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25 February 2012, Volume 32 Issue 1 Previous Issue    Next Issue

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Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints CHEN Jia-Wei, LI Jun, WANG Jing-Nan Acta mathematica scientia,Series A. 2012, 32 (1):  1-12.  Abstract ( 1473 )   RICH HTML PDF (356KB) ( 1000 )   Save In this work, a nonsmooth multiobjective optimization problem involving gen-eralized invexity with cone constraints (for short, (MOP)) is considered. The Kuhn-Tucker necessary and su?cient conditions for (MOP) are established by using a generalized alterna-tive theorem of Craven and Yang. The relationship between saddle points and weakly effcient solutions of (MOP) is developed. Furthermore, the Wolfe type and Mond-Weir type weak, strong and converse duality results for (MOP) are presented. These results extend and improve corresponding results of others. References | Related Articles | Metrics

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Stabilization of Multi-rate Sampled-data Nonlinear Systems with Quantization YU Hong-Wang, WANG Zhi-Ming, ZHANG Bao-Shan Acta mathematica scientia,Series A. 2012, 32 (1):  13-26.  Abstract ( 888 )   RICH HTML PDF (485KB) ( 827 )   Save This paper investigates multi-rate sampled-data stabilization of nonlinear control systems while the sampler produces quantization during sampling. The approximate DTD method is employed to design a (globally) stabilized controller based on the approximate discrete-time models of the nonlinear plant. It is shown that the multi-rate sampled-data nonlinearcontrolsystemswith quantizationareguaranteedtobe semi-globallypracticalasymp-totically stable while the approximate error and quantization level are restricted by a certain error condition. A simulation example illustrates the validity of obtained results. References | Related Articles | Metrics

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The Analysis of the Duration of the Negative Surplus for a Generalized Compound Poisson-Geometric Risk Model CUI Wei, YU Jing-Hu Acta mathematica scientia,Series A. 2012, 32 (1):  27-40.  Abstract ( 1023 )   RICH HTML PDF (440KB) ( 947 )   Save This paper mainly studies a generalized compound Poisson-Geometric risk model in which the income of insurance premiums is a compound Poisson process and the number of claims is a compound Poisson-Geometric process. This risk model has practical applications in the insurance industry. In this paper, the authors focus on the duration of the negative surplus(DNS) under the above risk model. By taking full advantage of the strong Markov property of the surplus process and the total expectation formula, they derive the distribution of the deficit at ruin, and the moment generating functions of the DNS. References | Related Articles | Metrics

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Precise Asymptotics in the Law of Logarithm for U-statistics ZHOU Hui, LIN Zheng-Yan Acta mathematica scientia,Series A. 2012, 32 (1):  41-54.  Abstract ( 1032 )   RICH HTML PDF (310KB) ( 784 )   Save Let {Xn; n ≥1} be a sequence of i.i.d. random variables, and Un be a U-statistic based on the symmetric kernel function h(x, y). Set Un =2/n(n-1) ∑1≤i<j≤n h(Xi, Xj), h1(x) =Eh(x, X2). Under someproperconditions, the exactmomentconvergenceratesof ∑n=2 ∞(logn)δ-1EUn2I {I U n |≥n 1/2√lognε} and ∑n=3∞(loglognε)δ-1/logn EUn2 I {|U n |≥n1/2 √log lognε } are showed. References | Related Articles | Metrics

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Numerical Computation of Eigenvalues of Self-adjoint Differential Operators by Using the Method of Separating Eigen-parameter CHEN Jin-She, SUN Jiong Acta mathematica scientia,Series A. 2012, 32 (1):  55-67.  Abstract ( 1098 )   RICH HTML PDF (444KB) ( 735 )   Save In this paper, a power series representation in λ and its method to solve for the general solution of eigen-equation ly(x, λ) = λy(x, λ) are discovered. Then, a new numerical method to get eigenvalues of self-adjoint ordinary di?erential operators is obtained. Also the analysis of stability and error for the algorithm are given. At last, the numerical examples are presented to verify the effciency of the method. References | Related Articles | Metrics

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The Product of Differentiation and Multiplication Operator from the Mixed-norm to the Bloch-type Space YU Yan-Yan, Liu-Yong-Min Acta mathematica scientia,Series A. 2012, 32 (1):  68-79.  Abstract ( 1105 )   RICH HTML PDF (328KB) ( 921 )   Save Let H(D) be the space of analytic functions on the unit disk D and u ∈ H(D). The boundedness and compactness of the product DMu of differentiation operator and multiplica-tion operator from the mixed norm to the Bloch-type space are investigated in this paper. References | Related Articles | Metrics

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The Schur Convexity and Inequalities for a Class of Symmetric Functions LONG Bo-Yong, CHU Yu-Ming Acta mathematica scientia,Series A. 2012, 32 (1):  80-89.  Abstract ( 928 )   RICH HTML PDF (267KB) ( 856 )   Save For x = (x1, x2,···, xn) ∈ (0,1) and r ∈ {1, 2,···, n}, the symmetric function Fn(x, r) is defined by Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1<i2<···<ir≤n ∑ j=1r(1+xi3/1- xi3)1/r, where i1, i2, ···, ir are integers. In this paper, it is proved that Fn(x,r) is Schur convex, Schur multiplicatively convex and Schur harmonic convex on (0,1)n. As applications, some inequalities are established by use of the theory of majorization. References | Related Articles | Metrics

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Optimal Harvesting of a Size-structured Predator-prey Model LIU Yan, HE Ze-Rong Acta mathematica scientia,Series A. 2012, 32 (1):  90-102.  Abstract ( 1125 )   RICH HTML PDF (406KB) ( 863 )   Save This work is concerned with an optimal harvesting problem for a predator-prey model, in which the prey population is described by a first order partial differential equation (PDE) in a density function and the predator by an ordinary di?erential equation in total size. The existence and uniqueness of solutions to the state system and the dual system is proven via fixed point theorem. Necessary optimality conditions of first order are established by use of tangent-normal cones and dual system technique. The existence of a unique optimal control pair is derived by means of Ekeland’s variational principle. The resulting conclusion extends some existing results involving age-dependent populations. References | Related Articles | Metrics

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On Rank Invariance of Generalized Block Pick Matrices of Matrix-valued Caratheodory Functions HE Qin, XU Qing-Zhou, CHEN Gong-Ning Acta mathematica scientia,Series A. 2012, 32 (1):  103-112.  Abstract ( 952 )   RICH HTML PDF (359KB) ( 1046 )   Save Lasarow[1] derived statements on the rank invariance of generalized block Pick matrices of matrix-valued Carath′eodory functions. In this paper, it is concluded that the rank of such generalized block Pick matrices can be related to and coincides with the rank of some block Toeplitz matrices in terms of the Toeplitz vector approach given in [2]. These results are used to improve the proof of the rank invariance of the generalized block Pick matrices in certain sence. References | Related Articles | Metrics

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Existence of Traveling Fronts for General Reaction Systems with Nonlinear Di?usion MA Man-Jun, HU Jian-Chao, YANG Dao-Ming Acta mathematica scientia,Series A. 2012, 32 (1):  113-125.  Abstract ( 831 )   RICH HTML PDF (357KB) ( 739 )   Save In this paper, the authors use the perturbation method to investigate the existence of traveling fronts for a general reaction system with nonlinear di?usion. Su?cient conditions for the existence of traveling wavefronts are obtained, which make the results in the related references derived easily. As an application the authors employ the obtained results to show the existence of traveling fronts for a specific reaction-di?usion system. References | Related Articles | Metrics

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Existence of Periodic Solution for Evolution Inclusion in Banach Space YU Jin-Feng, XUE Xiao-Ping Acta mathematica scientia,Series A. 2012, 32 (1):  126-136.  Abstract ( 999 )   RICH HTML PDF (312KB) ( 854 )   Save In this paper, using the Galerkin approximation method, the authors establish a theorem about the existence of periodic solution for a class of evolution inclusion. As an application of the results, a suffcient conditions for the existence of periodic solution to the parabolic differential equation with multivalued items is obtained. References | Related Articles | Metrics

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Optimal Proportional Reinsurance and Investment with Transaction Costs and Liability ZHANG Xin-Li, SUN Wen-Yu Acta mathematica scientia,Series A. 2012, 32 (1):  137-147.  Abstract ( 1200 )   RICH HTML PDF (415KB) ( 922 )   Save In this paper, the authorsconsidera problem ofoptimal reinsuranceand investment with multiple risky assets and a liability for an insurance company whose surplus is governed by a linear diffusion. The insurance company’s risk can be reduced through reinsurance, while in addition the company invests its surplus in a financial market with one risk-free asset and m risky assets. The risky assets’ prices are governed by geometric Brownian motions while the liability evolves according to a Brownian motion with drift. The correlations between the risky assets and the liability are considered. The transaction costs produced during the investmentaretaken into account. Te authors considerthe optimization problemof maximizing the expected exponential utility of terminal wealth and solve it by using the corresponding Hamilton-Jacobi-Bellman(HJB) equation. Explicit expression for the optimal value function and the corresponding optimal strategies are obtained. References | Related Articles | Metrics

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The Gel'f'and Approximations on Generalized Besov Classes Bp, θΩ in the Deterministic and Monte Carlo Settings DUAN Li-Qin Acta mathematica scientia,Series A. 2012, 32 (1):  148-160.  Abstract ( 978 )   RICH HTML PDF (396KB) ( 935 )   Save In this paper, the author studies the approximation problems on the generalized Besov classes Bp, θ Ω in the norm of Lq by the Gel’fand methods in the deterministic and Monte Carlo settings. Applying the Maiorov’s discretization technique and some properties of pseudo-s-scale, the author determines the asymptotic orders of this problem for some values of param-eters p, q, θ. References | Related Articles | Metrics

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Fast Discrete Galerkin Methods for Cauchy Integral Singular Equations with Constant Coe?cients CAI Hao-Tao Acta mathematica scientia,Series A. 2012, 32 (1):  161-170.  Abstract ( 1084 )   RICH HTML PDF (359KB) ( 948 )   Save The Petrov-Galerkin method based on Jacobi polynomials is the conventional and standard numerical method for solving the Cauchy singular integral equations with constant coeffcients. This conventional numerical method leads to a linear system with a full coeffcient matrix. When the order of the linear system is large, the computational cost for obtaining and then solving the fully discrete linear system is huge. So in this paper the author develops a fast fully discrete Petrov-Galerkinmethod for solving this kind of integral equations. First compress this full coe?cient matrix into a sparse matrix. Then apply the numerical integration scheme to obtain the fully discrete truncated linear system with a nearly linear computational cost. At last, the fully discrete truncated linear system is solved. It is established that the optimal convergence order of the approximation solution remains optimal. References | Related Articles | Metrics

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Some Extensions on Hardy-Littlewood Inequality and its Applications LIU Jian-Zhong Acta mathematica scientia,Series A. 2012, 32 (1):  171-185.  Abstract ( 1390 )   RICH HTML PDF (338KB) ( 978 )   Save By using the H\"{o}lder inequality and  β-function, some extensions and improvements on Hardy-Littlewood inequality are given. As applications, some generalzations and refinements of Hilbert  inequality are established by above results and matrix method. References | Related Articles | Metrics

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Stability for the Nonhomogeneous Timoshenko Beam with Local Memory Damping ZHANG Chun-Guo Acta mathematica scientia,Series A. 2012, 32 (1):  186-200.  Abstract ( 1711 )   RICH HTML PDF (361KB) ( 840 )   Save In this paper, the author studies the stability for the nonhomogeneous Timoshenko beam with one local memory damping. The exponential stability under certain hypothesis is proved. The method is based on the operator semigroup theory, the multiplier technique, and the contradiction argument of the frequency domain method. References | Related Articles | Metrics

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Discussion on the Existence of Solution to Nonlinear Boundary Value Problem with Generalized p-Laplacian Operator WEI Li, Ravi P Agarwal Acta mathematica scientia,Series A. 2012, 32 (1):  201-211.  Abstract ( 1394 )   RICH HTML PDF (366KB) ( 817 )   Save Two kinds of nonlinear boundary value problems with generalized p-Laplacian operator are studied in this paper. By using a result on the existence of solutions for variational inequalities, the result on the existence of solution of the nonlinear Dirichlet boundary value problem with generalized p-Laplacian operator is proved. Later, a kind of nonlinear Neumann boundary value problem with generalized p-Laplacian operator is presented. By digging deeply into the relationship between the above two kinds of nonlinear boundary value problems and by using a perturbation resulton the ranges of maximal monotone operators, an abstractresult for the existence of solution of the nonlinear Neumann boundary value problem with generalized p-Laplacianoperatoris obtained. In this paper, somenew prooftechniques areemployed, which extend and complement some of the previous research work. References | Related Articles | Metrics

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Some Properties on von Neumann-Jordan Type Constants of Banach Spaces YANG Chang-Sen, WANG Ya-Min Acta mathematica scientia,Series A. 2012, 32 (1):  212-221.  Abstract ( 1007 )   RICH HTML PDF (310KB) ( 815 )   Save In this paper, the authorsmainly givesome propertiesof vonNeumann-Jordantype constants. First, they characterize some equivalent conditions of uniformly non-square by von Neumann-Jordan constants. Second, they discuss the relation between von Neumann-Jordan type constant and normal structure. Finally, they give some relations among C1′(X), C1(X) and other constants. References | Related Articles | Metrics

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Oscillation Criteria for Third-order Emden-Fowler Delay Dynamic Equations on Time Scales LI Tong-Xin, HAN Zhen-Lai, ZHANG Cheng-Hui, SUN Yi-Bing Acta mathematica scientia,Series A. 2012, 32 (1):  222-232.  Abstract ( 1669 )   RICH HTML PDF (361KB) ( 791 )   Save By means of Riccati transformation technique, the authors establish some new oscillation criteria for the third-order Emden-Fowler delay dynamic equations (a(t)(r(t)x? (t))? ) ?+p(t)xγ (τ(t)) = 0 on a time scales , where γ > 0 is a quotient of odd positive integers, a, r, p are real-valued T positive rd-continuous functions defined on . Some new oscillation results which deal with T some cases not covered by existing results in the literature are obtained. Some examples are considered to illustrate the main results. References | Related Articles | Metrics

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Empirical Likelihood Confidence Regions of Parameters in Nonlinear EV Models under Missing Data LIU Qiang, XUE Liu-Gen Acta mathematica scientia,Series A. 2012, 32 (1):  233-245.  Abstract ( 1425 )   RICH HTML PDF (391KB) ( 782 )   Save The missing response problem in the nonlinear EV(error-in-variables) models is considered, where the explanatory variate X is erroneously measured. With the help of val-idation data, two empirical log-likelihood ratio statistics for the unknown parameters in the model are proposed. It is proved that the proposed statistics are asymptotically chi-square distribution under some mild conditions, and hence can be used to constructing the confidence regions of the parameters. References | Related Articles | Metrics

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Positive Solutions for Fractional m-Point Boundary Value Problem in Banach Spaces WANG Yong-Qing, LIU Li-Shan Acta mathematica scientia,Series A. 2012, 32 (1):  246-256.  Abstract ( 1298 )   RICH HTML PDF (331KB) ( 1199 )   Save In this paper, we concider a class of fractional m-point boundary value problem in Banachspaces. First, we get properties ofthe Green function, then construct a special cone and establish the existence results of positive solutions by using the cone expasion and compression fixed point theorem. Finally, an example is given to illustrate the main results of this paper. References | Related Articles | Metrics