关于(S)_+型映射的一个区域不变定理及其应用

本文运用拓扑度方法,获得一个关于(S)_+型映射的区域不变定理。作为它的应用,本文得到了扩张映射的满值性,从而部分地回答了著名数学家L.Nirenberg提出的一个关于扩张映射满值性的公开问题。     

二阶非线性常微分方程组边值问题的正解

研究一类二阶常微分方程组两点边值问题,利用Krasnoselskii’s不动点定理,得到当f和g满足超线性或次线性时边值问题一个正解存在的充分条件.     

Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r,s)‐out‐of‐(m,n):F system

A 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system consists of m × n components, and fails if and only if k or more components fail in an r × s submatrix. This system can be treated as a reliability model for TFT liquid crystal displays, wireless communication networks, etc. Although an effective method has been developed for evaluating the exact system reliability of small or medium‐sized systems, that method needs extremely high computing time and memory capacity when applied to larger systems. Therefore, developing upper and lower bounds and accurate approximations for system reliability is useful for large systems. In this paper, first, we propose new upper and lower bounds for the reliability of a 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system. Secondly, we propose two limit theorems for that system. With these theorems we can obtain accurate approximations for system reliabilities when the system is large and component reliabilities are close to one. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

稳定正规环分解定理

提出了稳定正规环的概念；推广了正规环的分解定理；给出了正则局部环整性的一个简单证明；指出了研究正则环的一条新途径。     

三维静磁场Lipschitz区域上Robin问题广义解的存在与唯一性

近年来,电磁场边值问题的数值解法取得了飞速的发展．由于电磁场边值问题是一类非线性偏微分方程,研究解的存在性、唯一性具有较大的困难．前人已讨论了B-H间的几个基本不等式,并由之证明了三雏静磁场带零边值问题广义解的存在与唯一性,作者也曾利用给出的B-H间的不等式证明了三维静磁场Neumann问题和二维时变场第一边值初值问题广义解的存在与唯一性．由于在一般区域讨论存在困难,作者利用Sobolev空间理论及单调算子理论证明了三雏静磁场Lipschitz区域上Robin问题广义解的存在与唯一性．     

导函数性质及其应用

处处有导数的函数（导函数）有两个很好的性质：（1）在一点处有极限,则该点必连续,若无极限则该点两侧或单侧必振荡;（2）可能有不连续点的导函数介值定理仍成立。如果函数某点的领域内处处可导,我们可得到如下三个推论：（1）当f^l（x0＋0）=f^l（x0-0）时,则存在且连续。（2）当f^l（x0＋0）≠f^l（x0-0）,或至少有一个单侧极限为无穷时,函数在该点不可导,（3）当f^l（x0＋0）和f^l（f0-0）中一个或同时振荡时,函数在该点可能可导。     

有关交簇超图的两个结论

本文结合超图中著名的EKR定理,充分利用补超图这一有力工具,论证了在限定条件下交簇超图的两个结论,从而推广了EKR定理。     

A location‐inventory model with lateral transshipments

We study an infinite horizon periodic stochastic inventory system consisting of retail outlets and customers located on a homogenous line segment. In each period, the total demand, generated by the customers on the line, is normally distributed. To better match supply and demand, we incorporate lateral transshipments. We propose a compact model in which the strategic decisions—the number and locations of retail outlets—are determined simultaneously with the operational decisions—the inventory replenishment and transshipment quantities. We find the optimal balance between the risk‐pooling considerations, which drive down the optimal number of retail outlets, and lateral transshipments, which drive up the optimal number of retail outlets. We also explore the sensitivity of the optimal number of retail outlets to various problem parameters. This article presents a novel way of integrating lateral transshipments in the context of an inventory‐location model. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

带紧扰动的集值(S)_+型映射的拓扑度及其应用

本文利用 Michael 连续选择定理与 F.E Browder 次连续(S)_+型映射度理论相结合的方法,构造了带紧扰动的1.s.c.集值(S)_+型映射的拓扑度,并讨论了作为其应用的不动点与值域问题.     

模拟电路子网络级故障诊断的新方法

针对目前模拟电路子网络级故障诊断方法普遍存在的问题,提出了一种新的诊断方法,阐述了该方法的诊断原理,给出了可诊断性条件,通过仿真例子,证明了该方法具有测试量少,方法简单,实时性好,适用于非线性电路等特点