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    The Inverse Problem of Symmetric Orthoantisymmetric Matrices
    HU Ti-Tan, ZHANG Lei, ZHOU Fu-Zhao
    Acta mathematica scientia,Series A    2004, 4 (5): 543-550.  
    Abstract2063)      PDF(pc) (346KB)(5659)       Save

    Given P∈OR\+\{n×n satisfying  P\+T=P. Set  SAR\+n\-P={A∈R\+\{n×n|A\+T=A, (PA)\+T=-PA}.
    This paper discusses the following problems
    Problem Ⅰ〓Given X∈R\+\{n×m, Λ=diag(λ\-1,λ\-2, …, λ\-m)∈R\+\{m×m. Find A∈SAR\+n\-P such that AX=XΛ.Problem ⅡGiven B, X∈R\+\{n×m.Find A∈SAR\+n\-P such that ‖AX-B‖=min.Problem Ⅲ〓Given [AKA~]∈R\+\{n×n. FindA\+*∈S\-E such that‖[AKA~]-A\+*‖=inf[DD(X]A∈S\-E[DD)]‖[AKA~]-A‖ where S\-E is the solution set of Problem Ⅱ, ‖\5‖ is the Frobenius norm.The necessary and sufficient conditions for the solvability of  Problem Ⅰ have been studied. The general form of the solution set S\-E of Problem Ⅱ has been given. For Problem Ⅲ the expression of the solution A\+* has been provided.

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    A Nonlinear Conjugate Gradient Method under Exact Line Search
    SHI Zhen-Jun
    Acta mathematica scientia,Series A    2004, 4 (6): 675-682.  
    Abstract1696)      PDF(pc) (349KB)(3005)       Save

    The paper presents a nonlinear conjugate gradient method for unconstrained optimization problem, and proves its global convergence under exact line searches. The linear convergence rate is investigated when the objective function is uniformly convex. Numerical experiments show that the new algorithm is effective in practice.

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    The Meaning of Quantum Finance
    CHEN Ze-Gan
    Acta mathematica scientia,Series A    2003, 23 (1): 115-128.  
    Abstract1900)      PDF(pc) (483KB)(2612)       Save

    This paper is the sequel of the author's papers [1], [2], and [3]. Quantum mechanics is involved to present a new version of hedging contingent claim The financial meaning of some results obtained in the sense of quantum theoryis studied. Finally, but not at last, the author tries his best to explain, in some details, why we should use quantum financial models in realworld financialmarkets.

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    ON THE CROSSING NUMBER OF THE COMPLETE TRIPARTITE GRAPH K1,8,n
    Huang Yuanqiu; Zhao Tinglei
    Acta mathematica scientia,Series A   
    Abstract1830)      PDF(pc) (204KB)(2357)       Save
    The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤ n) is Z(m,n), where Z(m,n)=\lfloor\frac{m}{2}\rfloor\lfloor\frac{m-1}{2}\rfloor\lfloor\frac{n}{2}\rfloor$$\lfloor\frac{n-1}{2}\rfloor$ (for any real number x, $\lfloor x\rfloor$ denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤ 6. In this article, the authors prove that if Zarankiewicz' conjecture holds for m≤ 9, then the crossing number of the complete tripartite graph K1,8,n is $Z(9, n)+ 12\lfloor\frac{n}{2}\rfloor$.
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    Some Properties on Currents in Metric Spaces
    Zhao Peibiao;Yang Xiaoping
    Acta mathematica scientia,Series A   
    Abstract2928)      PDF(pc) (352KB)(2171)       Save
    The authors study the representation theorem of current by using the view of algebra. The similar Radon-Nikodym theorem for completely invariant current is obtained by virtue of the constructing minimal triple.
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    Stability of Compacton Solutions and Backlund Transformation for One Type of Nonlinear Equations
    Yin Jiuli; Tian Lixin
    Acta mathematica scientia,Series A   
    Abstract3068)      PDF(pc) (368KB)(2168)       Save
    Introducing K(m,n,1) equation with linear fifth-order dispersion, the authors obtain sin-compacton solutions by Adomian decomposition method. Using the homogeneous balance(HB) method, the authors obtain a Backlund transformation of a special equation K(2,2,1) to determine some new solitary solutions of the equation. The authors finally show the linear stability of all obtained sin-typed multi-compacton solutions.
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    The Shock Solution for a Class of Nonlinear Equation
    HAN Xiang-Lin
    Acta mathematica scientia,Series A    2003, 23 (2): 253-256.  
    Abstract1599)      PDF(pc) (292KB)(2159)       Save

    By using the matching asymptotic expanding method, the shock solutions  and their locations of a nonlinear equation are considered. And the relation of  them with the boundary conditions is obtained.

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    Approximation of Convex Functions on the Dual Spaces
    RUAN Ying-Ban, CHEN Shao-Xiong
    Acta mathematica scientia,Series A    2004, 24 (1): 116-122.  
    Abstract1454)      PDF(pc) (354KB)(2158)       Save

    In this paper, the authors prove that for every w^* lower semicontinuous Lipschitzian convex function on the dual of a bistrictly convexifiable Banach space can be uniformly approximated by a  sequence of w^* lower semicontinuous monotone nondecreasing Lipschitzian convex function with the dense very smooth point  set.

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    Potential Function Model of Uniformity Measurement
    HU Dong-Hong, LI De-Hua, WANG Zu-Xi
    Acta mathematica scientia,Series A    2003, 23 (5): 607-612.  
    Abstract1791)      PDF(pc) (450KB)(2118)       Save

    The basic characteristics that  any criterion of uniformity measurement  should have are discussed. According to the model of physics potential and forc e, a new criterion of uniformity measurement, potential function model of unifor mity measurement, is proposed. The model  not only can solve the problems suc h as  computability and the adjustable character for uniformity, but also has all the  good characters, which a uniformity measurement should have, such as rotation s ymmetry , translation symmetry and center reflection symmetry. An example is shown and  the uniformity of lower dimension projection is discussed at the end.

     

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    Exponential Stability in Mean Square for Stochastic Hopfield Delay Neural Networks: an LMI Approach
    Chen Wuhua; Lu Xiaomei; Li Qunhong; Guan Zhihong
    Acta mathematica scientia,Series A   
    Abstract2818)      PDF(pc) (344KB)(2109)       Save
    By using a technique of model transformation of the system, a new type of Lyapunov functional is introduced. By applying this new Lyapunov functional, a novel delay-dependent sufficient condition of exponential stability in mean square for stochastic Hopfield delay neural networks is derived in terms of
    linear matrix inequalities (LMIs). A delay-independent sufficient condition is also presented. Numerical examples show that the proposed method is less conservative than the previous ones.
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    Research of the Motion Law on OneDimensional Relativistic Vibrator
    ZHU Ping
    Acta mathematica scientia,Series A    2004, 24 (1): 123-128.  
    Abstract1454)      PDF(pc) (314KB)(2084)       Save

    American R Penfield and Chinese Zhou Lingyun have discussed the approximate solutions to the motion law on one dimensional relativistic vibrator. In this thesis, utilizing the elliptical integrals theory, the authors have obtained the analytic soluti ons and the vibration period on one dimensional relativistic vibrator.

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    Generalized Inverses of Matrices on an Arbitrary Division Ring
    LIU Yong-Hui, SHU Chao, CHEN Guan-Liang
    Acta mathematica scientia,Series A   
    Factorization of Analytic Function of Order Less Than
    Deng Guantie
    Acta mathematica scientia,Series A   
    Abstract2347)      PDF(pc) (220KB)(2065)       Save
    In this paper, the author proves that an analytic function of order less than 2 in a half plane can be factored into the product of the three functions: weighted Blaschke product, weighted singular inner function and weighted outer function. This is a generalization of the classical factorization about analytic functions in the Hardy space.
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    Singular Perturbation for a Class of Reaction Diffusion Equation
    XIE Feng
    Acta mathematica scientia,Series A   
    不确定非线性系统的鲁棒自适应控制器
    CHEN Wei-Tian, YAN Shi-Tian, ZHANG Zheng-Qiang, ZHU Feng-Chun
    Acta mathematica scientia,Series A    2002, 22 (2): 194-202.  
    Abstract1397)      PDF(pc) (442KB)(2023)       Save

    在backstepping程序中,把非线性自适应控制和鲁棒控制连接起来,为参数化的严格反馈系统在不确定性存在的情况下,建立了一种鲁棒自适应控制方案.非线性自适应控制被用来处理系统的线性参数化部分,而鲁棒控制通过引进非线性阻尼项被用来处理不确定性部分.与现有的方案不同,作者给出了非线性阻尼项的无限种选择,而不是仅仅一种选择.通过使用一种合适的选择,能够设计一个鲁棒自适应控制器.它不仅能够保证对不确定性的鲁棒性,而且能够使输出误差任意小,以及用较小的控制努力取得较好的性能.

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    Estimates of Upper Bounds of the Spectral Radius for Some Iteration Matrix
    CHEN Chao-Rong, LI Wen
    Acta mathematica scientia,Series A    2001, 21 (1): 8-13.  
    Abstract1355)      PDF(pc) (312KB)(1993)       Save

    该文对一类广义对角占优矩阵M,给出了迭代矩阵M-1N 的谱半径的上界.特别,当M是严格对角占优时,证明了所得到的估计值总比通常用作谱半径的估计值要好.

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    Explicit Construction of Wavelet Tight Frames with Dilation factor α
    Huang Yongdong; Cheng Zhengxing
    Acta mathematica scientia,Series A   
    Abstract2378)      PDF(pc) (337KB)(1922)       Save
    This paper studies wavelet tight frames associated with given scaling functions with dilatin factor α. The wavelet tight frames consist of
    finite number of functions ψ12,...,ψn. First, the authors present sufficient conditions for existence of wavelet tight frames generated by the n functions, then give explicit constructing formula of wavelet tight frames. In particular, if mask of the scaling function are rational functions, the mask of the corresponding wavelet tight frames are rational. Finally, the paper derive the decomposition and reconstruction formulas, and give five numercial examples of wavelet tight frames.
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    Entropy of Cylindrical Black Hole
    ZHANG Zi-Zhen, ZHANG Li-Chun,ZHAO Ren
    Acta mathematica scientia,Series A    2005, 25 (7): 1061-1066.  
    Abstract1769)      PDF(pc) (318KB)(1914)       Save

    Using the new equation of state density motivated by the generalized uncertainty relation, the authors  derive the entropy of the black cylinder on the background of the cylindrically symmetric spacetime. When the new equation of state density is utilized to obtain that the entropy of the black cylinder is proportional to the horizon area, the divergence appearing in the brick wall model is removed, without any cutoff. It is shown that black cylinder's entropy is the entropy of quantum state on the surface of horizon. The black cylinder's entropy is a kind  of quantum effect. It is the intrinsic property of the black cylinder. Via the method of quantum statistics, the authors  directly derive the partition functions of Bosonic and Fermi field in black cylinder. The authors  also avoid the difficult to solve the wave equation of various particles. The authors  offer a new simple and direct way of calculating the entropy of black cylinders of different complicated spacetime.

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    On Singular Directions of |Meromorphic Algebroidal Functions
    ZHANG Hong-Shen
    Acta mathematica scientia,Series A    2009, 29 (6): 1642-1650.  
    Abstract1693)      PDF(pc) (275KB)(1906)       Save

    Let w(z) be a meromorphic algebroidal   function  for |z|<+∞. If limr →∞lg T(r, w)/lg r =0,  limr →∞lg T(r, w)/lg lg r =+∞, then there exists a direction arg z=θ0 such that, for any N>0, ∑i1/(lg|zi(a; ?(θ0δ))|)N=+∞, with 2 v possible exceptions for a. If limr →∞T(r, w)/lgKr =+∞,  limr →∞lg T(r, w)/lg lg r =M, then there exists a direction arg z=θ0 such that ∑1/lg|zi(a; ?(θ0δ))|)σ=∞ (σ=M-2 or σ=M-2-ε), with 2 v possible exceptions for a. For meromorphic functions, these singular directions have not been studied yet.

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    深切缅怀李国平院士——纪念李国平院士诞辰100周年
    FAN Wen-Tao, LIU Pei-De, OU Yang Cai-Heng
    Acta mathematica scientia,Series A    2010, 30 (5): 1185-1189.  
    Abstract1444)      PDF(pc) (457KB)(1902)       Save

    2010年11月15日, 是我们的恩师李国平院士诞辰100周年纪念日. 我们师从李先生凡数十年, 每聆教诲, 获益良多, 春风化雨, 受用终身. 今距李先生仙逝, 又过去了十四年, 先生的音容笑貌与人格魅力仍时时浮现于眼前. 值此先生百年诞辰之际, 谨以此文深切缅怀敬爱的李老师.

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