Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system

For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented.     

关于矩阵方程X+A*X-nA＝I的正定解

本文对任意正整数n界定了矩阵方程X A*X-nA=I的正定解的特征值的范围,给出了它的极大正定解一个充分条件.     

一种可能的简并谱NNS分布

利用随机矩阵理论,通过对一特殊情形的简并谱展开研究,得到了简并谱一种可能的最小相邻间距NNS分布函数．研究表明,由于简并的存在,简并谱不仅可分解成随机谱和规则谱两个子谱,同时还影响其规则谱,使规则谱的能级斥力减少．     

On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

关于圈的完全正矩阵实现

本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.     

On completely irreducible operators

Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more. The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section 2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties of completely irreducible operators are different from properties of unicellular operators. __________ Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29     

关于一类具有相同非负群逆和M-P逆的非负矩阵的进一步研究

1引言设A是n阶非负方阵．设矩阵方程(1)AXA=A,(2)XAX=X,(3)(AX)~T= AX,(4)(XA)~T=XA,(5)AX=XA．A具有非负广义逆是指存在非负方阵X满足方程(1)～(4),并记为A~(?)．A具有非负群逆是指存在非负方阵X满足方程(1),(2),(5),并记为A~#．在A~(?)存在的前提下,两者相同的充分必要条件有(a)AA~(?)=A~(?)A；(b)A~(?)=p(A),其     

无穷矩阵拓扑代数的理想(Ⅰ)(英文)

本文给出了所有弱紧算子 ,强紧算子 ,Mackey紧算子 ,构成无穷矩阵拓扑下相同紧集的特征的刻画 .     

一类无穷下三角矩阵的代数性质

修正了 [4,5]中的 Jabotinsky矩阵,得到并证明了一类无穷下三角矩阵T（f）的一些性质,最后,导出了一些与导数相关的反演关系和组合恒等式.     

High energy asymptotics of the scattering amplitude for the Schrödinger equation

We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover, the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables. This paper is dedicated to Jean-Michel Combes on the occasion of his sixtieth birthday.