中国科学院数学与系统科学研究院期刊网

15 March 2012, Volume 55 Issue 2
    

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  • A Generalization of Strassen's LIL for φ-Mixing Sequences and Its Application
    Ke Ang FU, Li Xin ZHANG
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 193-200. https://doi.org/10.12386/A2012sxxb0019
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The aim of this paper is to establish a general Strassen's law of the iterated logarithm (LIL) for φ-mixing random variables whose variance may be infinite, which extends previous results. As an application, a general Strassen's LIL for products of partial sums is derived.
  • On Inverse Moments for Nonnegative NOD Sequence
    Min XU, Ping Yan CHEN
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 201-206. https://doi.org/10.12386/A2012sxxb0020
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The asymptotic approximation of inverse moments of the normalized sums of the nonnegative NOD random variables is obtained under the finite first moments condition. In particular, the asymptotic approximation of inverse moments holds true for the partial sums. The main result extends the well-known results.
  • Eigenvalue Problems for Hemivariational Inequality Driven by the p-Laplacian
    Bin GE, Qing Mei ZHOU
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 207-218. https://doi.org/10.12386/A2012sxxb0021
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We consider a kind of nonlinear eigenvalue problem driven by the p-laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality), that is, 
    where 1 < p < ∞, and Ω ⊂ RN is a bounded domain. The purpose of this paper is to extend earlier existence and continuation results of nontrivial solutions of the problem in the superline case (i.e., p = 2) to the general case (i.e., 1 < p < ∞). We not only extend the existence results of nontrivial solutions for almost every parameter λ due to Miyagaki and Souto [Superlinear Problems without Ambrosetti and Rabinowitz Growth Condition, Jour. Diff. Equa., 245 (2008) 3628-3638], but also extend the existence results of nontrivial solutions for every parameter λ due to Schechter and Zou [Superlinear Problems, Pacific J. Math., 214 (2004) 145-160] to the general case when 1 < p < ∞. Our approach is based on the non-smooth critical point theory for locally Lipschitz functions.
  • Pricing Formulae for European Options under the Fractional Vasicek Interest Rate Model
    Wen Li HUANG, Xiang Xing TAO, Sheng Hong LI
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 219-230. https://doi.org/10.12386/A2012sxxb0022
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Under the assuming of the stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with stochastic interest rate. At the same time, we get the explicit expression for the European option price with stochastic interest rat and the call-put parity. The results in this paper extend as well as improve previously known results.
  • Removability of Compact Singularities of Left O-Analytic Functions
    Jin Xun WANG, Xing Min LI
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 231-234. https://doi.org/10.12386/A2012sxxb0023
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    In this paper, appeal to the algebraic method proposed by Adams et al., we prove the removability of compact singularities of left O-analytic functions of several octonionic variables and left O-analytic functions which satisfy a kind of partial differential equations.
  • Naturally Ordered Transformation Semigroups Preserving Order and an Equivalence Relation
    Hui Sheng PEI, Wei Na DENG
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 235-250. https://doi.org/10.12386/A2012sxxb0024
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let X be a set and TX the full transformation semigroup on X. Let E be an equivalence on X and define
    TE(X) = {f ∈TX: ∀(x,y)∈ E,(f(x),f(y))∈ E}. Then TE(X) is a subsemigroup of TX determined by the equivalence E. In this paper, the set X under consideration is a totally ordered finite set, while the equivalence E is non-trivial and all E-classes are convex. It is clear that
    OE(X) ={f ∈TE(X):∀x,y ∈ X,x ≤ y implies f(x) ≤ f(y)}
    is a subsemigroup of TE(X). We endow OE(X)) with the so-called natural order ≤ and discuss when two elements in OE(X)) are related under this order, then determine those elements of OE(X) which are compatible with ≤. Also, the maximal (minimal) elements and the covering elements are described.
  • Generalized Kato Decomposition and Topological Uniform Descent
    Qiao Fen JIANG, Huai Jie ZHONG
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 251-258. https://doi.org/10.12386/A2012sxxb0025
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    We discuss the generalized Kato decomposition and the topological uniform descent of an operator. We give a characterization of an operator which both admits a generalized Kato decomposition and has topological uniform descent. By means of this result, we obtain a new spectral structural diagram of an operator.
  • The Gerber-Shiu Function for a Risk Model Perturbed by Stable Lévy Motion
    Jin Yuan CHEN, Xin Bing KONG, Ze Hui LI
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 259-272. https://doi.org/10.12386/A2012sxxb0026
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    By following a weak convergence approach, the present paper for the first time gives the representation of the Gerber-Shiu expected discounted penalty function (the G-S function) of the risk process perturbed by an α-stable Lévy motion in terms of the Laplace transform. Using the same method, this paper also gives the ultimate ruin probability as a byproduct of our results. As a check, we find that the ultimate ruin probability of the risk process is indeed a special case of the G-S function.
  • Isometric Composition Operators on the Bloch Type Space in the Polydisk
    Zhong Shan FANG, Ze Hua ZHOU
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 273-280. https://doi.org/10.12386/A2012sxxb0027
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    We first give a brief survey on some results about surjective isometries on some Banach spaces of analytic functions. Then we characterize the isometries among the composition operators acting on the α-Bloch space in the polydisk, and necessar yand sufficient conditions are given for composition operators to be isometric.
  • Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic Equations
    Xiao Jun SONG, Yong Sheng MI, Chun Lai MU
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 281-292. https://doi.org/10.12386/A2012sxxb0028
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    The paper deals with the critical curve for a degenerate parabolic system coupled via nonlinear boundary flux. By constructing the self-similar super-solution and sub-solution, we obtain the critical global existence curve. And the critical curve of Fujita type is conjectured with the aid of some new results. An interesting feature of our results is that the critical global existence curve and the critical Fujita curve are determined by a matrix and by the solution of a linear algebraic system, respectively.
  • Systems of Complex Di erence Equations of Malmquist Type
    Ling Yun GAO
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 293-300. https://doi.org/10.12386/A2012sxxb0029
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In recent papers, Ablowitz, Halburd and Herbst et al. applied Nevanlinna theory to prove some results on complex di erence equations reminiscent of the classical Malmquist theorem in complex di erential equations. We will mainly investigate Malmquist theorem of a type of systems of complex di erence equations; improvements and extensions of such results are presented in this paper.
  • Self-adjointness of the Product of Two Hamiltonian Operators under the Limit Circle Case
    Zhao Wen ZHENG, Bao Sheng LIU
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 301-310. https://doi.org/10.12386/A2012sxxb0030
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the self-adjointness of the product of two Hamiltonian operators under the limit circle case is considered. Using the Calkin method and the construction of self-adjoint extension for singular Hamiltonian systems, the necessary and sufficient conditions which make the product of two Hamiltonian operators under the limit circle case being a self-adjoint operator are obtained.
  • Rough Singular Integrals Supported on Submanifolds of Finite Type
    Hong Hai LIU
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 311-320. https://doi.org/10.12386/A2012sxxb0031
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the author considers the mapping properties of rough singular integrals along submanifolds of finite type on some Triebel-Lizorkin spaces and Besov spaces, the lqlq-valued inequality is also established.
  • Balanced Categories and the Biorder in Semigroups
    Bing Jun YU
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 321-340. https://doi.org/10.12386/A2012sxxb0032
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper a natural relationship between categories and semigroups established by the biorder of idempotents in semigroups is investigated. For every semigroup S with idempotents, via the biorder ωl,ωr, the sets of left and right principal ideals generated by idempotents naturally determine two categories L(S),R(S) with subobjects and images in which every inclusion is right split. The properties of morphisms in these two categories naturally correspond to the abundance or regularity of elements in S. By applying this relationship, the concepts of “balanced, abundant or normal categories” are defined. For each balanced (abundant or normal) category C, the “cone semigroup” TC of C is constructed. It is proved that TC is a left abundant (abundant or regular) semigroup, a left abundant (abundant or regular) semigroup (monoid) S is isomorphic with a subsemigroup of TL(S) (with TL(S)), every balanced (abundant or normal) category C is isomorphic with the ideal category L(S) of some left abundant (abundant or regular) semigroup S, as categories with subobjects.
  • The Spread of Tetracyclic Graphs
    Lin CHEN
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 341-350. https://doi.org/10.12386/A2012sxxb0033
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    The spread of a graph is defined to be the difference between the greatest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. In this paper we determine the unique graph with maximum spread among all tetracyclic graphs on n vertices when n ≥ 84.
  • Hall-Type Criteria to Have a Transversal
    Hua MAO, San Yang LIU
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 351-354. https://doi.org/10.12386/A2012sxxb0034
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper provides some Hall-type criteria for a family of subsets of an arbitrary cardinality set to have a transversal, and simultaneously, answers to Welsh's open problem for the infinite case. The problem is to find necessary and sufficient conditions for a family of sets to have a transversal.
  • The Symmetric Mixed Isoperimetric Inequality of Two Planar Convex Domains
    Chun Na ZENG, Jia Zu ZHOU, Shuang Shan YUE
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 355-362. https://doi.org/10.12386/A2012sxxb0035
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let Kk(k=#em/em#,j) be domain of the area Ak, and of the perimeter Pk, respectively. The symmetric mixed isoperimetric deficit of K#em/em# and Kj is defined as σ(K#em/em#,Kj)=P#em/em#2Pj2-16π2A#em/em#Aj. We follow the ideas of Zhou, Ren (2010) and Zhou, Yue (2009) and obtain some Bonnesen-style symmetric mixed inequalities and the symmetric mixed isoperimetric inequality by the method of integral geometry. We also obtain some symmetric mixed isoperimetric upper limits. Some discrete Bonnesen-style symmetric mixed inequalities and one upper limit of the discrete symmetric mixed isoperimetric deficit for two domains are obtained. Finally we apply these symmetric mixed (isoperimetric) inequalities to estimate the complete elliptic integral of second class.
  • The Uniqueness of Meromorphic Functions that Share Two Sets with CM
    Bin YI, Yu Hua LI
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 363-368. https://doi.org/10.12386/A2012sxxb0036
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    We proved that there exist a set S1 with 2 elements and a set S2 with 5 elements, such that for any two nonconstant meromorphic functions f and g satisfying E(Sj,f)=E(Sj,g)(j = 1,2), then f ≡ g.
  • Weakly Lagrangian Minimal Immersions of S4 Into CPn with Constant Curvature
    Zhen Qi LI, Chun Yan LIAO
    Acta Mathematica Sinica, Chinese Series. 2012, (2): 369-384. https://doi.org/10.12386/A2012sxxb0037
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The weakly Lagrangian minimal immersions with constant curvature from S4 into CPn are studied. It is proved that if the induced metric has constant curvature c, than c = 4/[s(s + 3)] for some integer s ≥ 1. And the immersion φ : S4 → CPn is uniquely determined by two homogenous polynomials fs and fs-1 of four variables. If s = 1 or s = 2, or equivalently, if c = 1 or c = 2/5, the immersion φ is absolute real.
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