A SURFACTANT-ASSISTED APPROACH FOR PREPARING COLLOIDAL AZO POLYMER SPHERES WITH NARROW SIZE DISTRIBUTION

A surfactant-assisted method for preparing colloidal spheres with narrow size distribution from a polydispersed azo polymer has been developed in this work. The colloidal spheres were formed through gradual hydrophobic aggregation of the polymeric chains in THF-H2O dispersion media, which was induced by a steady increase in the water content. Results showed that the addition of a small amount of surfactant （SDBS） could significantly narrow the size distribution of the colloidal spheres. The size distribution of the colloidal spheres was determined by the concentrations of azo polymer and the amount of surfactant in the systems. When the concentrations of polymer and surfactant amount were in a proper range, colloidal spheres with narrow size distribution could be obtained. The colloidal spheres formed by this method could be elongated along the polarization direction of the laser beams to be a new type of the colloid-based functional materials. upon Ar^＋ laser irradiation. The colloidal spheres are considered     

On the stability of alternating‐direction explicit methods for advection‐diffusion equations

Alternating‐Direction Explicit (A.D.E.) finite‐difference methods make use of two approximations that are implemented for computations proceeding in alternating directions, e.g., from left to right and from right to left, with each approximation being explicit in its respective direction of computation. Stable A.D.E. schemes for solving the linear parabolic partial differential equations that model heat diffusion are well‐known, as are stable A.D.E. schemes for solving the first‐order equations of fluid advection. Several of these are combined here to derive A.D.E. schemes for solving time‐dependent advection‐diffusion equations, and their stability characteristics are discussed. In each case, it is found that it is the advection term that limits the stability of the scheme. The most stable of the combinations presented comprises an unconditionally stable approximation for computations carried out in the direction of advection of the system, from left to right in this case, and a conditionally stable approximation for computations proceeding in the opposite direction. To illustrate the application of the methods and verify the stability conditions, they are applied to some quasi‐linear one‐dimensional advection‐diffusion problems. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Comprehensive treatment of sphere-cap microelectrodes (SCMs) using digital simulations

The alternating direction implicit finite difference method (ADIFDM) is used to simulate the steady-state as well as the transient (chronoamperometric) behavior of sphere-cap microelectrodes (SCMs). The necessary steps to implement the ADIFDM for solving the rather complex geometry involved are described. The results for the steady-state behavior are in excellent agreement with a previously suggested analytical solution making the ADIFDM an excellent tool to develop a comprehensive theory for SCMs.     

亚纯函数的奇异方向

该文应用Ahlfors的覆盖曲面理论,讨论了复平面上超越亚纯函数的奇异 方向,证明了亚纯函数涉及一类有理函数的T方向的存在性,又一次证实了郑 建华的一个猜想.     

Geometric properties of the solutions of a Hele-Shaw type equation

This article deals with the application of the methods of geometric function theory to the investigation of the free boundary problem for the equation describing flows in an unbounded simply-connected plane domain. We prove the invariance of some geometric properties of a moving boundary.

     

A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems

In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems. Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O（△t2 ＋ h） and present some numerical examples at the end of the paper.     

Set Intersection Theorems and Existence of Optimal Solutions

The question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics, including the existence of optimal solutions, the validity of the minimax inequality in zero sum games, and the absence of a duality gap in constrained optimization. We consider asymptotic directions of a sequence of closed sets, and introduce associated notions of retractive, horizon, and critical directions, based on which we provide new conditions that guarantee the nonemptiness of the corresponding intersection. We show how these conditions can be used to obtain simple and unified proofs of some known results on existence of optimal solutions, and to derive some new results, including a new extension of the Frank–Wolfe Theorem for (nonconvex) quadratic programming.     

Asymptotic direction for random walks in random environments

In this paper we study the existence of an asymptotic direction for random walks in random i.i.d. environments (RWRE). We prove that if the set of directions where the walk is transient contains a non-empty open set, the walk admits an asymptotic direction. The main tool to obtain this result is the construction of a renewal structure with cones. We also prove that RWRE admits at most two opposite asymptotic directions.     

一种改进的基于小波方向对比度的无缝拼接算法

为了提高图像无缝拼接效果,对现有平滑算法进行分析,在此基础上提出一种基于小波方向对比度的中缝平滑算法。该算法首先对源图像进行基于统计参数的预处理,使得图像整体亮度趋于一致,然后利用小波变换对图像进行多分辨率分解,对于分解后的图像提出采用一种基于改进的小波方向对比度的规则进行平滑处理。文中还通过几种图像客观评价标准对仿真结果进行了评价,结果表明：该方法在两图像灰度相差较大时也能够取得较好的平滑效果,对光照具有鲁棒性,并且平滑后的图像可以保留原始图像的细节信息,使得图像在保证清晰度的前提下达到无缝拼接。     

具有弱正规结构的Orlicz空间

W.Kirk给出了弱正规结构（WNS）的概念,并证明了弱正规结构（WNS）蕴涵弱不动点性质,B.Sims给出了具有（k)性质的巴拿赫空间,并证明了（k)性质蕴函弱正规结构,陈述涛给出了伪－k(pseudo-(k))性质及弱各向一致凸（WURED）的概念,推广了B.Sims的结果,并讨论了Orlicz序列空间是弱各向一致凸的充要条件,本利用实变函数理论及赋范线性空间中有关知识,给出Orlicz函空间是弱各向一致凸的充分必要条件,所得以的结论和证明方法与序列空间情形都有实质不同。