任意多边形面积公式的推导及其应用

通过对Green公式的离散变形,建立了重积分到曲线积分的公式,用多种方法推导出任意多形的面积公式.     

Characterization of Stochastic Viability of Any Nonsmooth Set Involving Its Generalized Contingent Curvature

Abstract

Thanks to the Stroock and Varadhan “Support Theorem” and under convenient regularity assumptions, stochastic viability problems are equivalent to invariance problems for control systems (also called tychastic viability), as it has been singled out by Doss in 1977 for instance. By the way, it is in this framework of invariance under control systems that problems of stochastic viability in mathematical finance are studied. The Invariance Theorem for control systems characterizes invariance through first‐order tangential and/or normal conditions whereas the stochastic invariance theorem characterizes invariance under second‐order tangential conditions. Doss's Theorem states that these first‐order normal conditions are equivalent to second‐order normal conditions that we expect for invariance under stochastic differential equations for smooth subsets. We extend this result to any subset by defining in an adequate way the concept of contingent curvature of a set and contingent epi‐Hessian of a function, related to the contingent curvature of its epigraph. This allows us to go one step further by characterizing functions the epigraphs of which are invariant under systems of stochastic differential equations. We shall show that they are (generalized) solutions to either a system of first‐order Hamilton‐Jacobi equations or to an equivalent system of second‐order Hamilton‐Jacobi equations.     

Any admissible cycle‐convergence behavior is possible for restarted GMRES at its initial cycles

We show that any admissible cycle‐convergence behavior is possible for restarted GMRES at a number of initial cycles, moreover the spectrum of the coefficient matrix alone does not determine this cycle‐convergence. The latter can be viewed as an extension of the result of Greenbaum, Pták and Strako? (SIAM Journal on Matrix Analysis and Applications 1996; 17 (3):465–469) to the case of restarted GMRES. Copyright © 2010 John Wiley & Sons, Ltd.     

医用高等数学的教学现状及改革措施的研究

分析并阐述了目前医用高等数学教学过程中存在的一些问题,针对这些问题,提出了几条改革的措施.     

高级排程计划APS发展综述

高级排程计划(APS)是二十世纪信息技术与现代管理思想相结合的产物。本回顾了APS从萌芽到与ERP／SCM结合的过程，总结了APS的主要特点，并对我国企业应用APS的前景进行了分析与展望。     

The Viable System Model: Its Provenance,Development, Methodology and Pathology

It took the author 30 years to develop the Viable System Model, which sets out to explain how systems are viable-that is, capable of independent existence. He wanted to elucidate the laws of viability in order to facilitate the management task, and did so in a stream of papers and two (of his seven) books. Much misunderstanding about the V.S.M. and its use seems to exist; especially its methodological foundations have been largely forgotten, while its major results have hardly been noted. This paper reflects on the history, nature and present status of the V.S.M., without seeking once again to expound the model in detail or to demonstrate its validity. It does, however, provide a synopsis, present the methodology and confront some highly contentious issues about both the managerial and scientific paradigms.     

超前注水开发指标变化规律及跟踪调整研究

X区块为低渗透油藏,目前采用超前注水开发方式,在数值模拟历史拟合的基础上对试验区超前注水开发指标的变化规律进行研究,并对注采系统进行调整.通过相对渗透率曲线,得到无因次采液指数与含水率之间的变化规律,结果表明,含水率低于65%时,无因次采液指数呈下降趋势,可适当降低注水强度;当含水率达到65%以后,无因次采液指数开始上升,此时可通过放大生产压差对试验区进行提液生产;而含水率达90%以后,无因次采液指数迅速上升,此时应以稳油控水为主.在确定产液量的基础上,在下降期和上升期分别设计了四个方案进行注水强度调整,结果表明,在无因次采液指数下降期和上升期,当注水强度分别为1.65 m~3/d·m和2.10m~3/d·m时,地层压力保持较好,且试验区开发效果最好.     

微分概念的历史发展及教学启示

微分的形式化定义是学生学习微分概念的主要困难.微分概念的历史发展表明,形式化的微分定义是微积分严格化的产物,朴素的微分定义更能体现微积分思想,而非标准分析给微分概念带来重生.在微积分学中应用非形式化的方法构建微分概念,以微分为主线(传统教材一般以导数为主线)进行微积分教学可以促进学生学习效果.     

基于年龄分组的单种群收获模型及稳定性分析

本文建立了一种按年龄分组的单种群收获模型 ,详细分析了该模型的稳定性 ,并得到了该模型临界稳定的充分必要条件 ,还得到了在临界稳定平衡中的极限状态解及临界稳定的生物学意义     

一类超前型微分差分方程的有界解及其渐近性质

本文考虑具有扰动项的超前型微分差分方程,证明了当退化方程具有负指数阶的有界解且扰动项满足一定条件时,扰动方程也具有负指数阶的有界解.     

倒向随机微分方程的理论、发展及其应用

本文全面综述了倒向随机微分方程理论的出现、发展、应用及研究现状，介绍了作者博士论文的主要工作。