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Surface-induced interaction of colloidal particles in isotropic liquid crystals

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Communications in Theoretical Physics 2024年第7期76卷 114-122页

作者： Hualing Zhang kaifeng Weng Rui Ma department of Physics College of Physical Science and TechnologyXiamen UniversityXiamen 361005China Fujian Provincial Key Laboratory for Soft Functional Materials Research Research Institute for Biomimetics and Soft MatterXiamen UniversityXiamen 361005China

In this work,we study the interaction between two colloidal particles in a liquid crystal that is in the isotropic *** interaction is caused by surface-induced polarization of the liquid crystal molecules in the vicinity of the *** find that the interaction is short-ranged in both 2D and 3D *** symmetric homeotropic anchoring conditions,the interaction is *** under anti-symmetric homeotropic anchoring conditions,the interaction is repulsive at short distances but attractive at intermediate *** particle size has a strong impact on the effective interaction force.

关键词： surface-induced interaction colloidal particles liquid crystals

On the Exceptional Set for the Equation n=p+k^2

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Acta Mathematica Sinica,English Series 1995年第2期11卷 156-167页

作者： Wang Tianze department of mathematics henan university kaifeng, 475001 china lay.psych.mun.ca

Denote by E（X） the number of integers n≤X which are not a sum of a prime and a square. Set θ=1-0.994428b, where b≤min（0.9365/c3, 0.02578/c4）, c3, c4 being given in Lemma 8. The result E（x） xθ is proved in th... 详细信息

关键词： Lemma Square Denote Prime sums Integer Equation

Polynomial solutions of quasi-homogeneous partial differential equations

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Science china mathematics 2001年第9期44卷 1148-1155页

作者： LUO Xuebo ZHENG Zhujun Institute of Applied mathematics, Northwestern Polytechnical university, Xi’an 710072, china Institute of mathematics, henan university, kaifeng 475001, china 1. Institute of Applied mathematics Northwestem Polytechnical University 710072 Xi’an China 2. Institute of mathematics Henan University 475001 Kaifeng China

By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite

关键词： quasi-homogeneous partial differential operator polynomial solution, dimension of the space of solution method of analytic number theory

Influence of NH_3-treating temperature on visible light photocatalytic activity of N-doped P_(25)-TiO_2

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Science china Chemistry 2009年第8期52卷 1164-1170页

作者： CHEN WeiPing1,2,WANG Yan1,JIN ZhenSheng1,2,FENG CaiXia1,WU ZhiShen1 & ZHANG ZhiJun1 1 Key Laboratory for Special Functional Materials,henan university,kaifeng 475004,china 2 College of Chemistry and Chemical Engineering,henan university,kaifeng 475004,china Key Laboratory for Special Functional Materials Henan University Kaifeng 475004 China College of Chemistry and Chemical Engineering Henan University Kaifeng 475004 China

The influence of NH3-treating temperature on the visible light photocatalytic activity of N-doped P25-TiO2 as well as the relationship between the surface composition structure of TiO2 and its visible light photocatalytic activity were *** results showed that N-doped P25-TiO2 treated at 600℃ had the highest *** structure of P25-TiO2 was converted from anatase to rutile at 700℃.Moreover,no N-doping was detected at the surface of *** was no simply linear relationship between the visible light photocatalytic activity and the concentration of doped nitrogen,and visible light *** visible light photocatalytic activity of N-doped P25-TiO2 was mainly influenced by the synergistic action of the following factors:(i) the formation of the single-electron-trapped oxygen vacancies(denoted as Vo);(ii) the doped nitrogen on the surface of TiO2;(iii) the anatase TiO2 structure.

关键词： P25-TiO2 nitrogen doping NH3 treatment photocatalysis visible light photocatalytic activity

Existence of inner functions on classical domain

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Chinese Science Bulletin 1997年第1期42卷 84-85页

作者： LIU Taishun and ZHANG Wenjun1 department of mathematics, university of Science and Technology of china, Hefei 230026, china 2. department of mathematics henan university, kaifeng 475001, china

IN function of one complex variable, the inner function on the unit disc plays an important role in the theory of H^p functions. In the mid-1960s, W. Rudin and A. Vitushkin independently raised the question of whether there exist nonconstant inner functions on the unit ball B_n. Then quickly amassed considerable evidence indicated that such functions would be so pathological that they could not exist. Lately Rudin posed the conjecture on the nonexistence

关键词： In Existence of inner functions on classical domain

A conjecture on k-factor-critical and 3-γ-critical graphs

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Science china mathematics 2010年第5期53卷 348-354页

作者： WANG Tao1&YU QingLin2 1Institute of Applied mathematics,College of mathematics and Information Science,henan university,kaifeng 475001,china 2department of mathematics and Statistics,Thompson Rivers university,Kamloops,BC V2C5N3,Canada 1. Institute of Applied mathematics College of Mathematics and Information Science Henan University Kaifeng 475001 China2. Department of Mathematics and Statistics Thompson Rivers University Kamloops BC V2C5N3 Canada

For a graph G =(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in *** domination number γ(G) of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,if γ(G-v) 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is *** this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph.

关键词： domination critical graph factor critical bicritical

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2, WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics, Nanjing university, Nanjing 210093, china 2. department of mathematics, henan university, kaifeng 475001, china 3. department of Applied mathematics, Southeast university, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

Peak structure in the interlayer conductance of Moirésuperlattices

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Chinese Physics B 2024年第10期33卷 376-380页

作者： Yizhou Tao Chao Liu Mingwen Xiao henan Fang College of Electronic and Optical Engineering&College of Flexible Electronics(Future Technology) Nanjing University of Posts and TelecommunicationsNanjing 210023China department of Physics Nanjing UniversityNanjing 210093China

We investigate the peak structure in the interlayer conductance of Moirésuperlattices using a tunneling theory wedeveloped *** theoretical results predict that,due to the resonance of two different partial waves,the doublepeakstructure can appear in the curve of the interlayer conductance versus twist ***,we study the influencesof the model parameters,i.e.,the chemical potential of electrodes,the thickness of Moirésuperlattice,and the strength ofinterface potential,on the peak structure of the interlayer *** particular,the parameter dependence of the peakstructure is concluded via a phase diagram,and the physical meanings of the phase diagram is ***,thepotential applications of the present work is discussed.

关键词： Moirésuperlattice interlayer conductance electronic transport twistronics

ω-Gorenstein injective modules and dimensions

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Science china mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2 & DING NanQing3 1department of mathematics, Zhejiang university, Zhejiang 310027, china 2department of mathematics, Zhejiang university of Technology, Zhejiang 310023, china 3department of mathematics, Nanjing university, Nanjing 210093, china 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module