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25 August 2009, Volume 29 Issue 4 Previous Issue    Next Issue

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Relative Widths of Function Classes of L2(T) Determined by Fractional Order Derivatives in Lq(T) XIAO Wei-Wei, LIU Yong-Ping Acta mathematica scientia,Series A. 2009, 29 (4):  833-842.  Abstract ( 1435 )   RICH HTML PDF (338KB) ( 1229 )   Save The relative widths Kn(W2α(T), MW2β(T), L2(T)),  T=[0, 2π], is studied and the smallest number M which makes the equality Kn(W2α(T), MW2β(T), L2(T))=dn(W2α(T), L2(T)) valid is obtained, and the asymptotic order of relative widths Kn(W2α(T), W2α(T), Lq(T) ) is obtained, where α≥β>0, 1≤q ≤ ∞ , Kn (., ., Lq(T)) and dn(., Lq(T)) denote respectively the relative widths and the widths in the sense of Kolmogorov in Lq(T), and MWpα(T), 1≤ p ≤ ∞ , denotes the collection of 2π-periodic and continuous functions f representable as a convolution f(t)=c+(Bα* g)(t), where Bα* g denotes the convolution of Bα and g, for g ∈ Lp(T) satisfying ∫02πg(τ)dτ=0 and ||g||p ≤ M. Here Bα is in L1(T) with the Fourier expansion Bα(t) )=1/2π ∑' k∈ Z(ik)-αeikt, where ∑' means that  the term is omitted  when k=0. References | Related Articles | Metrics

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Spectral Analysis and Expansion of Solution to a Class of Delay Differential Equations WANG Lei, HU Gen-Qi Acta mathematica scientia,Series A. 2009, 29 (4):  843-857.  Abstract ( 1655 )   RICH HTML PDF (423KB) ( 1262 )   Save In this paper, the authors investigate the spectrum and expansion of solutions for a class of delay differential equations. The model under consideration comes from a practical problem, which describes machine tool vibration in cutting process. They tranform the model into a first order differential equation in a Hilbert state space. And then using the theory of C0 semigroup, they obtain the well-posed-ness of the sytem. By a detailed spectrum analysis, they give an explicit asymptotic expression of all eigenvalues. In addtion, they show that the eigenfunctions of the system do not form a basis for the state space; however, they get the exspansion of solution of the system according to the eigenfunctions. References | Related Articles | Metrics

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The Modified Characteristic Finite Difference Fractional Steps Method for Nonlinear Coupled System of Multilayer Fluid Dynamics in Porous Media Yuan Yirang Acta mathematica scientia,Series A. 2009, 29 (4):  858-872.  Abstract ( 1856 )   RICH HTML PDF (432KB) ( 1229 )   Save For nonlinear coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error of the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. Thus the author has thoroughly and completely solved the well-known problem. References | Related Articles | Metrics

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Pullback Attractors for Non-autonomous 2D Navier-Stokes Equations with Linear Dampness in Some Unbounded Domains WANG Xiao-Hu, LI Shu-Yong Acta mathematica scientia,Series A. 2009, 29 (4):  873-881.  Abstract ( 1765 )   RICH HTML PDF (353KB) ( 1354 )   Save In this paper,  the concept of pullback asymptotically compact non-autonomous dynamical system is firstly introduced. Then, a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system is given. Finally, the existence of a pullback attractor for a non-autonomous 2D Navier-Stokes equation with linear dampness in some unbounded domains is proved. Moreover, the upper bounds of  Fractal dimension of the pullback attractor is estimated. References | Related Articles | Metrics

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A New Model for Staircase Reduction in Image Restoration Problems Xing Li-Li, LI Wei-Guo Acta mathematica scientia,Series A. 2009, 29 (4):  882-890.  Abstract ( 1779 )   RICH HTML PDF (1000KB) ( 1259 )   Save In this paper, the authors propose a new model for image restoration problems, based on the total variation minimizing models proposed by Rudin, Osher, and Fatemi(ROF). Since the functional is nonquadratic, the dual method and Newton's method are used to compute the regularized solutions.The numerical experiments show the improvement is fairly valid. References | Related Articles | Metrics

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Study on Quaternary ZRM Codes PEI Jun-Ying, WANG Hai-Hua, CUI Jie Acta mathematica scientia,Series A. 2009, 29 (4):  891-897.  Abstract ( 1659 )   RICH HTML PDF (280KB) ( 1155 )   Save In the literature two classes of Z4 linear codes were defined to discuss the Z4 linearity of binary Reed-Muller codes, they are denoted by ZRM(r, m) and QRM(r, m), and their binary images under the Gray map are denoted by ZRM(r, m) and QRM(r, m) respectively. In this correspondence, the types of ZRM}(r, m) and QRM(r, m) are computed respectively. When 3 ≤ r ≤ m-1, it is shown that the binary image ZRM(r, m) is linear while QRM(r, m) is nonlinear. Moreover, the linear code spanned by QRM(r, m) is proved to be ZRM(r, m). Finally, the rank and the kernel are determined for the nonlinear code QRM(r, m). References | Related Articles | Metrics

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High Accuracy Analysis of Fully Discrete Galerkin Approximations for Parabolic Equations on Anisotropic Meshes Shi Dong-yang, GONG Wei Acta mathematica scientia,Series A. 2009, 29 (4):  898-911.  Abstract ( 1696 )   RICH HTML PDF (361KB) ( 1231 )   Save The aim of this paper is to study the higher order accuracy analysis of fully discrete Galerkin approximations to parabolic equations by biquadratic element under anisotropic meshes. Through the integral identity techniques and some novel approaches the superclose results are obtained. References | Related Articles | Metrics

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Some Explicit Examples of Lagrangian Submanifolds with Conformal Maslov Form in Complex Space Forms HAN Ying-Bo Acta mathematica scientia,Series A. 2009, 29 (4):  912-917.  Abstract ( 1439 )   RICH HTML PDF (260KB) ( 1221 )   Save In this paper, the author finds some new explicit examples of Lagrangian submanifolds with conformal Maslov form among the Lagrangian isometric immersions of a real space form into a complex space form. References | Related Articles | Metrics

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The Relation between Solutions of a Class of Differential Equations and Functions of Small Growth ZHANG Ran-Ran, CHEN Zong-Xuan Acta mathematica scientia,Series A. 2009, 29 (4):  918-928.  Abstract ( 2067 )   RICH HTML PDF (310KB) ( 1243 )   Save This paper investigates the relation between solutions, their 1st, 2nd and 3rd derivatives, differential polynomial of the equation f''+eaz f'+h(z)ebz f =0 with functions of small growth, where a, b are nonzero complex numbers such that a =cb~(c>1) and h(z) is a nonzero polynomial. References | Related Articles | Metrics

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Existence of Multiple Positive Solutions for General Sturm-Liouville Boundary Value Problems on the Half-line Xing Mei-Hong, ZHANG Ke-Mei, GAO He-Li Acta mathematica scientia,Series A. 2009, 29 (4):  929-939.  Abstract ( 2052 )   RICH HTML PDF (315KB) ( 1073 )   Save In this paper, by using the Leggett-Williams fixed point theorem, the authors discuss the existence of at least three solutions for a class of second order boundary value problems on the half-line as follows    (p(t)x'(t))'+Φ(t) f (t, x(t), x'(t))=0, t ∈ [0, +∞), α1x(0)-β1limt →0+ p(t) x'(t)=a1, α2limt →+∞ x'(t)+β2limt →+∞ p(t) x'(t)=a2.  References | Related Articles | Metrics

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Disruption Management for Single Machine Scheduling on Total Loss before Completion CAO Xiao-Gang, WEN Hui, HUANG Chong-Chao Acta mathematica scientia,Series A. 2009, 29 (4):  940-948.  Abstract ( 1495 )   RICH HTML PDF (388KB) ( 1010 )   Save This article addresses the problem of single machine scheduling on total loss before completion that arises under disruption environment. Such a problem deals with a situation when, at time t,  a disruption unexpectedly occurs after  a subset of jobs   processed. In such cases continuing with the original schedule is likely to be suboptimal and may be even infeasible. Therefore, a new schedule is needed to process the uncompleted jobs. The approach taken here differs from most rescheduling analysis in that the loss associated with the deviation between  the original and the new schedule is included in the model. The authors concentrate on the case in which the weighted shortest processing time (WSPT) rule is optimal for the original problem. According to type of disruption, type of disruption management policy, and objective function, several problems are studied in the paper. In each problem, the authors either find the optimal schedule or obtain some important results. References | Related Articles | Metrics

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The Best Invariant Estimator of a Symmetric Continuous |Distribution Function XIE Min-Yu, NING Jian-Hui Acta mathematica scientia,Series A. 2009, 29 (4):  949-957.  Abstract ( 1418 )   RICH HTML PDF (319KB) ( 1164 )   Save This paper considers the problem of invariant estimator of an unknown symmetric continuous distribution function. Though the group of all one to one monotone transformations of real values onto themselves leaves the parametric space of all continuous distribution functions invariant[1], it can not insure the parametric space of all the symmetric continuous distribution functions invariant. Thus, the decision problem is not invariant under the group of monotone transformations. In order to guarantee this invariance, the authors consider a new group of transformations -- the group of all the odd monotone transformations. It leaves the decision problem invariant. By noticing the special feature of a symmetric distribution function F at the zero point -F(0)=1/2 and viewing the zero point as a pseudo-observation value, the authors obtain all the nonrandomized invariant estimators and find the best invariant estimator in the invariant estimators. References | Related Articles | Metrics

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The Growth of Double Dirichlet Series LIU Jun, GAO Zong-Sheng Acta mathematica scientia,Series A. 2009, 29 (4):  958-968.  Abstract ( 1933 )   RICH HTML PDF (325KB) ( 1525 )   Save In this paper, the authors first study the relations between the coefficients, exponents, and growth of double Dirichlet series, and obtain a necessary and sufficient condition of $\theta$ linear lower order,  and further give an estimate of $\theta$ linear order of double Dirichlet series in every pair of horizontal straight lines. References | Related Articles | Metrics

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Generalized Differential Second Quantization Operator WANG Xiang-Jun, CAO Xue-Lian Acta mathematica scientia,Series A. 2009, 29 (4):  969-973.  Abstract ( 1629 )   RICH HTML PDF (274KB) ( 1117 )   Save In this paper, the authors define the differential second quantization operator of any continuous linear operator from Ec to Ec*. A Fock expansion by using Schwartz kernel theorem is obtained. The differential second quantization operator of composition operator by using tensor product is given. References | Related Articles | Metrics

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On the Approximate Control Criteria for Combinatorial Group Testing Procedure QI Ming-Nan, LIU San-Yang Acta mathematica scientia,Series A. 2009, 29 (4):  974-984.  Abstract ( 1252 )   RICH HTML PDF (393KB) ( 1038 )   Save The group testing problem for a given set is to determine a subset of the set by a series of  tests. In this paper,  firstly, the authors use the theory and method of dynamic programming to establish a proximate dominating criterion for controlling group testing procedures. Establishing the group testing procedure is optimal through the control. Secondly, the authors consider the problem of ascertaining the minimum average number of tests which suffice to determine one defective coin in a set of n coins by applying the proximate control criterion. In particular, this paper is concerned with proximate control problem on a group testing procedure, in which an optimal procedure for culling out the one subset of a given set is obtained. The desired procedure is optimal in the sense of minimizing the average number of steps. References | Related Articles | Metrics

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Local Strong Solutions of Navier-Stokes-Poisson Equations for Isentropic Compressible Fluids YIN Jun-Peng, TAN Zhong Acta mathematica scientia,Series A. 2009, 29 (4):  985-1000.  Abstract ( 2248 )   RICH HTML PDF (356KB) ( 1183 )   Save In this paper, the authors prove the existence, uniqueness, stability  of the local strong solutions for Navier-Stokes-Poisson equations in three dimensions. The important point is that they  allow the initial vacuum: the initial density may vanish in a boundary and open subset. The local existence is gotten by the extended Gronwall's inequality, then the authors prove the uniqueness in weaker condition. Finally, from the proof of the uniquenss, the stability can be concluded naturally. References | Related Articles | Metrics

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Infinite-dimensional Widths and Optimal Recovery of Besov-Wiener Classes of Multivariate Functions HU Gui-Qiao Acta mathematica scientia,Series A. 2009, 29 (4):  1001-1011.  Abstract ( 1306 )   RICH HTML PDF (338KB) ( 1055 )   Save This paper concerns the problem of the infinite-dimensional σ-widths and optimal recovery of Besov-Wiener classes Spqθr B(Rd) and Spqθr B(Rd) in the metric Lq(Rd) for 1≤ q ≤ p < ∞. By considering the approximation by spline functions and constructing a kind of continuous spline operators, the author obtains the weak asymptotic results concerning the infinite dimensional Kolmogorov widths, the infinite dimensional linear widths, the infinite dimensional Gel'fand widths  and optimal recovery, respectively. References | Related Articles | Metrics

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On the Time Value of Ruin for a Renewal Risk Model with Interest LV Yu-Hua, WANG Guang-Hua Acta mathematica scientia,Series A. 2009, 29 (4):  1012-1021.  Abstract ( 1464 )   RICH HTML PDF (320KB) ( 975 )   Save The  paper  studies the ruin problems for a renewal risk model with interest. An integral equation for the Gerber-Shiu discounted penalty function and an explicit infinite series expression for the Gerber-Shiu discounted penalty function are obtained. Then the authors generalize the Gerber-Shiu's formula$^{[4]}$   to this renewal risk process including the force of interest. Finally, as an application of the above results, an exponential upper bound for the ultimate probability is derived by recursive technique. References | Related Articles | Metrics

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Representations of Vertex Operator Superalgebras and Associative Algebras JIANG Wei, JIANG Qi-Fen, JIANG Cui-Bo Acta mathematica scientia,Series A. 2009, 29 (4):  1022-1032.  Abstract ( 1725 )   RICH HTML PDF (375KB) ( 1261 )   Save Let V be a vertex operator superalgebra. The authors construct a sequence of associative algebra An(V) for  n ∈ 1/2 Z+. It is also exposed that there is a pair of functors between the category of An(V)-modules which are not An-1/2(V)-modules and the category of admissible V-modules. The functors exhibit a bijection between the simple modules in each category. They also construct a generalized Verma admissible V-module Mn(U) by a An(V)-module which is not An-1/2(V)-module U. Futhermore, they study the theory of representations of vertex operator superalgebra by associative algebra An(V). References | Related Articles | Metrics

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A Concentration-Compactness Principle at Infinity on the Heisenberg Group and Multiplicity of Solutions for p-sub-Laplacian Problem Involving Critical Sobolev Exponents DOU Jing-Bo, GUO Qian-Qiao Acta mathematica scientia,Series A. 2009, 29 (4):  1033-1043.  Abstract ( 1654 )   RICH HTML PDF (374KB) ( 1144 )   Save The main results of this paper establish the concentration-compactness principle at infinity on the Heisenberg group. The authors consider the p-sub-Laplacian problem involving critical Sobolev exponents   -ΔH, pu=λg(ξ)|u|q-2u+f (ξ)|u|p*-2u,  in Hn,  u ∈ D1, p(Hn),  where ξ ∈ Hn, λ ∈ R,1<p<Q=2n+2, n ≥ 1, 1<q<p, p*=Qp/Q-p, g(ξ) and f(ξ) change sign and satisfy some suitable conditions. Under certain assumptions, they show the existence of m-j pairs of nontrivial solutions via variational  method,  where m>j, both m and j are   integers. The concentration-compactness principle allows  to prove the Palais-Smale condition is satisfied below a certain level. References | Related Articles | Metrics

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On the Distribution of Random Dirichlet Series in the Whole Plane JIN Qi-Yu, SUN Dao-Chun Acta mathematica scientia,Series A. 2009, 29 (4):  1044-1050.  Abstract ( 1347 )   RICH HTML PDF (245KB) ( 1184 )   Save For some random Dirichlet series of order(R) infinite almost surely every horizontal line is a strong Borel line of order(R) infinite and without exceptional little functions. References | Related Articles | Metrics

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Exponential Convergence Rates for Markov Processes with Markovian Switching XI Fu-Bao Acta mathematica scientia,Series A. 2009, 29 (4):  1051-1057.  Abstract ( 1420 )   RICH HTML PDF (325KB) ( 1018 )   Save Let (X(t), Z(t)) be a strong Markov process with the phase space [0, ∞) ×{1, 2, …, n0} such that the first component X(t) depends on the second component Z(t) which is a Markov chain. Using the coupling methods, the author evaluates the exponential convergence rates of the transition probability of (X(t), Z(t)) to its invariant probability measure in total variation norm. References | Related Articles | Metrics

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Strong Convergence Rates of the Maximum Quasi-Likelihood Estimator in Generalized Linear Models YIN Chang-Ming, LI Yong-Ming, WANG Peng-Yan Acta mathematica scientia,Series A. 2009, 29 (4):  1058-1064.  Abstract ( 2280 )   RICH HTML PDF (334KB) ( 1130 )   Save In a generalized linear model with q×1 responses, bounded and fixed p×q regressors Zi and general  link function, under  the moment  condition on responses as weak as possible and other conditions, the authors prove that with probability one, the quasi-likelihood equation has a solution βn for all large sample size n. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.  This result is an  improvement over the relevant results in literature. References | Related Articles | Metrics

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Two Φ-functions and Two Weights Inequalities for Maximal Operators in Martingale Spaces JIN Yan-Ming, YU Lin Acta mathematica scientia,Series A. 2009, 29 (4):  1065-1073.  Abstract ( 1711 )   RICH HTML PDF (264KB) ( 1023 )   Save In this paper, the weighted inequalities for the maximal functions in Orlicz martingale spaces are studied. It includes the strong and weak (Φ1, Φ2)-type weighed inequalities. The sufficient and necessary conditions on the part of the inequalities are given. References | Related Articles | Metrics

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Large Deviations for |Solutions to Stochastic Differential Equations Driven by Semimartingale with Non-Lipschitz Coefficients Fei Wei-Yin Acta mathematica scientia,Series A. 2009, 29 (4):  1074-1083.  Abstract ( 1537 )   RICH HTML PDF (306KB) ( 1164 )   Save In this paper, a class of stochastic differential equations (SDEs) driven by semimartingale with non-Lipschitz coefficients is established.   A  large deviation principle of Freidlin-Wentzell type is investigated. References | Related Articles | Metrics

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Forward-Backward Doubly Stochastic Differential Equations ZHU Qing-Feng, SHI Yu-Feng Acta mathematica scientia,Series A. 2009, 29 (4):  1084-1092.  Abstract ( 1532 )   RICH HTML PDF (284KB) ( 1057 )   Save A type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. Under some natural monotonicity assumptions, the existence and uniqueness result is established. References | Related Articles | Metrics

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Blow-up of |Solutions |of |an |Initial |Boundary |Value Problem for a Class of Nonlinear Wave Equation WANG Yan-Ping Acta mathematica scientia,Series A. 2009, 29 (4):  1093-1103.  Abstract ( 1519 )   RICH HTML PDF (324KB) ( 1100 )   Save In this paper, the following initial boundary value problem  of the nonlinear wave equation involving the nonlinear damping term and the nonlinear source term utt -uxxt -uxx -(σ(u2x)ux)x+δ|ut|p-1ut=μ|u|q-1u, 0 < x <1, 0 ≤ t ≤ T,       u(0, t)=u(1, t)=0,  0 ≤ t ≤ T,                                                                      u(x, 0)=u0(x),  ut(x, 0)=u1(x), 0 ≤ x ≤1                                            is discussed. This paper gives sufficient conditions of  blow-up of the solutions for the problem in finite time and proves the existence and uniqueness of the local generalized solution and classical solution of this problem. References | Related Articles | Metrics

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The Characterization of Compact Support of Fourier Transform for Scaling Function and Orthonormal Wavelets of L2(Rs) HUANG Yong-Dong, CHENG Zheng-Xing, HAN Hui-Li Acta mathematica scientia,Series A. 2009, 29 (4):  1104-1118.  Abstract ( 1721 )   RICH HTML PDF (364KB) ( 1023 )   Save In this paper, under a weaker condition, the authors give the sufficient and necessary condition that φ(x) is a scaling function of L2(Rs), in view of support of Fourier transform for  φ(x). Furthermore, suppose {Ψμ } is an orthonormal wavelet of L2(Rs) and the whole support of  its Fourier transform is     ∪μ  supp{ψμ} = ∏si=1[Ai, Di] - ∏si=1(Bi, Ci), Ai ≤ Bi ≤ Ci ≤ Di, i =1, 2, … , s. Under the weakest condition that each |ψμ| is continuous for ω ∈ ∂(∏si=1[Ai, Di]), the authors give results of the above whole support of {ψμ}, these results are characterized by some equalities and inequalities. They have improved completely Long's results and Zhang's results. References | Related Articles | Metrics

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Structure Classification of Hopf Path Coalgebras over Abelian Groups WU Mei-Yun Acta mathematica scientia,Series A. 2009, 29 (4):  1119-1131.  Abstract ( 1536 )   RICH HTML PDF (384KB) ( 1103 )   Save Let G be a group and kG be the group algebra of G  over a field k. It is well known that the kG-Hopf  bimodule category kGkG MkGkG is equivalent to the direct category ∏C ∈ K(G) MkZu(C) . For any Hopf quiver Q=(G, r), the kG-Hopf bimodule structures on the arrow comodule kQ1 can be derived from the right kZu(C)-module structures on u(C)(kQ1)1. In this paper, the author discusses the isomorphic classification of Hopf path coalgebra kQc and the structures of Hopf subalgebra of kG[kQ1] of kQc in case G is a cyclic group and G is a Klein quaternion group, respectively. References | Related Articles | Metrics

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Several Topologies on Semicontinuous Lattices WU Xiu-Hua, LI Qiang-Guo Acta mathematica scientia,Series A. 2009, 29 (4):  1132-1137.  Abstract ( 1612 )   RICH HTML PDF (280KB) ( 1042 )   Save In this paper, the authors give several topologies on semicontinuous lattices and investigate their properties and relations among them. References | Related Articles | Metrics

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Convergence Rate in the Law of |Logarithm for NA Random Fields JIN Jing-Sen Acta mathematica scientia,Series A. 2009, 29 (4):  1138-1143.  Abstract ( 1999 )   RICH HTML PDF (271KB) ( 1228 )   Save Let d be a positive ingter and N d denote  the d-dimensional lattice of positive integers. Let {Xn , n ∈ N d}be a same distribution NA random fields, put Sn = ∑k≤ n Xk, Sn(k)=Sn-Xk, if r >2, EX1 = 0 and σ2= Var(X1}, then there exists a positive constant M:=100√(r-2)(1+σ2) such that the following is equivalent: (I)   E |X1|r (log|X1|)d-1-r/2 < ∞; (II)   ∑n∈ Nd |n|r/2-2 P(max1≤ k≤ n |S n(k)| ≥ (2d+1 )ε √|n| log | n |) < ∞, ∨ε  > M;   (III)   ∑n ∈ N d |n|r/2-2 P(max1≤ k≤ n |Sk | ≥ ε √| n} log | n |) < ∞, ∨ε > M. References | Related Articles | Metrics