ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.     

A characterization of projective-planar signed graphs

A signed graph has a plus or minus sign on each edge. A simple cycle is positive or negative depending on whether it contains an even or odd number of negative edges, respectively. We consider embeddings of a signed graph in the projective plane for which a simple cycle is essential if and only if it is negative. We characterize those signed graphs that have such a projective-planar embedding. Our characterization is in terms of a related signed graph formed by considering the theta subgraphs in the given graph.     

广义C-R组的性质及两个边值问题

本文考虑广义C-R组^[1](H)的解f=u iv jw∈C^2的一些性质，提出与之相关的两个边值问题，用积分方程方法和调和函数性质证明了边值问题解的存在唯一性，并写出解的积分表达式．     

Computing Zeta Functions of Kummer Curves via Multiplicative Characters

We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such algorithms have recently been obtained using a method of Kedlaya based upon Monsky–Washnitzer cohomology, and are of interest in cryptography. We take a different approach. The problem is reduced to that of computing the L-function of a multiplicative character sum. This latter task is achieved via a cohomological formula based upon the work of Dwork and Reich. We show, however, that our method and that of Kedlaya are very closely related.Dedicated to the memory of Gian-Carlo Rota     

Integrability of subdifferentials of directionally Lipschitz functions

Using a quantitative version of the subdifferential characterization of directionally Lipschitz functions, we study the integrability of subdifferentials of such functions over arbitrary Banach space.

     

A subdomain boundary element method for high‐Reynolds laminar flow using stream function‐vorticity formulation

The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux’) is introduced for solving the general form of a parabolic diffusion‐convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward‐facing step flow and a square‐driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd.     

Tetrafunctional initiators for cationic polymerization of olefins

3,3′,5,5′‐Tetrakis(2‐chloro‐2‐propyl)biphenyl (biphenyl tetracumyl chloride, BPTCC) and 1,3‐bis[3,5‐bis(2‐chloro‐2‐propyl)phenoxy]propane (diphenoxypropane tetracumyl chloride, DPPTCC) were synthesized as initiators for quasiliving cationic polymerization of isobutylene (IB). In the synthesis of BPTCC, tetrafunctionality was achieved via the coupling of dimethyl 5‐bromoisophthalate (DMBI) using nickel dibromide bis(triphenylphosphine) and zinc in the presence of a base; in the synthesis of DPPTCC, two equivalents of dimethyl 5‐hydroxyisophthalate were linked via reaction with 1,3‐dibromopropane in the presence of potassium carbonate. Both initiators were used to initiate the polymerization of IB under quasiliving cationic polymerization conditions. PIB initiated from BPTCC revealed a chain end/molecule value (as determined by ¹H‐NMR) of 3.85, verifying the nearly exclusive production of 4‐arm polyisobutylene (PIB). GPC analysis revealed a narrow peak representing the target four‐arm PIB, with a slight shoulder at high elution volumes (low molecular weights). GPC analysis of the PIB initiated by DPPTCC revealed multimodal distributions, suggesting the formation of two‐, three‐, and four‐arm star polymers during the polymerization. This behavior was attributed to Friedel–Crafts alkylation of the initiator core after the addition of one IB unit, which was activated by the electron‐donating oxytrimethyleneoxy linking moiety. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5942–5953, 2004     

Ionic conductivity of multiarm star polymer/LiClO4 electrolytes

A series of polymer electrolytes based on multiarm polymers and lithium salt complexes were characterized by Fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), and impedance measurement. The relationships of conductivity with salt concentration, temperature, and arm numbers are discussed. It is suggested that the star polymer has a higher solvency and ion transfer ability on lithium salts than on linear polymers. The conductivity maximum appeared at a higher salt concentration ([EO]/[Li] = 4). Impedance measurement suggested that the optimum conductivity was 2 × 10^?4 s · cm^?1. The conductivity increased with temperature and the dependence of ionic conductivity on temperature fits the Arrhenius equation. Among the studied systems, the star polymer with a five arm number performs better than other structures. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4195–4198, 2004     

用格林函数法计算量子点中的应变分布

自组装量子点材料作为一种新型的光电材料无论在理论和实际应用都成为当今物理学界的研 究热点.由GaAs包围的InAs小岛，由于较大的晶格失配（≈-0.067），应变效应在量子点 的 形成过程中起主导作用.大部分计算量子点结构应变分布的方法都是基于数值解法，需要大 量的计算工作.给出用格林函数法推导各种常见形状量子点应变分布的解析表达式详细过程，讨论了弹性各向异性和形状各向异性对量子点应变分布的影响程度.结果表明对于不 同形状量子点结构中主要部分的应变分布都是相似的，流体静压变部分的特征值随量子点形状的变化不 关键词： 自组装量子点 格林函数 应变分布