A stackelberg model for Server-Proxies-Users systems

A Server-Proxies-Users communication system is studied by using Stackelberg strategy theory of game. A new model, in which the server, proxies and users are not equal is established, and that is a threelevel programming. The solution existence of the model is proved.     

Fuzzy metric spaces

In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research on fuzzy optimization and pattern recognition.     

A Class of Alternating Linearization Algorithms for Nonsmooth Convex Optimization

Acta Mathematicae Applicatae Sinica, English Series - We consider the problems of minimizing the sum of a continuously differentiable convex function and a nonsmooth convex function in this paper....     

广义随机KdV方程新的精确类孤子解

利用厄米(Hermite)变换求出了广义随机KdV方程新的类孤子解.这种方法的基本思想是通过厄米变换把Wick类型的广义随机KdV变成广义变系数KdV方程，利用特殊的截断展开方法求出 方程的解，然后通过厄米的逆变换求出方程的随机解. 关键词： 随机KdV方程 随机孤子解 白色噪音 截断展开方法 厄米变换     

A type of modified BFGS algorithm with any rank defects and the local Q-superlinear convergence properties

A modified BFGS algorithm for solving the unconstrained optimization, whose Hessian matrix at the minimum point of the convex function is of rank defects, is presented in this paper.The main idea of the algorithm is first to add a modified term to the convex function for obtain an equivalent model, then simply the model to get the modified BFGS algorithm. The superlinear convergence property of the algorithm is proved in this paper. To compared with the Tensor algorithms presented by R. B. Schnabel (seing [4],[5]), this method is more efficient for solving singular unconstrained optimization in computing amount and complication.     

Exact Solutions for (3+1)-Dimensional Wick-Type Stochastic KP Equation

In the paper, the (3+1)-dimensional Wick-type stochastic KP equation is considered. And the exact solutions for (3+1)-dimensional Wick-type stochastic KP equation are obtained via homogeneous balance principle and Hermite transformation.     

Intuitionistic fuzzy implication operators: Expressions and properties

The expressions of 32 fuzzy coimplication operators(FCO) and 32 intuitionistic fuzzy implication operators(IFIO) are given in this paper. The Co-D-P properties which the FCOs should satisfy are presented. The FCOs and IFIOs’situation of satisfying the properties which they should satisfy, respectively, are discussed in details.     

ABS algorithms for Diophantine linear equations and integer LP problems

The present article discusses the number of empty convex 4-gons and empty convex 5-gons in a finite planar point set. New proofs are provided for the two related important results.     

Single machine scheduling problems with controllable processing times and total absolute differences penalties

In this paper, we consider single machine scheduling problem in which job processing times are controllable variables with linear costs. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time, total absolute differences in completion times and total compression cost; minimizing a cost function containing total waiting time, total absolute differences in waiting times and total compression cost. The problem is modelled as an assignment problem, and thus can be solved with the well-known algorithms. For the case where all the jobs have a common difference between normal and crash processing time and an equal unit compression penalty, we present an O(n log n) algorithm to obtain the optimal solution.     

An ABS algorithm for solving singular nonlinear systems with rank one defect

A modified discretization ABS algorithm for solving a class of singular nonlinear systems, F(x) = 0, wherex, F ∈ Rⁿ, is presented, constructed by combining a discretization ABS algorithm and a method of Hoy and Schwetlick (1990). The second order differential operation ofF at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.