First Passage Time Distribution for Linear Functions of a Random Walk

In this paper, theorems about asymptotic behavior of the local probabilities of crossing the linear boundaries by a perturbed random walk are proved.     

最小平方距离法和隐式线性函数关系的参数估计

本文再次指出:最小平方距离法(LSD),也可叫最小模方法,是从解决多维空间n个点的超平面拟合问题而提取的;通过对p个随机变量的n组观测值,此方法是探求它们之间是否存在隐式线形函数关系的好方法;使用此法,可以得出隐式线形函数关系较好的参数估计。     

Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

Greedy Families for Linear Objective Functions

The following structures are characterized: for which families of feasible subsets of a finite set does the greedy algorithm return the optimum subset independent of the weighting of a linear objective function on the set? Characteristically, the family must then have as bases the bases of a matroid (even when the feasible family is not a system of independent sets), and for every accessible feasible set X, the subset of elements by which X can be augmented is the complement of a proper closed set of the matroid. Another characterization is given for a family in which the greedy algorithm gives the optimum subset at every stage: the family is that of the bases of a sequence of matroid strong maps resulting in a natural duality theory. Theoretical underpinnings are given for several classical instances such as the algorithms of Kruskal, Prim, and Dijkstra.     

Linear Differential Elimination for Analytic Functions

This paper provides methods to decide whether a given analytic function of several complex variables is a linear combination of finitely many given analytic functions with coefficients of the following special form: Each one of these coefficients is a composition of an unknown analytic function of less arguments than the function to be expressed, with fixed analytic functions. Methods which compute suitable coefficient functions in the affirmative case are presented as well.     

The Poisson Distribution for Linear Statistics of Random Permutations

We examine the asymptotic distribution laws of integer-valued linear statistics defined via the multiplicities of lengths of cycles comprising a random permutation taken with equal probability. We establish necessary and sufficient conditions for the weak convergence to the Poisson limit law. The approach can be applied to investigate other logarithmic structures. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 537–552, October–December, 2005.     

Distribution Functions in Risk Analysis: Response

Journal of the Operational Research Society -     

Linear Generalized Analytic Functions

Complex-valued continuous functions are approximated using solutions of complex partial differential equations of Vekua type.     

Formulas for Liapunov Functions for Systems of Linear Difference Equations

Explicit quadratic Liapunov functions that provide necessaryand sufficient conditions for the asymptotic stability of thesystem of linear difference equations x (t + 1) = Ax(t) areconstructed by transforming the original systems to y (t + 1)= Gy(t), where G is a companion matrix associated with the characteristicpolynomial of A. A necessary and sufficient condition for allroots of the characteristic polynomial to lie in the unit circle|z| < 1 on the complex plane is also derived. 2000 MathematicalsSubject Classification 39A11, 93D05.     

M—可加细函数的局部和整体线性无关性

讨论具有紧支集M的可加细函数的局部线性无关性和整体线性无关性的等价关系。     

分布余弦函数

本给出分布余弦函数的定义，其中包括生成元为多值算子情形，并讨论退化性型分布余弦函数与退化型二阶Cauchy问题、退化型积分余弦函数的关系，最后说明了非退化分布余弦函数的生成元亦生成正则余弦函数。     

收入分布曲线的线性正态插值函数拟合方法

用样本数据的分组均值与总体方差为参数的正态函数作为插值基函数,构造出线性正态插值函数曲线以拟合中国城乡居民收入的概率分布函数曲线,并论证了这样构造的线性正态插值函数存在且唯一,此插值函数任意阶可微.利用拟合的正态插值函数曲线计算出拟合的函数面积估计值并与相应的样本数据直方图面积做比较,进而得出正态插值函数拟合曲线面积与样本数据直方图的面积误差比率.     

无限级亚纯函数的幅角分布

本文研究了无限级亚纯函数的幅角分布,将有限级亚纯函数的两个分布定理推广到无限级亚纯函数中,     

一些完全非线性函数的原像分布值

确定完全非线性函数的原像分布值,是决定和分析完全非线性函数以及构造相应线性码的公开问题和重要课题之一.本文讨论了完全非线性函数的原像分布所满足的基本方程的求解问题,完全解决了该方程当m=5以及m=6时的情形.     

几种模拟逐日降水的分布函数比较分析

在模拟逐日降水方面,将马尔科夫链和某种分布函数相结合建立随机模型的方法在国外很多地区被证明是有效的,但该方法在我国的适用性研究并不多见.本文应用哈尔滨48年的实测降水资料,基于一阶马尔科夫两状态转移概率,分别采用皮尔逊Ⅲ型分布、伽玛分布和偏正态分布函数模拟了哈尔滨的1000年逐日降水过程.对比分析结果表明,伽玛分布更适合模拟哈尔滨的逐日降水过程,基于伽玛分布函数模拟的月份降水量和降水天数与实测降水数据符合较好.     

非均匀材料细观结构的定向分布函数（I）—定向分布函数和不可约张量

在最近研究非均匀材料的物理和力学性质的各种基于细观力学的方法中,定向分布函数（ODF）和晶体定向分布函数（CODF）的概念起着重要的作用,它们分别定义在单位球面和旋转群上,本文通过两部分的内空,具有不可约张量系数的傅立叶展开对它们分别作了深入的研究,群表示理论指出平面可积的定向分布函数可以展开为球谐数的绝对收敛的傅立叶级数,而其中的球谐函数又能进一步用不可约张量表示,这样一些不可约张一系数的基本重要性在于它们刻划了材料组元和缺陷的体积,形状,相,位置的宏观或全局影响,第（I)部分对定义在N维单位球上的定向分布函数的不可约张量Fourier展开了一般性质进行了研究,其中重点是构造二维和三维不可约张量的简单表示,以便于得到它们在各种点群（完全正交群的子群）对称性的约束形式,第（II）部分给出了晶体定向分布数的不可约张量展开的显式表示,产工且给出了不可约张量以及定向分布函数的晶体定向分布数不可约张量展开在各种点群下的约束形式。