Second order three boundary value problem in Banach spaces via Henstock and Henstock-Kurzweil-Pettis integral

Existence theorems and some properties of solutions set of three boundary value second order differential equations and inclusions in Banach spaces are obtained under Henstock, respectively Henstock-Kurzweil-Pettis integrability assumptions. Our results extend those obtained by Azzam, Castaing and Thibault in the Bochner integrability setting and in the Pettis integrability one. The continuity of the (unique) solution with respect to a parameter in the single-valued case is also studied.     

Separating points of measures on effect algebras

We prove the existence of separating points for every countable family of nonatomic σ-additive modular measures on a σ-complete lattice ordered effect algebra.      

Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack

The paper addresses the problem of a semi-infinite plane crack along the interface between two isotropic half-spaces. Two methods of solution have been considered in the past: Lazarus and Leblond [1998a. Three-dimensional crack-face weight functions for the semi-infinite interface crack-I: variation of the stress intensity factors due to some small perturbation of the crack front. J. Mech. Phys. Solids 46, 489-511, 1998b. Three-dimensional crack-face weight functions for the semi-infinite interface crack-II: integrodifferential equations on the weight functions and resolution J. Mech. Phys. Solids 46, 513-536] applied the “special” method by Bueckner [1987. Weight functions and fundamental fields for the penny-shaped and the half-plane crack in three space. Int. J. Solids Struct. 23, 57-93] and found the expression of the variation of the stress intensity factors for a wavy crack without solving the complete elasticity problem; their solution is expressed in terms of the physical variables, and it involves five constants whose analytical representation was unknown; on the other hand, the “general” solution to the problem has been recently addressed by Bercial-Velez et al. [2005. High-order asymptotics and perturbation problems for 3D interfacial cracks. J. Mech. Phys. Solids 53, 1128-1162], using a Wiener-Hopf analysis and singular asymptotics near the crack front.The main goal of the present paper is to complete the solution to the problem by providing the connection between the two methods. This is done by constructing an integral representation for Lazarus-Leblond's weight functions and by deriving the closed form representations of Lazarus-Leblond's constants.     

PuN基态分子势能函数与热力学函数的理论计算

在Pu的相对论有效原子实势近似和N原子 6 - 311G 全电子基函数下 ,用密度泛函B3LYP方法计算得到PuN分子基态X6Σ+ 的结构与势能函数、力常数与光谱数据 .同时计算得到PuN(g)分子在 2 98K时的标准生成热力学函数ΔfH0 、ΔS0 和ΔfG0 ,分别为 - 4 87.2 39kJ/mol、95 .345J/molK和 - 5 15 .6 6 6 1kJ/mol.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

Ultrathin Fe film on Cu(0 0 1): Exchange splitting of image states from first principles

The theoretical investigation of the image states in front of an ultrathin iron film grown on copper has been performed by means of the embedding method and a recently developed procedure for the inclusion of the image potential tail in a first principle calculation. From the electronic response to an applied electric field, the image plane position has been evaluated. This also allows one to obtain useful information about the spin dependent screening properties of the system. Exchange splitting, effective mass, and lifetime of such surface states result in good agreement with recently performed two-photon photoemission experiments [see A.B. Schmidt, M. Pickel, M. Wiemhöfer, M. Donath, M. Weinelt, Phys. Rev. Lett. 95 (2005) 107402].     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

Stone代数的Cayley表示定理

首先通过集代数得到了Stone代数的表示定理,然后证明了每一个Stone代数均嵌入到某个集合X上的一个Stone映射类S中.     

环上半线性椭圆型方程正解的存在性和唯一性

本文讨论了半线性椭圆方程△u+f(u)=0在三种边界条件下正解的存在性和唯一性,给出了正解存在和唯一的一些条件.