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25 April 2009, Volume 29 Issue 2 Previous Issue    Next Issue

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The Decay of Weak Solution of Pseudo-asymptotic Linear p&q-Laplacian Equation on RN HE Cheng-Jun, LI Gong-Bao Acta mathematica scientia,Series A. 2009, 29 (2):  217-222.  Abstract ( 1794 )   RICH HTML PDF (298KB) ( 1236 )   Save In this paper, the authors study the following equation { Δpu+m|u|p-2u-Δqu+n|u|q-2u=g(x, u),    x ∈ RN,   u ∈  W1, p(RN) ∩ W1, q(RN) where m, n>0,  N\ ≥ 3, 1 < q < p < N and g(x, u) satisfies some kind of asymptotic about u at infinity. They prove that the solution of this equation decays exponentially aoubt |x| at infinity. References | Related Articles | Metrics

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The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models XU Li-Wen, WANG Song-Gui Acta mathematica scientia,Series A. 2009, 29 (2):  223-232.  Abstract ( 2217 )   RICH HTML PDF (391KB) ( 1200 )   Save In this paper,   the estimation of a linear combination of fixed and random effects is investigated  in general linear mixed  models. Explicit expression of the best linear unbiased estimator(BLUE) of  the combination is derived and it is shown that this  BLUE is  essentially-unique where  the covariance matrix of the vector of observations may be singular. For the three small-area models that are all special cases of the general linear mixed model, spectral decomposition estimators(SDE) of small area mean, ui, and variance components are derived. Furthermore, second-order approximations to the MSE of two-stage estimators based on SDE are obtained. References | Related Articles | Metrics

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On the Largest Spectral Radius of Nonregular Graph Liu Bolian Acta mathematica scientia,Series A. 2009, 29 (2):  233-238.  Abstract ( 2206 )   RICH HTML PDF (220KB) ( 1105 )   Save The author discusses the upper bound for the largest eigenvalue of a  nonregular graph with order n and the maximum degree ? obtained by D.Stevanovi\'c and gives some new bounds in terms of  ?. References | Related Articles | Metrics

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Double-disk Property of Curves and Quasiconformal Mappings CHU Yu-Meng, WANG Gen-Di, ZHANG Xiao-Hui Acta mathematica scientia,Series A. 2009, 29 (2):  239-244.  Abstract ( 1556 )   RICH HTML PDF (279KB) ( 1109 )   Save Let f : R2→R2 be a homeomorphism with f (∝)=∝. In this paper, the authors prove that f is a quasiconformal mapping if and only if f preserves the double-disk property of curves. References | Related Articles | Metrics

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An Optimal Filtering Method for Solving a |Sideways Parabolic Equation LI Hong-Fang, FU Chu-Li, XIONG Xiang-Qiu, NA Nan Acta mathematica scientia,Series A. 2009, 29 (2):  245-252.  Abstract ( 2684 )   RICH HTML PDF (388KB) ( 1213 )   Save The authors  consider a sideways parabolic equation in the quarter plane, i.e., a non-standard inverse heat conduction  equation with convection term. People want determine the solution u(x, t) for 0 < x <1 from the data along the line x=1. This is an  ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. Some special regularization method is needed for solving this problem.  This paper considers an optimal filtering method and  gives the H\"{o}lder optimal error estimate between the exact solution and its regularized approximation solution. Furthermore, the convergence of  the regularized approximation solution at x=0 is also obtained. References | Related Articles | Metrics

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The Existence of Periodic Solutions for a Kind of Second Order Functional Differential Equations with Deviating Arguments ZHANG Chi, WANG Quan-Xi Acta mathematica scientia,Series A. 2009, 29 (2):  253-261.  Abstract ( 1931 )   RICH HTML PDF (321KB) ( 1189 )   Save In this paper, by using the abstract continuation theorem of k-set contractive operator and some analysis techniques, the authors study the existence of periodic solutions for a kind of second order functional differential equations with deviating arguments. The results improve and extend the main results of the papers [1-2]. References | Related Articles | Metrics

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Almost Sure Central Limit Theroem in Separable Metric Space FANG Yong-. Zhang-Chao-Xi Acta mathematica scientia,Series A. 2009, 29 (2):  262-271.  Abstract ( 1807 )   RICH HTML PDF (342KB) ( 1173 )   Save In this paper, the authors get the almost sure central limit theroems in separable metric space. As applications, they discuss the almost sure central limit theroems for the independent identically distributed random element sequence in separable Banach space, a certain independent identically distributed stochastic  processes sequence and  multidimension independent identically distributed random variables sequence. References | Related Articles | Metrics

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Drazin Spectra of 2×2 Upper-triangular |Operator Matrices ZHANG Hai-Yan, ZHANG Xi-Hua, DU Hong-Ke Acta mathematica scientia,Series A. 2009, 29 (2):  272-282.  Abstract ( 1952 )   RICH HTML PDF (318KB) ( 1233 )   Save Let MC=[A   C ;  0   B] be a 2×2 upper-triangular  operator matrix acting on the  Hilbert space H  K .  In this paper, the authors investigate the Drazin invertibility of MC and the Drazin spectrum of MC. Moreover,  for given operaters A ∈B}(H) and  B ∈B}(K), they shall give a  representation of ∩ σD (MC) under  certain condition. References | Related Articles | Metrics

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On Fractal Dimensions of some Level Sets of Random Walk XIONG Ying Acta mathematica scientia,Series A. 2009, 29 (2):  283-289.  Abstract ( 1981 )   RICH HTML PDF (263KB) ( 1009 )   Save For one-dimensional simple symmetric random walk, the Hausdorff and packing dimensions of level sets with prescribed rate of returns to the origin are determined. References | Related Articles | Metrics

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Fixed Point |Theorems for Asymptotically Nonexpansive Type Semigroups in General Banach Spaces SHU Lan-Ping, LI Gang Acta mathematica scientia,Series A. 2009, 29 (2):  290-296.  Abstract ( 369 )   RICH HTML PDF (246KB) ( 1097 )   Save This paper is first devoted to proving two existence theorems of fixed points  for  asymptotically nonexpansive type semigroups in general Banach  spaces. Based on these results, a strong convergence theorem of Mann's type sequences for the asymptotically nonexpansive type semigroups is given. The main results extend the results of Suzuki and Takahashi  to the case of  the non-Lipschitzian  semigroups. References | Related Articles | Metrics

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On Maximum γt - Critical Graphs WANG Chun-Xiang, LI Xiang-Wen Acta mathematica scientia,Series A. 2009, 29 (2):  297-302.  Abstract ( 342 )   RICH HTML PDF (281KB) ( 905 )   Save A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than that of G. These graphs are called γt-critical. If such a graph G has total domination number k,  it is called k-γt-critical. In this paper, the authors give the structure proof of those graphs satisfying n=Δ(G)(γt(G)-1)+1. References | Related Articles | Metrics

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Weak Limit Theorems for Ji\v{r}ina Processes with Immigration Li Yuqiang Acta mathematica scientia,Series A. 2009, 29 (2):  303-315.  Abstract ( 426 )   RICH HTML PDF (373KB) ( 1100 )   Save The author studies the limit theorems of Ji\v{r}ina processes with immigration under moment conditions. The moment conditions are classified according to the limiting processes. It is proved that under different moment conditions, a sequence of scaled Ji\v{r}ina processes with immigration converges weakly in the Skorokhod space to the continuous branching process, the continuous branching process with immigration, the branching process with immigration with jumps and the deterministic process, respectively. For the last case, a fluctuation limit theorem is also proved. References | Related Articles | Metrics

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Optimal Approximation Problem of Antireflexive Matrices under the Spectral Restriction GUAN Li, ZHANG Zhong-Zhi, XIE Dong-Xiu Acta mathematica scientia,Series A. 2009, 29 (2):  316-323.  Abstract ( 376 )   RICH HTML PDF (293KB) ( 1037 )   Save In this paper, the inverse eigenvalue problem of antireflexive matrices and relevant optimal approximation problem are considered. Some necessary and sufficient conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for solvable case. Furthermore, for any given complex matrix of dimension n, an expression of solution for its optimal approximation is presented. References | Related Articles | Metrics

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Finite Group and Laplician Qiu Weigang Acta mathematica scientia,Series A. 2009, 29 (2):  324-327.  Abstract ( 488 )   RICH HTML PDF (231KB) ( 1004 )   Save The eigenfunction of Laplacian with the symmetry of tetrahedral group Td and octahedron group Oh is constructed by representation and character. The eigenvalues are derived by the Dirichlet boundary condition. Finally, the parameter space of eigenvalues is discussed. References | Related Articles | Metrics

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Uniqueness for Parabolic Equations in Non-cylindrical Domains Li Jing Acta mathematica scientia,Series A. 2009, 29 (2):  328-333.  Abstract ( 319 )   RICH HTML PDF (266KB) ( 1099 )   Save This work concerns the uniqueness of solutions to parabolic equations in domains which are moving in time. Two uniqueness results are proved. The first one is the unique continuation property for parabolic equations in non-cylindrical domains. The second one is the backward uniqueness for parabolic equations in exterior domains with moving boundary. References | Related Articles | Metrics

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Observer-based Passive Control for Nonlinear Uncertain Time-delay Jump Systems HE Shu-Beng, LIU Fei Acta mathematica scientia,Series A. 2009, 29 (2):  334-343.  Abstract ( 484 )   RICH HTML PDF (391KB) ( 1122 )   Save Based on the robust control theory, the problem of passive control and the design of  the observer-based passive controller for a class of nonlinear uncertain time-delay Markov jump systems are dealt with by using linear matrix inequalities. By constructing proper Lyapunov functions, a sufficient condition for the system to be asymptotically stable with a passive index bound is presented for all admissible uncertainties, time-delays, and nonlinearities. The passive controller is obtained by solving a linear matrix inequality. Simulation results demonstrate the validity of the proposed approaches. References | Related Articles | Metrics

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Positve Solutions of Fourth Order Singular Superlinear p-Laplacian BVPs WANG Yan-Ling, SHI Guo-Liang Acta mathematica scientia,Series A. 2009, 29 (2):  344-352.  Abstract ( 418 )   RICH HTML PDF (276KB) ( 958 )   Save Necessary and sufficient conditions for existence of positive solutions of fourth order singular superlinear p-Laplacian BVPs are established by employing the fixed point theorem in cones. The conditions involve   the integral of the nonlinear terms. References | Related Articles | Metrics

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On the Existence and Decision Theorem of the Maximum Type Borel Point of Quasi-meromorphic Mappings in the Unit Circle XU Hong-Yan, YI Cai-Feng Acta mathematica scientia,Series A. 2009, 29 (2):  353-356.  Abstract ( 459 )   RICH HTML PDF (290KB) ( 961 )   Save In this paper, an inequality of K-quasimeromorphic mappings in the angular region in the unit circle is obtained, and by applying this inequality, the existence and decision theorem of the maximum type Borel point of K-quasimeromorphic mappings with finite order in the unit circle is studied. References | Related Articles | Metrics

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Studies on the Positive Operator Solutions to Operator Equations X+A*X-tA=Q YANG Kai-Fan, DU Hong-Ke Acta mathematica scientia,Series A. 2009, 29 (2):  359-364.  Abstract ( 390 )   RICH HTML PDF (248KB) ( 987 )   Save In this paper, the necessary conditions for the existence of positive operator solutions of the operator equation X+A*X-tA=Q are established. A sufficient and necessary condition for the existence of positive operator solutions for X+A*X-tA=Q is also derived. References | Related Articles | Metrics

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Extending Matchings in Odd Graphs DI Chao-Hui, GUO Xiao-Feng Acta mathematica scientia,Series A. 2009, 29 (2):  365-372.  Abstract ( 377 )   RICH HTML PDF (315KB) ( 1133 )   Save  Let G be  a graph, and let n, k and d be three nonnegative integers such that n+2k+d≤ |V(G)|-2 and, |V(G)| and n+d have the same parity. If after deleting any n vertices from G the remaining subgraph of G contains an k-matching and each k-matching of the subgraph can be extended to a defect-d-matching of the subgraph, then G is called an (n, k, d)-graph. Liu and Yu[1] first introduced (n, k, d)-graphs, and gave some properties and characterization of (n, k, d)-graphs. A (0, k, 1)-graph may be also called a near k-extendable graph. In the present paper, the authors improve the characterization of (n, k, d)-graphs, and consequently obtain a characterization of near k-extendable graphs. Furthermore, a characterization of near k-extendable bipartite graphs and the relations between near k-extendable graphs and n-factor critical graphs are investigated. References | Related Articles | Metrics

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General Theory of Radical Properties of Groups LI Xue-Mei, ZHANG Zhi-Rang Acta mathematica scientia,Series A. 2009, 29 (2):  373-377.  Abstract ( 308 )   RICH HTML PDF (250KB) ( 1046 )   Save In this paper, several examples of radical properties for arbitrary groups are given and the general theory of  radical properties of groups is studied. References | Related Articles | Metrics

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A Note on Strongly Separativity over Exchange Rings Chen Huanyin Acta mathematica scientia,Series A. 2009, 29 (2):  378-382.  Abstract ( 334 )   RICH HTML PDF (233KB) ( 1192 )   Save A ring R is strongly separative provided that, for any finitely generated projective right R-modules A and B, A    A ≌  A    B → A ≌ B. The author proves, in this note, that strongly separativity over exchange rings is invariant under subdirect products. As an application, the author proves that R/(IJ) is strongly separative if and only if so does R/(I∩J) for any ideals of an exchange ring. References | Related Articles | Metrics

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A Nonlinear Stochastic Evolution Equation in Hilbert Space Qiao Huijie Acta mathematica scientia,Series A. 2009, 29 (2):  383-391.  Abstract ( 397 )   RICH HTML PDF (289KB) ( 1016 )   Save This paper deals with a nonlinear stochastic evolution equation in a real separable Hilbert space. It is shown that the stochastic equation has a unique mild solution. Moreover, a time discretized approximation for the equation is proved to converge. References | Related Articles | Metrics

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Continuity for the Generators of some C0-semigroups and Cosine Families |in ∑e1 Type Banach Spaces SU Wei-Gang, ZHONG Fu-Jie Acta mathematica scientia,Series A. 2009, 29 (2):  392-398.  Abstract ( 345 )   RICH HTML PDF (334KB) ( 1056 )   Save This paper gives some sufficient conditions for the generators of uniformly bounded C0-semigroups to be bounded linear oprators in  ∑e1 type Banach spaces;  shows that the generator of  C0-semigroup  consisting of Hermitian operators or  isometries is always a bounded linear operator in such spaces;  shows that the generator of strongly continuous non-quasianalytic cosine family is necessarily a bounded linear operator in such spaces. References | Related Articles | Metrics

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A Krull-Schmidt Theorem for Lie Rings LIAO Jun, LIU Ge-Guo Acta mathematica scientia,Series A. 2009, 29 (2):  399-405.  Abstract ( 450 )   RICH HTML PDF (279KB) ( 1100 )   Save In this paper, the authors get the Krull-Schmidt theorem  for Lie rings. Let L be a Lie ring satisfying the maximal and minimal conditions on ideals. If                                   L = H1    H2    …     Hr=K1    K2    …    Ks are two Remak decompositions of L, then r=s and there is a central automorphism α of L such that, after suitable relabeling of the Kj's (if necessary), Hia = Ki and L = K1    K2    …     Kk    Hk+1    … Hr for k =1, 2, …, r. Furthermore,  L = H1    H2    …    Hr is the only Remak decomposition of L (up to the order of factors of  the direct sums) if and only if Hi0 ≤ Hi for every normal endomorphism θ of L and  i =1, 2, … , r. References | Related Articles | Metrics

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Application of the Diagonalization Method in the Robin Boundary Value Problem for the Vector Nonlinear Integro-differential Equations Lin Surong Acta mathematica scientia,Series A. 2009, 29 (2):  406-415.  Abstract ( 310 )   RICH HTML PDF (332KB) ( 1073 )   Save The singularly perturbed boundary value problem of scalar integro-differential equations was studied extensively by the differential inequality method. However, it is impossible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore, for n-dimensional vector integro-differential equations the problem has  not be solved fully. Here, the author studys this nonlinear vector problem by diagonalization method. Under appropriate conditions the existence of solution is proved and the asymptotic estimate is given as well. References | Related Articles | Metrics

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Noncreasy Orlicz-Bochner Function Spaces with Luxemburg Norm DONG Ge, WEI Wen-Zhan Acta mathematica scientia,Series A. 2009, 29 (2):  416-422.  Abstract ( 394 )   RICH HTML PDF (240KB) ( 1055 )   Save In this paper, the authors discuss the conditions for Orlicz-Bochner function spaces with Luxemburg norm to be noncreasy(NC) and obtain that, if X is a reflexive Banach space, then the Orlicz-Bochner spaces L(Φ)(X) is NC if and only if L(Φ)(X)is rotund or L(Φ)(X) is smooth. References | Related Articles | Metrics

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Generalized Bernstein Operators |Defined on a Simplex DING Chun-Mei, YANG Ru-Ru Acta mathematica scientia,Series A. 2009, 29 (2):  423-435.  Abstract ( 327 )   RICH HTML PDF (328KB) ( 972 )   Save In this paper, the authors introduce and study  generalized Bernstein operators  defined on a simplex in R. They first prove that these operators possess the symmetric property for a transformation from the simplex to itself and the Lipshcitz property.  Then,  by means of the multivariate Ditzian-Totik's modulus of continuity, they obtain a strong type direct estimate  and an inverse inequality of weak type for the operators approximating multivariate continuous functions. Finally, they  give some Voronovskaja type expansions when the parameters sn satisfy some conditions. The obtained results include the corresponding ones of the classical Bernstein operators as a corollary. References | Related Articles | Metrics

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Positive Solutions for a Class of Fourth Order Singular Superlinear Boundary Value Problems DIAO Ceng-Qi, LI Xiu-Zhen Acta mathematica scientia,Series A. 2009, 29 (2):  436-448.  Abstract ( 359 )   RICH HTML PDF (333KB) ( 1119 )   Save This paper investigates a kind of fourth order superlinear singular boundary value problem, which contains a second derivative item. The authors obtain the  existence   and some properties of the solutions. Lastly, a necessary and sufficient condition for the existence of C2[0,1] positive solutions as well as C3[0,1] positive solutions is given for the problems which do not contain derivative items. References | Related Articles | Metrics

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A Note on Matrix Extension for Multivariate Wavelet Filter Banks CA Jian-Hong, DAO Feng Acta mathematica scientia,Series A. 2009, 29 (2):  449-455.  Abstract ( 410 )   RICH HTML PDF (295KB) ( 1072 )   Save This note focuses on the problem of  matrix extension in the theory of  multivariate wavelets and filter banks. In [7], a matrix extension method was given for low-pass filter with linear phase in the bivariate case with special dilation matrix 2I2×2. The authors extend this result to general case with the determinant of the dilation matrix being 4. References | Related Articles | Metrics

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On (K1(x), K2(x)) - finite Distortion Mappings Gao Hongya; Wang Fang; Tong Yuxia; An Min Acta mathematica scientia,Series A. 2009, 29 (2):  456-464.  Abstract ( 311 )   RICH HTML PDF (324KB) ( 1034 )   Save In this paper, the authors first give the definition of K1(x), K2(x)) - finite distortion mappings, and then investigate their self-improving integrability property. Finally, they obtain novel result on the size of removable singularities for them by using the Caccioppoli-type inequality. References | Related Articles | Metrics

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The Existence of Positive Periodic Solutions for a Kind of Periodic Reaction-diffusion Equations Xie Qiangjun; Zhang Guangxin; Zhou Zekui Acta mathematica scientia,Series A. 2009, 29 (2):  465-474.  Abstract ( 278 )   RICH HTML PDF (350KB) ( 1064 )   Save By means of the property of periodic parabolic operators, Schauder estimates and global bifurcation theory, the coexistence state of time-periodic solutions for reaction-diffusion equations, a kind of two-species periodic predator-prey systems, are investigated. The necessary and sufficient conditions for the existence of positive periodic solutions are obtained. References | Related Articles | Metrics

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The Growth of Dirichlet Series and Random Dirichlet Series of Infinite Order in the Half Plane Luo Shile; Sun Daochun Acta mathematica scientia,Series A. 2009, 29 (2):  475-485.  Abstract ( 317 )   RICH HTML PDF (315KB) ( 1808 )   Save In this paper, the authors study the growth of Dirichlet series and random Dirichlet series of infinite  order in the half-plane. They prove several lemmas by using the Newton polygon and type-function U( r) of Hiong Kin-lai  under a much weaker coefficient condition. And  the relations between its order and low order and its coefficients are obtained. For some random Dirichlet series with non-uniformly distribution random variables there are almost surely (a.s.)  same relations. References | Related Articles | Metrics

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Factor-critical Graph  G with |V(G)|+2} Maximum Matchings Liu Yan；Yang Chunxia Acta mathematica scientia,Series A. 2009, 29 (2):  486-493.  Abstract ( 288 )   RICH HTML PDF (255KB) ( 1121 )   Save A connected graph G is said to be factor-critical if G-v has a perfect matching for  every vertex v of G. In this paper, the factor-critical graph G with |V(G)|+2 maximum matchings is characterized. By this, some special bicritical graphs are characterized. References | Related Articles | Metrics

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Numerical Approximation of Solution for the Initial-boundary Value Problem of the Klein-Gordon-Zakharov Equations Chen Juan; Zhang Luming Acta mathematica scientia,Series A. 2009, 29 (2):  494-504.  Abstract ( 328 )   RICH HTML PDF (310KB) ( 1205 )   Save In this work, a conservative difference scheme with a parameter $\theta$ is presented for the initial-boundary value problem of the Klein-Gordon-Zakharov equations. On the basis of a priori  estimates, convergence of the difference solutions is proved with order O(h2+τ2) in the energy norm. Numerical experiments emonstrate the accuracy and effectiveness of the  proposed scheme. References | Related Articles | Metrics

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Dual Hopf Algebras from a Quiver and Dual Quiver Quantum Groups Chen Lili; Li Fang Acta mathematica scientia,Series A. 2009, 29 (2):  505-516.  Abstract ( 364 )   RICH HTML PDF (363KB) ( 1083 )   Save In [3] and [6], the Hopf algebra structures of path algebra and path coalgebra on a Hopf quiver and a covering quiver respect to a weight sequence respectively were introduced independently. The main aim of this paper is to show the dually one-to-one correspondent relations between their structures (see Theorems 2.1 and 2.4). As applications, firstly, the authors obtain some important results about the Hopf algebra structure on the quotient of path algebra on a cycle; then, they prove that the Sweedler's fourdimensional Hopf algebra H4 is not only quasi-triangular but also co-quasi-triangular. Lastly, they characterize the graded automorphism group of the Hopf algebras on the path algebra of a Schurian covering quiver, according to that on the path coalgebra of a Schurian Hopf quiver. References | Related Articles | Metrics

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A Class of Small Deviation Theorems for the Sequences of N-valued Random Variables with Respect to mth-order Nonhomogeneous Markov Chains Yang Weiguo Acta mathematica scientia,Series A. 2009, 29 (2):  517-527.  Abstract ( 332 )   RICH HTML PDF (294KB) ( 988 )   Save Let {Xn, n ≥ 0} be a sequence of random variables on the probability space (Ω, F, P) taking values in alphabet S={1, 2, … , N}. Let Q be another probability measure on F, under which {Xn, n ≥ 0} is an mth-order onhomogeneous Markov chain. Let h(P|Q) be the sample divergence rate of P with respect to Q related to {Xn}. In this paper, the author first establishes a class of small deviation theorems for the averages of the functions of m+1 variables of {Xn}, n ≥ 0} with respect to $m$th-order nonhomogeneous Markov chains. As corollaries, the author obtains the small deviation theorems for the frequency of occurrence of the states and the entropy density of {Xn}, n ≥ 0} with respect to mth-order nonhomogeneous Markov chains. Finally, the author gets several strong laws of large numbers and a Shannon-McMillan theorem for mth-order nonhomogeneous Markov chains. References | Related Articles | Metrics