Moments of the Hermitian Matrix Jacobi Process

In this paper, we compute the expectation of traces of powers of the Hermitian matrix Jacobi process for a large enough but fixed size. To proceed, we first derive the semi-group density of its eigenvalues process as a bilinear series of symmetric Jacobi polynomials. Next, we use the expansion of power sums in the Schur polynomial basis and the integral Cauchy–Binet formula in order to determine the partitions having nonzero contributions after integration. It turns out that these are hooks of bounded weight and the sought expectation results from the integral of a product of two Schur functions with respect to a generalized beta distribution. For special values of the parameters on which the matrix Jacobi process depends, the last integral reduces to the Cauchy determinant and we close the paper with the investigation of the asymptotic behavior of the resulting formula as the matrix size tends to infinity.     

单纯形上Meyer-K{o}nig and Zeller算子矩量的一个递推公式

首先运用比文献[2]更简单的方法导出了一元Meyer-K\"{o}nig and Zeller算子矩量的一个积分表示, 然后利用这一方法建立了二元(单纯形上)Meyer-K\"{o}nig and Zeller算子矩量的一个递推公式, 最后作为这个递推公式的应用, 给出了该算子的二阶、三阶矩量的积分表示.     

单纯形上Meyer-Kōnig and Zeller算子矩量的一个递推公式

首先运用比文献[2]更简单的方法导出了一元Meyer-Kbnig and Zeller算子矩量的一个积分表示,然后利用这一方法建立了二元(单纯形上)Meyer-Konig and Zeller算子矩量的一个递推公式,最后作为这个递推公式的应用,给出了该算子的二阶、三阶矩量的积分表示.     

An Explicit Formula and its Application to the Selberg Trace Formula

We prove that the explicit formula in a symmetric case for a triple (Z, [(Z)\tilde]\tilde{Z} , Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates for the logarithmic derivative of the Selberg zeta function are considered.     

An Explicit Formula and its Application to the Selberg Trace Formula

We prove that the explicit formula in a symmetric case for a triple (Z, , Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates for the logarithmic derivative of the Selberg zeta function are considered.     

Minimal Moments and Cumulants of Symmetric Matrices: An Application to the Wishart Distribution

An algorithm is proposed and notions defined to determine the minimal sets of all possible higher order moments and cumulants of a random vector or a random matrix. The main attention has been paid to the case of symmetric matrices. Using the introduced notions, cumulants of arbitrary order for the Wishart distribution have been obtained.     

火场-结构联合分析简化模型及其应用研究

为在建筑结构火灾反应分析中考虑实际火场特性,并简化火场分析模型与结构有限元分析模型之间的复杂对应关系,提出并建立了火场温度及对流辐射边界的热传导分析时空模型(STM)和基于时空模型的火场-结构联合分析方法。该方法根据火场模型计算出室内火场温度分布场以及对流辐射边界场离散数据,通过双向正交多项式进行拟合来得到不同时刻的构件边界连续时空模型,再通过时空模型进行热传导分析和热力耦合分析,从而实现火场-结构联合分析方法。在验证其合理性的基础上,通过ABAQUS子程序UTEMP和DFLUX实现其分析过程,并进行了北京某档案馆工程的应用分析,结果表明该方法可以较好地联合火场模拟与结构分析用于结构火灾安全评价。     

A Schläfli-Type Formula for Polytopes with Curved Faces and Its Application to the Kneser-Poulsen Conjecture

We prove a Schl?fli-type formula for polytopes with curved faces lying in pseudo-Riemannian Einstein manifolds. This formula is applied to the Kneser-Poulsen conjecture claiming that the volume of the union of some balls cannot increase when the balls are rearranged in such a way that the distances between the centers decrease. Supported by the Hungarian National Science and Research Foundation OTKA T047102.     

Variational approach for a general financial equilibrium problem: The Deficit Formula,the Balance Law and the Liability Formula. A path to the economy recovery

Without using a technical language, but using the universal language of mathematics, we provide simple but significant laws, as Deficit Formula, Balance Law and Liability Formula, for the management of the world economy. Decisions, under these laws, for the recovery of the economy and for the good governance clearly appear. Further a simple but useful economical indicator E(t)$E(t)$ is provided and the results are illustrated with a significant example.     

Zonal Functions for the Unitary Groups and Applications to Hermitian Lattices

We study the decomposition of the space L²(Sⁿ⁻¹) under the actions of the complex and quaternionic unitary groups. We give an explicit basis for the space of zonal functions, which in the second case takes account of the action of the group of quaternions of norm 1. We derive applications to hermitian lattices.     

The Genetic Sums' Representation for the Moments of a System of Stieltjes Functions and its Application

This paper deals with the spectral problems for high-order nonsymmetric difference operators. The method of investigation is based on the analysis of the genetic sums formulas for the moments of the operator. The parameters of these sums are shown to be connected with coefficients of the introduced vector Stieltjes continued fraction. The connections with vector orthogonality, Hermite—Padé approximation, and Hankel determinants are investigated. This gives a tool for the analysis of the solution of the direct and inverse spectral problem of the operator. It is applied to the integration of hierarchy of the discrete KdV equations. The existence of a global solution is proved. July 13, 1998. Date revised: July 12, 1999. Date accepted: July 26, 1999.     

A Class of Generating Functions for the Jacobi and Related Polynomials

This paper aims at presenting a general class of mixed generating functions for the Jacobi polynomials. It is also shown how the main generating function can be suitably applied to yield numerous further results involving Jacobi polynomials and various other polynomials associated with them.     

Lundberg-type Bounds and Asymptotics for the Moments of the Time to Ruin

We obtain analogues of Lundberg’s inequality and the Cramér—Lundberg asymptotic relationship for the k-th moment of the time to ruin in the classical risk model. We also derive the asymptotic behaviour of the mean time to ruin when the claim size distribution has a heavy or intermediate tail.     

The projective rank of a Hermitian symmetric space: A geometric approach and consequences

The “Projective Rank” of a compact connected irreducible Hermitian symmetric space M has been defined as the maximal complex dimension of the compact totally geodesic complex submanifolds having positive holomorphic bisectional curvature with the induced K?hler metric. We present a geometric way to compute this invariant for the space M based on ideas developed in [1], [13] and [14]. As a consequence we obtain the following inequality relating the Projective Rank, the usual rank, and the 2-number (which is known to be equal to the Euler-Poincare characteristic in these spaces). Received: 6 June 2000 / Revised version: 6 August 2001 / Published online: 4 April 2002