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25 June 2011, Volume 31 Issue 3 Previous Issue    Next Issue

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ε-exact Penalty for Non-concave Bilevel Programming Problems LI Chang-Min, ZHU Dao-Li Acta mathematica scientia,Series A. 2011, 31 (3):  585-593.  Abstract ( 1405 )   RICH HTML PDF (370KB) ( 831 )   Save The main tool in the present literature  to treat the bilevel programming problems (BLPP)  is the method of  KKT conditions and value function. However, for the non-concave case, neither  technique can  be applied. In this paper,  the authors introduce the notions of ε-set, ε-error bounds, and use certain ε-uniform error bounds as ε-exact penalties to give single  level problems equivalent to the approximate BLPP. Furthermore, they show that any cluster of the approximate sequence is  the solution of the BLPP. References | Related Articles | Metrics

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Positive Solutions of Singular Fourth-order Periodic Boundary Value Problems TAO Qiang-Liu Acta mathematica scientia,Series A. 2011, 31 (3):  594-601.  Abstract ( 1467 )   RICH HTML PDF (326KB) ( 957 )   Save The purpose of this paper is to study the positive solutions to a class of nonlinear fourth-order periodic boundary value problems, where the nonlinear term f(t, u) is allowed to be singular at t = 0, t = 1 and u = 0. By introducing the height functions of nonlinear term and considering the integrations of the height functions, the growths of nonlinear term on some bounded sets are described. By applying the Hammerstein integral equations and the Guo-Krasnoselskii fixed point theorem of cone expansion-compression type, some new theorems concerned with the existence and multiplicity of positive solutions are obtained References | Related Articles | Metrics

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Numbers of Embeddings of Two Types of Regular Graphs on the Projective Plane LIU Xin-Qiu, HUANG Yuan-Qiu, WANG Jing, Ouyang Zhang-Dong Acta mathematica scientia,Series A. 2011, 31 (3):  602-610.  Abstract ( 1451 )   RICH HTML PDF (390KB) ( 921 )   Save Embedding numbers of graphs on distinct genus surfaces are always related. Therefore analyzing embedding numbers of graphs on lower genus surfaces is important to determine their genus distributions and their total genus distributions. Based on the model of joint tree introduced by Professor Liu, this paper calculates the embedding numbers of two types of necklace graphs on the projective plane. References | Related Articles | Metrics

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An Estimate for the Schr¨odinger Type Operators with Certain Nonnegative Potentials LIU Yu Acta mathematica scientia,Series A. 2011, 31 (3):  611-619.  Abstract ( 1048 )   RICH HTML PDF (320KB) ( 762 )   Save Let L = −Δ+ V be the Schr¨odinger operator on Rd with the potential V being a nonnegative polynomial. BMOL(Rd) is a dual space of the Hardy-type space H1 L(Rd) related to Schr¨odinger operator L = −Δ+V . In this article it is proved that the Schr¨odinger type operator (−Δ+ V )−β∇ is bounded from Lp(Rd) into BMOL(Rd) for p = d/2β−1 when the potential V is a nonnegative polynomial. References | Related Articles | Metrics

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Study on a Class of p-ary Sequences with Four-valued Crosscorrelation LI Nian, LI Sheng-Hua Acta mathematica scientia,Series A. 2011, 31 (3):  620-627.  Abstract ( 1473 )   RICH HTML PDF (306KB) ( 877 )   Save For an odd integer n > 0 and a prime p≡ 3 (mod 4), let be a primitive element of Fpn , where d = pn-1/2 + pk and 0 ≤ k < n. The crosscorrelation of p-ary sequences u(t) =Tr(aαdt), a ∈F*pn, and m sequences v(t) = Tr(αt) is proved to be four-valued. Moreover, the distribution is also completely determined. References | Related Articles | Metrics

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The Potentially Nilpotent Sign Patterns in the Set of Sign Patterns FSP(3, n-3) LI Hong-Hai, LI Jiong-Sheng, SU Li Acta mathematica scientia,Series A. 2011, 31 (3):  628-635.  Abstract ( 1372 )   RICH HTML PDF (355KB) ( 749 )   Save A matrix A whose entries come from the set {+, -, 0} is called a sign pattern matrix, or sign pattern. If A is a sign pattern and A is a real matrix for which each entry has the same sign as the corresponding entry of A, then A is said to be a realization of A. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, a class of sign patterns, denoted by FSP(3, n-3), is introduced. The authors determine all potentially nilpotent sign patterns in FSP(3, 4), and prove that no sign pattern of even order in  FSP(3, n-3) is potentially nilpotent. References | Related Articles | Metrics

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Inversion and Property Characterization on Generalized Transforms of Radon Type WANG Jin-Ping Acta mathematica scientia,Series A. 2011, 31 (3):  636-643.  Abstract ( 1272 )   RICH HTML PDF (346KB) ( 893 )   Save In this paper, the inversion formula and properties of generalized transforms of Radon type are discussed. Moreover, the numerical inversion is developed. Furthermore, the results of  Radon transform and exponential Radon transform in R2 are extended to $R^n$. References | Related Articles | Metrics

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Isotropic p-surface Area Measure YU Wu-Yang Acta mathematica scientia,Series A. 2011, 31 (3):  644-651.  Abstract ( 1164 )   RICH HTML PDF (313KB) ( 900 )   Save This paper studies the minimal p-surface area of a given convex body among its affine transformations of the same volume. A double-sided estimate for the volume of the polar Lp-projection body of p-surface isotropic convex body is given, and the p-isoperimetric inequality is given with its reverse form. Finally, the stability of the p-surface isotropic position for 1≤p≤2 is given. References | Related Articles | Metrics

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Patching Lemma and Deficiency Indices for |Singular Hamiltonian Differential Systems YANG Jie, QI Jian-Gang, JING Hai-Bin Acta mathematica scientia,Series A. 2011, 31 (3):  652-661.  Abstract ( 1488 )   RICH HTML PDF (346KB) ( 883 )   Save The "patching" lemma for singular Hamiltonian differential systems is obtained, which is the extension version of the corresponding result of H.D. Niessen and A. Zettl for second order differential equations. With applications, the non-oscillation criterion of Rellich and Rosenberger  type is generalized to singular Hamiltonian differential systems and the limit-point criteria of J. Qi and Sh. Chen, S.L. Clark and F. Gesztesy are improved. References | Related Articles | Metrics

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Higher Dimensional Matrices and Structure Constants for Hopf Algebras CHENG Dong-Ming Acta mathematica scientia,Series A. 2011, 31 (3):  662-669.  Abstract ( 969 )   RICH HTML PDF (233KB) ( 797 )   Save The concept of structure constants for Hopf algebras is introduced and studied in this paper. Higher dimensional matrices are introduced to describe the structure constants for Hopf algebras. The condition for a pre-coalgebra to be a coalgebra and the condition for a pre-bialgebra to be a bialgebra and a Hopf algebra are determined in form of higher dimensional matrices. References | Related Articles | Metrics

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Construction of Frames Based on Structured Admissible Covering LIU Guo-Jun, FENG Xiang-Chu, ZHANG Wei-Bin Acta mathematica scientia,Series A. 2011, 31 (3):  670-677.  Abstract ( 1192 )   RICH HTML PDF (376KB) ( 1134 )   Save Using the general theory of the structured admissible covering, a Ridgelet-type covering Q={QT}T∈T of the frequency space R2(ξ) is analogously introduced along with the constructed flow of Curvelet-type frame. The affine transformation T acts on the roles of dilation, translation, and modulation. Most of all, some different Ridgelet-type frames are given, such as Ridgelet-type tight frame, Dual Ridgelet-type frame, and Monoscale Dual Ridgelet-type frame, by combining the orthonomal Ridgelet with the constructed covering. Compared with Candes's Ridgelet tight frame, besides the analysis frames, their dual frames also have an explicit form. References | Related Articles | Metrics

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The Invariants of the Group of Lower Triangular Matrices over Finite Fields NAN Ji, CHEN Yin Acta mathematica scientia,Series A. 2011, 31 (3):  678-681.  Abstract ( 1056 )   RICH HTML PDF (255KB) ( 844 )   Save Let Fq be a finite field with characteristic p. The purpose of this note is to reconstruct an explicit set of generators of the ring of invariants of the group of lower triangular matrices with diagonal entries 1 over Fq. References | Related Articles | Metrics

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Adaptive Iterative Learning Control for Nonlinearly Parameterized Systems with Time-Varying Delays LI Jun-Min Acta mathematica scientia,Series A. 2011, 31 (3):  682-690.  Abstract ( 1444 )   RICH HTML PDF (422KB) ( 931 )   Save A new adaptive iterative learning control approach is proposed in this paper  for a class of nonlinear systems with unknown time-varying parameters and time-varying delays. By using the parameter separation technique combined with the signal replacement mechanism, the approach can be applied to   nonlinear systems with time-varying parameters and delay uncertainty. A novel adaptive control strategy is designed to ensure the tracking error converging to zero in the mean-square sense on the finite interval. A sufficient condition for the convergence is also given by constructing a Lyapunov-Krasovskii-like composite energy function. A simulation example is provided to illustrate the effectiveness of control algorithms proposed in this paper. References | Related Articles | Metrics

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The Inverse Eigenvalue Problem of Hermitian and Generalized Skew-Hamiltonian |Matrices with a Submatrix Constraint and Its Approximation MO Rong-Hua, LI Wen Acta mathematica scientia,Series A. 2011, 31 (3):  691-701.  Abstract ( 1394 )   RICH HTML PDF (343KB) ( 831 )   Save In this paper, the authors consider the inverse eigenvalue problem of Hermitian and generalized skew-Hamiltonian matrices with a submatrix constraint, provide an expression of the solution. The authors  also show that the best approximation is existed and unique and provide an expression of the solution. A numerical algorithm is given, and a numerical example is provided to illustrate the  results. References | Related Articles | Metrics

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Some New Kinematic Formulae and Their Applications ZU Du, LI De-Yi, XIE Feng-Fan Acta mathematica scientia,Series A. 2011, 31 (3):  702-708.  Abstract ( 1378 )   RICH HTML PDF (298KB) ( 876 )   Save By Minkowski differences of sets, the containment measures of line segments inside bounded Lebesgue measurable sets are studied and some new integral formulae are obtained. An application to the Buffon's needle problem leads to a new conclusion. References | Related Articles | Metrics

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Strong Periodic Solution for a Class of Non-local PDE Models for Population Dynamics with State-selective Delays LI Xiang, LI Zhi-Xiang Acta mathematica scientia,Series A. 2011, 31 (3):  709-719.  Abstract ( 1213 )   RICH HTML PDF (328KB) ( 1114 )   Save In this paper, a class of non-local PDE models for population dynamics with state-selective delays is considered and  the existence of strong periodic solutions is investigated via  Garlekin method. Moreover, the uniqueness and global attractivity of the periodic solution are discussed by using a Lyapnov function. References | Related Articles | Metrics

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Hybrid Algorithms of Common Elements for Equilibrium Problems and Fixed Point Problems GAO Xing-Hui, ZHOU Hai-Yun, GAO Gai-Liang Acta mathematica scientia,Series A. 2011, 31 (3):  720-728.  Abstract ( 1006 )   RICH HTML PDF (340KB) ( 919 )   Save In strictly convex and uniformly smooth Banach spaces with the K-K property, a new hybrid projection method is proposed to approximate common elements for the set of common fixed points of two quasi-Φ-nonexpansive mappings and the set of solutions of an equilibrium problem. A strong convergence theorem of the common elements is proved by using generalized projection operator, the K-K property and other analysis techniques. The results of this paper improve and extend recent some relative results. References | Related Articles | Metrics

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Representation of Bounded Linear Operators with Equal Spectral Projections at Zero ZHANG Yun, CHEN Dong-Jun, XIE Yong-Sheng Acta mathematica scientia,Series A. 2011, 31 (3):  729-736.  Abstract ( 1216 )   RICH HTML PDF (288KB) ( 834 )   Save In this paper, the authors  give the representation of all Drazin invertible operator B which shares the spectral projections at 0 with a given Drazin invertible operator A. Meanwhile, some related results for EP operators with closed range are  obtained. References | Related Articles | Metrics

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The Precise Large Deviations for a Risk Model Based on the Policy Entrance Process TANG Feng-Qin, LI Ze-Hui, CHEN Jin-Yuan Acta mathematica scientia,Series A. 2011, 31 (3):  737-751.  Abstract ( 1302 )   RICH HTML PDF (403KB) ( 881 )   Save Li and Kong[1] constructed a new risk model based on the policy entrance process which involves multiple kinds of independent policies, and studied the asymptotic behavior of the surplus when time goes to infinity. In this paper the authors investigate large derivations for this model. The authors obtain the precise large deviations with both single and multiple kinds of independent policies when the tail of the claim size is consistently varying. The  results extend the related large deviation results for shot noise processes. References | Related Articles | Metrics

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A New Representation of Efficient Point Sets and DEA Models LI Mao-Qin Acta mathematica scientia,Series A. 2011, 31 (3):  752-761.  Abstract ( 1012 )   RICH HTML PDF (354KB) ( 865 )   Save E(M, K) (Ew(M, K)), the set of efficient (weak efficient) points of a set M in Rn, is expressed as a difference of two sets M and (M+K\{0}). With the new representation, some properties of E(M, K) are proved more easily than that before. When M or K is in the form of union, intersection, sum or difference of two sets, some properties of E(M, K) are considered. Most of the properties are proved by the binary operations of sets, which is a new method in the multiobjective optimization. Then these properties are used to solve some types of multiobjective linear programming problems corresponding to DEA models. The structures of the DEA efficient solution sets of four input-orient DEA models are developed. Thereby the  relationship between efficiencies of four input-orient DEA models is deduced. References | Related Articles | Metrics

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Laws of Large Numbers for g-probabilities LI Wen-Juan Acta mathematica scientia,Series A. 2011, 31 (3):  762-768.  Abstract ( 1093 )   RICH HTML PDF (245KB) ( 798 )   Save The purpose of this article is to establish laws of large numbers  for g-probabilities, which are defined via Peng's g-expectations. By studying  the relationship of g-probabilities and  probability measures in a given set P, it is showed that  laws of large numbers in a broad sense for g-probabilities can be established via the corresponding laws for the  probability measures in the set P. References | Related Articles | Metrics

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A Reduced Finite Difference Scheme Based on POD Bases and Posteriori Error Estimation for the Three Parabolic Equation AN Jing, LUO Zhen-Dong Acta mathematica scientia,Series A. 2011, 31 (3):  769-775.  Abstract ( 1326 )   RICH HTML PDF (354KB) ( 977 )   Save In this article, the solution  space of three-dimensional parabolic equation finite difference scheme is studied. Firstly a group of proper orthogonal decomposition (POD) bases of solution space is obtained by using singular value decomposition. Secondly, by combining the Galerkin projection method, the finite difference scheme of three-dimensional parabolic equation is converted into a low dimensional mode with higher precise. Then, the error between the finite difference scheme solution and the POD scheme solution is presented. And it is shown by the numerical results that the error between the finite difference scheme solution and the POD scheme solution is consistents with theoretical results. Therefore, the POD method is effective and feasible. References | Related Articles | Metrics

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Coifman Type Weighted Inequalities for Commutators of Generalized Fractional Integral Operators YAN Xue-Fang, LI Wen-Ming Acta mathematica scientia,Series A. 2011, 31 (3):  776-784.  Abstract ( 1485 )   RICH HTML PDF (315KB) ( 810 )   Save Let Tα be the generalized fractional integral operator with kernel satisfying generalized  H\"{o}rmander condition. In this paper, the authors obtain the Coifman type weighted inequalities for commutators of generalized fractional integral operators and  give an application to the fractional integral operators with homogeneous kernel. References | Related Articles | Metrics

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Lyapunov Drift Conditions for General Symmetric Jump Processes WANG Jian Acta mathematica scientia,Series A. 2011, 31 (3):  785-795.  Abstract ( 1235 )   RICH HTML PDF (346KB) ( 886 )   Save This paper studies Lyapunov drift conditions for general symmetric jump processes. The author aims to derive Poincar´e, super-Poincar´e and weak-Poincar´e inequalities directly through Lyapunov functions controls. Birth death processes and symmetric L´evy type processes are presented to illustrate the power of the results. References | Related Articles | Metrics

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Regular Subsets of a Class of Self-affine Set GUI Yong-Xin, LI Wen-Xia Acta mathematica scientia,Series A. 2011, 31 (3):  796-804.  Abstract ( 1193 )   RICH HTML PDF (355KB) ( 847 )   Save A class of regular subsets of the self-affine set introduced by Gatzouras and Lalley are studied. Their Hausdorff and packing dimensions are explicitly obtained. References | Related Articles | Metrics

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Banach Spaces which are Dual to k Nearly Uniformly Convex Spaces Suya latu, Wudun qiqige, BAO Laiyou Acta mathematica scientia,Series A. 2011, 31 (3):  805-813.  Abstract ( 1451 )   RICH HTML PDF (342KB) ( 878 )   Save In this paper, we introduce two new classes of Banach spaces: k nearly uniformly smooth spaces and ω nearly uniformly smooth spaces, which are the dual notions to k nearly uniformly convex spaces and ω nearly uniformly convex spaces respectively, introduced by Denka Kutzarova. We give some characters and properties of these two kinds of Banach spaces. Apart from that we really distinguish the k uniformly smooth spaces, k nearly uniformly smooth spaces, ω nearly uniformly smooth spaces, fully k smooth spaces and nearly uniformly smooth spaces. References | Related Articles | Metrics

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2D Hilbert Transform and Bedrosian’s Principle Associated with Fractional Fourier Transform XU Guan-Lei, WANG Xiao-Tong, XU Xiao-Gang Acta mathematica scientia,Series A. 2011, 31 (3):  814-828.  Abstract ( 1622 )   RICH HTML PDF (404KB) ( 962 )   Save Hilbert transform (HT) plays an important role in signal processing. From the energy distributing of analytic signals in the FRFT domain and a few classical 2D elemen-tary Hilbert transform, the definitions of half-planed Hilbert transform, cross-orthant Hilbert transform and single-orthant Hilbert transform are yielded. Meanwhile, the expressions and the mapping in the time domain and the transformed domain are discussed. Moreover, some important properties and conclusions are obtained as well. Finally, we define and derive 2D Bedrosian’s principle in the FRFT domain, an important property of Hilbert transform.  References | Related Articles | Metrics

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Existence of Solutions for Fourth Order Boundary Value Problem with p-Laplace at Resonance JIN Shan, LU Shi-Ping Acta mathematica scientia,Series A. 2011, 31 (3):  829-836.  Abstract ( 1370 )   RICH HTML PDF (275KB) ( 904 )   Save This paper deals with the fourth order boundary value problem with p-Laplace at resonance (φ'p(u′′(t)))′′ = f(t, u(t), u′(t), u′′(t)), 0 < t < 1, u(0) = 0, u(1) = au(ξ), u′′(0) = 0, u′′(1) = bu′′(η), where 0 <  ξ，η < 1; a, b > 0 such that a ξ = 1 and bp−1η ≤ 1. The existence of solutions is obtained by means of Mawhin’s continuation theorem. References | Related Articles | Metrics

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A Class of Conformal Projectively Flat Finsler Manifolds ZHANG Jian-Feng Acta mathematica scientia,Series A. 2011, 31 (3):  837-844.  Abstract ( 1001 )   RICH HTML PDF (291KB) ( 892 )   Save In this paper, we study a class of Finsler manifolds defined by a Riemannian metric and a 1-form. we can get a projectively flat metric from a nonprojectively flat metric only through conformal transformation for some 1-forms and functions φ(s). References | Related Articles | Metrics

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Symplectic Vector Fields on Two Types of Special Symplectic Supermanifolds WANG Bao-Qi, ZENG Hui Acta mathematica scientia,Series A. 2011, 31 (3):  845-855.  Abstract ( 1551 )   RICH HTML PDF (355KB) ( 905 )   Save In this paper, an operator η is defined in the left A module DerA on symplectic supermanifoldM = (e, A) of dimension (0, n). Two sufficient and necessary conditions are given for vector fields on M being symplectic vecter fields, and some identities about the operator η are obtianed. Furthermore, three decision conditions are given to judge symplectic vector fields on cotangent supermanifold T*(M) = (e, S(DerA)), and their equivalences are proved. References | Related Articles | Metrics