在曲面上图嵌入的唯一性

在本文中，证明了图嵌入在一个已知曲面上的唯一性充分条件，这个条件比「４」中要弱些。     

与直径和围长有关的最大亏格的下界的一个注记

改正了文章"与直径和围长有关的最大亏格的下界(数学学报2004,47(6):1201-1204)"中的一个错误结论,并得到了如下结果:设G是直径为d(G)的简单图,若G的围长g(G)■d(G),则ξ(G)■2,从而γM(G)■(1/2)β(G)-1.     

On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus

In the present paper, the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given. In the meantime, the solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov’s positive annulus in ?³.     

PATHS AND CYCLES EMBEDDING ON FAULTY ENHANCED HYPERCUBE NETWORKS

Let Qn,k(n≥3,1≤k≤n-1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges,fv and fe be the numbers of faulty vertices and faulty edges,respectively.In this paper,we give three main results.First,a fault-free path P [u,v] of length at least 2n-2fv-1(respectively,2n-2fv-2) can be embedded on Qn,k with fv+fe≤n-1 when d Qn,k(u,v) is odd(respectively,d Qn,k(u,v) is even).Secondly,an Qn,k is(n-2) edgefault-free hyper Hamiltonian-laceable when n(≥3) and k have the same parity.Lastly,a fault-free cycle of length at least 2n-2fv can be embedded on Qn,k with fe≤n-1 and fv+fe≤2n-4.     

融合空间扩散与等级结构的种群系统的最优收获控制

分析一类基于个体等级差异和空间扩散的种群模型的最优收获控制问题,系统演化模型由二阶偏微分积分方程表征.运用Aubin引理和极值化序列方法建立了最优解的存在性,借助法锥理论和共轭系统技巧给出了最优控制器的特征刻画.所获成果为实际应用奠定基础.     

InSb的锂嵌入形成能第一原理计算

InSb材料在近来的锂离子电池负极材料研究中受到了重视.使用基于局域密度泛函理论的第一原理赝势法，计算了锂离子电池非碳类负极材料InSb各种锂嵌入情况时的形成能以及相应的电子结构.讨论了锂嵌入时的体积变化、能带结构、电子态密度以及电荷分布等性质.计算发现，闪锌矿结构的InSb材料，锂嵌入到主体材料的间隙位置时的形成能平均每个锂原子都在2.2eV左右. 关键词： InSb 锂嵌入形成能 电子结构 第一原理计算     

Molecular-Dynamics Simulations of Droplets on a Solid Surface

By using a semi-empirical Lennard-Jones embedded-atom-method potential, we study the influence of many-body forces and atomic size mismatch on the wetting behavior of nano droplets on a solid surface. With molecular dynamics simulations, we find that the contact angle decreases with increasing many-body forces. The increase of atomic size mismatch between solid and liquid results in the decrease of contact angles. Our calculation also shows that the interface structure is strongly affected by the interaction between liquid and solid as well as the atomic size mismatch. For weak solid-liquid interaction, the interface layer of the droplet nearest to the solid exhibits a typical simple liquid structure regardless of the size mismatch. For strong solid-liquid interaction, evident ordering in the interface layer is observed for well matched cases.     

与顶点A-划分有关的上可嵌入图类

图G的顶点A-划分是指:G的顶点集划分{V1,V2,···,Vs},其中G[Vi](1≤i≤s)为多重完全图或多重完全二部图.文中结合图的顶点A-划分,顶点度及边连通性等条件确定了一些新的上可嵌入图类,从而将已有类似结果进行了推广,且完整地刻画了这类图的上可嵌入性情况.     

多重圈梯图在射影平面上的嵌入个数

图在不同亏格曲面上的嵌入个数常常有相关关系,因此,分析一些图类在小亏格曲面上的嵌入个数对最终确定图的亏格分布和完全亏格分布有着重要意义,本文利用嵌入的联树模型得出了多重圈梯图在射影平面上的嵌入个数.     

The MAEAM Model and Anharmonic Theory for the Bulk Modulus of A1 Metal

The modified analytic embedded atom method （MAEAM） model and the anharmonic theory are used to study the bulk modulus of fcc A1 metal. The result shows that the bulk modulus can be described by a quadratic function of temperature. The result is in good agreement with the experimental data and theoretical results calculated by the first principle calculation etc. This outcome indicates that the temperature dependence of the bulk modulus for f cc A1 metal can be academically studied with the MAEAM model combining with the anharmonic theory.