FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation

This paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wave solutions are also obtained.     

θ*r,s,t-图与唯一2-列表染色图的特征化

如果一个图G存在一个k-列表安排使得G具有一个唯一列表染色,则称 G是唯一列表可染色图,简称UkLC图．我们称图G具有M(k)性质当且仅当G不 是UkLC图．本文在借鉴θr,s,t-图概念的基础上引入θr,s,t-图的定义,并证明:除了 r=s=t=2以外,θr,s,t-图都是U2LC图．利用如上结果我们给出M．Mahdian and E．S．Mahmoodian对U2LC图所作特征化的一个简单证明．     

热电物理的研究进展

热电效应在发电，致冷方面有巨大的应用潜力，这些年来，人们为提高热电能量转换效率进行了不懈的努力，文章概述了从机理上提高材料热性能的一般途径，在此基础上，介绍了最近几年在氧化物超导体，ＴＰｎ３化合物，富硼固体等新材料体系中，以及在非均匀材料，复合型材料，量子阱结构等新形式材料中的研究结果。     

Atom transfer radical polymerization directly from poly(vinylidene fluoride): Surface and antifouling properties

The direct preparation of grafting polymer brushes from commercial poly (vinylidene fluoride) (PVDF) films with surface‐initiated atom transfer radical polymerization (ATRP) is demonstrated. The direct initiation of the secondary fluorinated site of PVDF facilitated grafting of the hydrophilic monomers from the PVDF surface. Homopolymer brushes of 2‐(N,N‐dimethylamino)ethyl methacrylate (DMAEMA) and poly (ethylene glycol) monomethacrylate (PEGMA) were prepared by ATRP from the PVDF surface. The chemical composition and surface topography of the graft‐functionalized PVDF surfaces were characterized by X‐ray photoelectron spectroscopy, attenuated total reflectance/Fourier transform infrared spectroscopy, and atomic force microscopy. A kinetic study revealed a linear increase in the graft concentration of poly[2‐(N,N‐dimethylamino)ethyl methacrylate] (PDMAEMA) and poly[poly(ethylene glycol) monomethacrylate] (PPEGMA) with the reaction time, indicating that the chain growth from the surface was consistent with a controlled or living process. The living chain ends were used as macroinitiators for the synthesis of diblock copolymer brushes. The water contact angles on PVDF films were reduced by the surface grafting of DMAEMA and PEGMA. Protein adsorption experiments revealed a substantial antifouling property of PPEGMA‐grafted PVDF films and PDMAEMA‐grafted PVDF films in comparison with the pristine PVDF surface. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3434–3443, 2006     

Effect of glass bead packing on the fibrillation of liquid‐crystalline polymer in polycarbonate

Polycarbonate (PC) was melt blended with small amount of liquid‐crystalline polymer (LCP) and various contents of glass beads (GB) having different diameters. The rheological measurements indicated that the GB addition increased the viscosity ratio and seemed unfavorable to the LCP fibrillation. However, the morphological observation showed that the LCP fibrillation was promoted by the GB addition and varied with the GB packing. With the increased GB packing by increasing the GB content and/or decreasing the GB diameter, LCP deformed from spheres and ellipsoids into stretched ellipsoids at lower shear rates and into long fibrils at higher shear rates. Although higher content of smaller GB jammed into the larger LCP droplets and inhibited the LCP fibrillation, very long LCP fibrils formed at higher shear rates at a high enough packing of GB. The relationship between GB packing and LCP fibrillation revealed two kinds of hydrodynamic effects of GB promoting the LCP fibrillation: at lower GB packing, the shear flow was enhanced by the high local shear between GB, in quantity; and for a high enough GB packing, the shear flow was changed, in quality, into elongational flow, which was more effective for the LCP fibrillation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1020–1030, 2006     

Model and empirical study on some collaboration networks

In this paper we present an empirical study of a few practical systems described by cooperation networks, and propose a model to understand the results obtained. We study four non-social systems, which are the Bus Route Networks of Beijing and Yangzhou, the Travel Route Network of China, Huai-Yang recipes of Chinese cooked food, and a social system, which is the Collaboration Network of Hollywood Actors. In order to explain the results related to the degree distribution, act-degree distribution and act-size distribution (especially about the degree distribution, which may be better fitted using a stretched exponential distribution (SED)), we suggest a simple model to show a possible evolutionary mechanism for the emergence of such networks. The analytic and numerical results obtained from the model are in good agreement with the empirical results.     

经济增长与宏观经济运行模型

对国民经济进行宏观调控，如同经济增长问题一样是一个永恒问题，对宏观调控的基本内容，手段，方法，国内外学者已进行了较多的规范性讨论，尤其是在数理分析方面，也已有许多具有普遍意义的成果，但是，要把那些成果转化为“生产力”从而变成清晰的，简明的，可操作的手段和方法，尚需人们不断的探索，本文通过对国民经济运行过程中若干宏观经济变量之间的数量关系分析，并以此建立了的国民经济宏观数量模型，就是尝试性的探索。