中国科学院数学与系统科学研究院期刊网

15 May 2000, Volume 43 Issue 5
    

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  • Mu Fa CHEN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 769-772. https://doi.org/10.12386/A2000sxxb0100
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    A variational formula for lower bound of the principal eigenvalue of general Markov jump processes is presented. The result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov chains under some mild assumptions.
  • Shao Yi ZHANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 773-780. https://doi.org/10.12386/A2000sxxb0101
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    In this paper the existence theorem of the optimal measurable coupling of two transition probabilities on non-negative lower semi-continuous function is proved. As an application of this result, Strassen's theorem is generalized, moreover, it is proved that the existence of an order-preserving coupling of jump processes is equivalent to the stochastical comparability of jump processes.
  • Qiu Hui SHENG,Si Long PENG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 781-786. https://doi.org/10.12386/A2000sxxb0102
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    In this paper, we prove that if two multiresolutions satisfy a relation, then they the provide same accuracy in multivariate FSI case.
  • Zhong WANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 787-796. https://doi.org/10.12386/A2000sxxb0103
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    In this paper, we discussed the spectrum of J-selfadjoint operators that are extended by 2nth order differential expressions (2.1) with complex coefficients. We obtained that the essential spectrum of J-selfadjoint operators is contained in the set A when the coefficients of (2.1) satisfied conditions in theorem 3.2. Finally we gave some sufficient conditions for the discreteness spectrum of J-selfadjoint operators that are extended by (2.1) and Sturm-Liouville differential operations with complex coefficients.
  • Zhi Sui TAO,Yi HONG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 797-806. https://doi.org/10.12386/A2000sxxb0104
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    In this paper, the following result of a Heilbroon's problem is proved. Let S be a set consists of six points in R~3, its diameter being D. By d denote the minimum distance between any two points in S, then D≥ 2d. The equility holds if and only if S consists of the six venices of an octahedron or the six venices of the polygron △2 x △1, where by △1, △2 we denote the regular 1- and 2- simplex, with the same length of edges.
  • Zhao Jun LIANG,Xing An ZHANG,C
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 807-812. https://doi.org/10.12386/A2000sxxb0105
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    In this paper, we consider the Kolmogorov models which are the interaction of three species with the same intrinsic growthrate. We obtain the sufficient conditions which implies periodic orbits of a Kolmogorov system in R~3.
  • Qing Hua MA(1),En Hao YANG(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 813-820. https://doi.org/10.12386/A2000sxxb0106
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    In this paper, some priori bounds on continuous solutions to several n-variable nonlinear integral inequalities are established. They generalise five known theorems given by Pchpatte B. G.[5,9,10] for two-variable integral inequalities. An application example is also indicated.
  • Jie Cheng CHEN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 821-828. https://doi.org/10.12386/A2000sxxb0107
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    Let M be a complete Riemannian manifold, Strichartz R. S., Lohoue N., Bakry D. and the author proved the L~P (1 < p < ∞) and weak type (1,1)-boundedness of R. In this paper, we shall set up L,*-boundedness of R by an analytic method.
  • Guo Jun WANG(1),Wei WANG(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 829-832. https://doi.org/10.12386/A2000sxxb0108
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    How to enumerate Boolean functions representable by one perceptron is an open problem. The paper offered a new estimation to the problem by means of anti-chain method.
  • Gui Jing CHEN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 833-842. https://doi.org/10.12386/A2000sxxb0109
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    Extanding some Ibragimove-Hasminskii's idea, this paper points out that the phenomennon of superefficiency in Bahadur's sense can not be eliminated under one-parameter two-sided truncated distribution families. In order to eliminate this evil of superefficiency, a new kind of asymptotic efficiency have been established. Further the efficiencies of commonly used estimates have been calculated, and asymptotically median unbiased efficient estimates have been eonstructed.
  • Lun Chuan ZHANG(1),Xiao Xia ZH
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 843-846. https://doi.org/10.12386/A2000sxxb0110
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    In this paper, we gave some charasterizations of inner ideal in a unital concrete operator algebra, and obtained an isomorphism theorem between non-unital concrete operator algebras which have contractive approximate identities.
  • Ya Cheng LIU(1),Hong Xue XIN(2
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 847-854. https://doi.org/10.12386/A2000sxxb0111
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    This paper studies the initial value problem of Reaction-Diffusion system of Fujita type: ut - △u = a1u~α1-12u + b1v~β1-1v, vt - △v = a2u~α2-1u + b2v~β2-1v, u(x,0) = uo(x), v(x,0) = vo(x), (x,t) E R~N x R~+, where ai,bi≥ 0, on,αiβi≥ 1 (i = 1, 2), gives a series of sufficient conditions of the existence and nonexistence of the nonnegative global L~P solutions and classical solutions, and discusses the asymptotic behavior of solutions. The method used in this paper and obtained results are completly different from previous works [1-4], this paper not only generalies the results of [1-5], but also improves the results of [1] on some respect.
  • Xuan Hao DING(1),Cong Quan YAN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 855-860. https://doi.org/10.12386/A2000sxxb0112
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    In this paper, we characterize commuting and essentially commuting Toeplitz operators with bounded pluriharmophic symbols on Bergman space of the polydisk D~n for n > 1. A analytic Toeplitz operator and pluriharmophic Toeplitz operator essentially commute if and only if they commute.
  • Bing Jun YU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 861-870. https://doi.org/10.12386/A2000sxxb0113
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    A semigroup S is called strongly retractable, if each of its subsemigroups is a retract of S. In this paper, strongly retractable groups, strongly retractable completely simple semigroups, strongly retractable semilattices and strongly retractable regular semigroups are successively characterized and finally a structure theorem for general strongly retractable semigroups is given.
  • Zai Ping LU,Pin Chao WANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 871-874. https://doi.org/10.12386/A2000sxxb0114
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    In this paper, the concept of c-F automorphism is introduced. We obtain, on the basis of [1] and [2], three results which are some generalizations of Thompson's Theorem.
  • Chun SU(1),Han Ying LIANG(2),Y
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 875-886. https://doi.org/10.12386/A2000sxxb0115
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    Let X1, X2,... be independent identically distributed (iid) random variables, Un = 1≤i<j≤nXiXj is said to be pairwise products sum. In this paper, we give necessary and sufficient conditions for Un/n~2 → 0 (i.e. (0.3)). Though this question in this part has not been settled thoroughly yet, it reveals an essential distinction between this class conditions and these ones of Sn/n → 0 (Sn = n=1 Xi), i.e. this class conditions can not been characterized thoroughly by the moment of X1, it need to depend deeply on the tail probabality property of X1.
  • Feng De CHEN,Jin Lin SHI
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 887-894. https://doi.org/10.12386/A2000sxxb0116
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    In this paper, we use the theory of exponential dichotomy and fixed point to discuss the existence of periodic solution of the systems X = f(t, x) and X = A(t, x)x + b(t, x). Our theorems generalize the results of Wang Lian and Zeng Weiyao.
  • Xi ZHANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 895-906. https://doi.org/10.12386/A2000sxxb0117
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    In this paper, we will consider the non-linear parabolic equation: div (u~p-2 u) -u~p-2u = 0, for p > 1, on complete Riemannian manifolds. We derive a locally Harnack inequality for positive solution of this equation, then we generalize the results in [1, 2].
  • Deng Feng LI
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 907-920. https://doi.org/10.12386/A2000sxxb0118
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    In this paper, we study the construction of biorthogonal wavelet bases with arbitrary dilation matrix. In the result, we obtain biorthogonal wavelet bases {sj,k} and {sj,k } of L~2 (R~n), where sj,k (x)= det Aj2s(Ajx-k),sj,k(x) = det Aj2,s(Ajx- k) (.j Z, k Z~n) and A is an arbitrary dilation matrix.
  • Ming He Pei
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 921-930. https://doi.org/10.12386/A2000sxxb0119
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    In this paper, at first, we give some general results of existence and uniqueness of solutions of nonlinear two-point boundary value problems for nth-order nonlinear differential equations by using the shooting method, and then we give concrete sufficient conditions of the existence and uniqueness of solutions by applying the results to nonlinear two-point boundary value problems for nth-order Lipschitz equations.
  • Deng Yin WANG(1),Shang Zhi LI(
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 931-936. https://doi.org/10.12386/A2000sxxb0120
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    In this paper, Based on theory of root systems and Weyl groups, by using the commutator formula, for Chevalley groups of general type over arbitrary fields, we have determined in this paper all the overgroups of Levi subgroups in the maximal parabolic subgroups.
  • Zuo Huan ZHENG(1),Cheng Dong Z
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 937-946. https://doi.org/10.12386/A2000sxxb0121
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    In this paper, we discuss the global structure of the flows defined by a class of ecological systems, by computing the Conley index of their isolated invariant sets. Moreover, for the rest points which are all hyperbolic, we study the uniqueness of the connections between them. So the corresponding results in [4] have been improved.
  • Zhao Li LIU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 947-954. https://doi.org/10.12386/A2000sxxb0122
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    This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations. We obtain Nagumo type a priori bound for the periodic solutions and then by using this a priori bound prove the existence of at least one T-periodic solution under some general conditions.
  • Huan Guang ZHAO,Zhen Jie HONG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 955-960. https://doi.org/10.12386/A2000sxxb0123
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    In this paper, the method of vector measure is used to study the characteristics of dentable operator class and Radon-Nikodym operator class in Banach space. The results obtained are used to research into the structure of Banach space, giving out some new characteristics for Radon-Nikodym property of Banach space.