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25 April 2012, Volume 32 Issue 2 Previous Issue    Next Issue

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Ruin Probability in a Risk Model under Unexpected Random Heavy-tailed Claims BI Xiu-Chun, ZHANG Shu-Guang Acta mathematica scientia,Series A. 2012, 32 (2):  257-262.  Abstract ( 1412 )   RICH HTML PDF (350KB) ( 926 )   Save This paper sets up a generalized renewal risk model based on zhe reality of existing unexpected heavy-tailed claims and gives tail equivalence relationship for the ruin probability, which indicates that unexpected heavy-tailed claims can result in ruin. References | Related Articles | Metrics

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A Boundary Value Problem of Analytic Function by Finite Degree Parabolic Circle Packing LIU Fei-Lei, DAI Dao-Qing Acta mathematica scientia,Series A. 2012, 32 (2):  263-270.  Abstract ( 986 )   RICH HTML PDF (385KB) ( 853 )   Save We will discuss the relationship between finite degree circle packing mapping and the classical analytic function. We use finite degree parabolic circle packing to simulate polynomials and construct approximating sequence to the analytic function with given boundary condition and branch set. This extends earlier results of Carter and Rodin and of Dubejko on regular hexgonal circle packings. References | Related Articles | Metrics

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The Upwind Finite Difference Method for Three-dimensional Moving Boundary Value Problem YUAN Yi-Rang, LI Chang-Feng Acta mathematica scientia,Series A. 2012, 32 (2):  271-289.  Abstract ( 1164 )   RICH HTML PDF (1014KB) ( 784 )   Save The research of the three-dimensional compressible miscible (oil and water)  displacement problem with moving boundary values is of great value to the history of  oil-gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For a generic case of three-dimensional bounded region, the authors  put forward a kind of upwind finite difference schemes and make use the calculus of variations, the change of variables and the theory of a priori estimates and techniques. Optimal order estimates in l2  norm are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, model numerical method and software development. Thus, the well-known problem is solved. References | Related Articles | Metrics

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Automorphism Groups of Rank One Lattice Vertex Operator Superalgebras WANG Song Acta mathematica scientia,Series A. 2012, 32 (2):  290-296.  Abstract ( 775 )   RICH HTML PDF (306KB) ( 731 )   Save This paper studies automorphism groups of rank one lattice vertex operator superalgebras and  gives a complete description. References | Related Articles | Metrics

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Inferences in a Censored Single-index Model with Empirical Likelihood YANG Yi-Ping, XUE Liu-Gen, CHENG Wei-Hu Acta mathematica scientia,Series A. 2012, 32 (2):  297-311.  Abstract ( 1718 )   RICH HTML PDF (508KB) ( 1130 )   Save Empirical  likelihood method for single-index models with randomly censored data is investigated. An estimated empirical likelihood for the parameters by using a synthetic data approach is developed. An adjusted empirical log-likelihood ratio function is proven  to be asymptotically standard chi-squared, and the corresponding confidence regions of the parameters are then constructed. Furthermore,  since the index is of norm 1, this constraint is used to reduce the dimension of parameters, which increases the accuracy of the confidence regions.  A simulation study indicates that compared with a normal approximation method, the proposed method works better in terms of coverage probabilities and areas of confidence regions. References | Related Articles | Metrics

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Shock Solutions for Some Singularly Perturbed Quasilinear Boundary Value Problems LIU Shu-De, SUN Jian-Shan, XIE Yuan-Jing Acta mathematica scientia,Series A. 2012, 32 (2):  312-319.  Abstract ( 1147 )   RICH HTML PDF (284KB) ( 765 )   Save Some singularly perturbed quasilinear boundary value problems with interior shock layer properties are studied under certain conditions, the formal approximation of the problem is constructed using the mothed of composite expansions, and the existence and asymptotic behavior of solutions are proved by the fixed point theory . References | Related Articles | Metrics

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Endpoint Estimates for Higher Order Maximal Commutators QIAO Dan, YANG Mei-Jin, CHEN Jian-Ren Acta mathematica scientia,Series A. 2012, 32 (2):  320-335.  Abstract ( 944 )   RICH HTML PDF (358KB) ( 769 )   Save In this paper, the authors establish that higher order maximal commutators of singular integral operator Tb, m* satisfy the following inequality |{y∈Rn:Tb, m*f(y)>λ}|≤C||b||mBMO∫Rn|f(y)|/λ (1+log+|f(y)|/λ)mdy and are bounded on Lp(Rn), 1 < p <∞, when b is a BMO function. References | Related Articles | Metrics

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A Modified SQP Parallel Variable Distribution Algorithm FENG Ting-Ting, HAN Cong-Ying, HE Guo-Ping Acta mathematica scientia,Series A. 2012, 32 (2):  336-343.  Abstract ( 828 )   RICH HTML PDF (360KB) ( 733 )   Save Ferris and Mangasarian proposed a PVD(parallel variable distribution) algorithm for solving optimization problems, which divides variables into primary and secondary variables groups. According to the algorithm, the variables are distributed among p parallel processors with each processor having the responsibility for updating its primary variables while allowing the remaining "secondary" variables to change in a restricted fashion along some easily computable directions, which enhances robustness and flexibility of the algorithm. In this paper, we present a modified SQP type PVD algorithm based on [6], whose search direction is a suitable combination of a descent direction and a feasible direction, and give a second-order revised for such a  direction. This new algorithm is very effective in preventing Maratos effect from happening, and avoid constraints in subproblem are inconsistent. We show the global convergence under some suitable conditions. References | Related Articles | Metrics

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Coleman Automorphisms of Semidirect Products of Abelian Groups by p-groups of Maximal Class LI Zheng-Xing, HAI Jin-Ke Acta mathematica scientia,Series A. 2012, 32 (2):  344-348.  Abstract ( 813 )   RICH HTML PDF (273KB) ( 773 )   Save Let G=A×P be the  semidirect product of an abelian group A and a p-group P of maximal class, where P acts on A by leaving every cyclic subgroup of A invariant. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence, we obtain that the normalizer property holds for such group G. References | Related Articles | Metrics

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An Inequality on Parabolic M\"{o}bius Groups in Infinite Dimension and |Their Application LI Liu-Lan Acta mathematica scientia,Series A. 2012, 32 (2):  349-355.  Abstract ( 697 )   RICH HTML PDF (296KB) ( 816 )   Save In this paper, an inequality on parabolic M\"{o}bius transformations in infinite dimension is obtained by using Clifford algebra. An application is also given. References | Related Articles | Metrics

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Construction of Jacobi Matrix from its Submatrix and Spectrum and |its Expansion WEI Ying, DAI Hua Acta mathematica scientia,Series A. 2012, 32 (2):  356-363.  Abstract ( 1091 )   RICH HTML PDF (279KB) ( 748 )   Save This paper considers the following problem: how to construct a Jacobi matrix from its spectrum and a submatrix. The numerical algorithms are given. Then we expand the result to the method of expanding a spring mass system to double dimension and the inverse  problem of constructing  a tridiagonal quadratic pencil. References | Related Articles | Metrics

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Fixed Points and Variational Inequalities |with Lower and Upper Bounds in Topological Spaces PIAO Yong-Jie Acta mathematica scientia,Series A. 2012, 32 (2):  364-372.  Abstract ( 954 )   RICH HTML PDF (312KB) ( 729 )   Save Based on an KKM type theorem and a Fan-Browder type fixed point theorem on generalized convex space, some new fixed point theorems for  a Φ-map and a weak Φ-map defined on topological spaces without any convex and linear structure and any compact setting are obtained. As applications, some existence problems of solutions for variational inequalities with lower and upper bounds were discussed in non-compact topological spaces. References | Related Articles | Metrics

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Existence and Uniqueness on Random Fixed Points Theorems for a Class of Random Decreasing Operators and its Applications LI Xing-Chang, ZHAO Zeng-Qin Acta mathematica scientia,Series A. 2012, 32 (2):  373-378.  Abstract ( 1206 )   RICH HTML PDF (297KB) ( 804 )   Save The paper obtains a class of random fixed point theorems for decreasing operator. Here, we do not assume any continuity and compactness. As applications, two examples of random integral equations are given. References | Related Articles | Metrics

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Regular Growth of the Generalized Dirichlet Series NING Ju-Hong, YI Cai-Feng, HUANG Wen-Peng Acta mathematica scientia,Series A. 2012, 32 (2):  379-386.  Abstract ( 901 )   RICH HTML PDF (259KB) ( 731 )   Save In this paper, we study the growth and regular growth  of the generalized Dirichlet series, and the growth relation between the angle domain and the half real axis. References | Related Articles | Metrics

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On Extension of Isometries Between Unit Spheres in ALp-spaces (1<p<∞) GAO Jin-Mei, TAN Dong-Ni Acta mathematica scientia,Series A. 2012, 32 (2):  387-394.  Abstract ( 997 )   RICH HTML PDF (308KB) ( 758 )   Save In this paper, we discuss the 1-Lipschitz mappings between the unit spheres in vector valued spaces Lp(Ω, ∑, μ; Lq(X, A, ν)) (2≤q<p<∞) and anti-1-Lipschitz mappings between the unit spheres in  vector valued spaces Lp (Ω, ∑, μ; Lq(X, A, ν))(1<p<≤2), and obtain that every such mapping can be extended to be a real linear isometry on the whole space Lp(Ω, ∑, μ; Lq(X, A, ν)). References | Related Articles | Metrics

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Some Properties of Toeplitz Operators on Dirichlet Spaces XIA Jin, WANG Xiao-Feng, CAO An-Fu Acta mathematica scientia,Series A. 2012, 32 (2):  395-403.  Abstract ( 903 )   RICH HTML PDF (273KB) ( 762 )   Save In this paper, we investigate the compactness and the Fredholm properties of Toeplitz operators on the Dirichlet space Dp(D) (1 < p < ∞), where D is the unit disc in complex plane C. We also compute the Fredholm index of Toeplitz operator on Dirichlet space Dp(D). References | Related Articles | Metrics

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A Generalized Pachpatte Type |Inequality on Time Scales and Application to a Boundary Value Problem WANG Wu-Sheng, ZHOU Xiao-Liang Acta mathematica scientia,Series A. 2012, 32 (2):  404-413.  Abstract ( 1548 )   RICH HTML PDF (312KB) ( 782 )   Save In this paper, using a technique of monotonization, the authors  investigate a generalized Pachpatte type integral inequality on time scales, which includes both a non-constant term outside the integrals and three distinct nonlinear integrals without assumption of monotonicity. The result not only unifies some continuous inequalities and their discrete analogues but also extends some known dynamic inequalities on time scales. An application of the result to the estimation of a solution of boundary value problem on time scales is given. References | Related Articles | Metrics

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An Arrangement Problem of Subspaces of |Symplectic Space and Tighter |Bound of an Error-tolerant Pooling Design ZHAO Xiang-Hui, LI Li, ZHANG Geng-Sheng Acta mathematica scientia,Series A. 2012, 32 (2):  414-423.  Abstract ( 831 )   RICH HTML PDF (374KB) ( 706 )   Save In this paper, we design a class of new d z-disjunct matrices with the subspaces of the symplectic space and study the following arrangement problem. Given integers m, r, s, ν, d, q where ν ≥m≥r+2≥2s≥2, d≥2, q is  a prime power, and a subspace S of type (m, s) of symplectic space F2νq, we find d subspaces of type (m-1, s-1) H1, … Hd of S that maximize the number of the subspaces of type (r, s-1) contained in at least some  Hi (1\le i\le d). Then with obtained result, we give the tighter bound of pooling design. References | Related Articles | Metrics

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Novel Integrable Decomposition of the Super AKNS Equation JI Jie, YU Jing, DONG Ya-Juan Acta mathematica scientia,Series A. 2012, 32 (2):  424-432.  Abstract ( 1125 )   RICH HTML PDF (306KB) ( 783 )   Save In this paper, the approach to construct higher super matrix spectral problems from a 3×3 super matrix spectral problem is presented. As an example, we construct a 5×5 super spectral problem which is associated with the super AKNS equation from the 3×3 super AKNS spectral problem, by  use of the binary nonlinearization method, new constraint of super AKNS equation is obtained. The corresponding  new integrable decomposition of the super AKNS equation is presented also. References | Related Articles | Metrics

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Uniform Blow-up Profile for a Semilinear Parabolic System with Nonlocal Boundaries LING Zheng-Qiu, LU Wei-Ming, ZHOU Ze-Wen Acta mathematica scientia,Series A. 2012, 32 (2):  433-440.  Abstract ( 1376 )   RICH HTML PDF (290KB) ( 798 )   Save In this paper, the authors deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super- and sub-solution techniques,  the global existence and finite time blow-up of solution are proved. Moveover, the uniform blow-up profiles of solutions are discussed. References | Related Articles | Metrics