线性系统的块解耦与稳定块解耦

一、引言20多年来,对于线性多变量系统的解耦问题的讨论一直在进行.60年代中、后期,Morgan、Rekasius、Falb & Wolovich、Gilbert 等先后解决了解耦问题,用不同方法给出了问题有解的充要条件.前几年,我们曾用另外的方法给出了解耦及稳定解耦问题有解的充要条件.     

Super‐simple resolvable balanced incomplete block designs with block size 4 and index 3

The necessary conditions for the existence of a super‐simple resolvable balanced incomplete block design on v points with k = 4 and λ = 3, are that v ≥ 8 and v ≡ 0 mod 4. These conditions are shown to be sufficient except for v = 12. © 2003 Wiley Periodicals, Inc.     

循环矩阵的推广

1. 引言及记号 在[2]中,对循环矩阵作了系统的概述,但仅限于正方矩阵.[1]首次将循环矩阵推广到长方阵,并应用于CAGD中.本文进一步推广块循环阵,并可直接应用于解大型线性方程组.循环矩阵的其他应用,可见[3—6].     

多址可加信道分组码的唯一可译性

本文对多址可加信道分组编码进行了研究，得出了唯一可译性的充要条件及有关判别准则，并对译码算法进行了探讨．     

Super‐simple resolvable balanced incomplete block designs with block size 4 and index 2

The necessary conditions for the existence of a super‐simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and . These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007     

Embedding of quasi-residual designs

Geometriae Dedicata - A simple sufficient condition for embedding of a quasiresidual balanced incomplete block design into the corresponding symmetric balanced incomplete block design is obtained.     

Super-Simple Resolvable Balanced Incomplete Block Designs with Block Size 4 and Index 4

The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 4, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient.     

Block toeplitz products of block toeplitz matrices

Necessary and sufficient conditions for the product of two block Toeplitz matrices to be block Toeplitz are obtained. In the special case of two Toeplitz matrices, the conditions simplify considerably and, when combined with known necessary and sufficient conditions for a nonsingular Toeplitz matrix to have a Toeplitz inverse, provide a simple characterization of the additional matrix structure required by a subclass of Toeplitz matrices in order for it to be closed with respect to both inversion and multiplication.     

两类循环分块矩阵及其有关算法

本文利用多项式矩阵最大右公因式，给出R-循环分块矩阵的和对称R-循环分块矩阵非奇异以及线性方程组反问题有唯一解的充要条件，进而得到它们求逆、线性方程组唯一解、线性方程组在循环分块矩阵中的反总问题求唯一解的算法。     

The Spectrum of （gv,g, 3, λ）-dDF in Zgv

In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a （gv, g, 3, λ）-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.     

Virtually balanced incomplete block designs for v = 22, k = 8, and λ = 4

When basic necessary conditions for the existence of a balanced incomplete block design are satisfied, the design may still not exist or it may not be known whether it exists. In either case, other designs may be considered for the same parameters. In this article we introduce a class of alternative designs, which we will call virtually balanced incomplete block designs. From a statistical point of view these designs provide efficient alternatives to balanced incomplete block designs, and from a combinatorial point of view they offer challenging new questions. © 1995 John Wiley & Sons, Inc.     

非均匀Chemostat中非单食物链模型稳态正解的存在性

研究一类由反应扩散方程组描述的非均匀Chemostat中微生物之间既表现竞争关系又表现捕食被捕食关系的模型．用特征值理论确定了系统正稳态解存在的必要条件，用锥映射不动点指数方法给出了系统正稳态解存在的充分条件．     

Asynchronous pole assignment for linear systems with blocks of incomplete rank

We consider a linear periodic control system with constant matrix multiplying the control in the critical case under the assumption that the mean of the coefficient matrix is block triangular and some blocks of its nonstationary part have incomplete column rank. A linear state feedback control periodic with the same period as the system itself is considered. We obtain necessary and sufficient conditions for the solvability of the asynchronous pole assignment problem, that is, the problem of finding a feedback factor such that the closed-loop system has a strongly irregular periodic solution with desired frequencies.     

块中心对称H-矩阵的几个定理

1符号与定义 为了行文方便,首先作如下记号约定:n为自然数,In表示n阶单位矩阵,Rn×n表示所有n×n阶实数矩阵做成的集合.对A=(aij)n×n∈Rn×n,若aij≤0对所有的i,j=1,2,…,n,i≠j成立,则称A为Z-矩阵.     

Incomplete group divisible designs with block size four

The object of this paper is the construction of incomplete group divisible designs (IGDDs) with block size four, group‐type (g, h)^u and index unity. It is shown that the necessary conditions for the existence of such an IGDD are also sufficient with three exceptions and six possible exceptions. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 442–455, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10055     

The diameter and radius of simple graphs

This paper develops some properties of simple blocks—block graphs which are determined up to isomorphism by the degrees of their vertices. It is first shown that if G is a simple block graph on six or more points, then G cannot be minimal or critical and must contain a triangle—have girth three.Then the most useful necessary conditions for a graph to be simple are established; if a graph is simple, it has diameter less than or equal to three and dradius less than or equal to two.     

Kostin-type criterion for abstract linear differential equations of arbitrary order in banach spaces

We consider linear differential equations with operator coefficients in a Banach space. We construct necessary and sufficient conditions for the well-posedness of the Cauchy problem for these equations of arbitrary order that are analogous to the Kostin conditions for incomplete equations of the second order.     

Connectedness of PBIB designs having asymmetrical association schemes

Summary A necessary and sufficient condition for the connectedness ofm-associate partially balanced incomplete block (PBIB) designs having an asymmetrical association scheme is given, only in terms of design parameters, without inner structure parameters of designs. Supported in part by Grant 321-6066-58530013 (Japan).     

On some properties of Poisson processes

The Poisson process, i.e., the simple stream, is defined by Khintchine as a stationary, orderly and finite stream without after-effects. A necessary and sufficient condition for a stream to be a simple stream is that the interarrival times are independent random variables with identical exponential distributions. This paper gives a simple and rigorous proof of the necessary and sufficient condition, and discusses the other necessary and sufficient conditions for a renewal process to be a Poisson process.Institute of Applied Mathematics, Academia Sinica     

Ergodicity of Quasi-birth and Death Processes （Ⅰ）

Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.