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.     

非线性奇异边值问题的正解

利用锥映射的不动点指数定量，研究了一类非线性奇异边值问题多个正解的存在性问题。在构造的解的存在条件之下，证明了奇异边值问题至少有两个正解的存在性定理。     

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.     

混合判断矩阵排序方法研究

本文介绍了混合判断矩阵及完全一致性混合判断矩阵的概念，提出了混合判断矩阵排序的一种最小偏差法，并给出了其收敛性迭代算法，最后通过算例说明了方法的可行性。     

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.