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25 August 2008, Volume 28 Issue 4 Previous Issue    Next Issue

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Variance Component Testing in Semiparametric Generalized Linear Model for Longitudinal Data Zeng Linrui; Zhu Zhongyi Acta mathematica scientia,Series A. 2008, 28 (4):  585-594.  Abstract ( 1710 )   RICH HTML PDF (366KB) ( 1047 )   Save The variance component testing in the regression model is an important problem. In this paper, the authors study three cases in the variance component testing in semiparametric generalized linear model for longitudinal data, and the score statistic is obtained. In the first case, the authors just consider the nonconstant dispersion. Then in the second case, only the random effects are considered. In the last case, the authors consider both influences. Simulation studies are implemented to verify the efficiency of the method. Related Articles | Metrics

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Boundedness of Multilinear Operators Lin Yan Acta mathematica scientia,Series A. 2008, 28 (4):  595-602.  Abstract ( 1741 )   RICH HTML PDF (268KB) ( 1257 )   Save In this paper, the author studies a class of multilinear operators on product of Herz-type Hardy spaces. Moreover, as their special cases, the corresponding result of multilinear Calderón-Zygmund operators can be obtained. Related Articles | Metrics

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Nonexistence and Partial Existence of Rational First Integrals for General Nonlinear Systems Shi Shaoyun Acta mathematica scientia,Series A. 2008, 28 (4):  603-611.  Abstract ( 1945 )   RICH HTML PDF (296KB) ( 1277 )   Save The objective of this paper is to present some criteria for nonexistence and partial existence of rational first integrals for general nonlinear systems. The author first gives a necessary condition for general nonlinear systems to having rational first integrals. Then the author considers the case that the system have owed some rational integrals. Under certain conditions, the author proves that the system does not admit any other rational first integrals in the sense of functional independence, and thus the system is partially integrable. Related Articles | Metrics

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Strong Stability of Pairwise NQD Random Variable Sequences Gan Shixin; Chen Pingyan Acta mathematica scientia,Series A. 2008, 28 (4):  612-618.  Abstract ( 1690 )   RICH HTML PDF (236KB) ( 1517 )   Save In this paper the authors study the strong stability for pairwise NQD random variable sequences. The authors obtain some new strong stability results for such sequences. Some well-known results in independent case are extended to pairwise NQD random variable sequences. Related Articles | Metrics

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Three New Versions of the All-ones Problem Li Xueliang; Zhang Xiaoyan Acta mathematica scientia,Series A. 2008, 28 (4):  619-626.  Abstract ( 1682 )   RICH HTML PDF (360KB) ( 1175 )   Save The authors study three new versions of the all-ones problem and the minimum all-ones problem. The original all-ones problem is simply called the vertex-vertex problem, and the three new versions are called the vertex-edge problem, the edge-vertex problem and the edge-edge problem, respectively. The vertex-vertex problem is studied extensively. For example, the existence of solutions and efficient algorithms for finding solutions are obtained, and the minimum vertex-vertex problem for general graphs is shown to be NP-complete, however for trees, unicyclic and bicyclic graphs it can be solved in linear time, etc. In this paper, for the vertex-edge problem, the authors show that a graph has a solution if and only if it is bipartite, and therefore it has only two possible solutions and optimal solutions. For the edge-vertex problem, the authors show that a graph has a solution if and only if it contains even number of vertices. By showing that the minimum edge-vertex problem can be polynomially transformed into the minimum weight perfect matching problem, the authors obtain that the minimum edge-vertex problem can be solved in polynomial time in general. The edge-edge problem is reduced to the vertex-vertex problem for the line graph of a graph. Related Articles | Metrics

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Remark on the Regular and Singular Solutions to Nonlinear Parabolic-elliptic System Yuan Baoquan Acta mathematica scientia,Series A. 2008, 28 (4):  627-635.  Abstract ( 1841 )   RICH HTML PDF (333KB) ( 1268 )   Save This paper studies the existence of singular solutions to the nonlinear parabolic-elliptic system for initial data in Lorentz space Ln/2,∞ (Rn), n≥3, only by means of the norm of Lorentz space. The regularized solutions are also obtained by virtue of the time weighted Lorentz space. Moreover, the self-similar solutions are also obtained. Related Articles | Metrics

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Multivalued Solutions of an Iterative Equation Chen Li Acta mathematica scientia,Series A. 2008, 28 (4):  636-642.  Abstract ( 1836 )   RICH HTML PDF (278KB) ( 1278 )   Save The result on existence of solutions for a multivalued iterative equation given in [9] is extended to a larger class of multivalued functions which may be set-valued at end-points. Moreover, continuous dependence of the solution upon the given function is also obtained. Related Articles | Metrics

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Lévy Continuity Modulus of Brownian Sheet Via its Construction Liu Jicheng Acta mathematica scientia,Series A. 2008, 28 (4):  643-648.  Abstract ( 1397 )   RICH HTML PDF (242KB) ( 1304 )   Save In this paper, the author constructs a series representation of the Brownian sheet via Schauder functions. Related Articles | Metrics

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On the Evolution p-Laplacian Equation with Singular Coefficients Zeng Youdong Acta mathematica scientia,Series A. 2008, 28 (4):  649-660.  Abstract ( 1889 )   RICH HTML PDF (327KB) ( 1180 )   Save The author considers the solvability of the initial-boundary value problem in an n-ball for the evolution p-Laplacian equation with singular coefficients which are singular not only at the boundary of the n-ball but also at the origin x=0. The existence and nonexistence of global radial solutions are proved under some conditions related to parameters p, τ, λ and q. Related Articles | Metrics

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The Properties of Several Classes of Analytic Functions with Missing Coefficients Peng Zhigang Acta mathematica scientia,Series A. 2008, 28 (4):  661-669.  Abstract ( 1780 )   RICH HTML PDF (297KB) ( 1225 )   Save Let A be the class of functions, which are analytic in the unit disc D={z:|z|<1}, with f (0)=f′(0)-1=0. Let S* be the set of starlike functions, S*={f (z)∈A, Re zf′(z) / f(z)>0, z ∈ D}. Let K be the set of convex functions, K={f(z) ∈ A, Re(1+zf’’(z) / f ’(z)>0, z∈ D}. P denotes the class of functions p(z), which are analytic in D and satisfy p(0)=1, Rep(z)>0. Let Pn={p(z): p(z)=1+anzn+an+1zn+1+… ∈ P}, S*n={f (z): f(z)=z+anzn+an+1zn+1+… ∈ S*}, Kn={ f(z): f (z)=z+anzn+an+1zn+1+ … ∈K}. LSn*={g(z)=ln f(z) / z, f ∈ Sn*}, where the logarithmic function satisfy ln1=0. In this article the author investigated the properties of the classes S*n, Kn and LSn*. The author obstained the extreme points and support points of LSn*, and discussed the extreme points and support points of S*n and Kn. Related Articles | Metrics

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Growth of Solutions of a Class of Higher Order Linear Differential Equations Tu Jin; Chen Zongxuan Acta mathematica scientia,Series A. 2008, 28 (4):  670-678.  Abstract ( 1761 )   RICH HTML PDF (272KB) ( 1370 )   Save In this paper, the authors investigate the growth of solutions of a class of higher order differential equations, and improve and perfect the results of G. Gundersen7], J.K. Langley8], and Chen Zongxuan[10]. Related Articles | Metrics

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Super Efficiency of the ic-cone-convexlike Set-valued Optimization Problems in Locally Convex Spaces Yu Guolin; Liu Sanyang Acta mathematica scientia,Series A. 2008, 28 (4):  679-687.  Abstract ( 1867 )   RICH HTML PDF (302KB) ( 1261 )   Save This paper studies super efficient solution of the problem of minimizing a set-valued map subject to set-valued constraints in locally convex space. An useful property of ic-cone-convexlike set-valued maps is obtained. By using this property as the main tool, the optimality conditions and saddle point theorem for super efficient solution are proposed. Related Articles | Metrics

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Blow-up of Solution for an Initial Boundary Value Problem for a Nonlinear Hyperbolic Equation Wang Yanping; Guo Boling Acta mathematica scientia,Series A. 2008, 28 (4):  688-693.  Abstract ( 2060 )   RICH HTML PDF (263KB) ( 1312 )   Save This paper gives the sufficient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local solution of the problem. Related Articles | Metrics

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The Inverse Problem of Hermitian-Hamiltonian Matrices with a Submatrix Constraint Gong Lisha; Hu Xiyan; Zhang Lei Acta mathematica scientia,Series A. 2008, 28 (4):  694-700.  Abstract ( 1853 )   RICH HTML PDF (285KB) ( 1523 )   Save The paper discusses the solutions of inverse problem AX=B for Hermitian-Hamiltonian matrices with a submatrix constraint, the sufficient and necessary conditions under which the problem is solvable are obtained, and the general expression of the solutions is given. Moreover, to an arbitrary given matrix, the relative optimal approximation solution in the solution set is presented. Related Articles | Metrics

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One-step Estimation for Varying Coefficient Models with Unknown Functions of Different Degrees of Smoothness Tang Qingguo; Wang Jinde Acta mathematica scientia,Series A. 2008, 28 (4):  701-710.  Abstract ( 1905 )   RICH HTML PDF (314KB) ( 1354 )   Save An one-step estimation method is proposed to estimate all the unknown functions in varying coefficient models, of which the degrees of smoothness may be different from each other. In one-step estimation approach, the local estimators of all the unknown functions and their derivatives can be obtained by only one minimization operation. The asymptotic properties of the estimators, including bias, variance and asymptotic distribution, are derived. It is shown that all the one-step estimators achieve the optimal convergence rates. Related Articles | Metrics

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(n+1)-folds Periodic and Quasi-periodic Riemann Boundary Value Problems Gong Yafang Acta mathematica scientia,Series A. 2008, 28 (4):  711-718.  Abstract ( 1673 )   RICH HTML PDF (297KB) ( 1284 )   Save (School of Mathematics and Statistics, Wuhan University, Wuhan 430072) Related Articles | Metrics

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Existence of Positive Periodic Solutions of a Neutral Delay Competition Model with Diffusion and Stock Fang Hui; Wang Zhicheng Acta mathematica scientia,Series A. 2008, 28 (4):  719-730.  Abstract ( 1878 )   RICH HTML PDF (304KB) ( 1183 )   Save By means of Nussbaum degree theory, a sufficient condition is established for the existence of positive periodic solutions of a neutral delay competition model with diffusion and stock x′1(t)=x1(t)[a1(t)-b1(t)x1(t)-c1(t)y(t) ]+D1(t)[x2(t)-x1(t)]+S1(t), x′2(t)=x2(t)[a2(t)-b2(t)x2(t)]+D2(t)[x1(t)-x2(t) ]+S2(t), y′(t)=y(t)[a3(t)-b3(t)y(t)-α(t)y(t-τ1(t))-β(t) ∫0τ k(s)y(t+s)ds -γ(t)y’(t-τ2(t))-c3(t)x1(t)]. Related Articles | Metrics

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The Complete Elliptic Integrals and Hersch-Pfluger Distortion Function Wang Gendi; Zhang Xiaohui; Chu Yuming; Qiu Songliang Acta mathematica scientia,Series A. 2008, 28 (4):  731-734.  Abstract ( 1902 )   RICH HTML PDF (236KB) ( 1218 )   Save The authors establish the relationship between Hersch-pfluger distortion function ψK(r) and the second kind complete elliptic integral ε(r). By studying the monotonicity and convexity of complete elliptic integrals, the authors obtain inequalities for the complete elliptic integrals and sharp bounds for the Hersch-Pfluger distortion function. Related Articles | Metrics

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A New Family of Quadriphase Sequences with Optimal Correlation Properties Xia Yongbo; Zeng Xiangyong; Liu Heguo; Hu Lei Acta mathematica scientia,Series A. 2008, 28 (4):  735-741.  Abstract ( 1769 )   RICH HTML PDF (309KB) ( 1220 )   Save Based on sequences with two-level correlation and optimum quadriphase sequences, a new family of quadriphase sequences with parameter (22J-1,2J+1,2J+1) is proposed for a class of positive integers J. The new sequences family is optimal with respect to Welch’s lower bound on the maximum nontrival correlation value and it is suitable for CDMA. Related Articles | Metrics

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Optimal Portfolio in a Fractional Black-Scholes Model with Arbitrary Hurst Parameter Liu Shaoyue; Yang Xiangqun Acta mathematica scientia,Series A. 2008, 28 (4):  742-746.  Abstract ( 1707 )   RICH HTML PDF (265KB) ( 1329 )   Save Based on the mathematical model for a Black-Scholes market driven by frctional Brownian motion BH(t) with arbitrary Hurst parameter H ∈ (0,1), The authors solve the optimal portfolio problem in such a market for an agent with utility functions of power type by using quansi-conditional expectation and the stochastic-gradient. Related Articles | Metrics

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Almost Sure Central Limit Theorems for Functions of Random Variables Chen Shouquan; Lin Zhengyan Acta mathematica scientia,Series A. 2008, 28 (4):  747-756.  Abstract ( 1600 )   RICH HTML PDF (306KB) ( 1406 )   Save The authors prove a general almost sure central limit theorem for a sequence of random elements, and apply the result to the functionals of random variables. Related Articles | Metrics

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Genus Distribution for Cirle-like Graph Zhao Ximei; Liu Yanpei Acta mathematica scientia,Series A. 2008, 28 (4):  757-767.  Abstract ( 1787 )   RICH HTML PDF (374KB) ( 1437 )   Save The genus distribution of a graph G is defined to be the sequence {gk}, where gk is the number of different embeddings of G in the closed orientable surface of genus k. In this paper, a recurrence formula of the genus distribution for a standard circle-like graph is obtained,and a computing formula of the embedding for a circle-ike graph is given. Related Articles | Metrics

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Multiple Positive Solutions to a Singular Beam Equation Fixed at Both Ends Yao Qingliu Acta mathematica scientia,Series A. 2008, 28 (4):  768-778.  Abstract ( 2092 )   RICH HTML PDF (358KB) ( 1156 )   Save Let n be an arbitrary natural number. The existence of n positive solutions is proved for a singular beam equation fixed at both ends, where the nonlinear term is a Caratheodory function. Main tools are height functions concerned with nonlinear term and Guo-Krasnoselskii fixed point theorem of cone expansion-compression type. Further research shows that the equation may have positive solution if the growth limits of nonlinear term at zero and infinity are unbounded functions. Related Articles | Metrics

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Equilibrium States of Dynamical Systems Definded on Attractors of Iterated Function Systems Ma Dongkui Acta mathematica scientia,Series A. 2008, 28 (4):  779-784.  Abstract ( 1885 )   RICH HTML PDF (300KB) ( 1113 )   Save In this paper, let E denote the attrator of an iterated function system (X,T1,…, Tm). One can define a continuous self-mapping f : E→E by f(x)=T-1j(x), x∈ Tj(E), j=1, …, m . Given ψ ∈CR(E), let Kψ(δ, n = sup{∣∑n-1k=0[ψ(f kx)-ψ(f ky)]|:y ∈ Bx (δ, n)}, where Bx(δ, n) denotes the Bowen ball. Choosing an expansive constant ε, the authors write Kψ=supn Kψ(ε, n) and define ν(E)={ψ : Kψ < ∞}. For f : E → E, as some applications of a theorem by Ruelle[3,Theorem 2.1], the authors show that each ψ ∈ν(E) has a unique equilibrium state. The conclusions eneralize the main result of Zhou and Luo[12]. Related Articles | Metrics