g-循环矩阵的谱分解和Jordan块结构

首先证明了n级非奇异g-循环矩阵必定可以对角化，并且给出了它的谱分解。其次，当（n,g）=1时，给出了n级奇异g-循环矩阵相似于某些对角阵和某些幂零Jordan块的直和，进一步给出了其中幂零Jordan块的幂零指数的计算法。     

A big-M type method for the computation of projections onto polyhedrons

In a previous work (Ref. 1), we examined some active set methods for the computation of the projection of a point onto a polyhedron when a feasible point is known. In this paper, we assume that such a point is not known and examine a method similar to the big-M method developed for the solution of linear programming problems. Special attention is given to the study of computing error propagation.This research was supported partially by the Progetto Finalizzato Informatica del CNR, Sottoprogetto P1, Sofmat.     

用对角质量矩阵时有限单元特征值问题的准确度

本文讨论的对角化质量矩阵是在动能积分的公式中将积分点取在有限单元的结点上而得到的,本文给出了用这种矩阵时,固有频率、固有振型和对应的应力的对角化误差与动能积分的代数精确度、插值位移场的多项式的阶次、应变能中导数的最高阶数的关系,利用这些关系和多个算例讨论了对角化质量矩阵的应用性问题。     

Quadratic optimal control of stable well-posed linear systems

We consider the infinite horizon quadratic cost minimization problem for a stable time-invariant well-posed linear system in the sense of Salamon and Weiss, and show that it can be reduced to a spectral factorization problem in the control space. More precisely, we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution. If both the system and the spectral factor are regular, then the feedback operator can be expressed in terms of the Riccati operator, and the Riccati operator is a positive self-adjoint solution of an algebraic Riccati equation. This Riccati equation is similar to the usual algebraic Riccati equation, but one of its coefficients varies depending on the subspace in which the equation is posed. Similar results are true for unstable systems, as we have proved elsewhere.

     

图的(g,f)-因子分解

设Ｇ是一个图，ｇ（ｘ）和ｆ（ｘ）是定义在图Ｇ的顶点集上的两个整数值函数且ｇ≤ｆ．图Ｇ的一个（ｇ，ｆ）－因子是Ｇ的一个支撑子图Ｆ使对任意的ｘ∈Ｖ（Ｆ），有ｇ（ｘ）≤ｄＦ（ｘ）≤ｆ（ｘ）．如果图Ｇ的边集能划分为若干个边不相交的（ｇ，ｆ）－因子，则说图Ｇ是（ｇ，ｆ）－可因子化的．本文研究了图的（ｇ，ｆ）－可因子化的问题，给出了一个图Ｇ是（ｇ，ｆ）－可因子化的若干充分条件．     

A CLASS OF FACTORIZATION UPDATE ALGORITHM FOR SOLVING SYSTEMS OF SPARSE NONLINEAR EQUATIONS

ＡＣＬＡＳＳＯＦＦＡＣＴＯＲＩＺＡＴＩＯＮＵＰＤＡＴＥＡＬＧＯＲＩＴＨＭＦＯＲＳＯＬＶＩＮＧＳＹＳＴＥＭＳＯＦＳＰＡＲＳＥＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮＳＢＡＩＺＨＯＮＧＺＨＩ（ＩｎｓｔｉｔｕｔｅｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃ...     

Convergence Rate of the Distributions of Normalized Maximum Likelihood Estimators for Irregular Parametric Families

We study the convergence rate of the distributions of normalized maximum likelihood estimators defined by a parametric family of discontinuous multidimensional densities in the case of a vector parameter.     

QCD因子化在湮没衰变_(s,d)~0→J/ψγ中的应用

在QCD因子化框架下 ,对可能的辐射湮灭衰变 B0s ,d→J/ψγ进行研究 .在标准模型中 ,相对于简单因子化下领头阶的分支比 ,αs 阶非因子化辐射修正对分支比有显著的量级上的改变 ,这些衰变可用来检验因子化方法 .在理论上 ,B介子稀有辐射衰变对超出标准模型的新物理特别敏感 .作为一个例子 ,我们考虑右手带电流对标准模型中左手流可能的混合效应 ,这个混合对衰变分支比有显著的影响 .     

On a decomposition for infinite transition matrices

Heyman gives an interesting factorization of I-P, where P is the transition probability matrix for an ergodic Markov chain. We show that this factorization is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to be useful in the analysis of queues. This revised version was published online in June 2006 with corrections to the Cover Date.     

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations. Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992.