The first initial boundary value problem for a compound type equation in a three-dimensional multiply connected region

The method of boundary integral equations is used for solving the first initial boundary value problem for a compound type equation in a three-dimensional multiply connected region. The problem is reduced to a uniquely solvable integral equation. The solution of the problem is obtained in the form of dynamic potentials whose density satisfies this integral equation. Thus the existence theorem is proved. Moreover, the uniqueness of the solution is also studied. All the results are valid for both interior and exterior regions provided that the corresponding conditions at infinity are taken into account. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 249–265, August, 2000.     

A new process for constructing coefficients of elliptic complex equations in multiply connected domains

This article concerns the inverse problem for linear elliptic systems of first-order equations with Riemann–Hilbert-type map in multiply connected domains. First the formulation and the complex form of the problem for the systems are given, and then the coefficients of the elliptic complex equations for the above problem are constructed by a complex analytic method, where the advantage of the methods in other papers is absorbed, and the used method in this article is more simple and the obtained result is more general. As an application of the above results, we can derive the corresponding results of the inverse problem for second-order elliptic equations from Dirichlet to Neumann map in multiply connected domains.     

On the existence of multiply connected monolayered cyclofusenes with given parameters

For a given bipartite graph G its skewness is defined as the difference between the sizes of its classes of bipartition. We show that a multiply connected monolayered cyclofusene with m ≥ 2 internal holes and skewness k exists if and only if 0 ≤ k ≤ 2m − 2, thus settling in affirmative two conjectures raised in a recent paper by Karimi et al.     

INITIAL-OBLIQUE DERIVATIVE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS

This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved.     

苯胺衍生物式电位的QSAR研究

以AM1量子化学半经验分子轨道方法计算22个苯胺衍生物的分子结构参数,用多元线性回归的方法研究了13个式电位已知的苯胺衍生物的氧化式电位与其分子结构参数之间的关系.苯胺衍生物式电位与离子化电势(Ip),N原子上的净电荷(e(N),总的偶极矩(μt)和第四个碳上的净电荷(e(C4))有很好的相关性,回归方程为:E0′=-7.820 5 0.884 9(Ip-3.739(e(N)-0.093 56μt 0.925 1(e(C4)),(R=0.979,SD为0.023 6).依据回归方程合理地预测了其余9个苯胺衍生物的离子化电势和式电位,探讨了取代基性质和取代位置对离子化电势和式电位的影响.     

电离效率对激光电离团簇的高价离子产物的影响

纳秒激光与团簇相互作用产生高价离子逐渐成为分子物理界的热点之一, 为了深入研究团簇电离的本质, 本文以分子结构相似、元素组成相同的苯、环己烯和环己烷的分子团簇为对象, 利用飞行时间质谱研究了其与5 ns的532 nm激光相互作用时电离产物的价态和强度分布. 结果表明: 这三种化合物多光子电离效率苯>环己烯>环己烷, 但其高价离子的价态和比值苯是最低的, 环己烷的碳离子最高价态为4价, C³⁺和C²⁺的比值为1.1; 环己烯电离产物C³⁺和C²⁺ 的比值降低为0.6; 苯团簇的最高价态只有3价, C³⁺和C²⁺的比值约为0.4. 引起这种现象的原因可以归结于高的多光子电离效率会导致团簇多位点的电离, 引起团簇在电子加热到发生碰撞电离之前发生解离, 减小了团簇的尺寸, 进而减少了离子发生碰撞电离产生高价离子的反应时间, 最终阻碍了高价态离子的产生.     

A (T,ψ)‐ψe decoupled scheme for a time‐dependent multiply‐connected eddy current problem

The aim of this paper is to develop a fully discrete ( T ,ψ)‐ψ_e finite element decoupled scheme to solve time‐dependent eddy current problems with multiply‐connected conductors. By making ‘cuts’ and setting jumps of ψ_e across the cuts in nonconductive domain, the uniqueness of ψ_e is guaranteed. Distinguished from the traditional T ‐ ψ method, our decoupled scheme solves the potentials T and ψ‐ ψ_e separately in two different simple equation systems, which avoids solving a saddle‐point equation system and leads to a remarkable reduction in computational efforts. The energy‐norm error estimate of the fully discrete decoupled scheme is provided. Finally, the scheme is applied to solve two benchmark problems—TEAM Workshop Problems 7 and IEEJ model. Copyright © 2013 John Wiley & Sons, Ltd.