多椭圆孔有限大复合材料层板的热弹性分析

本文利用各向异性体平面热传导，热弹性理论中的复势方法，以保角映射，Ｆａｂｅｒ级数展开以及最小二乘边界配置技术为工具，导出了内边界条件精确满足，外边界条件近似满足的多椭圆孔复合材料层板的热传导以及热弹性问题的级数解，详细探讨了层板大小，孔径，相对孔距，孔的设置方式，椭圆度以及层板的铺层比例诸参数的影响规律，得到了一些有益结论。     

On the number of countable models of complete theories with finite Rudin-Keisler preorders

The aim of this article is to generalize the classification of complete theories with finitely many countable models with respect to two principal characteristics, Rudin-Keisler preorders and the distribution functions of the number of limit models, to an arbitrary case with a finite Rudin-Keisler preorder. We establish that the same characteristics play a crucial role in the case we consider. We prove the compatibility of arbitrary finite Rudin-Keisler preorders with arbitrary distribution functions f satisfying the condition rang f?ω∪{ω, 2^ω}.     

Robust linear optimization under general norms

We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.     

On inventory problems with arbitrary cost pattern,demand pattern and demand distribution

A detailed analysis of inventory models without setup costs, arbitrary demand distribution and arbitrary demand and cost pattern is given. First it is shown that the corresponding one-period model without ordering costs may be reduced to another simpler one with appropriately modified demand distribution. Several representations are given for the modified demand distribution. As one of the main results this reduction turns out to be robust in most cases. In a final chapter the results are applied to the determination of an optimal policy for a class of N-period inventory models with convex holding-and shortage costs and without setup costs.     

Robust probability updating

This paper discusses an alternative to conditioning that may be used when the probability distribution is not fully specified. It does not require any assumptions (such as CAR: coarsening at random) on the unknown distribution. The well-known Monty Hall problem is the simplest scenario where neither naive conditioning nor the CAR assumption suffice to determine an updated probability distribution. This paper thus addresses a generalization of that problem to arbitrary distributions on finite outcome spaces, arbitrary sets of ‘messages’, and (almost) arbitrary loss functions, and provides existence and characterization theorems for robust probability updating strategies. We find that for logarithmic loss, optimality is characterized by an elegant condition, which we call RCAR (reverse coarsening at random). Under certain conditions, the same condition also characterizes optimality for a much larger class of loss functions, and we obtain an objective and general answer to how one should update probabilities in the light of new information.     

On the controllability of the Vlasov-Poisson system

In this paper, we study the controllability of the Vlasov-Poisson system in a periodic domain, by means of an interior control located in an spatial subdomain.The first result proves the local exact zero controllability in the two-dimensional torus between two small acceptable distribution functions, with an arbitrary control zone.A second result establishes the global exact controllability in arbitrary dimension, provided the control zone satisfies the condition that it contains a hyperplane of the torus.     

On exceedances of record and order statistics

Exact, limiting distributions along with their rates of convergence of exceedance statistics for both order statistics and record statistics are provided when the underlying distribution is arbitrary. The exact distribution of record statistics for arbitrary underlying distributions is obtained as well.

     

两平行圆盘间或两圆球间存在二阶流体时的挤压流动

为了进行湿颗粒群的离散元模拟,研究两圆球颗粒间二阶流体在挤压流动时的法向粘性力．首先用小参数法对两平行圆盘间二阶流体挤压流动的速度场和正应力分布进行了近似分析,然后用类似的方法,分析任意两圆球间二阶流体的挤压流动,得到了压力分布和法向粘性力的解析解．     

梁受正弦分布压力作用的解析解

对梁受正弦分布压力作用的情况，本文以矩形截面简支梁为例，通过构造满足所有边界条件和双调和方程的应力函数给出了相应的解析解，这为求解梁受任意分布压力作用的解的问题打下了基础。     

Logarithmic potential <Emphasis Type="Italic">β</Emphasis>-ensembles and Feynman graphs

We present a diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with an arbitrary power of the Vandermonde determinant) to all orders of the 1/N expansion in the case when the limiting eigenvalue distribution spans an arbitrary (but fixed) number of disjoint intervals (curves) and when logarithmic terms are present. This diagrammatic technique is corrected and refined as compared to our first paper with B. Eynard of 2006.     

Temperature distribution in a parallelopiped under the influence of heat source with boundary conditions of second kind

In the present paper, the general expressions for temperature distribution in an orthotropic plate of finite dimensions have been derived under the influence of an arbitrary volume heat source and arbitrary initial temperature distribution. The boundary conditions prescribed on the faces are of second kind. The solution is obtained by constructing an eigen value problem. The expression for unsteady temperature distribution consists of two parts—steady and pseudo-steady. The pseudo-steady parts of the solution have been obtained with the help of finite integral transform technique. The general expressions are further studied under different cases. The whole analysis is presented in the dimensionless form with the help of various dimensionless parameters,viz., F _o , P _o , K _i , etc.     

解任意形状扁轴对称体Stokes流动的连续奇点分布法

本文以Sampson球形无穷级数作为基本奇点,采用分段等强度和分段二次抛物分布两种体内连续分布法解任意形状扁轴对称体的Stokes流动.通过扁球的无界绕流问题,对这两种方法的收敛性,精度和适用范围做了检验和比较.结果表明,在一定的范围内,无论是阻力系数或压力分布,它们的计算结果都和精确解符合得很好,而且,随着分布函数逼近程度的提高,其收敛性得到改善,适用范围也随之扩大.作为一般算例,分别用这两种方法解决了卡西尼扁卵形体的绕流问题,得到了一致的结果.最后,用分段二次连续分布法计算了具有一定生理意义的红细胞体的Stokes流动,首次得到了它的阻力系数和表面压力分布.     

On Sums of Overlapping Products of Independent Bernoulli Random Variables

We find the exact distribution of an arbitrary remainder of an infinite sum of overlapping products of a sequence of independent Bernoulli random variables.     

A generalization of the inspection paradox in an ordinary renewal process

The inspection paradox in an ordinary renewal process is investigated in the very general case of the time dependent problem and arbitrary distribution of inter–renewal times with finite mean and a probability density function     

Potential theory for finitely additive Markov chains

In this paper potential theory is developed for finitely additive Markov chains and this is used to obtain various characterization theorems for discrete time Markov chains with an arbitrary state space, with finitely additive stationary transition probabilities and a finitely additive initial distribution.     

Three-dimensional contact problem of the motion of a stamp with friction

There is considered the three-dimensional contact problem of elasticity theory with friction forces collinear to the motion direction. Such a case holds during stamp motion along the boundary of an elastic half-space with anisotropic friction /1/. In the case of an arbitrary friction surface, the mentioned force distribution is satisfied approximately during stamp motion.     

On zeros of polynomials orthogonal over a convex domain

We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result concerning the distribution of zeros of polynomials orthogonal on a convex domain.     

General linear-fractional branching processes with discrete time

We study a linear-fractional Bienaymé–Galton–Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads to the linear-fractional distribution formula for an arbitrary observation time, which allows us to establish transparent limit theorems for the subcritical, critical and supercritical cases. Our results extend recent findings for the linear-fractional branching processes with countably many types.     

Almost sure approximation theorems for the multivariate empirical process

Summary Let R(s,t) be the empirical process of a sequence of independent random vectors with common but arbitrary distribution function. In this paper we give an almost sure approximation of R(s,t) by a Kiefer process. The result continues to hold for stationary sequences of random vectors with continuous distribution function and satisfying a strong mixing condition.Supported in part by an NSF grant     

On the comparison of distribution functions of random variables

We prove a rather general comparison principle for the distribution functions of random variables. As a consequence, we obtain a criterion for the equivalence in distribution in the vector sense of an arbitrary sequence of random variables to the Rademacher system; we study the applications of this principle to special cases.