On almost sure max-limit theorems of complete and incomplete samples from stationary sequences

Let M _n denote the partial maximum of a strictly stationary sequence (X _n ). Suppose that some of the random variables of (X _n ) can be observed and let [(M)\tilde]_n\tilde M_n stand for the maximum of observed random variables from the set {X ₁, ..., X _n }. In this paper, the almost sure limit theorems related to random vector ([(M)\tilde]_n\tilde M_n , M _n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.     

具有界时滞和分布时滞的反应扩散神经网络的指数同步

本文研究了一类具有界时滞和分布时滞的反应扩散神经网络的状态变量在边界为零的条件下驱动系统和响应系统的指数同步性,得到了其驱动系统和响应系统指数同步的充分条件。     

罗尔定理应用中的辅助函数构造法

给出在利用罗尔定理证明等式时所需辅助函数的一种构造方法，并借助实例加以说明．     

双动点中的分类思想

分类是一种重要的数学思想方法,平面图形中双点运动时,常有某个元素不能确定,需作分类处理.     

数学课上的延时评价

课堂上,老师和学生始终面对面地共同构成教学活动的能动因素.居于主导地位的老师,自然会充分利用评价的手段对课堂活动进行掌握与调控.我们会看到:老师或表扬或批评、或肯定或否定、或诱导或劝止,学生的情绪、课堂的气氛、教学的速度与强度也就随之而或高昂或沉寂、或热烈或平淡、或飞流直下或缓缓而行,展现着波澜起伏、色彩纷呈动人的画卷.关于评价,各种流派的教育学专著都告诫我们,     

简解一道美国数学月刊征解题

问题设x,y,z∈(0,+∞),且x2+y2+z2=1,求函数f=x+y+z-xyz的值域.这是一道美国数学月刊征解题,贵刊文[1]给出一个三角代换的解法,求解过程中还运用到导数的知识,运算繁杂难度较大,不易掌握.文[2]给出一个     

二元函数连续性条件之探析

对二元函数连续性判定条件给出了详细分析，强调有关问题的关键点，纠正了常见的模糊认识，得到一系列连续性充分条件及其推广形式．     

分子动力学模拟研究聚乳酸/聚酰胺11共混物的相容性

采用分子动力学(MD)模拟方法在COMPASS力场下,研究了不同质量比(10/90,30/70,50/50,70/30和90/10)聚乳酸(PLA)/聚酰胺11(PA11)共混物的相容性.研究结果表明:不同比例下PLA/PA11共混物的Gibbs自由能变化均大于零,其共混物很难形成均相体系;共混体系结合能的计算以及不同组分分子间C—C原子对径向分布函数的分析揭示了PLA和PA11的相互作用主要源自其分子间的范德华力;此外,模拟得到的所有比例下共混物的Flory-Huggins相互作用参数(χ)均大于临界Flory-Huggins相互作用参数(χcritical),进一步证明PLA与PA11不能形成相容体系。     

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.