中国科学院数学与系统科学研究院期刊网

15 March 2001, Volume 44 Issue 3
    

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  • De Lang LI(1),Ye TIAN(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 385-392. https://doi.org/10.12386/A2001sxxb0051
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    It is proved in this paper that BSD conjecture holds for a certain kind of elliptic curves.
  • Sheng Hong LI(1),Xian Gao LIU(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 393-402. https://doi.org/10.12386/A2001sxxb0052
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    In this paper, we introduce the concept of G class of functions of the parabolic class, and show the Hǒlder continuity of G class of functions. The introduction of the concept contributes to the Proof of the regularity and existence of the solution for the first boundary Problem of parabolic equation in divergence form.
  • Si Lei WANG,Li Min SUN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 403-412. https://doi.org/10.12386/A2001sxxb0053
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    Let be a closed smooth hypersurface with non-vanishing Gaussian curvature, do the induced Lebesgue measure on S. If the density function then the Fouxier transform satisfies In this paper, It is showed that if op is non-smooth then the estimation is not valid in general. But, for , satisfying suitable conditions, still has certain decay rates. The restult is used to obtain the boundedness of a weighted maximal average operator on the sphere S~(n-1).
  • Jun YANG,Xin Ping GUAN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 409-416. https://doi.org/10.12386/A2001sxxb0054
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    This paper is concerned with the positive solutions a class of neutral type delay difference equations necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained.Various type of comparison theorems are also derived.
  • Zhen Gang ZHAO,Ming KOU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 417-428. https://doi.org/10.12386/A2001sxxb0055
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    In this artical, the Busemann function on the second classical domain is given and the following theorem is proved: for any geodesic curve passing the point 0 in RII(p) where U is a p x p unitary matrix, . Then, the Busemann function determined by r is: . where d-kk(z) is the diagonal element of the following matrix:
  • Jian Gang CHENG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 429-436. https://doi.org/10.12386/A2001sxxb0056
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    Without nonnegative assumptions and any monotonous assumptions on f, the existence of positive solutions of nonlinear boundary value problems have been studied in this paper, where q is nonnegative continuous and may be singular at end points.
  • Meng FAN,Ke WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 437-444. https://doi.org/10.12386/A2001sxxb0057
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    By using the method of coincidence degree theory, we study the existence of positive periodic solution of multispecies ecological competition system modeled by an integral differential equation system. Some new sufficient conditions are obtained.
  • Wen Feng QI,Xuan Yong ZHU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 445-452. https://doi.org/10.12386/A2001sxxb0058
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    Let Ω be the Teichlnuller represelltative set of Galois ring GR(2~d,r), then for each sequence a over GR(2~d,r), there exists a unique level decomposition , where a-i is a sequence over Ω and can be regarded as a sequence over the finite field F-(2~r) naturrally. Let f(x) be a strongly primitive polynomial over GR(2~d,r), G(f(x)) the set of sequences generated by f(x) over GR(2~d,r) and a polynomial of d -- 1 variables over F-(2~r). Set, then the compression mapping is injectiveness, that is, a = b if and only if for all a, b ∈ G(f(x)).
  • Ting Rong ZOU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 453-458. https://doi.org/10.12386/A2001sxxb0059
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    in this paper, by the contact has between BCK-algebra and axiom system of cubic lattices. The M-R open problem on infinite cubic lattices is answered in the affirmative.
  • Zhao Yong HUANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 459-468. https://doi.org/10.12386/A2001sxxb0060
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    Let R be a left and right coherent ring and R~ωR a faithfully balanced selforthogonal bimodule. For any finitely presented left R-module A and a positive integer n, we study in this paper the homological equations such as A = EXt-R~n(X,ω). The necessary and sufficient conditions of the category of modules {EXt-R~n(B, R) | B is any finitely presented right R-module} being submodule closed are given, and some examples are given to explain that such a category of modules as above is not always submodule closed.
  • Xiao Ying LIU,Cong Xin WU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 469-474. https://doi.org/10.12386/A2001sxxb0061
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    By establishing a comparison result and using the fiXed point theorem and the method of the upper and lower solutions, the maximal and minimal solutions of the initial value problem for the first order impulsive integro-differential equations of mixed type with discontinuous terms in Banach spaces are investigated. In the case that the nonlinearity satisfies the Caratheodory condition, we obtain the successive approximation of solutions. Our results improve and generalize those in some wellknown papers.
  • Zhi Lin YANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 475-480. https://doi.org/10.12386/A2001sxxb0062
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    This paper deals with the global structures of nontrivial solutions to the following Sturm-Liouville problems: where f: R→R is continuous and satisfies some additional conditions. The results obtained here generalize those of Berestycki.
  • Fu Liu ZHU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 481-490. https://doi.org/10.12386/A2001sxxb0063
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    in this paper, we investigate the asymptotic expressions of the elementary spherical functions on the non-compact Riemannian symmetric spaces of ranks one, and use the heat kernel obtained by Lohoue and Rychner to establish the central limit theorem for these spaces, our conclusion includes Terras theorem as a special case.
  • Zhong Yan LI,Bin Ren LI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 491-500. https://doi.org/10.12386/A2001sxxb0064
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    In this paper, we describe the standard matrix unit basis in the complexification of a finite dimensional real C~*-algebra, and we give the equivalent definition of a (AF) real C~*-algebra.
  • Li Hu DENG(1)(2),Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 501-506. https://doi.org/10.12386/A2001sxxb0065
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    In this paper, we study oscillation of solution for impulsive delay parabolic equation. Several oscillation criteria are obtained under two kinds of diffrent boundary conditons.
  • Shu Jie LI,Zhi Tao ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 507-516. https://doi.org/10.12386/A2001sxxb0066
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    In this paper, we use ordinary differential equation theory of Banach spaces and minimax theory, in particular, the relative mountain pass lemma to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity and get new multiple solutions and sign-changing solutions theorems, at last we get up to six nontrivial solutions.
  • Tong Seng QUEK(1),Da Chun YAN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 517-526. https://doi.org/10.12386/A2001sxxb0067
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    The authors introduce certain Calderón-Zygmund type operators and discuss their boundedness on spaces like weighted Lebesgue spaces, weighted weak Lebesgue spaces, weighted Hardy spaces and weighted weak Hardy spaces. Sharpness of some results are also investigated.
  • Yong DING(1),Da Shan FAN(2),Yi
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 527-534. https://doi.org/10.12386/A2001sxxb0068
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    We give the L~p-boundedness for a class of Marcinkiewicz integral operators and ,s related to the Littlewood-Paley g-function, -function ahd the area integral S, respectively. These operators have the kernel functions , the Hardy space on . The results in this paper substantially improve and extend the known results.
  • Jian Guo WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 535-540. https://doi.org/10.12386/A2001sxxb0069
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    in the case of not requiring the nonlinear terms non-positive, the existence of nontrivial solutions for the Hammerstein Integral Equations by using the partial ordering theory was discussed and some applications to ordinary differential equations with two-point bounded values.
  • Da Qing JIANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 541-548. https://doi.org/10.12386/A2001sxxb0070
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    For 1 ≤ k≤ n-1, the existence of solutions to the singular boundary value problem are reestablished under weaker and fewer restrictions on f(t, y), where f(t, y) may be singular at y = 0, t = 0 and t = 1. The arguments involve only positivity properties of the Green's function and a fixed point in cones. Moreover, the explicit formula of Green's function can be found in this paper.
  • Chang Mei TAN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 549-552. https://doi.org/10.12386/A2001sxxb0071
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    In this note we Present an inequality which implies the boundedness on weighted Lorentz spaces for the Littlewood-Paley operators.
  • Guo Long CHEN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 553-558. https://doi.org/10.12386/A2001sxxb0072
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    The inverses of infinite matrix on a division ring are discussed. The decomposition theorem of infinite matrix on a division ring is proved.
  • Yong Zhi CAO(1),Ping ZHU(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 559-566. https://doi.org/10.12386/A2001sxxb0073
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    In this paper,we give existential conditions and expressions for the (1,…, i)inverses of morphisms with universal- factoriztion in a Preadditive category. Particu- larly,we obtain some new necessary and sufficient conditions for the existence and new expressions of Moore-Penrose inverses and group inverses of this ciass of morphisms.
  • Di Xin ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(3): 567-576. https://doi.org/10.12386/A2001sxxb0074
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    In this paper, we study the conditional weak convergence of random weighted U-processes of 2 order indexed by a class of functions and deduce the random weighting approximation of U-processes.