中国科学院数学与系统科学研究院期刊网

15 September 2004, Volume 47 Issue 5
    

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  • Bing Wen LIU(1), Li Hong HUANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 833-836. https://doi.org/10.12386/A2004sxxb0106
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    In this parper, we study the boundedness of solutions of the following generalized Lienard system: dx/dt = p(y) - F(x), dy/dt = - g(x), and obtain two sufficient conditions for the existence of an unbounded solution to this system. Some mistakes in the corresponding papers are pointed out as well.
  • Song Xiao LI(1), Jun Yun HU(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 837-844. https://doi.org/10.12386/A2004sxxb0107
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    We prove that a bounded operator 5 on Lap(B) (p > 1) is compact if and only if the Berezin transform of S vanishes on the boundary of the unit ball B, when 5 satisfies some integrable conditions.
  • Ming Qiang WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 845-858. https://doi.org/10.12386/A2004sxxb0108
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    In this paper we prove that, with at most O(N13/30+ε) exceptions, all positive odd integers n ≤ N with n = 0 or 1 (mod 3) can be written as sum of a prime and two squares of prime.
  • Huo Yun WANG, Jin Cheng XIONG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 859-866. https://doi.org/10.12386/A2004sxxb0109
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    This paper deals with topologically ergodic maps. In terms of subshifts of finite type determined by an irreducible matrix, affine maps of compacted connected metric abelian group and by continuous maps of closed interval, the two concepts of topologically ergodic map and topologically transitive map are identical. Furthermore, examples show that the topologically ergodic map differs from the topologically mixing map and the topologically transitive map.
  • Pei Sheng JI,Li WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 867-872. https://doi.org/10.12386/A2004sxxb0110
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    We give a detailed description of the structure of a Lie ideal in GICAR algebra. Let A be the GICAR algebra, L be a closed Lie ideal of A. Then there is a closed ideal J of A such that [ J, J] L π-1(Z(A/J)), where π is the canonical quotient mapping from A onto A/J. On the other hand, every closed linear subspace L of A of this from is a Lie ideal of A.
  • Yun Xia LI, Jian Gao LI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 873-884. https://doi.org/10.12386/A2004sxxb0111
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    In this paper, we discuss weak convergence for partial sums of moving-average processes generated by ρ-mixing stochastic process of the form Xk(t) = ∑j=0∞ajεk-j(t), 0 ≤ t≤ 1, where {aj; j ≥ 0} is a sequence of real numbers with ∑j=0∞ |aj|<∞.Fur-thermore, weak convergence of stochastic process of the form Yn(s,t) =1/n~(1/2) ∑k=1[ns]Xk(t), 0 ≤ s, t ≤ 1 and weak convergence of stochastic subscript sums of SNn(t) = ∑k=1Nn Xk(t) are also discussed.
  • Cui Lian YOU, Zhen HE
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 885-898. https://doi.org/10.12386/A2004sxxb0112
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    By defining some operators and studying their properties, we take nonlinear elliptic equation and nonlinear parabolic equation into consideration in which we make use of the related results on sums of ranges in Reich. Meanwhile, we establish the existence conditions of the above two equations, thus extending the related results in Pascali.
  • En Hui SHI(1), Li Zhen ZHOU(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 899-904. https://doi.org/10.12386/A2004sxxb0113
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    In [9], we considered the problem of whether a continuum admits expansive group actions, and proved that the free Abelian group Z ×Z can not act expansively on the unit intenval I; an example of expansive Z * Z action on was also given where Z * Z denotes the free product of two copies of Z. That is to say, though the group generated by two commutative homeomorphisms can not act on an arc expansively, there still exists an expansive group action which is generated by two noncommutative homeomorphisms. In this paper, we prove that there exists no expansive Z2 actions on graphs, which answers one of the quenstions in paper [9].
  • Xiao Chun LIU, Hua CHEN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 905-914. https://doi.org/10.12386/A2004sxxb0114
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    In this paper, we give the Littlewood-Paley decomposition of the cone Sobolev spaces, and then discuss its applications to nonlinear partial differential equations.
  • Hai Tao YANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 915-920. https://doi.org/10.12386/A2004sxxb0115
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    We show that the ideals of non-degenerate JC*-algebras and JVN-algebras are symmetrc. We alsol give two class of symmetric and non-symmetric ideal, and show that the JVN-algebras on the π1 spaces have not non-symmetric ideal without third class algebras. Finally, we construct two examples of ideal symmtry of JC*-algebras.
  • Guang Shan XU, Tian Qin WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 921-930. https://doi.org/10.12386/A2004sxxb0116
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    In this paper we give some p-adic measures for algebraic independece of the values of Mahler type functions.
  • Jian Ping OU(1), Fu Ji ZHAO(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 931-940. https://doi.org/10.12386/A2004sxxb0117
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    For Moor-Shannon network models, those that have greater edge connectivity and restricted edge connectivity usually have better reliability and fault-tolerance. It is proved in this paper that undirected Kautz graphs UK(d,n), the topologies of undirected Kautz networks, are super restricted edge connected except for two trivial cases. And so, they have better restricted edge connectivity than undirected De Bruijn networks.
  • Han Fang ZHANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 941-946. https://doi.org/10.12386/A2004sxxb0118
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    In this paper, we first use basic derivayive rule, prove a geometric inequality involoving n -1 dimensional and n dimensional volume of simplex, from this a result we can obain a k-n type Neuberg-Pedoe inequality in Euclidean space En.
  • Ji Wei HE
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 947-956. https://doi.org/10.12386/A2004sxxb0119
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    We provide a "deformation complex" CH*(H, A) associated to a given module algebra HA, and use the cohomology of CH*(H,A) to describe the infinitesimal deformation of HA. We show that there is an one-to-one correspondence between the equivalence classes of the infinitesimal deformations and HH2(H,A), and HA is rigid if the 2-cohomology of the deformaton complex HH2(H, A) = 0.
  • Xing Bo LIU, De Ming ZHU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 957-964. https://doi.org/10.12386/A2004sxxb0120
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    The problem of homoclinic bifurcation under perturbation is studied for the high dimensional system with nonhyperbolic equilibrium. By constructing local coordinate systems near the unperburbed homoclinic orbit, we get Poincare maps of the system in new coordinate systems, and discuss the persistence of generic homoclinic orbit and the bifurcation of periodic orbit from the homoclinic orbit for the system accompanied with transcritical bifurcation. Some known results are extended.
  • Feng Yang CHENG, Yue Bao WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 965-972. https://doi.org/10.12386/A2004sxxb0121
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    Let {X, Xi : i ≥ 1} be a sequence of iid random variables which belongs to the domain of attraction of a nondegenerate stable distribution and let Sn = ∑i=1n Xi. A result on the precise asymptotics of Sn for wide range weighted functions and boundary functions is obtained. The results of precise asymptotics of partial sums for strictly stationary NA sequence are obtained. The results in Wang etc. are improved and extended. Many important results from the literatures are obtained easily as corollaries.
  • Feng De CHEN, De Xian SUN, Jin
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 973-984. https://doi.org/10.12386/A2004sxxb0122
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    In this paper, nonlinear integro- differential equations with both continuous delay and discrete delays of the form x'(t) = A(t,x(t))x(t) + f-∞t C(t,s)x(s)ds + + b(t) are considered, where the n × n matrix function A(t,x) and the n-vectors f(t,x),gi(t,x) (i = 1,2, ...,l) are continuous in (t,x) ∑ R × Rn, C(t,s) ∑ C(R ××R, Rn×n). By combining the theory of exponential dichotomies of linear system and the method of functional analysis, some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the systems are obtained. We not only make an essential improvement and extension of the main results but also obtain some new criteria which guarantee the existence and uniqueness of peroidic solution of the sytems; these criteria can not be obtained by the existing methods (see [1-30]).
  • Zi Long ZHANG, Bing Ling CAI,
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 985-992. https://doi.org/10.12386/A2004sxxb0123
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    Let S be a semi-group. For a semi-group S-set, we discuss some properties of modules graded by 5-sets and present a collection of finitely generated projective generators for (S, A, R)-gr, the category consisting of the left R-modules graded by a 5-set A with degree preserving .R-linear maps for the morphisms. For the smash product R#S*, we mainly prove the category of unital left R#S*-module is isomorphic to the category of graded .R-module on certain conditions.
  • Xue Jun ZHANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 993-100. https://doi.org/10.12386/A2004sxxb0124
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    In this paper, we will discuss some equivalent characterizations of mixed norm space, Dirichlet type space, Bloch type space in several complex variables and obtain a series of sufficient and necessary conditions.
  • Ying Zhe WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 1001-101. https://doi.org/10.12386/A2004sxxb0125
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    Algebraic convergence in L2-sense is studied for diffusion processes on Rn. Some criteria for the convergence are presented. Furthermore, some special cases are studied in order to be compared with ordinary cases. The results are effective since the convergence region can be completely covered, as illustrated by two examples.
  • Xian ZHANG, Chong Guang CAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 1013-101. https://doi.org/10.12386/A2004sxxb0126
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    Suppose F is a field of characteristic other than 2. Let Mn(F) be the set of n × n matrices over F. We show that f : Mn(F) → Mn(F) is an additive preserver of {1}-inverses or {1,2}-inverses of matrices on Mn(F) if and only if f has one of the following forms: (a) f = 0; (b) f(A) = εPAτP-1 for any A ∈ Mn(F), where P ∈GLn(F), τ is some injective endomorphism on F with τ(1) = 1, and ε = ±1; (c) f(A) = εP(Aτ)TP-1 for any A ∈ Mn(F), where r, e and P are as in (b).
  • Guo Hua ZOU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 1019-102. https://doi.org/10.12386/A2004sxxb0127
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    This paper considers the admissibility of the estimators for finite population when the parameter space is restricted. We obtain all admissible linear estimators of an arbitrary linear function of the characteristic values of a finite population in a class of linear estimators under the criterion of the expectation of mean square error.
  • Qi Xiang YANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 1025-103. https://doi.org/10.12386/A2004sxxb0128
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    In the fifties, Calderon established a formal relation between symbol and kernel distribution, but it is difficult to. establish an intrinsic relation. The Calderon-Zygmund. (C-Z) school studied the C-Z operators, Hormander, Kohn and Nirenberg et al. studied the symbolic operators. Here we apply a refinement of Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces OpS1,δm and kernel distributions spaces with other spaces composed by some almost diagonal matrix, then one gets an isometric between OpS1,δm and kernel distribution spaces.
  • De Ming LI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(5): 1031-103. https://doi.org/10.12386/A2004sxxb0129
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    The notion of star chromatic number of a graph is a generalization of the chromatic number. In this paper, we calculate the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel by subdivisions, their star chromatic numbers being 2 + 2/(2n + 1), 2 + 3/(3n + 1) and 2 + 3/(3n - 1) separately. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 + 1/n, which is a generalization of the result of Gao et al.