期刊：
Stochastic Analysis and Applications,1996年14(2):165-185 ISSN：0736-2994
通讯作者：
Mao, X.
作者机构：
[X.X. Liao; X. Mao] Department of Mathematics , University of Strathclyde , Glasgow Gl 1XH, Wuhan, U.K
通讯机构：
Department of Statistics and Modelling Science, University of Strathclyde, United Kingdom
摘要：
In this paper we shall discuss stochastic effects to the stability property of a neural network Suppose the stochastically perturbed neural network is described by an Itô equation [ILM002]The Geral theory on the almost sure exponential stability and instability of the stochastically perturbed neural network is first established. The theory is then applied to investigate the stochastic stabilization and destabilization of the neural network. Several interesting examples are also given for illustration
作者机构：
CENT CHINA NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.;WUHAN UNIV TECHNOL,DEPT MATH & PHYS,WUHAN 430070,PEOPLES R CHINA.;[Yu, XP] 华中师范大学数学系;[Jian, M] 武汉工业大学数学物理系
摘要：
In this paper, it is proved that if A is a normal proper contraction on Hilbert space H and F(z) = U(z) + iV(z) is operator-valued analytic on the unit disc Delta and 0 < p < 1, then parallel to F(A)parallel to(p) less than or equal to parallel to F(0)parallel to(p) + C-p (1 - parallel to A parallel to)(-2) [GRAPHICS]
作者机构：
[Lu G.] Department of Mathematics, Huazhong Normal University, Wuhan, 430070, China;[Sleeman B.D.] Department of Mathematics and Computer Science, The University of Dundee, Dundee, DD1 4HN, United Kingdom
通讯机构：
[Lu, G.] D;Department of Mathematics, Huazhong Normal University, China
摘要：
Competitive systems defined by Lotka-Volterra equations
(I)
$$\dot x_i = x_i \left( {r_i - \sum\limits_{j = 1}^n {a_{ij} x_j } } \right),i = 1,2,...n,$$
wherer
i>0,a
ij>0, have been extensively studied in the literature. Much attention has been drawn to, among other things, the non-periodic oscillation phenomenon, or May-type trajectory as it is called by some authors, since the discovery of that kind of trajectories in competitive Lotka-Volterra systems made by May and Leonard[2]. Recently, the same phenomenon was reported to be existing in prey-predator systems. In this paper it is clear that one can expect the appearance of such phenomenon in a broader class of Lotka-Volterra systems, namely quasi-competitive systems (i.e.r
i>0. (a
ij/ajj)+(a
ji/aii)>0 in (I)), which cover both competitive and some prey-predator systems in addition to others. Conditions are established in terms of the parameters of the systems for the existence of stable equilibrium, periodic oscillation and non-periodic oscillation.
通讯机构：
[HU, XY ] ;CENT CHINA NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
关键词：
RANDOM;CANTOR;set;SUBORDINATOR;stable;process;HAUSDORFF;MEASURE;FUNCTION;packing;MEASURE;function.;RANDOM CANTOR SET;SUBORDINATOR;STABLE PROCESS;HAUSDORFF MEASURE FUNCTION;PACKING MEASURE FUNCTION
摘要：
Let （Ω, F, P）=（[0, 1], [0, 1], μ）<sup>N</sup> （μ is the Lebesque measure, N={1, 2,…}）.{X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are independent random variables on （Ω, F, P） with X<sub>n</sub>（ω）=ω<sub>n</sub>, where ω=（ω<sub>1</sub>, ω<sub>2</sub>,…）. The {X<sub>n</sub>}<sub>n=1</sub><sup>∞</sup> are almost surely distinct. Thus to almost all sample points ω there is a random partial order 【 of the integers given by
作者机构：
[KONG, QK; LIAO, XX] HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.;[KONG, QK] NO ILLINOIS UNIV,DEPT MATH SCI,DE KALB,IL 60115, USA.
通讯机构：
[KONG, QK] N;NO ILLINOIS UNIV,DEPT MATH SCI,DE KALB,IL 60115, USA.
期刊：
Journal of Mathematical Analysis and Applications,1995年189(3):617-630 ISSN：0022-247X
通讯作者：
WANG, XJ
作者机构：
HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.;ZHEJIANG UNIV,INST MATH,HANGZHOU,PEOPLES R CHINA.;[WANG, XJ] ZHEJIANG UNIV,DEPT MATH,HANGZHOU,PEOPLES R CHINA.
通讯机构：
[WANG, XJ] Z;ZHEJIANG UNIV,DEPT MATH,HANGZHOU,PEOPLES R CHINA.
关键词：
Positive solutions
摘要：
In this paper, by means of a priori estimates and topological degree theory, we prove the existence of two or more solutions to nonlinear elliptic equations of nondivergence form. (C) 1995 Academic Press, Inc. [References: 9]
摘要：
This paper deals with a problem proposed by H. Brezis on the existence of positive solutions to the equation DELTAu + u((n+2)/(n-2)) + f(x, u) = 0 under the Neumann boundary condition D(gamma)u = u((n/(n-2)), where f(x,u) is a lower order perturbation of u((n+2)/n-2)) at infinity.
作者：
Li Jialiang Central China Normal University, China Department of Mathematics Central Normal University
期刊：
分析理论与应用：英文刊,1994年10(2):74-82 ISSN：1672-4070
通讯作者：
Jialiang, L.
作者机构：
[Li Jialiang Central China Normal University, China Department of Mathematics Central Normal University] Department of Mathematics, Central Normal University, PR China
通讯机构：
[Jialiang, L.] D;Department of Mathematics, China
关键词：
Rational Function;Analytic Function;Rational Approximation;Fraction Continue;Orlicz Space
作者机构：
[XIE, MY] CENT CHINA NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
关键词：
多元线性模型;回归;线性估计
摘要：
In this paper, we discuss admissibility for linear estimates on regression coefficients in a general multivariate linear model. Eight kinds of definition for admissibility are given. We have proved that they can be divided into three identical subclasses in the class of linear estimates, and got necessary and sufficient conditions for admissible estimates on each subclass. Particularly, the eight kinds of admissibility are identical under a special case of the model.
摘要：
Let X1,...,X(N) (where N > m) be independent N(m)(mu, SIGMA) random vectors, and put [GRAPHICS] where T is upper-triangular with positive diagonal elements. The author considers the problem of estimating SIGMA, and restricts his attention to the class of estimates D = {T' DELTA*T + Nb* XBAR XBAR':DELTA* is any diagonal matrix and b* is any nonnegative constant} because it has the following attractive features: (a) Its elements are all quadratic forms of the sufficient and complete statistics (XBAR, T). (b) It contains all estimates of the form aA + NbXBARXBAR' (a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0), which construct a complete subclass of the class of nonnegative quadratic estimates D* = {X'BX : B greater-than-or-equal-to 0} (where X = (X1,...,X(N)') for any strict convex loss function. (c) It contains all invariant estimates under the transformation group of upper-triangular matrices. The author obtains the characteristics for an estimate of the form T' DELTAT + NbXBARXBAR' (DELTA = diag{delta1,...,delta(m)} greater-than-or-equal-to 0 and b greater-than-or-equal-to 0) of SIGMA to be admissible in D when the loss function is chosen as tr(SIGMA-1 SIGMA - I)2, and shows, by an example, that aA + NbXBARXBAR' (a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0) is admissible in D* can not imply its admissibility in D.
期刊：
Journal of Combinatorial Designs,1994年2(5):325-339 ISSN：1063-8539
通讯作者：
Xia, M.‐Y.
作者机构：
[Tian-Bing Xia; Tian-Bing Xia Tian-Bing Xia Tian-Bing Xia] Computer Bureau, Hubei Branch, The People's Construction Bank of China, Wuhan 430071, People's Republic of China;[Ming-Yuan Xia; Ming-Yuan Xia Ming-Yuan Xia Ming-Yuan Xia] Department of Mathematics, Huazhong Normal University, Wuhan 430070, People's Republic of China
通讯机构：
Department of Mathematics, Huazhong Normal University, China
摘要：
A fundamental comparison theorem is established for general semilinear parabolic systems via the notions of sectorial operators, analytic semigroups and the application of the Tychonoff Fixed Point Theorem. Based on this result, we establish a maximum principle for systems of general parabolic operators and general comparison theorems for parabolic systems with quasimonotone or mixed quasimonotone nonlinearities. These results cover and extend most currently used forms of maximum principles and comparison theorems. A global existence theorem for parabolic systems is derived as an application which, in particular, gives rise to some global existence results for Fujita type systems and certain generalisations.
