This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and e...This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and exerted his influence on other scholars in the translation and diffusion of ancient Greek texts.Second,investigating Lagrange's style in doing and writing history of mathematics,this paper takes a new perspective and elucidates his motivation in these activities.In particular,it focuses on Lagrange's presentation of the history of calculus while he was teaching analysis at the Ecole Polytechnique(1795-1799)so as to clarify the function of history in Lagrange's mathematical works.My thesis is that Lagrange's intention in examining the different methods employed by his predecessors was to find inspiration and useful contents in his search for the proper approach to mathematical problems.I thus argue in this paper that history served as a guide or methodology for Lagrange's mathematics.Meanwhile,through an analysis of his historical writing,this paper points to four epistemological values according to which Lagrange judged various historical methods of differential calculus:generality,simplicity,clarity,and rigor.Lagrange's move to rigorize analysis was connected to his interest in and research of Greek texts;he was attempting to introduce the rigor of the ancient Greeks'demonstration in his works of analysis.展开更多
The micro/nano structures of the wing scales in Morpho butterfly are responsible for the structural coloration,with a major part ascribed to interference and diffraction of light.The optical properties of the butterfl...The micro/nano structures of the wing scales in Morpho butterfly are responsible for the structural coloration,with a major part ascribed to interference and diffraction of light.The optical properties of the butterfly wings were investigated by simulating a two-dimensional model using rigorous coupled-wave analysis technique.It is proved that they depend strongly on the structural parameters,incidence angle and refractive index.The peak value and the peak wavelength of the reflection efficiency increase as the vertical periodic thickness increases.The peak value decreases observably,while both of the bandwidth and the peak wavelength increase when the number of the vertical periods decreases.Increase of the horizontal periodic width causes a decrease of the peak value and an increase of the peak wavelength,although the variations are small.The peak value decreases distinctly and the peak wavelength increases as the ambient refractive index increases,which corresponds to the variation in ambient conditions.The research reveals the mechanisms of the brilliant structural color in Morpho butterfly,and is of great significance to the design,manufacture and applications of the bionic micro/nano structures for gas detection.展开更多
With high energy density and improved safety,rechargeable battery chemistries with a zinc(Zn)metal anode offer promising and sustainable alternatives to those based on lithium metal or lithium-ion intercalation/alloyi...With high energy density and improved safety,rechargeable battery chemistries with a zinc(Zn)metal anode offer promising and sustainable alternatives to those based on lithium metal or lithium-ion intercalation/alloying anode materials;however,the poor electrochemical reversibility of Zn plating/stripping,induced by parasitic reactions with both aqueous and non-aqueous electrolytes,presently limits the practical appeal of these systems.Although recent efforts in rechargeable Zn metal batteries(RZMBs)have achieved certain advancements in Zn metal reversibility,as quantified by the Coulombic efficiency(CE),a standard protocol for CE has not been established,and results across chemistries and systems are often conflicting.More importantly,there is still an insufficient understanding regarding the critical factors dictating Zn reversibility.In this work,a rigorous,established protocol for determining CE of lithium metal anodes is transplanted to the Zn chemistry and is used for systematically examining how a series of factors including current collector chemistry,current density,temperature,and the upper voltage limit during stripping affect the measured reversibility of different Zn electrolytes.With support from density functional theory calculations,this standardized Zn CE protocol is then leveraged to identify an important correlation between electrolyte solvation strength toward Zn2+and the measured Zn CE in the corresponding electrolyte,providing new guidance for future development and evaluation of Zn electrolytes.展开更多
We present quasi-exact ab initio path integral Monte Carlo(PIMC)results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime,from solid density conditions to the...We present quasi-exact ab initio path integral Monte Carlo(PIMC)results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime,from solid density conditions to the strongly compressed case.The full dynamic treatment of electrons and protons on the same footing allows us to rigorously quantify both electronic and ionic exchange–correlation effects in the system,and to compare the results with those of earlier incomplete models such as the archetypal uniform electron gas or electrons in a fixed ion snapshot potential that do not take into account the interplay between the two constituents.The full electronic density response is highly sensitive to electronic localization around the ions,and our results constitute unambiguous predictions for upcoming X-ray Thomson scattering experiments with hydrogen jets and fusion plasmas.All PIMC results are made freely available and can be used directly for a gamut of applications,including inertial confinement fusion calculations and the modeling of dense astrophysical objects.Moreover,they constitute invaluable benchmark data for approximate but computationally less demanding approaches such as density functional theory or PIMC within the fixed-node approximation.展开更多
Balanoposthitis(BP),a common male genitalia inflammation,is managed by clinicians from different specialties,including urology,pediatrics,dermatology,and venereology.Due to this diverse array of clinicians involved,th...Balanoposthitis(BP),a common male genitalia inflammation,is managed by clinicians from different specialties,including urology,pediatrics,dermatology,and venereology.Due to this diverse array of clinicians involved,there exists a lack of consistent,evidence-based recommendations for BP.The development of the consensus engaged 19 representative hospitals and it adhered to rigorous protocols,encompassing international registration(IPGRP-2021CN003)and the application of evidence grading criteria and recommendation standards[Appendix S1,Supplementary File,http://links.lww.com/CM9/C42].Over the period from December 2020 to October 2022,consensus on 12 clinical issues was reached through comprehensive evidence searches and two iterations of Delphi surveys[Supplementary File,http://links.lww.com/CM9/C42].展开更多
文摘This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and exerted his influence on other scholars in the translation and diffusion of ancient Greek texts.Second,investigating Lagrange's style in doing and writing history of mathematics,this paper takes a new perspective and elucidates his motivation in these activities.In particular,it focuses on Lagrange's presentation of the history of calculus while he was teaching analysis at the Ecole Polytechnique(1795-1799)so as to clarify the function of history in Lagrange's mathematical works.My thesis is that Lagrange's intention in examining the different methods employed by his predecessors was to find inspiration and useful contents in his search for the proper approach to mathematical problems.I thus argue in this paper that history served as a guide or methodology for Lagrange's mathematics.Meanwhile,through an analysis of his historical writing,this paper points to four epistemological values according to which Lagrange judged various historical methods of differential calculus:generality,simplicity,clarity,and rigor.Lagrange's move to rigorize analysis was connected to his interest in and research of Greek texts;he was attempting to introduce the rigor of the ancient Greeks'demonstration in his works of analysis.
文摘The micro/nano structures of the wing scales in Morpho butterfly are responsible for the structural coloration,with a major part ascribed to interference and diffraction of light.The optical properties of the butterfly wings were investigated by simulating a two-dimensional model using rigorous coupled-wave analysis technique.It is proved that they depend strongly on the structural parameters,incidence angle and refractive index.The peak value and the peak wavelength of the reflection efficiency increase as the vertical periodic thickness increases.The peak value decreases observably,while both of the bandwidth and the peak wavelength increase when the number of the vertical periods decreases.Increase of the horizontal periodic width causes a decrease of the peak value and an increase of the peak wavelength,although the variations are small.The peak value decreases distinctly and the peak wavelength increases as the ambient refractive index increases,which corresponds to the variation in ambient conditions.The research reveals the mechanisms of the brilliant structural color in Morpho butterfly,and is of great significance to the design,manufacture and applications of the bionic micro/nano structures for gas detection.
基金supported by the Joint Center for Energy Storage Research(JCESR),a Department of Energy,Energy Innovation Hub,under an Interagency Agreement No.IAA SN2020957Forch Distinguished Postdoctoral Fellowship administered by the National Research Councilsupport from Oak Ridge Associated Universities(ORAU)
文摘With high energy density and improved safety,rechargeable battery chemistries with a zinc(Zn)metal anode offer promising and sustainable alternatives to those based on lithium metal or lithium-ion intercalation/alloying anode materials;however,the poor electrochemical reversibility of Zn plating/stripping,induced by parasitic reactions with both aqueous and non-aqueous electrolytes,presently limits the practical appeal of these systems.Although recent efforts in rechargeable Zn metal batteries(RZMBs)have achieved certain advancements in Zn metal reversibility,as quantified by the Coulombic efficiency(CE),a standard protocol for CE has not been established,and results across chemistries and systems are often conflicting.More importantly,there is still an insufficient understanding regarding the critical factors dictating Zn reversibility.In this work,a rigorous,established protocol for determining CE of lithium metal anodes is transplanted to the Zn chemistry and is used for systematically examining how a series of factors including current collector chemistry,current density,temperature,and the upper voltage limit during stripping affect the measured reversibility of different Zn electrolytes.With support from density functional theory calculations,this standardized Zn CE protocol is then leveraged to identify an important correlation between electrolyte solvation strength toward Zn2+and the measured Zn CE in the corresponding electrolyte,providing new guidance for future development and evaluation of Zn electrolytes.
基金supported by the Center for Advanced Systems Understanding(CASUS),financed by Germany’s Federal Ministry of Education and Research(BMBF)and the Saxon State Government out of the State Budget approved by the Saxon State Parliamentfunding from the European Research Council(ERC)under the European Union’s Horizon 2022 Research and Innovation Program(Grant Agreement No.101076233,“PREXTREME”).
文摘We present quasi-exact ab initio path integral Monte Carlo(PIMC)results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime,from solid density conditions to the strongly compressed case.The full dynamic treatment of electrons and protons on the same footing allows us to rigorously quantify both electronic and ionic exchange–correlation effects in the system,and to compare the results with those of earlier incomplete models such as the archetypal uniform electron gas or electrons in a fixed ion snapshot potential that do not take into account the interplay between the two constituents.The full electronic density response is highly sensitive to electronic localization around the ions,and our results constitute unambiguous predictions for upcoming X-ray Thomson scattering experiments with hydrogen jets and fusion plasmas.All PIMC results are made freely available and can be used directly for a gamut of applications,including inertial confinement fusion calculations and the modeling of dense astrophysical objects.Moreover,they constitute invaluable benchmark data for approximate but computationally less demanding approaches such as density functional theory or PIMC within the fixed-node approximation.
基金National Natural Science Foundation of China(No.82273538)Public Health Research and Development Program of the Shenyang Science and Technology Bureau(No.22-321-33-12)National Key R&D Program of China(No.2023YFC2508200)
文摘Balanoposthitis(BP),a common male genitalia inflammation,is managed by clinicians from different specialties,including urology,pediatrics,dermatology,and venereology.Due to this diverse array of clinicians involved,there exists a lack of consistent,evidence-based recommendations for BP.The development of the consensus engaged 19 representative hospitals and it adhered to rigorous protocols,encompassing international registration(IPGRP-2021CN003)and the application of evidence grading criteria and recommendation standards[Appendix S1,Supplementary File,http://links.lww.com/CM9/C42].Over the period from December 2020 to October 2022,consensus on 12 clinical issues was reached through comprehensive evidence searches and two iterations of Delphi surveys[Supplementary File,http://links.lww.com/CM9/C42].
