Some Conditions for a C0-Semigroup to Be Asymptotically Finite-Dimensional

We study the class of bounded C ₀-semigroups T=(T _t ) _t0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X ₀(T)<, where X ₀(T):={x X:lim_t T _t x=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.     

Choquet-type Integral Representation of Invariant Functions for some Product Semigroups

We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions.     

Matrix Rings with Summand Intersection Property

A ring R has right SIP (SSP) if the intersection (sum) of two direct summands of R is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of R by M has SIP if and only if R has SIP and (1 – e)Me = 0 for every idempotent e in R. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.     

关于算子方程AX=XAX与AX=XA=XAX

用A的不变子空间作参数，给出了算子方程AX＝XAX的全部解。当A是单射或稠值域时，或者当A是正规算子时，给出了算子方程AX＝XA＝XAX的全部解。我们还给出正规算子X是算子方程AX＝XZ＝XAX的解的充分必要条件。     

一类混杂动态系统的能控性（I）——基本结果

首次将时滞现象引入到线性切换系统的模型中，研究含有时滞线性切换系统的能控性及其判定条件．全部工作由三部分组成，第I部分首先，提出含时滞的线性切换系统的数学模型，并介绍切换系统的基本概念——切换序列．其次，引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念，给出一些有关概念的基本性质，特别是分离引理．然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系，这个引理将在能控性的判定中起关键作用．这些概念和引理都将作为以后展开能控性分析所必需的研究工具．     

一类混杂动态系统的能控性(Ⅲ)——含多时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅲ部分,主要研究含多时滞的线性切换系统的能控性及其判定规则。首先给出周期型系统的单周能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。最后,研究时滞大小不一致的情形,指出能控性与时滞大小无关。     

A quasilinear Neumann problem with discontinuous nonlinearity

In this paper we study a quasilinear boundary value problem of Neumann type with discontinuous terms. In particular we consider a problem in which the p–Laplacian is involved. In order to prove the existence of solutions we replace this problem with a multivalued approximation of it and, using a variational approach for locally Lipschitz functionals, we prove two existence results for it.     

OnM-ideals and best approximation

In this paper we will prove some theorems on theM-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].This work is supported in part by the National Natural Science Foundation of China.     

Semi-empirical likelihood ratio confidence intervals for the difference of two sample means

We all know that we can use the likelihood ratio statistic to test hypotheses and construct confidence intervals in full parametric models. Recently, Owen (1988,Biometrika,75, 237–249; 1990,Ann. Statist.,18, 90–120) has introduced the empirical likelihood method in nonparametric models. In this paper, we combine these two likelihoods together and use the likelihood ratio to construct confidence intervals in a semiparametric problem, in which one model is parametric, and the other is nonparametric. A version of Wilks's theorem is developed.     

Tests of ordered hypotheses in linkage in heredity

The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases.