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25 June 2007, Volume 27 Issue 3 Previous Issue    Next Issue

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The Discussion and Application of the Non-surjective Isometries between the Unit Spheres of Two l∞-spaces Liu Rui Acta mathematica scientia,Series A. 2007, 27 (3):  385-391.  Abstract ( 1672 )   RICH HTML PDF (278KB) ( 1187 )   Save In this paper, the author gives some properties of non-surjective isometries between the unit spheres of two l∞-spaces, and discribes the characters of the range set in this condition. At the end, the author answers the question when the non-surjective isometries between the unit spheres of c0(\Gamma)$ and l∞-space can be extended to a linear isometry on the whole space. Related Articles | Metrics

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Analysis of Reliability of a System with Repair and Multiple Critical and Noncritical Errors Yin Shuxin; Xu Genqi Acta mathematica scientia,Series A. 2007, 27 (3):  392-413.  Abstract ( 1959 )   RICH HTML PDF (497KB) ( 1183 )   Save In this paper the authors study reliability of a system with repair and multiple critical and non-critical errors. Under the functional frame work, they rewrite the system into an eqvolutionary equation in the state Banach space. Using the theory of semigroup of bounded linear operators, they investigate the well-poseness and the stability of the system. They prove that, under certain assumptions, the system is wellposed and associates a positive C0 semigroup; There is a steady state of the system and solution of the system converges asymptotically to this steady state in the sense of norm. And hence the indices of the system determined by the steady state are reliable. Related Articles | Metrics

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Closure of Exponential Polynomials in a Half Strip Deng Guantie Acta mathematica scientia,Series A. 2007, 27 (3):  414-419.  Abstract ( 1541 )   RICH HTML PDF (266KB) ( 1084 )   Save In this paper, the author obtains a necessary and sufficient condition for the incompleteness of complex exponential polynomials in the Banach space Hα consisting of all continuous functions f on the closed right half strip Iα={z=x+iy: x≥ 0, |y|≤α} (α > 0 ), analytic in its interior and such that f(z) vanishing uniformly at infinity. The author also proves that, if some conditions of incompleteness hold, then each function in the closure of the set of complex exponential polynomials can be extended to an analytic function represented by a Dirichlet series. Related Articles | Metrics

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Blow-up Profiles to a Nonlocal Reaction-diffusion System Chen Qiong; Xiang Zhaoyin; Mu Chunlai Acta mathematica scientia,Series A. 2007, 27 (3):  420-427.  Abstract ( 2083 )   RICH HTML PDF (302KB) ( 1212 )   Save This paper deals with a reaction-diffusion system with nonlocal sources. The authors first show that the solution blows up in finite time T if the initial data is large enough, then establish the estimates of the blow-up rates and the asymptotic behavior of the solution. Finally the size of the boundary layer is given. Related Articles | Metrics

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On Projectives over Radical Total Rings Feng Lianggui; Piao Zhihui Acta mathematica scientia,Series A. 2007, 27 (3):  428-433.  Abstract ( 1842 )   RICH HTML PDF (306KB) ( 1126 )   Save The decomposition theorems on projective modules over radical total rings are built in this paper. For a total free ring $R$ with $u.{\rm dim}_{R}R < \infty$, it is showed that $R$ is Noetherian with gldim$R \leqslant 1$, and any projective module $P$ over $R$ is isomorphic to $ \bigoplus\limits_{i\in I}Re_{i}$, in which each $e_{i}$ is a nonzero idempotent in $R$. Some examples are also given. Related Articles | Metrics

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Diffusion Wave for Navier-Stokes Equations in Even Space Dimensions Xu Hongmei; Yang Xiongfeng Acta mathematica scientia,Series A. 2007, 27 (3):  434-441.  Abstract ( 1680 )   RICH HTML PDF (292KB) ( 1167 )   Save The authors study the large time behavior of solutions to general Navier-stokes equations in even space-dimension. Through the pointwise estimate of the Green function of the linearized system, the authors obtain explicit expressions of the time-asymptotic behavior of the solutions. The result coincides with weak Huygen's principle. Related Articles | Metrics

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The Inverse Eigenvalue Problem of Hamiltonian Matrices Meng Chunjun; Hu Xiyan Acta mathematica scientia,Series A. 2007, 27 (3):  442-448.  Abstract ( 2338 )   RICH HTML PDF (276KB) ( 1156 )   Save In this paper the authors mainly discuss the inverse eigenvalue problem of Hamiltonian matrices. The necessary and sufficient conditions of solvability for the problem are conducted. And the general form of solutions is presented. Further, the authors research the optimal approximation solution to any given matrix, prove that such solution is unique and provide the formula to compute it. Some examples are given to demonstrate that the results are right and the algorithm is feasible. Related Articles | Metrics

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Iterative Solution for Systems of a Class of Abstract Operator Equations and Applications Su Hua; Liu Lishan; Wu Congxin Acta mathematica scientia,Series A. 2007, 27 (3):  449-455.  Abstract ( 1962 )   RICH HTML PDF (299KB) ( 1216 )   Save In this paper, by using partial order method, the existence and uniqueness of solutions for systems of a class of abstract operator equations in Banach spaces are studied. The results obtained in this paper improve and unify many recent results. Applications to the system of nonlinear integral equations in Banach space are given. It is proved that the unique solution exists by the iterative sequence which converges to the unique solution is constructed and the error estimate is given. Related Articles | Metrics

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Properties of the Birth and Death Processes with Zero as Their Leap-reflecting Barriers before Explosion Zhu Quanxin; Dai Yonglong Acta mathematica scientia,Series A. 2007, 27 (3):  456-469.  Abstract ( 1579 )   RICH HTML PDF (397KB) ( 1188 )   Save This paper first deals with some properties of birth and death processes with state 0 as their leap-reflecting barriers before explosion. By proposing a system of linear equations and shift operator, the authors obtain some precise expressions of both probability and average time when the processes move from state i to state n(i ≤ n ≤∞ or n≤ i) in several cases. On the other hand, the authors not only give a new definition of the characteristic numbers such as mi,ei,Ni,R etc, but also show their probability meanings. Related Articles | Metrics

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Orthogonal Multiscaling Functions and Multiwavelets with General Cardinal Property Yang Shouzhi; Yang Xiaozhong Acta mathematica scientia,Series A. 2007, 27 (3):  470-475.  Abstract ( 1728 )   RICH HTML PDF (280KB) ( 1114 )   Save A general scheme for constructing a class of orthogonal multiscaling functions with general cardinal property is presented. The corresponding orthogonal multiwavelets also have the same general cardinal property. The multiwavelets sampling theorem is established. Finally, the authors give some examples. Related Articles | Metrics

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Detection of Mutiple-outliers in Random-effects Model of Balanced One-way Classification Shi Lei; He Liping; Huang Mei Acta mathematica scientia,Series A. 2007, 27 (3):  476-487.  Abstract ( 2010 )   RICH HTML PDF (353KB) ( 1170 )   Save This paper studies the detection of multiple-outliers in balanced random-effects model of one-way classification. The authors derive the likelihood ratio test under the mean-shift model in random-effects. The distribution of test statistic is given and employed to obtain the test procedure. The authors also study the test of mean-shift outlier model in error variables, and a score test is used to identify the multiple-outliers in the data. Related Articles | Metrics

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Expected Bayesian Estimation of Failure Probability and Its Character Han Ming Acta mathematica scientia,Series A. 2007, 27 (3):  488-495.  Abstract ( 1961 )   RICH HTML PDF (342KB) ( 1300 )   Save This paper develops a new method of parameter estimation, which is named as E-Bayesian estimation method. In the case of zero-failure data, the defined of E-Bayesian estimation of the failure probability is provided, and more the formulas of E-Bayesian estimation of the failure probability is provided also on the base. Then discusses the character of E-Bayesian estimation-----the relations between E-Bayesian estimation and hierarchical Bayesian estimation. Finally, calculations are performed according to simulation example, which show that the method provided in the paper is practicable and easy to operate. Related Articles | Metrics

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Global Stability of Single-species Diffusion Models with Time Delay Gui Zhanji; Jia Jing; Ge Weigao Acta mathematica scientia,Series A. 2007, 27 (3):  496-505.  Abstract ( 2236 )   RICH HTML PDF (332KB) ( 1270 )   Save In this paper, single-species diffusion models with time delays are investigated. It can have a positive equilibrium by homotopy techniques. It is showed that the system is uniformly persistent under appropriate conditions, and sufficient conditions are obtained for local stability and global stability of the equilibrium of the system. Related Articles | Metrics

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Sufficient Conditions for Almost Starlike Mappings of Order α Feng Shuxia; Liu Taishun Acta mathematica scientia,Series A. 2007, 27 (3):  506-514.  Abstract ( 2048 )   RICH HTML PDF (303KB) ( 1004 )   Save In this paper, the authors establish some partial differential inequalities on bounded starlike circular domains and the unit ball of Banach norm in cn. Then using these inequalities, the authors get two sufficient conditions for almost starlike mappings of order α. Related Articles | Metrics

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Two-weight Integral Inequalities for Differential Forms Li Juan Acta mathematica scientia,Series A. 2007, 27 (3):  515-523.  Abstract ( 1616 )   RICH HTML PDF (284KB) ( 1082 )   Save In this paper, some two-weight integral inequalities for differential forms satisfying A-harmonic equation are proved. As applications of the local result, the global cases on a domain are obtained. Related Articles | Metrics

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Generalized Gaussian Quadrature Formulas Cao Lihua Acta mathematica scientia,Series A. 2007, 27 (3):  524-534.  Abstract ( 2201 )   RICH HTML PDF (311KB) ( 1455 )   Save The purpose of this paper is to construct a generalized Gaussian quadrature rule based on the divided differences of the integrand at the zeros of the n-th Chebyshev polynomial of the first kind. Another similar quadrature rule based on the divided differences at the zeros of the n-th Chebyshev polynomial of the second kind is also considered. The obtained results include some existing results as special cases. The interesting thing here is that these new results are closely related to the so-called Gauss-Turan quadrature formulas. Related Articles | Metrics

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An Active Constraints Identification Technique-based SSLE Algorithm and Its Convergence Analysis Zhou Changyin; He Guoping; Wang Yongli Acta mathematica scientia,Series A. 2007, 27 (3):  535-540.  Abstract ( 2406 )   RICH HTML PDF (331KB) ( 1328 )   Save In this paper, based on an active set identification technique, a new feasible sequential system of linear equations (SSLE) algorithm is proposed for nonlinear optimization problems with inequality constraints. At each iteration, only two or three systems of linear equations with a common coefficient matrix are solved to obtain the search direction. Under mild conditions, the suggested algorithm converges globally to a KKT point of the problem. Without assuming the strict complementarity, the convergence rate is proved to be superlinear under a condition weaker than the strong second-order sufficiency condition. Related Articles | Metrics

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Hochschild Cohomology of l-hereditary Algebras Xu Yunge; Zeng Xiangyong Acta mathematica scientia,Series A. 2007, 27 (3):  544-548.  Abstract ( 1566 )   RICH HTML PDF (299KB) ( 1026 )   Save Let $\Lambda$ be a finite-dimensional $k$-algebra over a field $k$. The low dimensional Hochschild cohomological groups $H^i(\Lambda)~(i \leq 2)$ have a classical interpretation and play an important role in representation theory of finite-dimensional algebras. In this note the formulae on the dimensions of the first and the second Hochschild cohomology groups of $l$-hereditary algebras are obtained explicitly. Related Articles | Metrics

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Positive Solutions for Singular Two-point Boundary Value Problem for p-Laplacian Equation Xiong Ming; Liu Jiaquan; Zeng Pingan Acta mathematica scientia,Series A. 2007, 27 (3):  549-558.  Abstract ( 2157 )   RICH HTML PDF (286KB) ( 1144 )   Save Some results on existence of positive solutions for singular boundary value problem -(|u'(t)|p-2u'(t))'=a(t)f(u(t)), t∈(0,1) u(0)=u(1)=0 have been given, where the function a(t) may be singular at t=0,1. Related Articles | Metrics

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Periodic Solutions for a Class of Neutral Functional Differential Equations with Infinite Delay Liu Guirong; Yan Jurang Acta mathematica scientia,Series A. 2007, 27 (3):  559-567.  Abstract ( 1807 )   RICH HTML PDF (307KB) ( 1092 )   Save Discuss the periodic solutions of the following neutral functional differential equation with infinite delay $$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t). $$ Some results on the existence and uniqueness of periodic solutions are obtained by using continuation theorem in coincidence degree. Especially, when $g(s,x)\equiv 0$ and $A(t,x)=A(t)$, the conditions which guarantee the existence of the unique and stable periodic solution are derived. Related Articles | Metrics

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Multiplication of Orthogonal Arrays Pang Shanqi; Zhang Yingshan Acta mathematica scientia,Series A. 2007, 27 (3):  568-576.  Abstract ( 2126 )   RICH HTML PDF (273KB) ( 1130 )   Save A kind of multiplication of orthogonal arrays is presented by exploring orthogonal decomposition of projection matrices. Using this multiplication, one can construct some new larger orthogonal arrays from smaller ones. Related Articles | Metrics