关于nZ的理想及商环

给出了nZ的全部理想、极大理想和素理想,并研究了nZ的商环的构造以及为域的条件,解决了Z<,n>的子域的存在和个数问题.     

Confined modified realizability

We present a refinement ofthe bounded modified realizability which provides both upper and lower bounds for witnesses. Our interpretation is based on a generalisation of Howard/Bezem's notion of strong majorizability. We show how the bounded modified realizability coincides with (a weak version of) our interpretation in the case when least elements exist (e.g. natural numbers). The new interpretation, however, permits the extraction of more accurate bounds, and provides an ideal setting for dealing directly with data types whose natural ordering is not well‐founded (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Decomposition Method with a Variable Parameter for a Class of Monotone Variational Inequality Problems

In this paper, we focus on a useful modification of the decomposition method by He et al. (Ref. 1). Experience on applications has shown that the number of iterations of the original method depends significantly on the penalty parameter. The main contribution of our method is that we allow the penalty parameter to vary automatically according to some self-adaptive rules. As our numerical simulations indicate, the modified method is more flexible and efficient in practice. A detailed convergence analysis of our method is also included.     

A control problem governed by a second-order differential inclusion

This article studies some Bolza-type problems governed by second-order differential inclusions with two boundary conditions, where the controls are Young measures.     

Regularization inertial proximal point algorithm for common solutions of a finite family of inverse-strongly monotone equations

The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.     

A Hybrid Approximate Extragradient – Proximal Point Algorithm Using the Enlargement of a Maximal Monotone Operator

We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, an approximate extragradient-type step is performed using information obtained from an approximate solution of a proximal point subproblem. The algorithm is of a hybrid type, as it combines steps of the extragradient and proximal methods. Furthermore, the algorithm uses elements in the enlargement (proposed by Burachik, Iusem and Svaiter) of the operator defining the problem. One of the important features of our approach is that it allows significant relaxation of tolerance requirements imposed on the solution of proximal point subproblems. This yields a more practical proximal-algorithm-based framework. Weak global convergence and local linear rate of convergence are established under suitable assumptions. It is further demonstrated that the modified forward-backward splitting algorithm of Tseng falls within the presented general framework.     

Runge–Kutta Methods for Monotone Differential and Delay Equations

Classes of Runge–Kutta methods preserving the monotonicity of ordinary and delay differential equations are identified. Essentially, the vector b and the matrix A from the Butcher tableau should be such that all components of b are positive and all components of the matrix B(r)A, where B(r) is the inverse of the matrix I+rA, are nonnegative for sufficiently small positive r. The latter is satisfied by all explicit, diagonally-implicit and fully implicit Runge–Kutta methods for which all of the components of the matrix A, except those that are zero by definition, are positive.     

Banach代数L∞(T;X)

讨论向量值函数的Banach代数L∞（T；X）的极大理想空间的拓扑性质和代数性质，得到了若干结果；给出了Banach空间H∞（D；X）中闭单位球的端点的一条性质．     

Applying simulated annealing to location-planning models

Simulated annealing is a computational approach that simulates an annealing schedule used in producing glass and metals. Originally developed by Metropolis et al. in 1953, it has since been applied to a number of integer programming problems, including the p-median location-allocation problem. However, previously reported results by Golden and Skiscim in 1986 were less than encouraging. This article addresses the design of a simulated-annealing approach for the p-median and maximal covering location problems. This design has produced very good solutions in modest amounts of computer time. Comparisons with an interchange heuristic demonstrate that simulated annealing has potential as a solution technique for solving location-planning problems and further research should be encouraged.     

k＜1时Cartan-Hartogs域上的极值问题

本文讨论两种类型的极值问题,其中一种类型的极值问题可以认为是复平面上经典的Schwarz引理在高维的一个推广;另一种类型的极值是某空间上的度量,可以用来考虑域的双全纯等价分类问题．在本文中,k＜1时Cartan-Hartogs域与单位超球间的极值与极值映照被得到。