_JJ scaling_NN1 ,_, in_II agreement_NN1 with_IW the_AT predictions_NN2 of_IO dynamic_JJ RG_NP1 analysis_NN1 for_IF local_JJ growth_NN1 process_NN1 without_IW quenched_JJ disorder_NN1 or_CC additional_JJ symmetries_NN2 &lsqb;_( 20_MC &rsqb;_) ._. 
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The_AT fast_JJ 3He_FO ion_NN1 slowing_VVG down_RP distributions_NN2 at_II the_AT midplane_NN1 edge_NN1 of_IO the_AT plasma_NN1 on_II the_AT low_JJ field_NN1 side_NN1 have_VH0 the_AT strong_JJ pitch-angle_JJ anisotropy_NN1 in_II both_DB2 cases_NN2 ._. 
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The_AT agreement_NN1 with_IW Zhou_NP1 et_RA21 al_RA22 ._. 
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&lsqb;_( 14_MC &rsqb;_) and_CC with_IW the_AT low-energy_JJ data_NN <Chart>_FO ._. 
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The_AT author_NN1 thanks_NN2 Kazuya_NP1 Fujimoto_NP1 for_IF useful_JJ discussion_NN1 ._. 
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Having_VHG warmed_VVN up_RP with_IW case_NN1 of_IO time-reversal_JJ symmetry_NN1 ,_, we_PPIS2 now_RT move_VV0 on_RP to_TO discuss_VVI systems_NN2 with_IW both_DB2 charge_VV0 conservation_JJ and_CC time-reversal_JJ symmetry_NN1 ,_, i.e._REX ,_, U(1)_FO ZT_NP1 2_MC symmetry_NN1 ._. 
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Three_MC of_IO the_AT FLASH1_FO beamlines_VVZ ,_, BL1_FO ,_, BL2_FO and_CC PG2_FO ,_, are_VBR equipped_VVN with_IW permanently_RR installed_VVN SDUs_NN1 with_IW time_NNT1 resolution_NN1 down_RP to_II 100_MC as_CSA and_CC maximum_JJ delay_NN1 times_NNT2 ranging_VVG from_II several_DA2 picoseconds_NNT2 (_( BL2_FO ,_, PG2_FO )_) to_II almost_RR a_AT1 nanosecond_NN1 (_( BL1_FO )_) ._. 
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In_II the_AT literature_NN1 ,_, several_DA2 composites_NN2 have_VH0 been_VBN engineered_VVN to_TO produce_VVI bio-implants_NN2 ._. 
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The_AT electron_NN1 temperature_NN1 is_VBZ determined_VVN by_II a_AT1 Thomson_NP1 scattering_VVG diagnostic_JJ ._. 
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Rather_CS21 than_CS22 study_VVI high_JJ order_NN1 harmonic_JJ generation_NN1 for_IF my_APPGE Ph.D._NP1 ,_, we_PPIS2 decided_VVD to_TO study_VVI multiphoton_NN1 ionization_NN1 ._. 
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