A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform conv...A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform convergence.展开更多
Based on the Hirota bilinear and long wave limit methods,the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI)equation are constructed.Then,by approximating soluti...Based on the Hirota bilinear and long wave limit methods,the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI)equation are constructed.Then,by approximating solutions of the GHSI equation along some parallel orbits at infinity,the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied,and the expressions of phase shift for lump wave before and after collisions are given.Furthermore,it is revealed that collisions between the lump wave and other waves are elastic,the corresponding collision diagrams are used to further explain.展开更多
The isotope shifts of the 282 1S0 to 2s2p 1P1 and 3P1 transitions in the four-electron beryllium atom are calcu- lated by using the multi-configuration Dirac-Hartrce-Fock method and the relativistic configuration inte...The isotope shifts of the 282 1S0 to 2s2p 1P1 and 3P1 transitions in the four-electron beryllium atom are calcu- lated by using the multi-configuration Dirac-Hartrce-Fock method and the relativistic configuration interaction approach for the stable and short-Bved beryllium isotopes. The results provided herein can be employed for the consistency check with the nuclear rms charge radii from the experimental isotope shifts by using the correspond- ing transitions for the short-lived nuclei 7,10-12Be and 14 Be. The analogous isotope shift results could also be obtained for the beryllium-like ions by the methods used here.展开更多
Wavelength-dependent AC Stark shifts and magic wavelengths of the terahertz clock transitions between the metastable triplet states 6s5d3D1 and 6s5d3D2are investigated with considering the optical lattice trapping of ...Wavelength-dependent AC Stark shifts and magic wavelengths of the terahertz clock transitions between the metastable triplet states 6s5d3D1 and 6s5d3D2are investigated with considering the optical lattice trapping of barium atoms with the linearly polarized laser. The trap depths and the slopes of light shift difference with distinct magic wavelengths of the optical lattices are also discussed in detail. Several potentially suitable working points for the optical lattice trapping laser are recommended and selected from these magic wavelengths.展开更多
Magic wavelengths for laser trapping of barium atoms in the optical clock transition at l107nm between the 6s2 1So state optical lattices are calculated with considering the and 6s5d 3D1 state. Theoretical calculation...Magic wavelengths for laser trapping of barium atoms in the optical clock transition at l107nm between the 6s2 1So state optical lattices are calculated with considering the and 6s5d 3D1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated, Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser.展开更多
We study the phase-conjugate polarization interference in a V-type three-level system and obtain an analytic closed form for the second-order stochastic correlation of sum-frequency polarization beat. In our Na vapour...We study the phase-conjugate polarization interference in a V-type three-level system and obtain an analytic closed form for the second-order stochastic correlation of sum-frequency polarization beat. In our Na vapour atomic system pumped by laser pulse of nano-second timescale duration, we experimentally demonstrate an ultrafast modulation of the four-wave mixing signal intensity with a sub-femtosecond timescale period, corre- sponding to the sum-frequency of the resonant transitions from 3S1/2 to 3Pl/2 and 3P3/2.展开更多
A high optical magnification three-dimensional imaging system is proposed using an optic microscope whose ocular （eyepiece） is retained and the structure of the transmission mode is not destroyed. The elemental imag...A high optical magnification three-dimensional imaging system is proposed using an optic microscope whose ocular （eyepiece） is retained and the structure of the transmission mode is not destroyed. The elemental image array is captured through the micro lens array. Due to the front diffuse transmission element, each micro lens sees a slightly different spatial perspective of the scene, and a different independent image is formed in each micro lens channel. Each micro lens channel is imaged by a Fourier lens and captured by a CCD. The design translating the stage in x or y provides no parallax. Compared with the conventional integral imaging of micro-objects, the optical magnification of micro-objects in the proposed system can enhanced remarkably. The principle of the enhancement of the image depth is explained in detail and the experimental results are presented.展开更多
This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is ...This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is presented.展开更多
Electrocatalytic reduction of CO_(2) to produce high value-added products is an important way to achieve sustainable production of green energy,but it is limited by high complexity of the catalyst structure and reacti...Electrocatalytic reduction of CO_(2) to produce high value-added products is an important way to achieve sustainable production of green energy,but it is limited by high complexity of the catalyst structure and reaction process,making the rational design of the catalyst and the targeted generation of specific products a huge challenge.Herein,based on the penta-octa-graphene(POG)with sp~2 and sp~3 hybrid as the prototype,we theoretically guide the design of CO_(2) electrocatalytic reduction(CO_(2)RR)catalyst over pure POG and TM doping POG(TM@POG).Our mechanistic study highlights two key factors in new pathway for CH_(4) production and catalytic performance,i.e.,TM provides electron transfer for the key intermediate*CHO,promoting the activation of CO_(2),and the type of protonation for CO_(2)RR is determined by the charge accumulation on the O atom of the intermediates.This reduces the complexity of the reaction and provides a predictive effect on the formation of intermediates.More importantly,the proper values of the Gibbs free energy indicate that TM@POG is an ideal catalyst candidate,especially the Fe@POG,which is superior to Cu(211)material.On this basis,three simple descriptors(Bader charge,d-band centerε_dand descriptorφ)based on the inherent properties of atoms were constructed to reveal the underlying causes of the improvement of catalytic activity.Our results provide a new understanding of the’structure-performance’relationship of carbon-based electrocatalysts,thus providing a useful strategy for the design of catalysts for CO_(2)RR.展开更多
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A（u, Ux）Uxx ＋ B（u, ux） is studied by using the conditional Lie-Blicklund symmetry method. The variant forms o...The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A（u, Ux）Uxx ＋ B（u, ux） is studied by using the conditional Lie-Blicklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie--Biicklund symmetries, are characterized. To construct functionally gener- alized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided.展开更多
基金the Basic Research Foundation of Xi'an University Architecture Technology(JC0620)the Youth Science and Technology Foundation of Xi'an University of Architecture and Technology(QN0736)
文摘A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform convergence.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12001424 and 12271324)the Natural Science Basic Research Program of Shaanxi Province,China(Grant No.2021JZ-21)+1 种基金the Chinese Post Doctoral Science Foundation(Grant No.2020M673332)the Three-year Action Plan Project of Xi’an University(Grant No.2021XDJH01)。
文摘Based on the Hirota bilinear and long wave limit methods,the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI)equation are constructed.Then,by approximating solutions of the GHSI equation along some parallel orbits at infinity,the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied,and the expressions of phase shift for lump wave before and after collisions are given.Furthermore,it is revealed that collisions between the lump wave and other waves are elastic,the corresponding collision diagrams are used to further explain.
基金Supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 14JK1402
文摘The isotope shifts of the 282 1S0 to 2s2p 1P1 and 3P1 transitions in the four-electron beryllium atom are calcu- lated by using the multi-configuration Dirac-Hartrce-Fock method and the relativistic configuration interaction approach for the stable and short-Bved beryllium isotopes. The results provided herein can be employed for the consistency check with the nuclear rms charge radii from the experimental isotope shifts by using the correspond- ing transitions for the short-lived nuclei 7,10-12Be and 14 Be. The analogous isotope shift results could also be obtained for the beryllium-like ions by the methods used here.
基金Project supported by the Science Fund from the Shaanxi Provincial Education Department,China(Grant No.14JK1402)
文摘Wavelength-dependent AC Stark shifts and magic wavelengths of the terahertz clock transitions between the metastable triplet states 6s5d3D1 and 6s5d3D2are investigated with considering the optical lattice trapping of barium atoms with the linearly polarized laser. The trap depths and the slopes of light shift difference with distinct magic wavelengths of the optical lattices are also discussed in detail. Several potentially suitable working points for the optical lattice trapping laser are recommended and selected from these magic wavelengths.
基金Supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 14JK1402
文摘Magic wavelengths for laser trapping of barium atoms in the optical clock transition at l107nm between the 6s2 1So state optical lattices are calculated with considering the and 6s5d 3D1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated, Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser.
基金Supported by the National Natural Science Foundation of China under Grant Nos 60308002 and 60678005, the Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No 200339, the Foundation for Key Programme of Ministry of Education of China under Grant No 105156, the For Ying-Tong Education Foundation for Young Teachers in the Institutions of Higher Education of China under Grant No 101061, and the Specialized Research Fund for the Doctoral Programme of Higher Education of China under Grant No 20050698017.
文摘We study the phase-conjugate polarization interference in a V-type three-level system and obtain an analytic closed form for the second-order stochastic correlation of sum-frequency polarization beat. In our Na vapour atomic system pumped by laser pulse of nano-second timescale duration, we experimentally demonstrate an ultrafast modulation of the four-wave mixing signal intensity with a sub-femtosecond timescale period, corre- sponding to the sum-frequency of the resonant transitions from 3S1/2 to 3Pl/2 and 3P3/2.
基金Supported by the Scientific Research Fund Project of the Education Department of Shaanxi Province under Grant No 15JK1732the Natural Science Foundation of Shaanxi Province under Grant No2014JQ1044the Science Foundation of Northwest University under Grant No 12NW01
文摘A high optical magnification three-dimensional imaging system is proposed using an optic microscope whose ocular （eyepiece） is retained and the structure of the transmission mode is not destroyed. The elemental image array is captured through the micro lens array. Due to the front diffuse transmission element, each micro lens sees a slightly different spatial perspective of the scene, and a different independent image is formed in each micro lens channel. Each micro lens channel is imaged by a Fourier lens and captured by a CCD. The design translating the stage in x or y provides no parallax. Compared with the conventional integral imaging of micro-objects, the optical magnification of micro-objects in the proposed system can enhanced remarkably. The principle of the enhancement of the image depth is explained in detail and the experimental results are presented.
基金Supported by the Natural Science Foundation of Shaanxi Province（2007A12） Supported by the Scientific Research Foundation of Shaanxi Educational Committee（11JK0507）
文摘This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is presented.
基金supported by the Natural Science Basic Research Program of Shaanxi(2023-JC-YB-065,2024JC-YBMS-788)the Foundation of Laboratory of Computational Physics(6142A05QN22017)。
文摘Electrocatalytic reduction of CO_(2) to produce high value-added products is an important way to achieve sustainable production of green energy,but it is limited by high complexity of the catalyst structure and reaction process,making the rational design of the catalyst and the targeted generation of specific products a huge challenge.Herein,based on the penta-octa-graphene(POG)with sp~2 and sp~3 hybrid as the prototype,we theoretically guide the design of CO_(2) electrocatalytic reduction(CO_(2)RR)catalyst over pure POG and TM doping POG(TM@POG).Our mechanistic study highlights two key factors in new pathway for CH_(4) production and catalytic performance,i.e.,TM provides electron transfer for the key intermediate*CHO,promoting the activation of CO_(2),and the type of protonation for CO_(2)RR is determined by the charge accumulation on the O atom of the intermediates.This reduces the complexity of the reaction and provides a predictive effect on the formation of intermediates.More importantly,the proper values of the Gibbs free energy indicate that TM@POG is an ideal catalyst candidate,especially the Fe@POG,which is superior to Cu(211)material.On this basis,three simple descriptors(Bader charge,d-band centerε_dand descriptorφ)based on the inherent properties of atoms were constructed to reveal the underlying causes of the improvement of catalytic activity.Our results provide a new understanding of the’structure-performance’relationship of carbon-based electrocatalysts,thus providing a useful strategy for the design of catalysts for CO_(2)RR.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11371293,11401458,and 11501438)the National Natural Science Foundation of China,Tian Yuan Special Foundation(Grant No.11426169)the Natural Science Basic Research Plan in Shaanxi Province of China(Gran No.2015JQ1014)
文摘The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A（u, Ux）Uxx ＋ B（u, ux） is studied by using the conditional Lie-Blicklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie--Biicklund symmetries, are characterized. To construct functionally gener- alized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided.
