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25 April 2013, Volume 33 Issue 2 Previous Issue    Next Issue

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Groups of Self-equivalences in Category ZHAO Hao, YU Hai-Bo, SHEN Wen-Huai Acta mathematica scientia,Series A. 2013, 33 (2):  201-205.  Abstract ( 646 )   RICH HTML PDF (256KB) ( 586 )   Save Groups of self-equivalences of the objects in category MAP and fibrewise category TOPB are studied. We show that these two kinds of groups are connected via an exact sequence which is split in some cases. References | Related Articles | Metrics

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Internal Transition Layer Solution of Singularly Perturbed Optimal Control Problem  WU Li-Meng, NI Ming-Kang, LIU Hai-Bo Acta mathematica scientia,Series A. 2013, 33 (2):  206-215.  Abstract ( 584 )   RICH HTML PDF (352KB) ( 536 )   Save The existence of internal transition layer solution for a class of optimal control problem is proved by the singularly perturbed theory. In the framework of this paper, the authors not only give the conditions under which there exists an internal transition layer but also determine where an internal transition time is. Meanwhile, the uniformly valid asymptotic solution for the optimal control problem is constructed by the direct scheme method, which is based on the boundary function method. Finally, an example is presented to show the result. References | Related Articles | Metrics

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Sign-changing Solutions to Third-order Two-point Boundary Value Problem ZHANG Qi Acta mathematica scientia,Series A. 2013, 33 (2):  216-223.  Abstract ( 623 )   RICH HTML PDF (312KB) ( 530 )   Save In this paper, we use the fixed point index theory and the Leray-Schauder degree theory to discuss the third-order boundary value problem -u'''(t)=f(t, u(t)) for all t ∈[0,1] subject to u(0)=u'(0)=u''(1)=0, where f ∈C([0,1]×R, R). By computing hardly the eigenvalues and their algebraic multiplicities of the associated linear problem, we obtain some new existence results concerning sign-changing solutions to this problem. If f satisfies certain conditions, then the problem has at least six different nontrivial solutions: two positive solutions, two negative solutions and two sign-changing solutions. Moreover, if f(t, •) is odd for all t ∈[0,1], then the problem has at least eight different nontrivial solutions, which are two positive, two negative and four sign-changing solutions. References | Related Articles | Metrics

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The Upper Bound of Second Order Item Coefficients of Homogeneous  Expansion for Spirallike Mappings Relative to A LIU Hao, CHANG Shui-Zhen Acta mathematica scientia,Series A. 2013, 33 (2):  224-229.  Abstract ( 562 )   RICH HTML PDF (283KB) ( 455 )   Save In this thesis, with the properties of Loewner chains,  the upper bound of second order item coefficients of homogeneous expansion for spirallike mappings relative to A was obtained via the characters of spirallike mappings relative to A on the unit ball Bn in Cn. References | Related Articles | Metrics

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The Stability of the Riemann Solutions for Aw-Rascle Model ZHANG Ting-Ting Acta mathematica scientia,Series A. 2013, 33 (2):  230-241.  Abstract ( 1087 )   RICH HTML PDF (532KB) ( 464 )   Save In this paper, we propose an entropy inequality, and using it, the stability of the Riemann solutions for the Aw-Rascle model is gotten  when the initial data include vacuum. The entropy in the inequality is strong and locally strictly convex, which is a new phenomenon. References | Related Articles | Metrics

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Shared Value and Normality of Families of Meromorphic Functions DUAN Xi-Sheng, XIE Li Acta mathematica scientia,Series A. 2013, 33 (2):  242-245.  Abstract ( 819 )   RICH HTML PDF (206KB) ( 620 )   Save This paper proved some theorems on the normality of families of meromorphic functions which share values along with their derivatives. The results improved a theorem of holomorphic functions. References | Related Articles | Metrics

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The Koszulity of the Trivial Extension of Selfinjective Algebras WAN Jian-Hong, GUO Jin-Yun Acta mathematica scientia,Series A. 2013, 33 (2):  246-252.  Abstract ( 656 )   RICH HTML PDF (269KB) ( 502 )   Save Let Λ be a connected finite-dimensional selfinjective algebra, we obtain that the trivial extension T(Λ) of Λ is a Koszul algebra if Λ is a Koszul algebra. References | Related Articles | Metrics

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Integrals on Matrix Spaces WANG Cheng-Yong, QU Gang-Rong, WANG Rui-Min Acta mathematica scientia,Series A. 2013, 33 (2):  253-259.  Abstract ( 721 )   RICH HTML PDF (230KB) ( 505 )   Save In this paper we calculate some classical integrals on hyperbolic matrix spaces. From these integrals we can obtain the volumes of real symmetric classical domains of hyperbolic matrix spaces. References | Related Articles | Metrics

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Stochastic Stability for the Nonlinear Autoregressive Series ZHANG Ren, ZHANG Shao-Yi Acta mathematica scientia,Series A. 2013, 33 (2):  260-266.  Abstract ( 613 )   RICH HTML PDF (288KB) ( 445 )   Save In this paper, we discuss existence of the stationary distribution and moment of nonlinear autoregressive model with conditional heteroscedasticity by the Markov theory. Especially,only assume that random variable has density function in the innovation, but not positive everywhere. References | Related Articles | Metrics

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A Note on Strong Approximation for Trimmed Sums FU Ke-Aong Acta mathematica scientia,Series A. 2013, 33 (2):  267-275.  Abstract ( 644 )   RICH HTML PDF (310KB) ( 460 )   Save Let {X, Xn; n≥1} be a sequence of independent and identically distributed random variables, and let Xn(r)}=Xm if |Xm| is the r-th maximum of {|Xk|; k≤n} . Define Sn==∑k=1nXk and (r)Sn=Sn-(Xn(1)+…+Xn(r)). This paper aims to establish a general strong approximation for the trimmed sums (r)Sn without variance, and as applications, general functional laws of the iterated logarithm for trimmed sums and products of trimmed sums are derived. References | Related Articles | Metrics

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Algebro-Geometric Solutions of the D-AKNS Equations SUN Yu-Juan, DING Qi, MEI Jian-Qin, ZHANG Hong-Qing Acta mathematica scientia,Series A. 2013, 33 (2):  276-284.  Abstract ( 767 )   RICH HTML PDF (323KB) ( 625 )   Save The D-AKNS equations are decomposed into system of partial differential equations which is easier to solve. The Abel-Jacobi coordinates and Abel map are introduced to straighten out the flows, from which algebro-geometric solutions of the D-AKNS equations are obtained  by means of the Riemann theta function. References | Related Articles | Metrics

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Blow-up and Global Boundedness for a Weakly Coupled Parabolic System with Variable Exponents SONG Wen-Jing, GUO Bin, GAO Wen-Jie Acta mathematica scientia,Series A. 2013, 33 (2):  285-291.  Abstract ( 749 )   RICH HTML PDF (287KB) ( 456 )   Save The aim of this paper is to study the properties of solutions of a reaction-diffusion system with variable exponents. The authors obtained sufficient conditions for the existence of global and non-global solutions. References | Related Articles | Metrics

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Optimal Subspace of Bernstein n-Widths for Some Classes of Periodic Functions FENG Guo Acta mathematica scientia,Series A. 2013, 33 (2):  292-297.  Abstract ( 588 )   RICH HTML PDF (269KB) ( 495 )   Save In this paper, we consider Bernstein n-width of the  classes of 2π-periodic convolution functions Kp and Bp, obtain their optimal subspaces in Lp for n odd and p∈(1, ∞). References | Related Articles | Metrics

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Inequalities Between Generalized Logarithmic, Arithmetic and Geometric Means CHU Yu-Ming, WANG Miao-Kun Acta mathematica scientia,Series A. 2013, 33 (2):  298-308.  Abstract ( 725 )   RICH HTML PDF (256KB) ( 578 )   Save In this paper, we establish the best lower and upper bounds for combination of the arithmetic and geometric means by the generalized logarithmic mean. These results solve two open problems posed in the paper [21]. References | Related Articles | Metrics

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Tangle of Arbitrary Dimensional Bipartite Quantum States LI Bin, SHEN Guang-Yan Acta mathematica scientia,Series A. 2013, 33 (2):  309-316.  Abstract ( 667 )   RICH HTML PDF (327KB) ( 713 )   Save We derive two analytical lower bounds for one of entanglement measures called tangle (squared \emph{I}-concurrence) of a bipartite quantum state in arbitrary dimension by two different ways. They are achieved by an important connection among the concurrence, the well-known Peres-Horodecki, and realignment criteria. At last we give a comparison and find their internal relation of this two bounds. References | Related Articles | Metrics

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Optimal Excess of Loss Reinsurance for a Correlated Risk Model with Thinning-Dependence Structure HU Feng-Qing Acta mathematica scientia,Series A. 2013, 33 (2):  317-326.  Abstract ( 550 )   RICH HTML PDF (348KB) ( 528 )   Save In this paper, we investigate the optimal excess of loss reinsurance under the correlated risk model with thinning-dependence structure, that maximizes the expected exponential utility and the adjustment coefficient respectively. Correspondingly, we derive the optimal solutions and give a numerical example to analyze the impacts of the thinning factor for each strategy. References | Related Articles | Metrics

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Normal Structure and the Generalized Modulus of U-convexity in Banach Spaces ZUO Zhan-Fei Acta mathematica scientia,Series A. 2013, 33 (2):  327-332.  Abstract ( 687 )   RICH HTML PDF (255KB) ( 440 )   Save Some sufficient conditions for which a Banach space X has normal structure in term of the generalized modulus of U-convexity, the coefficient of weak orthogonality and the coefficient R(1, X) were studied in this paper. Our results extend and improve some recent results. References | Related Articles | Metrics

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A Uniqueness Theorem for Diffusion Operators on the Finite Interval WANG Yu-Ping Acta mathematica scientia,Series A. 2013, 33 (2):  333-339.  Abstract ( 576 )   RICH HTML PDF (279KB) ( 591 )   Save In this paper, we discuss the inverse problem for diffusion operators on the finite interval [0, π].  For a fixed integer n (n∈Z),  the potentials (q(x), p(x)) and coefficient h of the boundary condition can be uniquely determined  by the spectral set of the n-th eiginvalues of the diffusion operator for distinct Hk.  References | Related Articles | Metrics

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A New Generalized Sum-Difference Inequality with Two Variables and Applications to BVP WANG Wu-Sheng, LI Zi-Zun, ZHOU Xiao-Liang Acta mathematica scientia,Series A. 2013, 33 (2):  340-353.  Abstract ( 623 )   RICH HTML PDF (368KB) ( 446 )   Save In this paper, we establish a general form of sum-difference inequality in two variables, which contains both a nonconstant term outside the sums and k terms of nonlinear sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to solve those discrete inequalities considered in the work of  Cheung W S (2006) and  Wang W S (2008). Furthermore, we apply our result to a boundary value problem of a partial difference equation for boundedness, uniqueness and continuous dependence. References | Related Articles | Metrics

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Multiple Solutions for Biharmonic Equations with Concave-Convex Nonlinearities ZHANG Ya-Jing Acta mathematica scientia,Series A. 2013, 33 (2):  353-365.  Abstract ( 645 )   RICH HTML PDF (307KB) ( 454 )   Save In this paper, we consider biharmonic equations involving concave-convex nonlinearities and sign-changing weight function. With the help of Nehari manifold, we prove the existence of two solutions for the biharmonic equation.   References | Related Articles | Metrics

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On Logarithmic Order and Logarithmic Proximate Order of the Analytic Function Defined by Laplace-Stieltjes Transformations XU Hong-Yan, YI Cai-Feng, HU Yi Acta mathematica scientia,Series A. 2013, 33 (2):  366-376.  Abstract ( 665 )   RICH HTML PDF (340KB) ( 546 )   Save The purpose of this paper is to study precisely the growth of the analytic functions of zero order which are defined by Laplace-Stieltjes transformations and are analytic in the right half  plane. The  concepts of logarithmic order and logarithmic proximate  order have been introduced and some results of the growth of such functions are obtained.   References | Related Articles | Metrics