The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

L-fuzzifying topology

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang’s fuzzy topology, is presented in the paper. Some basic properties are discussed.     

微分方程公式的机器推导(Ⅰ)

本文阐述了微分方程公式推导程序系统的算法,这个系统已经实现,并成功地用于极限环的研究工作.作为一个具体例子和验证,文中给出了右方为二次多项式方程的机器结果,并指出了Н.Н.Баутин所发表结果中的符号错误. 本文是微分方程公式推导研究成果的第一部分.     

Relation between Demyanov difference and Minkowski difference of convex compact subsets inR 2

A necessary and sufficient condition for Demyanov difference and Minkowski difference of compact convex subsets inR ² being equal is given in this paper. Several examples are computed by Matlab to test our result. The necessary and sufficient condition makes us to compute Clarke subdifferential by quasidifferential for a special of Lipschitz functions.     

Exact solutions to generalized Wick-type stochastic Kadomtsev–Petviashvili equation

An auto-Bäcklund transformation (BT) to generalized Wick-type stochastic Kadomtsev–Petviashvili equation (GWSKPE) is obtained by using extended homogeneous balance method. Making use of the auto-BT and Hermite transformation, we obtain many families of exact solutions of the GWSKPE by choosing a special seed solution, which include single soliton-like solutions, multi-soliton-like solutions and special-soliton-like solutions.     

An ABS algorithm for a class of systems of stochastic linear equations

This paper is to explore a model of the ABS algorithms dealing with the solution of a class of systems of linear stochastic equations Aξ=η when η is a m-dimensional normal distribution. It is shown that the stepsize α _i is distributed as N(u _i ,σ _i ) (being u _i the expected value of α _i and σ _i its variance) and the approximation to the solutions ξ _i is distributed as N _n (U _i ,Σ _i ) (being U _i the expected value of ξ _i and Σ _i its variance), for this algorithm model.     

A superlinear space decomposition algorithm for constrained nonsmooth convex program

A class of constrained nonsmooth convex optimization problems, that is, piecewise C² convex objectives with smooth convex inequality constraints are transformed into unconstrained nonsmooth convex programs with the help of exact penalty function. The objective functions of these unconstrained programs are particular cases of functions with primal-dual gradient structure which has connection with VU space decomposition. Then a VU space decomposition method for solving this unconstrained program is presented. This method is proved to converge with local superlinear rate under certain assumptions. An illustrative example is given to show how this method works.     

Symmetry reductions and soliton-like solutions for stochastic MKdV equation

In this paper, the Wick-type stochastic MKdV equation is researched by using symmetry reduction. And some stochastic soliton-like solutions are given via Hermite transformation.     

Stochastic exact solutions to (2 + 1)-dimensional stochastic Borer–Kaup equation

(2 + 1)-dimensional Wick-type stochastic Borer–Kaup equations are researched by homogeneous balance method and tanh-function method. And some stochastic exact solutions of (2 + 1)-dimensional Wick-type stochastic Borer–Kaup equations are obtained via Hermite transformation.