渐近非扩张映象的修正Reich-Takahashi迭代的收敛定理

研究Banach空间中渐近非扩张映象和非扩张映象的具随机误差的修正的Reich-Takahashi的迭代序列的收敛问题,给出了第一型具随机误差的修正Reich-Takahashi迭代序列强敛到不动点的充要条件,所得结果推广和改进了已有文献的相关结果．     

Bayes DLM 递推方程中未知参数分布假定的理论证明

贝叶斯动态线性模型（简称为ＢａｙｅｓＤＬＭ）是一种特殊的预测方法,它以一个动态方程组和先验信息为基础,通过一组递推修正方程预测指标的变化情况。本文给出递推修正方程的一个假定前提的理论证明,从而说明ＢａｙｅｓＤＬＭ的合理性和严密性     

On the origins and foundations of Laplacian determinism

In this paper I examine the foundations of Laplace’s famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace’s statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace’s determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace’s determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation.     

函数具有最小值的充分和必要条件

给出了广义的实值函数f分别在R^N和在R^N的闭子集S上具有局部最小值点x的一阶和二阶充分和必要条件．     

线性互补问题的若干注记

首先给出Murthys等在[SIAM J.Matrix Anal.Appl.22(2000)]中提出的公开问题的肯定回答,然后讨论了R0－矩阵和Q－矩阵的一些关系。     

具有齐次核的Hilbert型积分不等式的构造特征及应用

利用实分析技巧,研究具有齐次核的Hilbert型积分不等式的构造特征及取最佳常数因子的充要条件,得到了最佳常数因子的解析表达式.     

Essential Independent Condition for Graphs to Be Hamiltonian

Let G be a graph of order n．For graph to be Hamiltonian,beginning with Dirac’s classic result in １９５２,Dirac’s theorem was followed by that of Ore in１９６０．In１９８４,Fan generalized Dirac’s theorem and Ore’s theorem as if G is a２-connected graph of order n and max｛d（u）,d（v）｝≥n/２for each pair of vertices u and v with d（u,v）＝２,then G is hamiltonian．In１９９１,Faudree et al proved that if G is a２-connected graph and,| N（u）∪N（v）|＋δ（G）≥n for each pair of nonadjacent vertices u,v∈V（G）,then G is hamiltonian．This paper generalizes the above onditions of Dirac,Ore,Fan and Faudree et al in the case of３-connected graph and proves that if G is a３-connected graph of order n and max｛｜N（x）∪ N（y）｜＋d（u）,｜N（w）∪N（z）｜＋d（v）｝≥n for every choice of６Essential independent vertices,then G is hamiltonian．     

基于凸组合技术的加速FR型共轭梯度算法

为高效求解非线性方程组问题,利用凸组合技术设计一个新型搜索方向,同时结合加速线搜索技术,提出一个新的加速FR型共轭梯度算法.在合理的假设下,新算法拥有全局收敛的良好性质.数值试验结果表明,新算法总体上优于经典FR算法和三项FR算法.新算法继承了修正FR方法的良好数值效果、充分下降性及信赖域特征,并具有计算简单和存储量小...     

Theoretical construction in physics – The role of Leibniz for Weyl's ‘Philosophie der Mathematik und Naturwissenschaft’

This paper aims at closing a gap in recent Weyl research by investigating the role played by Leibniz for the development and consolidation of Weyl's notion of theoretical (symbolic) construction. For Weyl, just as for Leibniz, mathematics was not simply an accompanying tool when doing physics—for him it meant the ability to engage in well-guided speculations about a general framework of reality and experience. The paper first introduces some of the background of Weyl's notion of theoretical construction and then discusses particular Leibnizian inheritances in Weyl's ‘Philosophie der Mathematik und Naturwissenschaft’, such as the general appreciation of the principles of sufficient reason and of continuity. Afterwards the paper focuses on three themes: first, Leibniz's primary quality phenomenalism, which according to Weyl marked the decisive step in realizing that physical qualities are never apprehended directly; second, the conceptual relation between continuity and freedom; and third, Leibniz's notion of ‘expression’, which allows for a certain type of (surrogative) reasoning by structural analogy and which gave rise to Weyl's optimism regarding the scope of theoretical construction.     

形如d2x/dt2+f(x)dx/dt+sinx=0方程解的有界性

研究了系统d2x/dt2 f(x)dx/dt sinx=0的有界性,给出了该系统存在无界解的若干新的判据,并用实例说明结果的正确性和方法的有效性.