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25 October 2006, Volume 26 Issue 5 Previous Issue    Next Issue

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On the Set of Indices of Convergence for the Class of s-Cycle Boolean Matrices Han Hyuk Cho; Suh Ryung Kim Acta mathematica scientia,Series A. 2006, 26 (5):  641-646.  Abstract ( 1641 )   RICH HTML PDF (276KB) ( 1172 )   Save Using Boolean arithmetic, the index of convergence and period of a Boolean matrix A are respectively the least non-negative integer k and the least positive integer p respectively such that Ak=Ak+p. The knowledge about the period is quite completed. Given positive integers n and s satisfying a certain inequality, the authors apply combinatorial arguments to determine which numbers are attainable as the indices of convergence of n× n Boolean matrices whose digraphs contain at least one s-cycle. Related Articles | Metrics

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Modifying the Proof of a Lemma in Mixture Models Tan Xianming; Zhang Runchu Acta mathematica scientia,Series A. 2006, 26 (5):  647-652.  Abstract ( 1606 )   RICH HTML PDF (442KB) ( 1197 )   Save Motivated by a real life example from neuroscience, the authors present a theoretical frame for feature selection in discriminant analysis of very high-dimensional data. In light of a theorem, the authors provide a modification to a procedure, which is commonly-employed, of discriminant analysis of very high-dimensional data. The modified procedure works are better thantwo other popular procedures in this example in that it needsfewer features and the classification error is smaller Related Articles | Metrics

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The Spaces Whose Products is a D -space Peng Liangxue Acta mathematica scientia,Series A. 2006, 26 (5):  653-658.  Abstract ( 1337 )   RICH HTML PDF (269KB) ( 1224 )   Save It is known that every C-like space is a D -space, and every regular weakly θ-refinable C-scattered space is also a D-space. Is the product of these spaces also a D-space? In this paper the above question is discussed. It is proved that the finite product of regular weakly θ-refinable C -scattered spaces is aD -space, and the countable product of regular Lindel\"of C-scattered spaces is aD -space Related Articles | Metrics

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Rectangular Crouzeix-raviart Anisotropic Finite Element Method for Nonstationary Stokes Problem with Moving Grids Shi Dongyang; Zhang Yiran Acta mathematica scientia,Series A. 2006, 26 (5):  659-670.  Abstract ( 2052 )   RICH HTML PDF (362KB) ( 1200 )   Save This paper is devoted to the study of rectangular Crouzeix-Raviart anisotropic finite element method with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. Anisotropic error estimations of the velocity and the pressure are derived based on some novel techniques. Related Articles | Metrics

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On the Factorization of Meromorphic Functions Huang Zhibo ; Sun Daochun Acta mathematica scientia,Series A. 2006, 26 (5):  671-674.  Abstract ( 1734 )   RICH HTML PDF (234KB) ( 1237 )   Save In this paper, the authors study the factorization of meromorphic functions under the condition of composition of functions, obtain a perfect proof of the Theorem 1 in [1]and the necessary conditions of some pseudo-prime or E-pseudo-prime functions Related Articles | Metrics

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Precise Asymptotics in the Law of Large Numbers of Moving-average Processes Li Yunxia Acta mathematica scientia,Series A. 2006, 26 (5):  675-687.  Abstract ( 1629 )   RICH HTML PDF (301KB) ( 1123 )   Save In this paper, the author discusses moving-average process $X_k=\sum\limits_{i=-\infty}^\infty a_{i+k}\varepsilon_i$, where $\{\varepsilon_i; -\infty $\varphi$-mixing or negatively associated random variables with mean zeros and finite variances, $\{a_i;-\infty $S_n=\sum\limits_{k=1}^nX_k, n\geq 1$, the author proves that, if $E|\varepsilon_1|^r<\infty$, then, for $1\leq p<2$ and $r>p$ $$\lim_{\epsilon\searrow 0}\epsilon^{2(r-p)/(2-p)}\sum\limits_{n=1}^\infty n^{r/p-2} P\{|S_n|\geq \epsilon n^{1/p}\}=\frac{p}{r-p}E|Z|^{2(r-p)/(2-p)},$$ where $Z$ has a normal distribution with mean 0 and variance $\tau^2=\sigma^2\cdot(\sum\limits_{i=-\infty}^\infty a_i)^2. Related Articles | Metrics

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A Note on Pugh's Problem Tian Desheng;Zeng Xianwu Acta mathematica scientia,Series A. 2006, 26 (5):  688-694.  Abstract ( 1841 )   RICH HTML PDF (299KB) ( 1007 )   Save In this paper the authors construct a quartic Abelian equation with coefficients beingtrig onometric polynomials of degree ≤3, in which there exist six periodic solutions. In other words, the authors give an example on Pugh's problem, in which K(n)=6 for n=4. The authors propose to comparethe example with Nirenberg's example, of which Smale spoke in[1]. Related Articles | Metrics

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Multiple Fixed Points of Quasi-monotone Nondecreasing Operator Sun Jinli;Sun Jingxian Acta mathematica scientia,Series A. 2006, 26 (5):  695-699.  Abstract ( 1770 )   RICH HTML PDF (222KB) ( 1216 )   Save By using variational method and the theory of ordinary differential equations in Banach spaces, a three fixed points theorem of quasi-monotone nondecreasing operator is proved. Related Articles | Metrics

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Multiple Positive Solutions for Even Order Sturm-Liouville Boundary Value Problems Sun Hongrui ; Li Wantong Acta mathematica scientia,Series A. 2006, 26 (5):  700-706.  Abstract ( 2098 )   RICH HTML PDF (267KB) ( 1174 )   Save In this paper the authors discuss the existence of positive solution to the following even order boundary value problem (-1)m y(2m)=f(t,y), 0≤t≤1, ai+1y(2i) (0)-βi+1y (2i+1) (0)=0, γi+1y(2i) (1)+δi+1y(2i+1) (1)=0,0≤i ≤m-1 Sufficient conditions are obtained for existence of three or arbitrary odd positive solutions of the above problem by using Leggett-Williams fixed point theorem. Related Articles | Metrics

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Finitely Extending Rings Zhou Dexu Acta mathematica scientia,Series A. 2006, 26 (5):  707-715.  Abstract ( 1641 )   RICH HTML PDF (295KB) ( 1176 )   Save Finitely extending property is shown to carry over to matrix rings, and non-singular finitely extending rings are characterized via PP rings, semihereditary rings and finitely co-non-singular rings, these extend [2, Theorem 2.1]; a partial positive answer is provided to the FGF and CF Conjectures, that is, every right finitely extending right CF ring is right CEP (so right aritian), which improve [6, Theorem 3.7]. Related Articles | Metrics

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Nontrival Solutions for a Singular Critical Elliptic Equations Kang Dongsheng Acta mathematica scientia,Series A. 2006, 26 (5):  716-720.  Abstract ( 1528 )   RICH HTML PDF (241KB) ( 1061 )   Save In this paper, a semilinear elliptic equation with critical Sobolev-Hardy exponents is studied,the existence of nontrival solutions for which is proved by the linking theorem in variational calculus. Related Articles | Metrics

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A Sufficient and Necessary Condition for Quasi-Proximatable of Algebra of Bitopology Li Qingguo; Chen Xueyou; Cai Haitao Acta mathematica scientia,Series A. 2006, 26 (5):  721-724.  Abstract ( 1429 )   RICH HTML PDF (245KB) ( 1155 )   Save In this paper the authors study the connections between quasi-proximities and pairwise completely reguler on completely distributive lattice with order reversing involution. The authors obtain a sufficient and necessary condition for quasi-proximatable of algebra of bitopology. Related Articles | Metrics

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Maximal Inequalities for Identically Distributed ρ Mixing Random Variables and Applications Chen Pingyan Acta mathematica scientia,Series A. 2006, 26 (5):  725-730.  Abstract ( 1653 )   RICH HTML PDF (246KB) ( 965 )   Save Let $\{X_n,n\geq1\}$ be a sequence of identically distributed $\tilde{\rho}$ mixing random variables and $S_n=\sum\limits^n_{i=1}X_i(n\geq1)$. The paper discusses the upper bound of the distributions of $\max\limits_{1\leq i\leq n}\frac{|S_i|}{i}(n\geq1)$, and the sufficient and necessary conditions of the 1-$th$ and $p$-$th(p>1)$ moments of $\sup\limits_{n\geq1}\frac{|S_n|}{n}$ are obtained, which are as same as the case of the independent identically distributions. Related Articles | Metrics

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Blow-up and Global Existence for a Nonlocal Degenerate Parabolic System Chen Yujuan Acta mathematica scientia,Series A. 2006, 26 (5):  731-740.  Abstract ( 1820 )   RICH HTML PDF (324KB) ( 1047 )   Save This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. The sub and super solutions method and the regularization skill are used. The critical exponent of the system is gained. It's proved that if pc=(p1+p2)(q1+q2)- mn, every nonnegative solution is global, whereas if pc>0, there exists both global and blow-up nonnegative solution. When pc=0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain is large enough that is, if it contains a sufficiently large ball, there is no global solution. The related results of papers [8,10,11] are the special cases of this paper. Related Articles | Metrics

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Asymptotic Upper Bounds for Wheel: Complete Graph Ramsey Numbers Song Hongxue ; Bai Lufeng; Liu Shuyan Acta mathematica scientia,Series A. 2006, 26 (5):  741-746.  Abstract ( 1755 )   RICH HTML PDF (258KB) ( 1253 )   Save It is shown that r(Wm,Kn)≤l(1+o(1))C1(m) (n/logn ) (2m-2)/(m-2) for fixed even r(Wm,Kn)≤(1+o(1))C2(m) (n2m/m+1/log n)(m+1)/(m-1) for fixed odd m≥5 and n→∞. In particular, C2(5)=12 . Also, c(n/logn)5/2≤r(K4,Kn)≤ (1+o(1)) n3/(logn)2. Moreover, in this paper, the authors discuss some generalizations for wheel: complete graph Ramsey numbers. Related Articles | Metrics

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Statistical Analysis on Evolutionary Behaviors of Games Gong Xiaoqing Acta mathematica scientia,Series A. 2006, 26 (5):  747-752.  Abstract ( 1538 )   RICH HTML PDF (360KB) ( 1093 )   Save Average selection operators in random environments are introduced in the first place, and it is proved that the sequence of probability distributions in agents' strategies set, when repeatedly operated by average selection operator, converges to the probability distribution in the subset of strategies that takes the largest value of average fitness. Then, the concept of average selection operator is extended to the multi-agents game problems, and it is proved that the fixed points of such an operator are just the Nash equilibria of games. Related Articles | Metrics

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Global Existence and Uniform Decay Rates of Solutions for a Class of Strongly Damped Wave Equations Fang Daoyuan ; Xu Jiang Acta mathematica scientia,Series A. 2006, 26 (5):  753-765.  Abstract ( 1515 )   RICH HTML PDF (361KB) ( 1180 )   Save In this paper the authors study the existence and uniqueness of global strong solutions and global weak solutions for a class of strongly damped wave equations with nonlinear source term and nonlinear boundary damping term. The authors also discuss the uniform decay of solutions. Related Articles | Metrics

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Generalized Hamming Weights and Semilinear Equivalence of Codes Liu Hongwei Acta mathematica scientia,Series A. 2006, 26 (5):  766-772.  Abstract ( 1641 )   RICH HTML PDF (256KB) ( 1220 )   Save Let σ be an automorphism on a field ( F. It is proved in this paper that any σ-semilinear isomorphism between two linear codes which preserves one generalized Hamming weight is a σ -semilinear monomial equivalence. Related Articles | Metrics

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A Note on a Discrete Schrodinger Spectral Problem Liu Qingping;Wang Yuqing Acta mathematica scientia,Series A. 2006, 26 (5):  773-777.  Abstract ( 1528 )   RICH HTML PDF (257KB) ( 1069 )   Save For a discrete Schrodinger spectral problem, the authors associate a bi-Hamiltonian structure for the related hierarchy. A simple Darboux transformation is also presented. Related Articles | Metrics

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The Set of Non-weakly Almost Periodic Recurrent Points on Wang Lidong;Chu Zhenyan;Liao Gongfu Acta mathematica scientia,Series A. 2006, 26 (5):  778-784.  Abstract ( 1546 )   RICH HTML PDF (302KB) ( 1221 )   Save In this paper, the authors discuss the shift of the one-sided symbolic space and prove that there exists an uncountable SS chaotic set, in which each point is recurrent, but is not weakly almost periodic. Related Articles | Metrics

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Local Strassen's Law of the Iterated Logarithm for Diffusion Processes in H Liu Yonghong; Gao Fuqing Acta mathematica scientia,Series A. 2006, 26 (5):  785-793.  Abstract ( 1769 )   RICH HTML PDF (270KB) ( 1105 )   Save In this paper, the authors obtain the functional law of the iterated logarithm for diffusion processes by large deviations in Holder norm. As an application, the authors obtain the functional law of the iterated logarithm for iterated Ito integrals. Related Articles | Metrics

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The Existence of Multile Positive Solutions for a Class of Third-order p-Laplacian Operator Singular Boundary Value Problems Chen Shunqing Acta mathematica scientia,Series A. 2006, 26 (5):  794-800.  Abstract ( 1869 )   RICH HTML PDF (267KB) ( 1001 )   Save In this paper, the existence of multile positive solutions for a class of third-order p -Laplacian operator singular boundary value problems is discussed by using the fixed point index, and so yield sone new conclusions. Related Articles | Metrics