中国科学院数学与系统科学研究院期刊网

15 April 2001, Volume 44 Issue 4
    

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  • Wei Ping SUN,Wei Gao GE
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 577-580. https://doi.org/10.12386/A2001sxxb0075
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    In this paper, the existence of positive solutions for some boundary value problem of p-Laplacian operator were studied. Several sufficient conditions were given by a fixed point theorem on cones.
  • Lu Chuan ZENG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 581-594. https://doi.org/10.12386/A2001sxxb0076
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    In this paper, let C be a nonempty closed covex subset of a uniformly convex Banach space E and r = {Tt: t∈ S} be a self-mapping family of asymptotically nonexpansive type on C such that for each t∈E S, Tt: C - C is continuous, where S is a commutative topological semigroup with identity. Let {u(t): t∈ S} be an almost- orbit ofГ . It is shown that if Г is asymptotically regular at the asymptotic center c∈ C of {u(t): t ∈ S} with respect to C, then the following statements are equivalent: (i) the set F(Г) of all common fixed points of Tt, t∈e S is nonempty; (ii) {u(t): t∈E S} is locally bounded; (iii) limt||Ttc-c|| = 0; (iv) c∈E F(Г). As an application we establish the result on the asymptotic behavior of almost-orbits of asymptotically nonexpansive families.
  • Li Feng XI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 587-592. https://doi.org/10.12386/A2001sxxb0077
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    In the paper, the continuity and singularity of the invariant measure uλ,α with uλ,α = (1/3) ∑3i=1uλ,αo Si-1 were discussed, where the self-similar maps S1 (x) =λx, S2(x) = λx + a, S3(x)0 = λx + 3 (λ,α are parameters). The main results of the paper are following: (1) If the parameter λ∈E (1/3, 2/5) is ford, then for almost all α (0, 1), the measure uλ,α is absolutely continuous with a density in L2(R). (2) If λ-1 is a P.V. number, and the parameter a is a rational polynomial of λ,ie, a = ∑ni=0 qiλi (qi∈ Q, Vi), then the measure uλ,α is singular.
  • Bo Ling GUO(1),Jia Sheng XING(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 593-604. https://doi.org/10.12386/A2001sxxb0078
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    In this paper, we consider the Cauchy problem of the Wigner-Poisson equa- tions. In the attratice potential, we prove quasi decay estimates for the particle density, the potential and the solutions.
  • Hong Ya GAO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 605-610. https://doi.org/10.12386/A2001sxxb0079
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    A regularity property for very weak solutions of quasilinear partial differential equations of second order is proved. If u is a very weak solution to (1) and belongs to a proper space, which contains W(), then u W( ), i.e., u is a weak solution to (1) in the usual sense. Similar result is given to weak minima of variational integrals.
  • Man You XUAN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 611-618. https://doi.org/10.12386/A2001sxxb0080
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    in this paper, we give the position vector field of a special surface about given principal curvature function in R3 and R2.1 in field of definitions, so that the problems discussed in section [1] can be solved satisfactorily.
  • Su Wen JIAN,Feng Zao YANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 619-626. https://doi.org/10.12386/A2001sxxb0081
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    In this paper, Hardy-Hilbert's integral inequalities are all-sidely generalized, and many fine and new inequalities are obtained.
  • Lun Hai LONG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 627-632. https://doi.org/10.12386/A2001sxxb0082
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    In this article, in the representing system of Rn, a new criteria for the self-affine sets verifying the Moran's open conditions, the lower and upper bounds for the Hausdorff dimensions of the self-similar sets which is not necessary to verify the open set conditions are given, and using two examples, the equality of the upper lower bounds is estimated.
  • Hui XU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 633-640. https://doi.org/10.12386/A2001sxxb0083
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    in this article, we determine the Hausdorff dimension of the comformal graphdirected set, prove that the associated Hausdorff measure is positive o-finite, and give the sufficient and necessary condition that makes Hausdorff measure be positive finite.
  • Xian ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 641-646. https://doi.org/10.12386/A2001sxxb0084
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    A partial ordering is defined in metric space. Some fixed point theorems of monotone mappings and coupled fixed point theorems of mixed monotone mappings are peoved.
  • Zai Hong WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 647-656. https://doi.org/10.12386/A2001sxxb0085
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    We provide two sufficient conditions for the existence of periodic solutions of Lienard equations with weaker damping terms.
  • Xiao Ping ZHAN(1)(2),Hai Tao C
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 657-668. https://doi.org/10.12386/A2001sxxb0086
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    Since Lehto O.[1] presented the concept of exceptional set of entire functions and meromorphic functions, many results have been got. But these results are only on entire functions, the main reasoin is the difficult to prove caused by poles. The paper proves the following result which extended the result of Hayman. Suppose that f is a transcendental meromorphic function such that δ(∞, f) > 3/4, Q[f] is a differential polynomial in f of weight ГQ, and k is an integer not less than 15/8 + 1/2ГQ. Then fkQ[f] assumes ail Values w∈ C, except possibly zero,infinitely often, outside the union of the discs which do not contain the poles of f and Q[f].
  • Wen Guang ZHAI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 667-672. https://doi.org/10.12386/A2001sxxb0087
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    Let t(G) be the number of unitary factors of finite Abelian group G. In this paper, we obtain an asymptotic formula of t(G) with a better error term.
  • Jian Gang CHENG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 673-678. https://doi.org/10.12386/A2001sxxb0088
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    We consider the existence and nonexistence of positive solutions to the singular boundary value problems y" =μF(t, y), y(0) = a > 0, y(1) = 0, where μ≥ 0 is a constant, F(t, y) ≥ 0 and may be singular at (t, y) = (1, 0).
  • Hong You YIN(1),Cheng Xian XU(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 679-686. https://doi.org/10.12386/A2001sxxb0089
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    In this paper, the F-complementarity problem is introduced in the Banach space. The existence of its solutions is discussed. The conditions of its feasible set being a ∧-sublattice are given in the vector lattice. The equivalence between this problem and the least element problem is studied.
  • Xian Tao WANG,Yue Ping JIANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 687-692. https://doi.org/10.12386/A2001sxxb0090
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    In this paper, by using the Clifford matrix expression of higher dimensional sense preserving Mbius transformations, we obtain geometric characterizations for n dimensional nonelementary subgroups and discontinuous subgroups, respectively.
  • Zhen Lin GAO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 693-700. https://doi.org/10.12386/A2001sxxb0091
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    Green's *-relations on po-semigroups and abundant po-semigroups are introduced and studied. By using these results, we show that the structure theorem of weakly commutative abundant po-semigroups as follows: If N then S is a weakly commutative abundant po-semigroup if and only if S is a semilattice of left (resp. right) simple semigroups {(e)), for some (s),
  • Ren Xing NI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 701-712. https://doi.org/10.12386/A2001sxxb0092
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    In the present paper, by virtue of a concept of generalized Lipschitzian map- ping introduced by Zhou and Chen[4], we discuss problem of iterative approximation of fixed points for generalized Lipschitzian - strong pseudo-contractive mappings and of solutions of the equation for generalized Lipschitzian - strongly accretive operators in real Banach spaces. Our results improve and extend the recent corresponding resullts,and answer partly the open problem pat forward by Zhou[3].
  • Guo Bin ZHANG(1),Jian Ming YU(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 713-726. https://doi.org/10.12386/A2001sxxb0093
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    The discussion of various stabilities of smooth map-germs is an important part of singularity theory. While Thorn R. [1] established catastrophe theory, he gave a theory of stability of r-unfoldings of map germs. Wassermann G.[2] developed a theory of (r, s)-stability of unfoldings. In this paper we generalize them to (r1 ,... ,rd)-stability. For any Integer d, we prove equivalence of strong-, weak- and infinitesimal stabilities among other basic results.
  • Kun Hui LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 727-736. https://doi.org/10.12386/A2001sxxb0094
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    This paper studies some complex analysis problems assoiated with differien- tial equations and obtains a series of conclusions, these conclusions will be key in the studing of variational equations of (Ⅱ) in this article.
  • Wei Xing SONG(1),Ping CHENG(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 737-746. https://doi.org/10.12386/A2001sxxb0095
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    In the common support distribution and one side truncated distribution families, Bickle, Ibragimov I. A. and Hasminskii R. Z. proved two important convolution theorems. In this paper, we consider the following two side truncated distribution families: dPθ(x) = j(x;θ1,θ2)I(θ1 ≤x≤θ2)dx, where θ= (θ1,θ2), θ1 <θ2 are unknown. Under some weak conditions, we get convolution theorem, furthermore, based on the result, a new asymptotic efficiency definition is proposed. At the end of the paper, we construct some asymptotic efficient estimators for one class of two side truncated distribution families.
  • Song Fa YOU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 747-752. https://doi.org/10.12386/A2001sxxb0096
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    We research some properties on the essential (one-sided) ideals and the maximal quotient rings of smiprime PI-rings. The main resu is proved in this paper are that if R is a semiprine PI-rings then every essential one-sided ideal of R contains an essential two-sided ideal of R (Th7, Cor8), the connection between essential one sided ideals of R and essential ideals of the center are indicated (Th9 Cor10), the maximal quotient ring of R is also PI (Th12), every regular element in R is invertible in maximal quotient ring (Th14).
  • Ming Sheng SHANG(1),Qing Xian
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 753-760. https://doi.org/10.12386/A2001sxxb0097
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    This paper studied a new generalized set-valued variational inclusions: 0 ∈ N(w,y) + A(z,u), which included many variational inclusions studied by others in recent years. Using the resolvent technique, we established the equivalence between the generalized set-valued variational inclusions and the fixed point problems, and some perturbed iterative algorithms, proved that its proximate solution converge to its exact solution in real Hilbert space. Our results improve and generalized many known corresponding algorithms and results.
  • Hui Jing CAI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(4): 761-768. https://doi.org/10.12386/A2001sxxb0098
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    In this paper, it is proved that the period-doubling bifurcation of the solutions of the first order exponential Logistic iterative equation is existent. The equation that must be satisfied by critical bifurcation parameters is given. And it is showed that the critical bifurcation parameter sequence has a limit. Then, it is proved that the first order exponential Logistic iterative equation has a chaotic solution when the parameter is over the limit.