中国科学院数学与系统科学研究院期刊网

15 September 2010, Volume 53 Issue 5
    

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  • Yu Hui ZHANG, Qian Qian ZHAO
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 833-846. https://doi.org/10.12386/A2010sxxb0093
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the explicit criteria for uniqueness, recurrence, ergodicity, strong ergodicity of the single birth processes with immigration are presented. Meanwhile, an explicit sufficient condition for exponential ergodicity of the processes is obtained. In addition, the explicit expressions on the polynomial moments of the first hitting time are also founded. As an application, some properties are obtained on the birth death processes with immigration. Some examples are illustrated at the end.

     

  • Dong Dong SUN, Guo Wei ZHANG, Tie ZHANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 847-852. https://doi.org/10.12386/A2010sxxb0094
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    This paper presents a retract in Banach spaces by means of concave functional and gives a fixed point theorem about cone expansion and compression of concave functional type which extends and complements the previous results.

     

  • Yan Ni LIU, Xiao Yan GUO
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 853-856. https://doi.org/10.12386/A2010sxxb0095
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    The main purpose of this paper is using the elementary method and the divisible properties of the integers to study this problem, and solve it completely. That is, we shall prove that the Diophantine equation xy + yz + zx = 0 has and only has six integer solutions. They are: (x, y, z) = (-2, 1, 1), (1, -2, 1), (1, 1, -2), (1,-1,-2), (-1, -2, 1), (-2,1,-1).

     

  • Zhi Bin LIANG, Jun Yi GUO
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 857-870. https://doi.org/10.12386/A2010sxxb0096
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    In this paper, we study the optimal retentions for an insurance company, which intends to reinsure its risk by means of a pure proportional treaty, a pure excess of loss treaty or any combination of the two. Under the criterion of maximizing the adjustment coefficient, the closed form expressions of the optimal results are given not only for the Brownian motion risk model but also for the compound Poisson risk model. Moreover, a smallest exponential upper bound for the ruin probability is obtained. We also conclude that, under some conditions, there exists a pure excess of loss reinsurance strategy which is better than any combinational reinsurance strategy. Some numerical examples are presented, which illustrate the results of this paper.

     

  • Jin Feng YU, An Ni CHEN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 871-880. https://doi.org/10.12386/A2010sxxb0097
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    In this paper, controllability problems of second-order differential inclusion with nonlocal conditions have been researched. We consider this problem and establish sufficient conditions for convex field. The problem is converted into fixed pointed problem of set-valued integral operators, then the controllability theorem is obtained by using Kakutani fixed point theorem.

     

  • Wei LI, Ping Yan CHEN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 881-890. https://doi.org/10.12386/A2010sxxb0098
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    In this paper, we obtain the mean convergence, Kolmogrov strong law of large numbers and the exist of the normed partial sums for the sequence of B-valued ρ-mixing random elements, which extend and generalize the well-known results.

     

  • Jin Ke HAI, Zheng Xing LI
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 891-896. https://doi.org/10.12386/A2010sxxb0099
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    A finite group G is called an ATI-group if for any abelian subgroup A of G, AAg=1 or A for all gG. In this paper, it is shown that a class-preserving automorphism of an ATI-group G of p-power order whose restriction to any Sylow subgroup of G is equal to the restriction of some inner automorphism of G is necessarily an inner automorphism. As an immediate consequence, we obtain that the normalizer property holds for finite ATI-groups.

     

  • Su Ping GU, Zhuang Chu LUO, Hua CHEN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 897-904. https://doi.org/10.12386/A2010sxxb0100
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    In this paper, we study a class of first order nonlinear partial differential equation with irregular singularity in the domain . Under certain assumptions, we prove the existence and uniqueness of the formal solution in formal Gevrey class.  
  • Yong Wen ZHU, Da Liang CHEN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 905-910. https://doi.org/10.12386/A2010sxxb0101
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    Some sufficient and necessary conditions are given for a monogenic semigroup or monoid to be reducible, indecomposable and completely reducible respectively. Then the reducibility of commutative semigroups of matrices are discussed over an arbitrary field, and especially over the field of real numbers, and the irreducible commutative semigroups of some symmetric and skew symmetric matrices over the field of real numbers are completely determined.

     

  • Lin ZHANG, Yin Sheng JIANG, Lin TANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 911-924. https://doi.org/10.12386/A2010sxxb0102
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    In this paper, we establish a priori weighted h1-estimate in a bounded domain for a elliptic equations with vanishing LMO coefficients via a corresponding estimate for the commutator of a singular integral with an LMO function.

     

  • Zun Wei FU, Yan LIN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 925-932. https://doi.org/10.12386/A2010sxxb0103
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    In this paper, we obtain the best constant in the boundedness of higher dimensional Hardy operators on λ-central BMO spaces, and establish λ-central BMO estimates for commutators of higher dimensional fractional Hardy operators on central Morrey spaces.

     

  • HaiPeng QU, Xiao Hong ZHANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 933-944. https://doi.org/10.12386/A2010sxxb0104
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    Assume N and H are groups. If there is a group G which has a normal subgroup Ñ≤ Z(G) such that ÑN and G/ÑH, then G is called a central extension of N by H. In this paper, we classify all groups which are central extensions of N by H, where N is a cyclic p-group and H is an inner abelian p-group.

     

  • Hai Feng XU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 945-952. https://doi.org/10.12386/A2010sxxb0105
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    Fischer-Colbrie and Schoen have studied the equation Δg-aKg=0 on unit disc in complex plane in 1980. The disc is endowed with a complete conformal metric. They got a sufficient condition for the nonexistence of positive solution on such disc and applied this result to the study of complete stable minimal surfaces in 3-dimensional manifolds of non-negative scalar curvature. Here Δ is Laplace operator, K is Gauss curvature, a is a constant, and g is a function defined on the unit disc. In this paper, we obtain a more weaker sufficient condition which also ensures the nonexistence of positive solution on such unit disc.

     

  • Xiao Hong CAO, Jun Ying LIU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 953-962. https://doi.org/10.12386/A2010sxxb0106
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    In this note, we define a class operators called consistent Fredholm and index operators and give a complete characterization of this class operators, also, we define the generalized property (ω'), a variant of Weyl's theorem. By means of the new spectrum defined in view of the property of consistence in Fredholm and index, we establish for a bounded linear operator T defined on a Hilbert space the sufficient and necessary conditions for which the generalized property (ω') holds. We also study the stability of generalized property (ω') under perturbations. In addition, the relation between the generalized property (ω') and hypercyclicity is discussed.

     

  • Feng Lü, Jun Feng XU, Hong Xun YI
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 963-974. https://doi.org/10.12386/A2010sxxb0107
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    In this paper, we prove two theorems of normal family which greatly improve a results of G. Zhang, W. Sun, X. Pang and a result of Y. Xu, respectively.

     

  • Cui YANG, Jian Hua ZHANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 975-980. https://doi.org/10.12386/A2010sxxb0108
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    Let H be a Hibert space over the real or complex field , N be a non-trivial nest on H and τ(N) be the associated nest algebra. Suppose φ:τ(N)→τ(N) is an additive map and m, n, p are positive integers such that (m+n)φ(Ap+1)=mφ(A)Ap+nApφ(A)  or φ(Am+n+1)=Amφ(A)An holds for all Aτ(N), then there exists a λ∈ such that φ(A)=λA for all Aτ(N).  
  • Dong Ni TAN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 981-988. https://doi.org/10.12386/A2010sxxb0109
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    We show that every 1-Lipschitz map having DOPP between two unit balls of normed spaces is the restriction of a linear isometry on the whole space under the assumption that the map is surjective or the target space is strictly convex. We also present some applications of this result and a generalized result when both of the normed spaces are assumed to be strictly convex.

     

  • Jin Bo YANG, Xiao Quan XU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 989-996. https://doi.org/10.12386/A2010sxxb0110
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    In this paper, we discuss some properties of locally strongly compact spaces, especially the properties of their Hoare spaces and Smyth spaces. It is proved that a T0 space is locally strongly compact if and only if its Hoare space is locally strongly compact and the Smyth space of a locally strongly compact space is a C-space. Analogous results are obtained for strongly locally compact spaces.

     

  • Kai Yun WANG, Bin ZHAO
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 997-1006. https://doi.org/10.12386/A2010sxxb0111
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    In this paper, the theory of set system is applied to quantale theory. We introduce the notion of Z-quantale which is a generalization of Quantale. Z-quantales and their categorical properties are studied. we mainly prove that the category of Z-quantales is a reflective subcategory of the category of ordered semigroups and the category of coherent Z-quantales is a coreflective subcategory of the category of Z-quantales. Projective objects in the category of Z-quantales are studied. We prove that a Z-quantale A is E-projective if and only if it is stable Z-continuous.

     

  • Zhi Zheng ZHANG , Ji Zhen YANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 1007-1018. https://doi.org/10.12386/A2010sxxb0112
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    The purpose of this paper is to construct two new finite q-exponential operators with two parameters and obtain several operator identities. Applying these operator identities to q-Chu-Vandermonde summation, we derive several curious q-series identities involving a generalization of Jackson's transformation.

     

  • Xiang Qun YANG, Lin XIAO, He Song WANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 1019-1026. https://doi.org/10.12386/A2010sxxb0113
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    The qualitative theory for birth and death processes with barrier (BDP) is researched. According to kinds of barrier 0, kinds of boundary point Z, BDP is whether or not honest, whether or not satisfying backward equations or forward equations, there are many combinations and there are many types of BDPs. For each type there is not or only one, or there are infinitely many BDFs. A table obtained in detail.

     

  • Yang Li HU, Qing Ping WU, Ying Qiu LI
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 1027-1034. https://doi.org/10.12386/A2010sxxb0114
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    The problem of explosiveness of age-dependent branching processes in random environments is discussed, then some sufficient and necessary conditions and more sufficient conditions of explosiveness are obtained. It is seen that explosiveness is essentially determined by the steepness of random life-length distribution function near the origin and random family-size generating function near 1. Also it's shown ways to compare two different processes.

     

  • Rui Xiang DAI, Chao LIU, Ding Guo WANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(5): 1035-1040. https://doi.org/10.12386/A2010sxxb0115
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    In this paper coconvolution product, linear form, cocentral elements, cotwist, coquasitriangular bimonad are defined. Then a bijection between linear forms of T and braidings C of T-module categories and a bijection between cotwists for T and twists on T-module categories are given.