CM分担三个公共值的亚纯函数的进一步结果

进一步研究了具有三个cM公共值的亚纯函数的唯一性，改进了H．Ueda和仪洪勋等人的有关结果．     

一个耦合系统自由边界问题的整体古典解

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Duffing-van der Pol振子随机分岔的全局分析

应用广义胞映射方法研究了参激和外激共同作用的Duffing-van der Pol振子的随机分岔.以 系统参数通过某一临界值时，如果系统的随机吸引子或随机鞍的形态发生突然变化，则认为 系统发生随机分岔为定义，分析了参激强度和外激强度的变化对于随机分岔的影响.揭示了 随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的.分析表明，广义 胞映射方法是分析随机分岔的有力工具，这种全局分析方法可以清晰地给出随机分岔的发生 和发展. 关键词： 随机分岔 全局分析 广义胞映射方法 随机吸引子 随机鞍     

共轭下降法的全局收敛性

本文提出了一种Armijo型的线搜索，并在这种线搜索下讨论了共轭下降法的全局收敛性，且可得方法在每次迭代均产生一个下降搜索方向．     

Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon

Recently, the authors have proposed a new necessary and sufficient condition for turnpike optimality in calculus of variations with singular Euler equation. The method is based on a characterization of the value function and generalizes the well known method based on the Green theorem. Furthermore, it allows the optimality of a competition between several turnpikes to be characterized. For a class of such problems not enjoying the turnpike property, we give an explicit formula for the value function and show how to characterize the optimal solution as the limiting solution of a family of perturbed problems satisfying the turnpike property. The considered problems are scalar with infinite horizon.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

Solving a class of multiplicative programming problems via c-programming

In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques.     

New solitons and kink solutions for the Gardner equation

The Gardner equation, also called combined KdV–mKdV equation, is studied. New hyperbolic ansatze are proposed to derive solitons solutions. The tanh method is used as well to obtain kink solutions.     

The concentration effect on the ‘hydrophobic’ and ‘hydrophilic’ behaviour around DMSO in dilute aqueous DMSO solutions. A computer simulation study

We have carried out a molecular dynamics study of dimethyl sulfoxide (DMSO) in water at 298 K at two different densities by simulating two different concentrations: 0.055 and 0.19 mole fraction. We have found an enhancement in the structure of water, an effect that becomes more pronounced as the concentration of DMSO increases. At both concentrations there is a well-defined hydration structure around the oxygen atom of DMSO, which is able to establish strong hydrogen bonds with surrounding water molecules. An increase in the concentration of DMSO depletes the solution of bulk water molecules, reducing the number of hydrogen bonds that water can have in the immediate vicinity of DMSO but increasing the strength of the hydrogen bonds made between the oxygen atom of DMSO and water. There is clear evidence of ‘hydrophobic’ hydration around the methyl groups of DMSO, which is enhanced as the concentration of DMSO increases.