关于齐次树上随机场的一类强偏差定理

通过引进渐近对数似然比作为齐次树上任意Markov随机场逼近的一种度量,通过构造鞅的方法,建立了关于随机场的一类强偏差(也称小偏差)定理.所得结论推广了一个已知的结果.     

Hermite型多元样本定理及Sobolev类上混淆误差的估计

本文证明了Hermite型多元样本定理,并由此确定了Sobolev类上混淆误差阶的精确估计．     

广义Bethe树上关于随机选择系统的一类极限定理

本文将随机选择系统的概念在广义 Bethe 树上进行了推广,同时研究了广义Bethe树上选择子序列的状态序偶出现频率的一类极限定理,它是 Bernoulli序列无规则性概念的进一步推广.     

Local Limit Theorems for Sums of Power Series Distributed Random Variables and for the Number of Components in Labelled Relational Structures

A Local limit theorem for the distribution of the number of components in random labelled relational structures of size n (e.g., a type of random graphs on n vertices, random permutations of n elements, etc.) is proved as n→∞. The case when the corresponding exponential generating functions diverge at their radii of convergence is considered.     

Theorems on the representation of nonlinear mapping families and implicit function theorems

We derive a result on local representations of a nonlinear mapping family in a neighborhood of a 2-regular singularity. Theorems of this kind are special forms of implicit function theorems and contain many very important results of local nonlinear analysis. Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 57–68, January, 2000.     

Cayley树上随机场的马尔可夫逼近与一类小偏差定理

通过引进样本相对熵率作为Cayley树上任意随机场与马尔可夫链场之间的偏差的一种度量, 建立了关于状态序偶频率的一类小偏差定理. 证明中应用了研究马尔可夫链强极限定理的一种新的分析方法.     

三相滞后对有球形空腔无限介质双温广义热弹性的影响

就各向同性的无限弹性体,具有一个球形空腔时,从双温广义热弹性理论（2TT）角度,研究三相滞后热方程的热弹性相互作用问题．在三相滞后理论中,热传导方程是一个含时间四阶导数的、双曲型的偏微分方程．假设无限介质初始时静止,通过Laplace变换,将基本方程用向量矩阵微分方程的形式表示,然后通过状态空间法求解．将得到的通解应用于特殊问题:空腔边界上承受着热荷载（热冲击和坡型加热）和力学荷载．使用Fourier级数展开技术,实现Laplace变换的求逆．计算了铜类材料物理量的数值解．图形显示,两种模型:带能量耗散的双温Green-Naghdi理论（2TGNIII）和双温3相滞后模型（2T3相）明显不同．还对双温和坡型参数的影响进行了研究．     

On a generalization of the Schauder and Krasnosel'skii fixed points theorems on Dunford–Pettis spaces and applications

In this paper, we give a generalization of the Schauder and Krasnosel'skii fixed point theorems in Dunford–Pettis spaces. Both of these theorems can be used to resolve some open problems posed by Jeribi (Nonlinear Anal.: Real World Appl. 2002; 3 :85–105); and Latrach (J. Math. Phys. 1996; 37 :1336–1348). Further, we applied our work to prove some existence results for a source problem with general boundary conditions in L₁ spaces. Copyright © 2005 John Wiley & Sons, Ltd.     

Some Recent Developments in the Theory and Applications of a Class of Finite Fourier Transformations

In this talk we shall investigate various properties of a class of finite Fourier transformations (that is, Fourier transformations on finite intervals), not as Fourier coefficients, but as functions of a continuous variable. Some of these potentially useful properties of finite Fourier exponential, finite Fourier sine, and finite Fourier cosine transformations will then be applied to several families of special functions including (for example) Bessel functions, parabolic cylinder functions, and Chebyshev and Legendre (or spherical) polynomials.     

Optimal control of a large dam with compound Poisson input and costs depending on water levels

This paper studies a discrete model of a large dam where the difference between lower and upper levels, L, is assumed to be large. Passage across the levels leads to damage, and the damage costs of crossing the lower or upper level are proportional to the large parameter L. Input stream of water is described by compound Poisson process, and the water cost depends upon current level of water in the dam. The aim of the paper is to choose the parameters of output stream (specifically defined in the paper) minimizing the long-run expenses that include the damage costs and water costs. The present paper addresses the important question: How does the structure of water costs affect the optimal solution? We prove the existence and uniqueness of a solution. A special attention is attracted to the case of linear structure of the costs. As well, the paper contributes to the theory of state-dependent queueing systems. The inter-relations between important characteristics of a state-dependent queueing system are established, and their asymptotic analysis that involves analytic techniques of Tauberian theory and heavy traffic approximations is provided.     

给定密度随机数的生成的通用方法与球面和球体上均匀随机向量的生成法

本文首先介绍基于垂直概率密度表示的,给定密度函数的随机数生成的通用方法;然后介绍球面及球体上均匀随机向量的生成算法。     

Error Estimation and Optimization of the Functional Algorithms of a Random Walk on a Grid Which Are Applied to Solving the Dirichlet Problem for the Helmholtz Equation

We consider the algorithms of a random walk on a grid which are applied to global solution of the Dirichlet problem for the Helmholtz equation (the direct and conjugate methods). In the metric space C we construct some upper error bounds and obtain optimal values (in the sense of the error bound) of the parameters of the algorithms (the number of nodes and the sample size).     

转移概率流图的概率理论基础与应用方法(Ⅵ)——中止规则对调整型抽样方案复合OC函数影响的进一步讨论

解顺强．转移概率流向图的概率理论基础与应用方法（Ⅵ）—中止规则对调整型抽样方案复合ＯＣ函数影响的进一步讨论．数理统计与管理．１９９８．１７（６）本文运用转移概率流向图及其粘接方法，证明了当检查始于加严抽样方案时，不带中止规则的调整型抽样方案与带中止规则的相应的调整型抽样方案，两者的复合ＯＣ函数相同     

The Effects of Flexion and Torsion on a Fluid Flow Through a Curved Pipe

We consider an injection of incompressible viscous fluid in a curved pipe with a smooth central curve γ . The one-dimensional model is obtained via singular perturbation of the Navier—Stokes system as ɛ , the ratio between the cross-section area and the length of the pipe, tends to zero. An asymptotic expansion of the flow in powers of ɛ is computed. The first term in the expansion depends only on the tangential injection along the central curve γ of the pipe and the velocity as well as the pressure drop are in the tangential direction. The second term contains the effects of the curvature (flexion) of γ in the direction of the tangent while the effects of torsion appear in the direction of the normal and the binormal to γ . The boundary layers at the ends of the pipe are studied. The error estimate is proved. Accepted 21 March 2001. Online publication 9 August 2001.