中国科学院数学与系统科学研究院期刊网

15 March 2004, Volume 47 Issue 3
    

  • Select all
    |
    论文
  • Hong Bin CHEN(1),Kai Tai LI(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 417-424. https://doi.org/10.12386/A2004sxxb0053
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we consider the Lienard equation +f(x) +g(x) =p(t), where g∈C~1(R), f∈C(R), p(t)∈C_(2π). A necessary and sufficient condition to ensure the existence and uniqueness of a 2π-periodic solution is obtained, for the Duffing type equation. For the Ambrossetti-Prodi type, +c+ g(x,t) =s, the existence of exactly two periodic solutions is confirmed by Sturm theory.
  • Liu Chuan ZENG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 425-432. https://doi.org/10.12386/A2004sxxb0054
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let X be a uniformly convex Banach space with a Frechet differentiable norm, C be a nonempty bounded closed convex subset of X, and T = {T (t): t≥0} be a semigroup of self-mappings of C which is asymptotically nonexpansive in the intermediate sense. If u (·): [0, ∞)→C is an almost-orbit of T = {T(t): t≥0} which is continuous in t∈[0, ∞) then {u (t): t≥ 0} almost converges. weakly to the unique point of the set∩t≥0 {u (r): r≥t}∩ F (T).
  • Huai Xin CAO(1),Zong Ben XU(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 433-440. https://doi.org/10.12386/A2004sxxb0055
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, let (K, d) be a given compact metric space, A a unital Banach algebra and φ: [0, +∞)→ [0, ∞) a continuous function with ker φ= {0}. Noncommu- tative Banach algebras L~φ(K, A) and l~φ(K, A), consisting of Lipschitz-φ operators and of little Lipschitz-φ operators from K into A, respectively are introduced and discussed. It is proved that these algebras are both subalgebras of noncommutative Banach alge- bra C(K, A), consisting of all continuous operators from K into A, and Banach algebras with respect to norm ||f||_φ = L_φ(f) +||f||_∞. Secondly, inclusion relationships between L~φ(K,A) and L~ψ(K,A) (resp. l~φ(K,A) and l~ψ(K,A)) are given. Especially when φ(t) = t~α, the limit algebras lim_(α→0~+)l~α(K, A), lim_(α→+∞)l~α(K, A), lim_(α→-o~+)L~α(K, A) and lim_(α→+∞)L~α(K,A) are defined and studied. Thirdly, Lipschitz connectedness of a metric space is introduced and is applied to give necessary condition and sufficient condition for lim_(α→+∞)l~α(K, A) =A. Conditions for lim_(α→0~+)L~α(K, A) = C(K, A) are also obtained.
  • Guang Gan CHEN(1),Zhi Lin PU(2
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 441-448. https://doi.org/10.12386/A2004sxxb0056
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the KDV type equation is considered on an unbounded domain R~1.By applying the theory of decomposing operator and the method of constructing some compact operator in weighted space, the existence of exponential attractor on R~1 is Obtained.
  • Yi WANG,Li Zhong ZHAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 449-454. https://doi.org/10.12386/A2004sxxb0057
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Denote by N(m, n;λ,μ) the number of lattice paths from the lower left corner to the upper right corner in an m×n grid with the Ferrers diagrams of two partitions λ and μ being removed from the upper left corner and the lower right corner respectively. Simion's conjectured that N(e-k, k;λ,θ) is log-concave in k. Here we show that if the sequence x_0, x_1,..., x_n is log-concave, then the sequence y_k x_i is also log- concave, and present an application of this result to Simion's conjecture. Furthermore, we show that N(e-k, k;λ,μ) is log-concave in k for all partitions λand μ
  • Feng Quan LI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 455-466. https://doi.org/10.12386/A2004sxxb0058
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we study the existence and regularity of entropy solutions of nonlinear elliptic boundary value problem with equivalued surface and improve previous original result.
  • Qiang Jun XIE,Jian Hua WU,Li J
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 467-478. https://doi.org/10.12386/A2004sxxb0059
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, by means of calculating the indices of fixed points of compact maps in cones, in combination with the maximum principles, lower-upper solutions methods and spectrum analysis of operators, we consider the coexistence of steady states for a kind of reaction-diffusion systems.
  • Shi Huang HOU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 479-486. https://doi.org/10.12386/A2004sxxb0060
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the aim is to give sufficient conditions for the existence of solutions to nonlinear boundary value problems of multivalued differential equations in complete metric spaces and to a class of functional equations arising in dynamic pro- gramming. By using fixed point theorems, our results lead to new existence principles.
  • Zhao Xiang LI(1),Yan Pei LIU(2
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 487-494. https://doi.org/10.12386/A2004sxxb0061
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we study the chromatic and dichromatic sum functions of rooted general maps on the plane. The chromatic and dichromatic sum function equa- tions of such maps are obtained. From the chromatic sum equation of such maps, the enumerating function equation of rooted loopless maps, bipatite maps and Eulerian maps on the plane are also derived. Moreover, some explicit expressions of enumerating functions are also derived.
  • Ming Xue LIU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 495-498. https://doi.org/10.12386/A2004sxxb0062
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we obtain a new equivalent condition for the existence of a nontrivial closed invariant subspace for a subalgebra A of B(X) in a reflexive Banach space X.
  • Jia Yun ZHOU,Yu LIU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 499-504. https://doi.org/10.12386/A2004sxxb0063
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper explores the property of frame and atomic decomposition for Banach space in terms of the theory of frame for Hilbert space. Besides, it gives a suppicient condition for Banach frame and atomic decomposition, and discusses the relation between Banach frame and atoAnc decomposition.
  • Wan Gui SUN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 505-510. https://doi.org/10.12386/A2004sxxb0064
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The sufficient conditions are given for the continuous calculus of U-scalar operators to be bounded. And for a certain U-scalar operator T, we prove that operator u(T) is bounded if u′(t) is continuous. Yet there exists a continuous function u(t) such that u(T) is unbounded.
  • Jing An CUI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 511-520. https://doi.org/10.12386/A2004sxxb0065
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we consider the permanence and periodic solation of a peri- odic predator-prey system, and a sufficient and necessary condition is obtained for the permanence of this system. The system has a positive w periodic solution under this condition, and we improve some known results.
  • Long Chun WANG,Guo Jun WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 521-526. https://doi.org/10.12386/A2004sxxb0066
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper concerns an extension of the theory of generalized tautologies in revised Kleene system. The theory of generalized tautologies for all kinds of infinite subalgbras of R_0-algebra [0,1] is considered. It is proved that, in R_0-subalgebra E_2, the system L~* has countable different generalized tautologies.
  • Deng Feng LI(1),Dun Yan YAN(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 527-530. https://doi.org/10.12386/A2004sxxb0067
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we prove that if wavelets which arise in multidimensional multiresolution analysis with an arbitrary dilation matrir are orthonormal, then the corresponding scaling function is also orthonormal, where orthonormality of functions f_s(x)∈L~2(R~n) (s= 1, 2,...,r, r being a positive integer) means that the function family consisting of all integer translations of f_s (x) is an orthonormal system in L~2 (R~n). This result shows that if we want to construct orthonormal wavelets from a multireso- lotion, then that multiresolution must have an orthonormal scaling function.
  • Zheng Qiu ZHANG,Zhi Cheng WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 531-540. https://doi.org/10.12386/A2004sxxb0068
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, a class of predator-prey diffusive system of three species with ratio-dependence is studied. By using coincidence degree theory,we establish the exis- tence result of positive periodic solution for the predator-prey diffusive system.
  • Li Xin ZHANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 541-552. https://doi.org/10.12386/A2004sxxb0069
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let {X_n;n≥ 1} be a strictly stationary sequence of negatively associ- ated random variables with mean zeros and finite variances. Set S_n=sum from k=1 to n X_k, M_n =max_k≤n |S_k|, n≥1. Suppose σ~2 =EX_1~2 +2 sum from k=2 to ∞ EX_1X_k>0. We study the precise asymptotics of a kind of weighted infinite series of P{M_n≥∈σ(2n loglogn)~(1/2)} as ∈ 0, and the precise asymptotics of a kind of weighted infinite series of P{M_n≤ ∈σ(π~2n/(8loglogn))~(1/2)} as ∈ ∞. The results are related to the convergence rates of the law of the iterated logarithm and the Chung type law of the iterated logarithm.
  • Xian Neng DU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 553-558. https://doi.org/10.12386/A2004sxxb0070
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let A be a finite dimensional algebra, R the dual extension algebra of A. In this paper, we investigate the Shod subcategories of R, the relations between tilting ob- jects in A-module category D and these in R-module category , and the contravariant finite subcategories of R.
  • Zhi Gui LIN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 559-568. https://doi.org/10.12386/A2004sxxb0071
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the three-species food chain is discussed, in which the third species is the predator of the second one and the second species is the predator of the first one. The dynamics of coupled systems of semilinear parabolic equations with time delays are investigated by using the method of upper and lower solutions, and the asymptotic behavior of the solution is given.
  • Ling Li REN(1),Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 569-578. https://doi.org/10.12386/A2004sxxb0072
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, by using the theorem of coincidence degree, the authors study periodic solution to a class of second order functional diffrential equation x"(t) + f(t, x_t)x'" +β(t)g(x(t-T(t))) =p(t). Some new results for the existence of the periodic solution are obtained.
  • Ju Rang YAN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 579-586. https://doi.org/10.12386/A2004sxxb0073
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, oscillation properties of solutions under two boundary condi- tions for impulsive delay parabolic equations with oscillatory coefficients are studied. Several oscillation criteria are obtained. The results of this paper improve some known onse.
  • Tong Zhu LI,Zhen GUO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 587-592. https://doi.org/10.12386/A2004sxxb0074
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let f: M~n→ (c) be an isometric immersion of a Riemannian manifold with parallel Ricci curvature into a constantly curved manifold. In this paper, we present the classification of this kind of hypersurfaces. In addition, if (M~n, f) is a minimal immersion, we also classify this class of hypersurfaces and extend the results of Lawson.
  • Zhi Shan DONG,Xiao Yun YANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 593-600. https://doi.org/10.12386/A2004sxxb0075
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we give the almost sure central limit theorem, under the coudition of existence of second order moment, for NA and LNQD random variables with stationary distribution, where W is the standard Brownian motion on [0, 1].
  • Wei HE(1),Shou Li JIANG(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 601-606. https://doi.org/10.12386/A2004sxxb0076
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We introduce the concept of weakly topological spaces, and show that the relationship between the category of locales and the category of weakly topological spaces is similar to the relationship between the category of topological spaces and the category of locales. The category of locales is strictly contained in the category of weakly topological spaces, and is equivalent to the category of sober weakly topological spaces.
  • Lr Qun PENG(1),Xian Gao LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 607-614. https://doi.org/10.12386/A2004sxxb0077
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    People could be confronted with the mappings into R~∞ when they consider the maps from Riemannian manifold into Hilbert loop Lie groups. However, some properties of the maps, such as the renowned Arzela-Ascoli theorem, are not clear. We shall give the norms of the space of the maps into Hilbert loop group, and prove the Arzala-Ascoli theorem in this article.
  • Ping An HUANG(1),Guo Hua QIAN(
    Acta Mathematica Sinica, Chinese Series. 2004, 47(3): 615-620. https://doi.org/10.12386/A2004sxxb0078
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we classify finite groups G satisfying the following hypothesis: |Aut(G)| = prq~2, q > 2, where p, q, r are distinct primes.