Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace

We consider the problem of efficient integration of an n-variate polynomial with respect to the Gaussian measure in ℝⁿ and related problems of complex integration and optimization of a polynomial on the unit sphere. We identify a class of n-variate polynomials f for which the integral of any positive integer power f^p over the whole space is well approximated by a properly scaled integral over a random subspace of dimension O(log n). Consequently, the maximum of f on the unit sphere is well approximated by a properly scaled maximum on the unit sphere in a random subspace of dimension O(log n). We discuss connections with problems of combinatorial counting and applications to efficient approximation of a hafnian of a positive matrix.     

抽样调查的设计与分析(Ⅰ)

本文讨论抽样调查实践中有关设计和数据分析的若干问题．第一部分主要涉及设计问题．     

On Statistical Properties of the Lerch Zeta-Function. II

A discrete limit theorem for the Lerch zeta-function with an integer parameter in the space of meromorphic functions is proved.     

哈密顿系统的低维环面的保存性

本文给出了关于哈密顿系统低维环面的一个推广的KAM定理,它适用于同时存在法向频率和双曲法向分量的情况.其证明基于尤建功的一个定理的光滑性表述及法向双曲不变流形理论的应用.文中还给出了另外两种情况下的推广.     

Sea and Wind: Multivariate Extremes at Work

Multivariate extreme value theory is used to estimate the probability of failure of a sea-wall near the town of Petten in Noord Holland, The Netherlands. The sample consists of 828 observations of still water levels and wave heights collected during storm events over a 13-year period. The paper sketches the probabilistic and statistical theory behind the estimation procedures used. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于彩色图象 RGB分析的自动对焦技术

参照人眼的特点,作者将传统的双焦评价函数分别作用于目标图象的R、G、B分量得到三个数值,然后由这三个值计算出一个新的评价值.对一般对焦目标,这种新方法能增强传统对焦评价函数结果.本文中作者对这一方法进行了详尽的讨论.     

Multiple existence of non-radial solutions with group invariance for sublinear elliptic equations

We deal with sublinear elliptic equations in a ball and prove the existence of infinitely many solutions which are not radially symmetric but G invariant. Here G is any closed subgroup of the orthogonal group and is not transitive on the unit sphere.     

Infinitely divisible probabilities on discrete linear groups

We investigate the structure of infinitely divisible probability measures on a discrete linear group. It is shown that for any such measure there is an infinitely divisible elementz in the centralizer of the support of the measure, such that the translate of the measure byz is embeddable over the subgroup generated by the support of the measure. Examples are given to show that this reult is best possible.     

The connectivity of a graph on uniform points on [0,1]

A random graph G_n(x) is constructed on independent random points U₁,…,U_n distributed uniformly on [0,1]^d, d1, in which two distinct such points are joined by an edge if the l_∞-distance between them is at most some prescribed value 0<x<1. The connectivity distance c_n, the smallest x for which G_n(x) is connected, is shown to satisfy

(1)

For d2, the random graph G_n(x) behaves like a d-dimensional version of the random graphs of Erdös and Rényi, despite the fact that its edges are not independent: c_n/d_n→1, a.s., as n→∞, where d_n is the largest nearest-neighbor link, the smallest x for which G_n(x) has no isolated vertices.     

Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue

We are concerned with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. It is known that an analytical solution of this queueing model is difficult and does not lead to numerical implementation. Based on appropriate understanding of the physical behavior, an efficient and numerically stable algorithm for computing the stationary distribution of the system state is developed. Numerical calculations are done to compare our approach with the existing approximations.