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25 October 2005, Volume 25 Issue 5 Previous Issue    Next Issue

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Stability and Boundedness of Neutral Functional Differential Equations with Infinite Delay DI Shen-Jia-Bo, FAN Meng, WANG Ke Acta mathematica scientia,Series A. 2005, 25 (5):  593-603.  Abstract ( 2265 )   RICH HTML PDF (393KB) ( 1307 )   Save With the help of the phase space sufficient and necessary criterias are established for the uniform stability and uniformly asymptotic stability of solutions to neutral functional differential equations with infinite delay. In addition, the author also prove that the uniformly asymptotic stability of solutonsimplies the existence of the bounded solutions when the equation satisfies Lipschitz assumption. References | Related Articles | Metrics

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The Minimax Estimator of Stochastic Regression Coefficients and Parameters in Normal Linear Model XU Li-Wen, YU Qing-Hua Acta mathematica scientia,Series A. 2005, 25 (5):  604-611.  Abstract ( 1592 )   RICH HTML PDF (357KB) ( 1181 )   Save In this paper the authors investigate estimation problem of stochastic regression coefficients and parameters in the general normal random effects linear model. Under the quadratic loss, the authors obtain the unique minimax estimator of linear estimable functions in the class of all estimators. References | Related Articles | Metrics

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Entire Functions That Share a Value CM with Their Two Derivatives WANG Jian-Beng, YI Hong-Xun Acta mathematica scientia,Series A. 2005, 25 (5):  612-620.  Abstract ( 1576 )   RICH HTML PDF (365KB) ( 1199 )   Save This paper studies the uniqueness problem on entire functions that share a finite, nonzero value with two of their derivatives and gives the definite expressions of the functions which appear to be a proper answer to the question proposed by Yi H X and Yang C C References | Related Articles | Metrics

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Global Stability for Neural Networks with Unbouned Time Varying Delays CENG Zhi-Gang, LIAO Xiao-Cuan Acta mathematica scientia,Series A. 2005, 25 (5):  621-626.  Abstract ( 1747 )   RICH HTML PDF (334KB) ( 1034 )   Save This paper studies the global stability of the neural network with unbounded time varying delays and time varying coefficients.Using two kinds of methods,some sufficient conditions have been obtained to guarantee that such neural network is globally stable. Moreover,when time delay is constant or doesn't exist,the results given in the paper extend the existing relevant stability results in the existing literature. References | Related Articles | Metrics

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Multivariate Weighted Modulus of Smoothness and Bernstein-Durrmeyer Operators in B_a Space DING Chun-Mei, CAO Fei-Long- Acta mathematica scientia,Series A. 2005, 25 (5):  627-636.  Abstract ( 1428 )   RICH HTML PDF (383KB) ( 1234 )   Save In this paper, the authors introduce a new multivariate weighted modulus of smoothness in B_a space,which generalizes the Ditzian Totik's modulus in L^p space. The equivalence relationship between the modulus and certain K functional is shown. As an application, the relationship between the multivariate Bernstein Durrmeyer operators defined on the simplex and the modulus is discussed as well. Namely, with the modulus as a metric, the upper and lower bounds of degree of approximation by the operators are estimated in B_a space. References | Related Articles | Metrics

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Perturbation Theorems for Linear Operators CAO Xiao-Gong, GUO Mao-Zheng, MENG Bin Acta mathematica scientia,Series A. 2005, 25 (5):  637-642.  Abstract ( 1465 )   RICH HTML PDF (330KB) ( 1391 )   Save In this paper, the authors use two subspaces which are introduced by Mbekhta M in 1987 to study the perturbation of linear operators on a Banach space X.  The main result is: suppose that X=K(T)+W, K(T) and W are all closed,dim［K(T)∩N(T)］<∞.If TWW, TW is closed, and there exists a closed subspace N in X such that W=［W∩N(T)］N, and if S∈B(X) is invertible, ST=TS, SWW, and S has sufficiently small norm, then T-S is an upper semi Fredholm operator. If in addition K(T′) is closed and dim N< ∞, then T-S is a Fredholm operator. References | Related Articles | Metrics

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The Rate of Uniformly Asymptotic Normality for Probability Density Estimator under Negatively Associated Samples LI Yong-Meng, YANG Shan-Chao Acta mathematica scientia,Series A. 2005, 25 (5):  643-651.  Abstract ( 1591 )   RICH HTML PDF (374KB) ( 1316 )   Save In this paper, the authors  discuss the  uniformly asymptotic normality for an u nknown pro bability density function estimator under stationary and negatively associated s amples. Under suitable conditions, the authors  give the rate of the uniformly a symptotic normality that can get near n^{-1/6} References | Related Articles | Metrics

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The Self similar Solution and its Limit Behavior for the Complex Ginzburg Landau Equation ZHANG Xiao-Yi Acta mathematica scientia,Series A. 2005, 25 (5):  652-662.  Abstract ( 1719 )   RICH HTML Save The author proves there exists unique global solution in the non standarct funct ion space X_{s,p} for complex Ginzburg Landau equation. The author also  shows that the self similar solution of Ginzburg Landau equation converges to  the self similar solution of the limit equation as the parameter ε→0++  or ε→0++, a→0 References | Related Articles | Metrics

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Equivalent Norms on Weighted Analytic Lipschitz Spaces HUANG Ling-Di, CHEN Ze-Qian Acta mathematica scientia,Series A. 2005, 25 (5):  663-672.  Abstract ( 1942 )   RICH HTML PDF (383KB) ( 1179 )   Save In this paper, the authors first extend Theorem 1 in [3] and obtain the characterization of weighted analytic Lipschitz functions in terms of p Garsia modules. Secondly, the authors characterize them by using higher derivatives and Bergman Carleson measures, respectively. Finally, the authors show the associated expondntial decay effect as similar to John Niren berg's theorem of BMO spaces. References | Related Articles | Metrics

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The Maximality Borel Direction of Zero Order Algebroid Functions GAN Hui-Lin, SUN Dao-Chun Acta mathematica scientia,Series A. 2005, 25 (5):  673-677.  Abstract ( 1603 )   RICH HTML PDF (314KB) ( 1136 )   Save It is proved that the nu; value algebroid functions of zero order satisfying certain conditions on the plane possess at least one maximality Borel direction, and the maximality Borel direction is also the general Borel directions on their type functions. References | Related Articles | Metrics

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Synthetic Expected Bayesian Estimation of the Failure Rate HAN Meng, DING Yuan-Yao Acta mathematica scientia,Series A. 2005, 25 (5):  678-684.  Abstract ( 1603 )   RICH HTML PDF (356KB) ( 1320 )   Save The paper gives a new estimation method of reliability parameters, which is named as synthetic expected Bayesian estimation method . In the case of zero failure data, the definition of expected Bayesian est imation and the expected Bayesian estimation of failure rate are given. After introducing failure information, the expected Bayesian estimation of failure rate is given, the synthetic expected Bayesian estimation for failure rate and other reliability parameters are given also on the base. Finally, calculations are performed regarding to a practical problem, which show that the synthetic expected Bayesian method is feasible and easy to operate. References | Related Articles | Metrics

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Regularity of Solutions to Second Order Elliptic Equations with Discontinuous Coefficients XIN Mei Acta mathematica scientia,Series A. 2005, 25 (5):  685-693.  Abstract ( 1577 )   RICH HTML PDF (385KB) ( 1354 )   Save The mathematical problem discussed in the paper is derived from the electric field with discontinuous dielectric constants arising in biology and physics. The author will study the existence and regularity of solutions to semi linear second order elliptic equations with discontinuous coefficients. The pseudo differential operator is a basic tool in the present paper. References | Related Articles | Metrics

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Kullback Leibler's Divergence between Two Multivariatet Distributions BAI Peng Acta mathematica scientia,Series A. 2005, 25 (5):  694-709.  Abstract ( 1622 )   RICH HTML PDF (452KB) ( 1214 )   Save The paper is devoted to extension of results obtained in paper ［1］to mul tivariate t distributions case. It is shown that the divergence between two mul tivariate t distributions closely depends on the maximum eigenvalue of the rati o of scale matrices in the distributions. As an application, a kind of e ntropy loss function in estimating the unknown positive definite matrix is establis hed. References | Related Articles | Metrics

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The Induction Control of a Single Species Model with Stage Structure DIAO Li-Chun, ZHANG Qiang-Ling, YANG Qi-Chang Acta mathematica scientia,Series A. 2005, 25 (5):  710-717.  Abstract ( 1339 )   RICH HTML PDF (398KB) ( 1152 )   Save Three different induction control are exerted on a single species model with stage structure. The corresponding induction control domains are got. The rela tion between induction control domain and ultimately bounded domain which makes the system persist is given. Some induction control laws which make the system p ermanent are obtained.  References | Related Articles | Metrics

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Dissections of Quadrilaterals into Triangles of Equal Areas SU Zhan-Jun, DING Ren Acta mathematica scientia,Series A. 2005, 25 (5):  718-721.  Abstract ( 1771 )   RICH HTML PDF (302KB) ( 1516 )   Save In 1970 Monsky proved the famous Richman conjecture that a square can not be divided into an odd number of triangles of equal areas. In recent  years Stein studied the dissections of quadrilaterals into triangles of equal areas and obtained a lot of important results. In the present paper the authors study some open problems about the equidissections of quadrilaterals.  References | Related Articles | Metrics

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Positive Solutions of Sigular Sublinear Emden Fowler Boundary Value Problems with Impulse YAN Bao-Jiang, DAI Li-Mei Acta mathematica scientia,Series A. 2005, 25 (5):  722-733.  Abstract ( 1834 )   RICH HTML PDF (382KB) ( 1101 )   Save This paper considers the Dirichlet boundary value problem of the singular sublin ear Emden Fowler equations with impulse. A necessary and sufficient condition f or the existence of positive solutions to this problem is obtained by the method of lower and upper solutions. Moreover, under the influence of the impulse, a result on the existence of multiple solutions is also given. References | Related Articles | Metrics

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Marcinkiewicz Laws of Large Numbers and Complete Convergence with Multidimensional Indices WANG Jian-Feng, JIN Jing-Sen Acta mathematica scientia,Series A. 2005, 25 (5):  734-743.  Abstract ( 2072 )   RICH HTML PDF (377KB) ( 1253 )   Save In this paper, the authors consider a set of pairwise NQD multidimensional index  random sequ ences X_k-∈N^d(d≥2) The classical strong and weak  Marcinkiewicz laws are generalized to this case. Also, the complete convergence of part ial sums is derived. References | Related Articles | Metrics

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Singular Point Quantities and Bifurcations of Limit Cycles for a Class of Quintic Polynomial Systems HUANG Wen-Tao, LIU Yi-Reng, TANG Qing-An Acta mathematica scientia,Series A. 2005, 25 (5):  744-752.  Abstract ( 1841 )   RICH HTML PDF (375KB) ( 1615 )   Save In this article, the bifurcations of limit cycles at the degenerate critical point and at infinity for a class of quintic polynomial sy stem are investigated. In the system, the origin is degenerate critical point and the equator contains no real critical point. Firstly,algebraic recursive formulas for computing singular point quantities of the origin and infinity are derived resp ectively . The first five singular point quantities at the origin and first four singular point quantities at infinity for the system are given in order to get conditions of center and investigate bifurcations of limit cycles. At last, the authors construct a quintic system which allows the appearance of five limit cycles in the neighborhood of the origin and two limit cycles around infinity. As far as the authors know, this is the first time that the problem of limit cycles bifurcated from a degenerate singular point and from infinity under the sync hronous perturbed conditions is investigated. References | Related Articles | Metrics