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25 October 2009, Volume 29 Issue 5 Previous Issue    Next Issue

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Minimum Moment Aberration Majorization in Non-isomorphic Asymmetrical Saturated Designs ZHOU Yong-Dao, LIU Yao-Mei Acta mathematica scientia,Series A. 2009, 29 (5):  1145-1152.  Abstract ( 1356 )   RICH HTML PDF (457KB) ( 1101 )   Save For distinguishing non-isomorphic orthogonal saturated designs, Fang and Zhang[2]proposed the minimum aberration majorization approach to distinguish non-isomorphic symmetrical orthogonal saturated designs. However, their method can not distinguish the asymmetrical cases. In this paper, the authors consider the criterion of minimum moment aberration majorization (MMAM) and extend the results in [2]. On the basis of  this criterion, a new algorithm is given to detect the non-isomorphism of both symmetrical and asymmetrical designs. Examples show the MMAM approach is useful for distinguishing non-isomorphic saturated designs. References | Related Articles | Metrics

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The Normality Criterion of a Class of Meromorphic Functions HUANG Xiao-Jun Acta mathematica scientia,Series A. 2009, 29 (5):  1153-1159.  Abstract ( 2049 )   RICH HTML PDF (271KB) ( 1294 )   Save In this paper, the author studies the normality of a family of meromorphic functions and general criteria for normality of families of meromorphic functions. The  results improve the earlier Hayman's conjecture. References | Related Articles | Metrics

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The Method of Green Function for a Holder Continuity of Elliptic Equations with Divergence LU Han-Fang, ZHENG Shen-Zhou Acta mathematica scientia,Series A. 2009, 29 (5):  1160-1166.  Abstract ( 1609 )   RICH HTML PDF (289KB) ( 1458 )   Save According to the estimates and comparison of Green function of nonlinear elliptic operators with Laplacian operators, the authors  establish locally H\"older continuity  for a class of nonlinear elliptic equations with divergence under the condition of natural growth. References | Related Articles | Metrics

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A Class of Multiplier Convergent Series Spaces LEI Qiang, LI Rong-Lu Acta mathematica scientia,Series A. 2009, 29 (5):  1167-1174.  Abstract ( 1641 )   RICH HTML PDF (286KB) ( 1152 )   Save Depending only upon the intrinsic properties of a sequence space λ, the authors endow a locally convex topology TΒ on λ-multiplier convergent series space X(λ) and obtain that (X(λ), TΒ) is an AK-space and has sequentially completeness and Banach-Steinhaus properties. In particular, the authors give a generalization of the Orlicz-Pettis theorem for the series in X(λ). References | Related Articles | Metrics

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Parameter Identification for a Model of Tumor Growth in the Presence of Inhibitors TAO You-Shan, BIAN Bao-Jun Acta mathematica scientia,Series A. 2009, 29 (5):  1175-1186.  Abstract ( 1854 )   RICH HTML PDF (381KB) ( 1183 )   Save In this paper, the authors consider a model of tumor growth in the presence of inhibitors. The tumor is assumed to be spherically symmetric and its surface is a moving boundary denoted by a function r=R(t). Since multicellular tumor spheroids (MTS) are routinely used as in vitro models of cancer growth and they can be observed and controlled in the laboratory, the authors study the following inverse problem: Given observed dynamics of MTS growth (i.e., given R(t)), the authors determine the inhibitor's parameter. The authors first prove the uniqueness of solution to the inverse parabolic problem by the maximum principle. Then the authors develop an optimal control framework for studying the reconstruction of the inhibitor's parameter. The authors prove the existence of solution to the optimal control problem, and the authors derive the necessary optimality conditions which have to be satisfied by each optimal control. References | Related Articles | Metrics

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Single and Multiple Positive Solutions to Second-order Discrete Periodic Boundary Value Problems LI Xiao-Yue, WANG Li-Ying Acta mathematica scientia,Series A. 2009, 29 (5):  1187-1195.  Abstract ( 2295 )   RICH HTML PDF (305KB) ( 1137 )   Save This paper gives a existence theory for single and multiple positive solutions to a kind of second-order discrete periodic boundary value problems by employing a fixed point theorem in cones. This paper obtains some new results about nonlinear difference equations on a finite discrete segment with periodic boundary conditions. References | Related Articles | Metrics

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Compact Operators on Dirichlet Space XIA Jin, WANG Xiao-Feng, CAO Guang-Fu Acta mathematica scientia,Series A. 2009, 29 (5):  1196-1205.  Abstract ( 1677 )   RICH HTML PDF (280KB) ( 1172 )   Save If S is a Hankel operator or a finite sum of finite products of Toeplitz operators  on Dirichlet space of unit disk, some equivalence conditions of compactness of operator S are obtained. References | Related Articles | Metrics

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Asymptotics for the Density of the Supremum of a Certain Kind of Random Walks CHENG Dong-Ya, WANG Yue-Bao Acta mathematica scientia,Series A. 2009, 29 (5):  1206-1212.  Abstract ( 1825 )   RICH HTML PDF (304KB) ( 1156 )   Save Kluppelberg[1], Asmussen et al. [2] obtained asymptotics for the density of the supremum of a random walk with a finite negative mean. While this paper further investigates the case of a random walk with negative infinite mean on the basis of Denisov et al. [3] and Wang and Cheng[4]. To illustrate that some common distributions satisfy the conditions of the obtained results,  the authors discuss some properties of certain density classes. References | Related Articles | Metrics

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Darboux Transformation of Generalized Coupled KdV Soliton Equation and its Even-soliton Solutions LIU Ping Acta mathematica scientia,Series A. 2009, 29 (5):  1213-1222.  Abstract ( 1492 )   RICH HTML PDF (976KB) ( 1175 )   Save Based on  the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using the Darboux transformation, the generalized even-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given. References | Related Articles | Metrics

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Global Bifurcation of Periodic Solutions to Second Order Ordinary Differential Equations MA Ru-Yun, GAO Cheng-Hua Acta mathematica scientia,Series A. 2009, 29 (5):  1223-1232.  Abstract ( 1877 )   RICH HTML PDF (311KB) ( 1223 )   Save We are concerned with determining values of r, for which there exist nodal solutions of the periodic boundary value problem {u''+r f(u)=0,  u(0)-u(2π)=u'(0)-u'(2π)=0.  The proof of our main result is based upon global bifurcation techniques. References | Related Articles | Metrics

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Twin Positive Solutions for a Singular Semipositone Boundary Value Problem YU Hui-Min, LIU Yan-Sheng Acta mathematica scientia,Series A. 2009, 29 (5):  1233-1239.  Abstract ( 2057 )   RICH HTML PDF (285KB) ( 1066 )   Save By using the fixed point index theory, the authors investigate the existence of multiple positive solutions for third-order three-point singular semipositone BVP {x'''(t)-f(t, x)=0,    t ∈(0, 1);  x(0)=x'(η)=x''(1)=0, 1/2 < η <1, The nonlinear term f (t, x) may be singular at t =0,  t =1, and x =0, also may be negative for some values of  t and  x. References | Related Articles | Metrics

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On the Cardinality of Generating Subsets of Finite Abelian Groups CHEN Xue-Sheng, HU Ya-Hui, TANG Meng-Jun Acta mathematica scientia,Series A. 2009, 29 (5):  1240-1245.  Abstract ( 1308 )   RICH HTML PDF (276KB) ( 1073 )   Save Suppose G =Zm1   Zm2    …    Zmr be an Abelian group of type (m1, m2, …, mr) (Zmi is a cyclic group of order mi, 1≤ i ≤ r, m1|m2| …| mr). Let S be a symmetrically closed set (S is symmetrically closed if 0 ∈ S =-S) and a generating set of G. If |S|>|G|/ρ, where ρ ≥lmr /2 land mr=e(G) denotes the least common multiple of the orders of all elements of  group G, then ρS=G. And if G=Z2    Zm is an Abelian group of type (2, m) (m ≥ 8), then t m /2}(G)=0, which extends the related results of Klopsch and Lev[1]. References | Related Articles | Metrics

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Stochastic Delay Lotka-Volterra Model LIAN Bao-Sheng, HU Shi-Geng Acta mathematica scientia,Series A. 2009, 29 (5):  1246-1255.  Abstract ( 1726 )   RICH HTML PDF (319KB) ( 1122 )   Save This paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process, namely, the delay  Lotka-Volterra model. The stochastic version of this process appears to have some intriguing properties such as pathwise estimation and asymptotic moment estimation. Indeed, their solutions are  stochastically ultimately bounded. References | Related Articles | Metrics

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The Adjusted of Parameter Estimation in Seemingly Unrelated Regression MA Tie-Feng, WANG Song-Gui Acta mathematica scientia,Series A. 2009, 29 (5):  1256-1264.  Abstract ( 1281 )   RICH HTML PDF (382KB) ( 1124 )   Save For a seemingly unrelated regression with m linear regression models,the literature [7] propose a new method which based on iterative information step by step. Based on this method, this paper obtain a farther adjusted form which also has congruence. At the same time, a new estimator is proposed by using the idea in literature [7]. It is a feasible estimator having small sample property. The simulation result also indicates that our estimator is effective. The literature [10] gave a concise two-stage estimator by using the covariance adjusted approach of literature [8]. This paper improves on it which shows the more power of small sample optimality by comparing with least square estimator. References | Related Articles | Metrics

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Existence and Uniqueness of Weak Solutions for a Fourth Order Regularized YK Equation JIN Zheng-Meng, YANG Xiao-Ping Acta mathematica scientia,Series A. 2009, 29 (5):  1265-1273.  Abstract ( 1950 )   RICH HTML PDF (334KB) ( 1020 )   Save In this paper the authors propose the regularized YK equation based on the ill posed properties for the YK equation in image processing. They prove the existence and uniqueness of weak solution of the regularized equation in bounded domains. Furthermore, it is only assumed that the initial data belong to L2, which is more natural in image processing. References | Related Articles | Metrics

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Solving Nonlinear Singular Two-point Boundary-value Problem in the Reproducing Kernel Space LV Xue-Qin, CUI Ming-Gen Acta mathematica scientia,Series A. 2009, 29 (5):  1274-1282.  Abstract ( 1495 )   RICH HTML PDF (321KB) ( 1109 )   Save In this paper, the authors establish an iterative method to compute solution for a class of singular two-point boundary value problems (xαu')'=f(x, u, u'), where x ∈(0,1), and α< 2. Representation of the solution is given in the form of series in the reproducing kernel space W2[0,1]. The n-term approximation un(x) is proved to converge to the exact solution. Furthermore, the approximate error of un(x) is monotone decreasing. Some numerical examples are illustrated  to demonstrate the accuracy of the present method. References | Related Articles | Metrics

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A Test for an Umbrella Order Against Unrestricted Alternative in Stratified Contingency Tables FENG Yan-Qin, QIU Xiao-Xia, MA Cheng-Gang Acta mathematica scientia,Series A. 2009, 29 (5):  1283-1290.  Abstract ( 1910 )   RICH HTML PDF (368KB) ( 1053 )   Save Stochastic order between probability distributions is an important concept in applied probability and statistical inference, and it is often used in many situations. Trend test based on cross-classified data was widely studied, and stratified contingency tables are common in practice. Likelihood ratio test is often used to test involving stochastic order. For stratified contingency tables with ordered categories, this paper introduces a model-free test method by using likelihood ratio test statistic and gives the asymptotic distribution of this statistic. References | Related Articles | Metrics

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Local Regularity for Very Weak Solutions of Obstacle Problems to the A-Harmonic Operators GAO Hong-Y, HE Qian, NIU Hong-Ling, CHU Yu-Ming Acta mathematica scientia,Series A. 2009, 29 (5):  1291-1297.  Abstract ( 1693 )   RICH HTML PDF (300KB) ( 1224 )   Save This paper gives a local regularity result for very weak solutions of obstacle problems to the A-Harmonic operator div A(x, u,   u)=0 with nonnegative obstacle by using the method of Hodge decomposition. References | Related Articles | Metrics

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Minimization Problem for Hermitian Matrices over the Quaternion Field YUAN Shi-Fang, LIAO An-Ping, LEI Yuan Acta mathematica scientia,Series A. 2009, 29 (5):  1298-1306.  Abstract ( 1681 )   RICH HTML PDF (315KB) ( 1138 )   Save In this paper, the canonical correlation decomposition of quaternion matrices (CCD-Q) is established. Based on the CCD-Q, GSVD-Q, and the projection theorem in the finite dimensional inner product space, the expression of minimization problem for Hermitian matrices associated with the quaternion matrix equation AXB=C is derived. References | Related Articles | Metrics

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Braided Monoidal Category of Entwined Modules JIA Ling, JIANG Xiu-Yan Acta mathematica scientia,Series A. 2009, 29 (5):  1307-1310.  Abstract ( 1216 )   RICH HTML PDF (230KB) ( 991 )   Save In this paper,the authors mainly consider how to make the category of entwined modules into a braided monoidal category and give the necessary and sufficient conditions. References | Related Articles | Metrics

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Composition Operators from Hyperbolic α-Bloch Spaces into Hyperbolic QK Type Spaces YU Yan-Yan, LIU Yong-Min Acta mathematica scientia,Series A. 2009, 29 (5):  1311-1320.  Abstract ( 1767 )   RICH HTML PDF (341KB) ( 1230 )   Save Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ : Cφ (f)=f ο φ , for all f  ∈ X. In this paper, the boundedness of the composition operators from hyperbolic α-Bloch spaces into hyperbolic QK type spaces are discussed, where 0 < α ≤ 1. Moreover, a necessary and sufficient condition for Cφ from weighted Dirichlet space Dp, α to QK(p, q) to be bounded or compact is given in terms of the map φ. References | Related Articles | Metrics

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The Boundary Value Problem of k}-monogenic Functions in Clifford Analysis BU Yo-De, DU Jin-Yuan Acta mathematica scientia,Series A. 2009, 29 (5):  1321-1330.  Abstract ( 1658 )   RICH HTML PDF (290KB) ( 1096 )   Save In this paper, the authors  give the solution of boundary value problem of  k-monogenic functions by Euler operator. And   some applications of Euler operator in Clifford analysis also be given. References | Related Articles | Metrics

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Generalizations of Busemann's Inequality with Applications WANG Wei, YUAN Jun, HE Bin-Wu Acta mathematica scientia,Series A. 2009, 29 (5):  1331-1337.  Abstract ( 1924 )   RICH HTML PDF (266KB) ( 1075 )   Save In this paper, we  generalize the Busemann's inequality. As applications, we get the dual Brunn-Minkowski inequality of the generalized intersection bodies. References | Related Articles | Metrics

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Empirical Likelihood Confidence Regions of the Parameters in Nonlinear Semiparametric Regression Models FENG San-Ying, XUE Liu-Gen, FAN Cheng-Hua Acta mathematica scientia,Series A. 2009, 29 (5):  1338-1349.  Abstract ( 1913 )   RICH HTML PDF (399KB) ( 1268 )   Save In this paper, we consider the nonlinear semiparametric regression model, and construct the empirical log-likelihood ratio statistic for the unknown parameter. It is shown that the proposed statistics have the asymptotic standard chi-square distribution, and hence it can be used to construct the confidence region of the parameter. In addition, the least squares estimator of unknown parameter is constructed, and its asymptotic behavior is proved. A simulation study is carried out to compare the proposed methods with the least-squares method in terms of the confidence regions and its coverage probabilities. References | Related Articles | Metrics

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Collection of Neighborhoods of Normal Tiling LI Hao, LUO Jun, ZHOU Zuo-Ling Acta mathematica scientia,Series A. 2009, 29 (5):  1350-1354.  Abstract ( 1245 )   RICH HTML PDF (345KB) ( 1145 )   Save In this paper, by using the topological graphs and the edge-neighbor graphs of tiling, we give a sufficient and necessary condition of two tiles of normal tiling having a same collection of neighborhoods. And it is proved that there exist impossibly three tiles with a same collection of neighborhoods in every normal tiling via the condition. Therefore, an open problem of Grünbaum is solved  in some sense. References | Related Articles | Metrics

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Lazy Cocycles for Commutative Algebras JU Teng-Xia Acta mathematica scientia,Series A. 2009, 29 (5):  1355-1363.  Abstract ( 1429 )   RICH HTML PDF (260KB) ( 1080 )   Save In this paper, the author defines the lazy left 2-cocycles σ: H     H → A for a Hopf algebra H and a commutative algebra A, and shows that there exists a correspondence between the lazy 2-cocycles and the lazy H-cleft objects. References | Related Articles | Metrics

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The Diffusive Behavior of Accupation Time Function in Exclusion Process LI Zhi-Min, MAO Ming-Zhi Acta mathematica scientia,Series A. 2009, 29 (5):  1364-1375.  Abstract ( 1357 )   RICH HTML PDF (353KB) ( 1003 )   Save In this paper, the authors consider the diffusive behavior of exclusion process, under the condition that the mean value m ≠ 0 and ρ = 1/2, the authors give an upper bound of the diffusive behavior. References | Related Articles | Metrics

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Graphic Sequences that Have a Realization Containing an K r+1 YIN Jian-Hua Acta mathematica scientia,Series A. 2009, 29 (5):  1376-1389.  Abstract ( 1634 )   RICH HTML PDF (320KB) ( 1113 )   Save Let K r+1 be the complete graph on r+1 vertices. A graphic sequence π =(d_1,d_2,\cdots ,d_n) is said to be potentially K r+1-graphic if there exists a realization of π containing K r+1 as a subgraph. In this paper, we further investigate a number of new conditions for π to be potentially K r+1-graphic, which imply some previous results in [14,10,11] and the values of σ(K r+1, n) for n ≥ 5r/2 +1, which was conjectured in [2] and was confirmed in [6,7,8,3]. Moreover, we also determine F(4), the set of all graphic sequences π=(d1, d2, …, dn) with n ≥ 5 and d5 ≥ 4 so that π is not potentially K5-graphic. References | Related Articles | Metrics

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Moments of the Discounted Dividends and Related Problems in a Markov-dependent Risk Model LIU Juan, XU Jian-Cheng Acta mathematica scientia,Series A. 2009, 29 (5):  1390-1397.  Abstract ( 1503 )   RICH HTML PDF (324KB) ( 1050 )   Save In this paper, a Markov-dependent risk model with a constant dividend barrier is considered. A system of integro-differential equations with boundary conditions satisfied by the expected present value of the total dividends prior to ruin and the moments of the discounted dividends, given the initial environment state, are derived and solved. In two-state model, explicit solutions to the integro-differential equations are obtained when claim size distributions are exponentially distributed. . References | Related Articles | Metrics

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Neumann Problem for Coupled Nonlinear Schrödinger Equations WEI Gong-Ming Acta mathematica scientia,Series A. 2009, 29 (5):  1398-1414.  Abstract ( 1547 )   RICH HTML PDF (395KB) ( 1100 )   Save In this paper, we consider  existence and concentration phenomena of least energy solutions of coupled  nonlinear Schrödinger systems  with Neumann boundary conditions. The focus  is on  the locations of  peaks (maximum points) of the least energy solutions. Following  Tai-Chia Lin and Juncheng Wei's procedure  for  Dirichlet  problem,  least energy solutions for Neumann problem are obtained. As the small perturbed parameter goes to zero, we prove that the peaks of the least energy solutions  approach to the boundary of domain and the energy concentrates around these peaks. On the other hand, peaks of  the two states attract or repulse each other depending on the interaction between them  to be   attractive or repulsive. References | Related Articles | Metrics

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Positive Solution of Semipositone Singular Dirichlet Boundary Value Problems for Second Order Impulsive Differential Equations GAI Yong-Jie, JIANG Da-Qing, ZU Li, WENG Shi-You, WEI Jun Acta mathematica scientia,Series A. 2009, 29 (5):  1415-1425.  Abstract ( 1794 )   RICH HTML PDF (291KB) ( 1032 )   Save In this paper, the existence of positive solution to semipositone singular  Dirichlet boundary value problems with impulsive effects is discussed. Our analysis relies on a cone fixed point theorem. References | Related Articles | Metrics

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Optimal Positive Solutions of a Nonlinear Fourth Order Periodic Boundary Value Problem ZHANG Li-Li Acta mathematica scientia,Series A. 2009, 29 (5):  1426-1433.  Abstract ( 2188 )   RICH HTML PDF (253KB) ( 1195 )   Save The fourth order periodic boundary value problem u(4)-m4u+F(t, u(τ(t)))=0, 0<t<2π, with u(i)(0)=u(i)(2π), i=0,1, 2, 3,  is studied by using the fixed point theorem in cones, where F:[0, 2π]×R+→ R+ and τ: [0, 2τi]→[0, 2π] are continuous and  0<m<1. Under suitable conditions on F, it is proved  that the problem  has at least two positive solutions if m ∈  (0, M), where M is the smallest positive root of the equation tan mπ=-tanh mπ, which takes the value 0.7528094 with an error of ±10-7. References | Related Articles | Metrics

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Nonexistence Results for a Class of Sub-P-Laplacians JIN Yong-Yang Acta mathematica scientia,Series A. 2009, 29 (5):  1434-1441.  Abstract ( 1312 )   RICH HTML PDF (300KB) ( 1073 )   Save The purpose of the present paper is to establish some nonexistence results of nonnegative solutions for the problem {Lp, k u+f(u)=0, in Ω,  u|∂Ω=0, where Ω is a domain (bounded or unbounded) in an H-type group G and  Lp, k u= divX (|   X u|p-2    X u) is a sub-P-Laplacian  associated with Greiner type vector fields X. References | Related Articles | Metrics

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Existence and Uniqueness of Positive Periodic Solution for a Kind of Generalized Logistic Model of Single Species YANG Xin-Song, RUI Wei-Guo Acta mathematica scientia,Series A. 2009, 29 (5):  1442-1452.  Abstract ( 2019 )   RICH HTML PDF (321KB) ( 1163 )   Save By using the method of Krasnoselskii's fixed point theorem and Schwarz inequality, new results on the existence and uniqueness of positive ω-periodic solution for the nonautonomous generalized Logistic model of single species of the form x=x(t){a(t)-b(t)x(t)-∑ni=1ci (t)x(t-τi(t))-∫0-∞k(t, s)x(t+s)ds} are obtained. References | Related Articles | Metrics

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Berry-Esseen Bounds for Wavelet Estimator of Regression Function under Strong Mixing Process LI Yong-Ming, WEI Cheng-Dong Acta mathematica scientia,Series A. 2009, 29 (5):  1453-1463.  Abstract ( 1891 )   RICH HTML PDF (362KB) ( 1226 )   Save Consider the nonparametric regression model Yni=g(tni)+εni~ (i=1, …, n) with wavelet method, where the design points {tni} are known and nonrandom,  g(?) is an unknown function defined on the closed interval [0,1],  and  {εni} are  strictly stationary strong mixing processes.  Under appropriate conditions,  we derive Berry-Esseen bounds for wavelet estimator of g(?).  As a corollary, we give the Berry-Esseen bounds that can attain  O(n-1/6). References | Related Articles | Metrics