矩阵特征值的几个不等式

研究矩阵特征值的上、下界以及特征值的实部、虚部的不等式 ,给出了特征值一些新的上界和下界     

Toda Chains in the Jacobi Method

We use the Jacobi method to construct various integrable systems, such as the Stäckel systems and Toda chains, related to various root systems. We find canonical transformations that relate integrals of motion for the generalized open Toda chains of types B _n, C _n, and D _n.     

Concerning seven and eight mutually orthogonal Latin squares

In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 419. © 2003 Wiley Periodicals, Inc.     

GA optimization on multi-segments muffler under space constraints

Whilst the space volume of muffler in noise control system is often constrained for maintenance in practical engineering work, the maximization on muffler’s performance becomes important and essential. In this paper, a novel approach genetic algorithms (GAs) based on the principles of natural biological evolution will be used to tackle this optimization of muffler design [M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, Cambridge, MA, 1996]. Here, the shape optimization of multi-segments muffler coupled with the GA searching technique is presented. The techniques of binary genetic algorithms (BGA) together with the commercial MATLAB package [G. Lindfield, J. Penny, Numerical Method Using Matlab, second ed., Prentice Hall, Englewood Cliffs, NJ, 2000] are applied in GA searching. In addition, a numerical case of pure tone elimination with 2-5 segments on muffler is introduced and fully discussed. To achieve the best optimization in GA, several GA parameters are on trial in various values. Results show that the GA operators, including crossover mutation and elitism, are essential in accuracy. Consequently, results verify that the optimal sound transmission loss at the designed frequency of 500 Hz is exactly maximized. The GA optimization on multi-segments muffler proposed in this study surely provides a quick and correct approach.     

Finite-Dimensional PT-Symmetric Hamiltonians

This paper investigates finite-dimensional PT-symmetric Hamiltonians. It is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian.     

标度系统一致性矩阵容量的计算方法

本文研究正互反矩阵的变换性质 ,提出一种保持正互反矩阵一致性程度的等价分类 ,为计算各种标度系统下的一致矩阵容量提供了计算方法     

Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi elliptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

一个来自振动理论反问题的矩阵方程

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＲｎ×ｍｄｅｎｏｔｅｔｈｅｒｅａｌｎ×ｍｍａｔｒｉｘｓｐａｃｅ ,Ｒｎ×ｍｒ ｉｔｓｓｕｂｓｅｔｗｈｏｓｅｅｌｅｍｅｎｔｓｈａｖｅｒａｎｋｒ ,ＯＲｎ×ｎｔｈｅｓｅｔｏｆａｌｌｎ×ｎｏｒｔｈｏｇｏｎａｌｍａｔｒｉｃｅｓ,ＳＲｎ×ｎ(ＳＲｎ×ｎ≥ ,ＳＲｎ×ｎ>)ｔｈｅｓｅｔｏｆａｌｌｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃ (ｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｓｅｍｉｄｅｆｉｎｉｔｅ ,ｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ)ｍａｔｒｉｃｅｓ.ＴｈｅｎｏｔａｔｉｏｎＡ>0 (≥ 0 ,<0 ,≤ 0 )ｍ…