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25 April 2011, Volume 31 Issue 2 Previous Issue    Next Issue

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The Existence of Smooth Solutions for a Nonlinear Beam with Distributed Damping JIA Chao-Hua, FENG De-Xing Acta mathematica scientia,Series A. 2011, 31 (2):  273-288.  Abstract ( 1256 )   RICH HTML PDF (414KB) ( 1105 )   Save This article is devoted to the study of the existence of local smooth solutions to a nonlinear beam with distributed damping. Applying the theory of evolution equations, we first show that related linear systems admit unique smooth solutions. Then some energy estimates for the linear systems are established. Finally we prove the existence of local smooth solutions to the nonlinear system by the fixed point argument. References | Related Articles | Metrics

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Eistence of Solutions for Nonlinear Fractional Order Functional Differential |Equations ZHANG Hai, ZHENG Zu-Xiu, JIANG Wei Acta mathematica scientia,Series A. 2011, 31 (2):  289-297.  Abstract ( 2236 )   RICH HTML PDF (321KB) ( 1066 )   Save This paper is concerned with the initial value problems for nonlinear fractional functional differential equations. The results of existence of solutions are derived based on Banach fixed point theorem, Schauder fixed point theorem and successive approximations technique, respectively. These results extend the corresponding ones of ordinary differential equations and functional differential equations of integer order. An example is also given to illustrate the validity and practicability of our main results. References | Related Articles | Metrics

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Completely Distributionally Chaotic Maps on Countable Metric Spaces YUAN Da-Lian, LV Jie Acta mathematica scientia,Series A. 2011, 31 (2):  298-304.  Abstract ( 1188 )   RICH HTML PDF (313KB) ( 961 )   Save Let X={x0, x1, …} be a countable metric space without isolate point. Then for every 0<δ<diam X there exists a homeomorphism φ on X such that (a) X={φix0: i ∈Z} and either {φix0: i ≥0} and {φ-ix0: i ≥0} is dense in X and (b) X is a distributionally δ-chaotic set of either φ or φ-1. References | Related Articles | Metrics

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Global and Pointwise Estimates for Approximation by Rational Functions with Polynomials of Positive Coefficients as the Denominators YU Dan-Sheng, ZHOU Song-Ping Acta mathematica scientia,Series A. 2011, 31 (2):  305-319.  Abstract ( 1596 )   RICH HTML PDF (349KB) ( 988 )   Save For non-negative continuous function f(x) defined on [0,1], and f≠0, the present paper proves that, there is a polynomial Pn(x)∈Πn(+), such that $$\left|f(x)-\frac{1}{P_n(x)}\right|\leq C\omega_{\varphi^\lambda}\big(f,n^{-1/2}A_n^{1-\lambda}(x)\big),$$ where An(x)=\sqrt{x(1-x)}+1/\sqrt{n},\;0\leq \lambda\leq 1,$and$\Pi_n(+)$ indicates the set of all polynomials of degree n with positive coefficients. When $f(x)$ has exact $l$ sign change points in (0, 1), we also construct a rational function $r(x)\in R_n^l(+)$ such that $$\left|f(x)-r(x)\right|\leqC(l+1)^{2}\omega_{\varphi^\lambda}\big(f,n^{-1/2}A_n^{1-\lambda}(x)\big).$$ References | Related Articles | Metrics

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Procrustes Problem of Hermitian Degree k R-symmetric Matrix and Its Approximation Problem JIA Zhi-Gang, WEI Mu-Sheng, ZHAO Mei-Xiang Acta mathematica scientia,Series A. 2011, 31 (2):  320-327.  Abstract ( 1381 )   RICH HTML PDF (293KB) ( 1063 )   Save The class of Hermitian degree k R-symmetric matrices is characterized. Necessary and sufficient conditions and explicit formulations   of   Hermitian degree k R-symmetric solutions of | AX-V|=min and AX=V are respectively derived, where X, V in Cnχm are known matrices. For given matrix Cnχn, the unique common Hermitian degree k R-symmetric solution of | AX-V| and | A-B| is obtained. References | Related Articles | Metrics

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Property U of Orlicz Space LIU Chun-Yan, SHI Zhong-Rui Acta mathematica scientia,Series A. 2011, 31 (2):  328-334.  Abstract ( 1163 )   RICH HTML PDF (282KB) ( 951 )   Save In this paper, a result that a finite dimensional subspace of Orlicz space with Orlicz norm [or Luxemburg norm] has property U if and only if each element of the subspace is a smooth point is obtained. References | Related Articles | Metrics

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Bilinear Pseudodifferential Operators with Forbidden Symbols on Morrey Type |Spaces ZHOU Jiang, CAO Yong-Hui, MA Bai-Lin Acta mathematica scientia,Series A. 2011, 31 (2):  335-342.  Abstract ( 1561 )   RICH HTML PDF (318KB) ( 986 )   Save In this paper, the authors prove that the bilinear pseudodifferential operators with forbidden symbols  are bounded on products of Morrey type Sobolev spaces and Morrey type Besov spaces. References | Related Articles | Metrics

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Lp Boundedness of |Parabolic Littlewood-Paley Operator with Rough Kernel Belonging to Fα(Sn-1) CHEN Dong-Xiang, LU Shan-Zhen Acta mathematica scientia,Series A. 2011, 31 (2):  343-350.  Abstract ( 1301 )   RICH HTML PDF (274KB) ( 848 )   Save In this paper, the authors establish the Lp-boundedness for  parabolic Littlewood-Paley operator under a weaker condition. Some known results are essentially improved. References | Related Articles | Metrics

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Practical Stability of Nonlinear Differential Equations Relative to Initial Time Difference via Perturbing Lyapunov Functions LI An, SONG Xin-Yu, WANG Zhi-Xiang Acta mathematica scientia,Series A. 2011, 31 (2):  351-359.  Abstract ( 1421 )   RICH HTML PDF (305KB) ( 933 )   Save In this paper, the practical stability of nonlinear differential equations with solutions starting off with different initial times is investigated. Several practical stability criteria of nonlinear dynamical systems relative to initial time difference are presented by perturbing Lyapunov functions. The  results enrich the theory on practical stability of nonlinear differential equations relative to initial time difference. References | Related Articles | Metrics

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Empirical Likelihood Inferences for Covariate Adjusted Regression ZHAO Pei-Xin, XUE Liu-Gen Acta mathematica scientia,Series A. 2011, 31 (2):  360-368.  Abstract ( 1379 )   RICH HTML PDF (381KB) ( 980 )   Save In this paper, an empirical likelihood inference for the covariate adjusted regression is investigated. Based on the empirical likelihood method, a corrected empirical likelihood ratio method is proposed and the Wilks' phenomenon is derived. Then, the confidence intervals for the regression coefficients are constructed. A simulation study and a real data application are undertaken to assess the finite sample performance of the proposed method. References | Related Articles | Metrics

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Generalization of |Phelps' Lemma to Bornological Vector Spaces HE Fei, QIU Jing-Hui Acta mathematica scientia,Series A. 2011, 31 (2):  369-377.  Abstract ( 1337 )   RICH HTML PDF (310KB) ( 987 )   Save Phelps' lemma is extended to bornological vector spaces. An immediate application is to re-establish Wong's generalization of Ekeland variational  principle to bornological vector spaces. And Ng and Zheng's result on existence of efficient points in topological vector spaces is easily achieved. Meanwhile, a Phelps' lemma in locally convex spaces is obtained. References | Related Articles | Metrics

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Regularity Results for Div-Curl Fields and Applications GAO Hong-Ya, HAN Xiao-Fan Acta mathematica scientia,Series A. 2011, 31 (2):  378-386.  Abstract ( 1275 )   RICH HTML PDF (294KB) ( 972 )   Save The aim of the present paper is to prove higher integrability results for div-curl vector fields B, E)∈Llocq(1-ε)(Ω, Rn)×Llocp(1-ε) (Ω, Rn) , 1< p, q <∞, 1/p + 1/q =1, ε sufficiently small, such that divB =0, E= 0 satisfying a reverse inequality of the type | B |q + | E |p ≤C <B, E> + | F |q, with F ∈Lr (Ω, Rn), r > q (1-ε) . Applications to the theory of weak quasiregular mappings and very weak solutions of nonhomogeneous A -harmonic equations divA (x, \nabla u) = div F are given. References | Related Articles | Metrics

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Optimization of Adaptive Direct Method for Approximate Solution of Integral Equations with Bounded Mixed Derivative Kernels DUAN Li-Qin Acta mathematica scientia,Series A. 2011, 31 (2):  387-393.  Abstract ( 1291 )   RICH HTML PDF (315KB) ( 954 )   Save In this paper, the author  considers the problem of optimization of adaptive direct methods for approximate solution of operator equations. For some classes of Fredholm integral equations of the second kind with kernels belonging to the Sobolev classes with bounded mixed derivative, the author  determines the exact error orders on optimization of adaptive direct methods for approximate solution, and also gives an optimal algorithm in the sense of order. References | Related Articles | Metrics

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Piecewise-Koszul-Type Algebras LV Jia-Feng, CHEN Miao-Sen Acta mathematica scientia,Series A. 2011, 31 (2):  394-400.  Abstract ( 1115 )   RICH HTML PDF (291KB) ( 938 )   Save Piecewise-Koszul-type algebras, including some Artin-Schelter regular algebras of global dimension five, are introduced in this paper. It is showed  that the `piecewise-Koszul-type property' of an algebra can be characterized by its minimal graded free resolution and the associated generalized Castelnuovo-Mumford regularity. The structure of the Yoneda algebra $\bigoplus\limits_{i\geq0}{\rm Ext}_A^i({\Bbb K},{\Bbb K})$ of a piecewise-Koszul-type algebra is investigated. In particular, a necessary and sufficient condition for a graded algebra to be piecewise-Koszul-type is given in terms of the Yoneda algebra. References | Related Articles | Metrics

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Existence of Positive Solutions for |Boundary Value Problems with Nonlinear Fractional Differential Equations XU Xiao-Jie, SUN Xin-Guo, LV Wei Acta mathematica scientia,Series A. 2011, 31 (2):  401-409.  Abstract ( 1719 )   RICH HTML PDF (288KB) ( 1107 )   Save In this paper, the authors  consider the properties of Green's function for the nonlinear fractional differential equation boundary-value problem Dα0+u(t)=f(t, u(t)), 0<t<1,  u(0)=u(1)=u'(0)=u'(1)=0, where 3<α≤4 is a real number, and Dα0+ is the standard Riemann-Liouville differentiation, and f: [0,1]×[0, ∞)→[0, ∞) is continuous.  As an application of Green's function, the authors give some multiple positive solutions for nonlinear by means of some fixed-point theorem on cones. References | Related Articles | Metrics

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On Buffon Problem for Bounded Lattices in E3 XIE Feng-Fan, HU Shi-Geng Acta mathematica scientia,Series A. 2011, 31 (2):  410-414.  Abstract ( 1692 )   RICH HTML PDF (292KB) ( 931 )   Save Two new concepts, the restricted chord function and the restricted chord projection function, both referring to the convex body in En, were  introduced in Reference[1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex body in En,  were established based on these concents and a discussion was given with respect to right parallelepiped domain in E3. In this paper, by using restricted chord projection method, the authors could solve Buffon needle problem for three kinds of bounded lattices in E3.  References | Related Articles | Metrics

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Asymptotic Estimates of the Discounted Penalty Function in a Perturbed Risk Model ZHANG Zhen-Zhong, ZU Jie-Zhong, LIU Yuan-Yuan Acta mathematica scientia,Series A. 2011, 31 (2):  415-421.  Abstract ( 1527 )   RICH HTML PDF (301KB) ( 985 )   Save In this paper, the authors focus on asymptotic behavior of the discounted penalty function in the classical risk model perturbed by diffusion when the claim size is sub-exponentially distributed. They obtain the exact asymptotic expressions for  the discounted penalty function caused by  a claim, in two cases: δ>0 and δ=0, where δ denotes the interest force. Moreover, it is showed  that the discounted penalty function caused by oscillation vanishes when the initial reserve goes to infinity. References | Related Articles | Metrics

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Almost Periodic Solutions for Cellular Neural Networks with Distributed Delays ZHANG Ruo-Jun, WANG Lin-Shan Acta mathematica scientia,Series A. 2011, 31 (2):  422-429.  Abstract ( 1496 )   RICH HTML PDF (325KB) ( 910 )   Save In this paper, cellular neural networks with distributed delays are considered. Without assuming the global Lipschitz conditions of neuron signal functions, sufficient conditions for the existence, uniqueness and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality technique. The authors extend and improve previously known results. Moreover, an example is also worked out to illustrate the advantages of the results. References | Related Articles | Metrics

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Generalized Weighted Mean Values and r-Convex Functions in Carnots Groups SUN Ming-Bao, YANG Xiao-Ping Acta mathematica scientia,Series A. 2011, 31 (2):  430-438.  Abstract ( 1368 )   RICH HTML PDF (318KB) ( 1093 )   Save In this paper, we establish the relationship between generalized weighted mean values and r-convex functions on Carnot group $G$, which is a generalization of the classical Hadamard's inequality for convex functions. References | Related Articles | Metrics

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The Solutions of Linear Dynamical Equations in Commutative Banach Algebra on Time Scales FENG Yao-Ling Acta mathematica scientia,Series A. 2011, 31 (2):  439-446.  Abstract ( 1341 )   RICH HTML PDF (338KB) ( 1044 )   Save In this paper, using functional calculus and spectrum theory of Banach algebra, we give an explicit formula of the general exponential function in Banach algebra on time scales which improves the one in real number. We also prove it to be the unique solution of the IVP of linear dynamical equations in unital commutative Banach algebra on time scales. References | Related Articles | Metrics

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Uniqueness of Meromorphic Functions Concerning Differential Polynomials ZHANG Xiao-Yu, CHEN Jun-Fan, LIN Wei-Chuan Acta mathematica scientia,Series A. 2011, 31 (2):  447-454.  Abstract ( 1711 )   RICH HTML PDF (294KB) ( 915 )   Save In this paper, we discuss the uniqueness problems of meromorphic functions concerning differential polynomials by the idea of weighted sharing introduced by I.Lahiri, improve and generalize some previous results. References | Related Articles | Metrics

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Existence of Solutions to a Semipositone Third-order Three-point BVP on Time Scales SANG Yan-Bin, WEI Zhong-Li Acta mathematica scientia,Series A. 2011, 31 (2):  455-465.  Abstract ( 1428 )   RICH HTML PDF (356KB) ( 1009 )   Save In this paper, by constructing an auxiliary function concerned with nonlinear term and considering the properties of this auxiliary function on bounded sets, the existence of solutions is established for a semipositone third-order three-point BVP on time scales, where the nonlinear term is lower bounded. The main tool is based on Krasnosel'skii fixed point theorem of cone expansion-compression type. References | Related Articles | Metrics

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The First Cartan Invariant of Sp(4, 3n) WU Sui-Chao, YE Jia-Chen Acta mathematica scientia,Series A. 2011, 31 (2):  466-477.  Abstract ( 1755 )   RICH HTML PDF (295KB) ( 1012 )   Save It is a very important aspect in modular representations of finite groups that how one can calculate the Cartan invariant, especially, the first Cartan invariant for a finite group of Lie type. By using a series of results from modular representations of algebraic groups, and by using MATLAB software, the authors compute the first Cartan invariant of the finite symplectic group Sp(4, 3n) over a field with 3n elements. References | Related Articles | Metrics

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Perturbations of Standard Generalized Frames in Hilbert  W*-Module FU Huan-Kun, MENG Bin, DONG Fang-Fang Acta mathematica scientia,Series A. 2011, 31 (2):  478-491.  Abstract ( 1378 )   RICH HTML PDF (321KB) ( 888 )   Save In this paper, the stability of Hilbert W*-modular standard generalized frames under perturbations are studied intensively by using operator-theoretic-methods, and some useful conditions of perturbation and results which are similar to the frames in Hilbert space are given. References | Related Articles | Metrics

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Lattices Associated with Distance-Regular Graphs I LI Zeng-Ti Acta mathematica scientia,Series A. 2011, 31 (2):  492-499.  Abstract ( 1196 )   RICH HTML PDF (260KB) ( 893 )   Save Let L be a finite set associated with cliques of a distance-regular graph of order (s,t),  with d-cliques of the Johnson graphs J(dm,d) and antipodal distance-regular graphs of diameter d, respectively. If we partially order L by the reverse inclusion, three families of finite lattices are obtained. This article discusses their atomicity, and computes their character polynomials. References | Related Articles | Metrics

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The Minimum Selections of Set-Valued Mappings and Applications ZHU Xing-Hua, Xiao-Jian-Zhong Acta mathematica scientia,Series A. 2011, 31 (2):  500-507.  Abstract ( 1555 )   RICH HTML PDF (337KB) ( 1037 )   Save In this paper, the continuation properties of the minimum selections of set-valued mappings are studied by utilizing the theory of geometry in Banach space, and some continuity theorems depended on geometric properties of spaces are given. On the basis of these, the problem concerning the continuation properties of minimum right inverses for surjective linear operators is discussed. References | Related Articles | Metrics

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Some Strong Limit Theorems of Geometric Average of Transition Probabilities |and Their Function for Markov Chains in Markovian Environments LI Ying-Qiu, WANG He-Song, WANG Zhong Acta mathematica scientia,Series A. 2011, 31 (2):  508-517.  Abstract ( 1269 )   RICH HTML PDF (368KB) ( 949 )   Save By using analytic method, the strong limit theorems expressed by inequalities relative to geometric average of transition probabilities for fintie state Markov chains in single infinitely Markovian environments are obtained. Furthermore, their functional limit properties are studied and a class of strong laws of large numbers different from usual ones are obtained. References | Related Articles | Metrics

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Local Influential Analysis in Contingency Tables HE Li-Ping, SHI Lei Acta mathematica scientia,Series A. 2011, 31 (2):  518-527.  Abstract ( 1255 )   RICH HTML PDF (427KB) ( 1002 )   Save This paper studies the local influence in contingency tables. Based on power-divergence statistics, the I distance function, associated influential graph and the conformal normal curvature are constructed, and a new local influence method is proposed to detect the influential cells in r×c contingency table. The results are applied to detect the influential observations in the independent model of the contingency tables. Finally an example  is used for illustration. References | Related Articles | Metrics

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An Embedding Theorem of a Class of Bidimensional Frame Multiresolution Analyses ZHUNG Zhi-Tao, LI Yun-Zhang Acta mathematica scientia,Series A. 2011, 31 (2):  528-539.  Abstract ( 1300 )   RICH HTML PDF (372KB) ( 1038 )   Save This paper addresses the embedding relation of a frame multiresolution analysis (FMRA) into a multiresolution analysis (MRA) associated with a 2×2 dilation matrix with determinant ±2. It is well-known that 2×2 dilation matrices with  determinant ±2 can be classified as six classes according to integral similarity. For three classes of them, it is proved that an arbitrary FMRA must be contained in some MRA. References | Related Articles | Metrics

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A Normal Criterion Concerning Shared Values HUANG Xiao-Jie, LIU Zhi-Xiu Acta mathematica scientia,Series A. 2011, 31 (2):  540-545.  Abstract ( 1468 )   RICH HTML PDF (263KB) ( 993 )   Save Let F be a family of meromorphic functions on a plane domain D, let a, e be two finite complex numbers, and b, c, d be three nonzero finite complex numbers. If, for each F, all the zeros of f-e are of multiplicity at least k≥2, f(z)=a↔ (z)=a↔ f (k)(z)=b, and f(k)(z)=c→f (k+1)(z)=d, then F is a normal family on D. The same result holds for k=1so long as b≠(n+1)c, n=1, 2…. References | Related Articles | Metrics

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The Discrete Time Geomx/G/1 Repairable Queueing System with Delay Multiple Vacations---Some Queueing Indices TANG Ying-Hui, YU Miao-Miao, LI Cai-Liang, HUANG Shu-Juan, YUN Xi Acta mathematica scientia,Series A. 2011, 31 (2):  546-558.  Abstract ( 1299 )   RICH HTML PDF (643KB) ( 917 )   Save This paper firstly considers the discrete time Geomx/G/1 repairable queue system with delay multiple vacations. It's assumed that both the inter-arrival times and the life of the service station are independent random variables with geometric distribution, while the service time, the delayed vacation time, the vacation time and the repair time have general discrete distribution. By introducing the server busy period and using the total probability decomposition technique we discuss the transient properties of the queue length from the beginning of  any initial state i~(i=0,1,…), and obtain the z-transformation of the transient distribution of the queue length. Furthermore, we obtain the recursion expressions of the steady distribution and the stochastic decomposition of the queue length at a random point in equilibrium. Especially we can obtain some corresponding results of the discrete queue system under some special cases. References | Related Articles | Metrics

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Galois Theory for Partial Group Entwining Structure GUO Qiao-ling Acta mathematica scientia,Series A. 2011, 31 (2):  559-566.  Abstract ( 1222 )   RICH HTML PDF (271KB) ( 923 )   Save In this note, we  develop Galois theory  for partial  group entwining structures, generalizing the corresponding theory  of Caenepeel et.al.. References | Related Articles | Metrics

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Behaviors of Vertex Neighbors of Trees Under Some Graph Colorings YAO Bing, CHENG Hui, YAO Meng, ZHANG Zhong-Fu Acta mathematica scientia,Series A. 2011, 31 (2):  567-576.  Abstract ( 1387 )   RICH HTML PDF (466KB) ( 1117 )   Save Behaviors of vertex neighbors of trees under certain graph colorings show some interesting problems. These behaviors of vertex neighbors of trees give  stronger properties for known total colorings, and reveal some relations between the coloring conjectures, more or less. It is hoped to apply these behaviors to study deeply graph coloring problems. References | Related Articles | Metrics

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E-Bayesian Estimation of Failure Probability in the Case of Data Only One Failure HAN Ming Acta mathematica scientia,Series A. 2011, 31 (2):  577-583.  Abstract ( 1550 )   RICH HTML PDF (345KB) ( 1004 )   Save This paper introduces a new parameter estimation method, named E-Bayesian estimation method, to estimate failure probability. In the case of data only one failure, the definition of E-Bayesian estimation of the failure probability is provided, moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation, and the properties of E-Bayesian estimation of the failure probability are also provided. Finally, calculations are performed according practical problem, which shows that the provided method in the paper is practicable and easy to operate. References | Related Articles | Metrics