中国科学院数学与系统科学研究院期刊网

15 May 2001, Volume 44 Issue 5
    

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  • Shan Zhen LU,Dun Yan YAN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 769-776. https://doi.org/10.12386/A2001sxxb0099
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    In this paper, we study multilinear oscillatory singular integrals with rough kernel, and give a criterion of certain boundedness for this kind of operators.
  • Xiao Sheng ZHU(1),Jing Hua YAN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 777-784. https://doi.org/10.12386/A2001sxxb0100
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    The authors of Sandomierski F. L., Small L. W., Fields K. L.[1-3] studied homological dimensions of rings and residuce rings under "nilpotent" conditions. But, for some rings (for example, R is a commutative Von Neuman regular ring) the "nilpo- tent" conditions don't hold. Hence, in this paper, we consider homological dimensions of rings and residuce rings under "no-nilpotent" conditions such as R(R/t)((R/I)R) is R-projective of R(R/I)R is R-flat.
  • Li Ning JIANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 785-790. https://doi.org/10.12386/A2001sxxb0101
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    Let A be a right complemented Banach algebra,and LA, Ml(A) the left regu- lar and left mulplier algebra of A respectively In this paper, we get some necessary and sufficient conditions about when Ml(A) is right complemented or annihilator algebra. Also, under the given conditions, we obtain the relation between the representations for A and LA based on the relation between the complementors on them.
  • Ting Fang ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 791-804. https://doi.org/10.12386/A2001sxxb0102
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    With the method of Moving Frames this paper has proved: If Mn (n ≥2) is a nondegenerate affine hypersurface in An+1, (1) Suppose ■K = 0 (The difference tensor K is parallel), then M is an affine hypersphere with J = 0 and G is an Einstein's affine metric, Here J is Pick invariant of M and G is the Blaschke metric. (2) R' K = 0 (The difference tensor K is semi-parallel) if and only if S = 0 (M is an Amproper affine hypersphere), or K = 0 (M is a quadric).
  • Zong Sheng GAO,Feng Zhu WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 805-814. https://doi.org/10.12386/A2001sxxb0103
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    In this paper, we firstly improve one of the well-known Tsuji's theorems on the simply-connected finite covering surfaces of a sphere, and make use of it to prove a basic inequality on the multiple values of algebroid function. Then, we obtain the precise results of the sequence of filling disks and Borel direction dealing with multiple values of algebroid function of positive order finite.
  • Yao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 815-822. https://doi.org/10.12386/A2001sxxb0104
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    The algebraic independence of values of certain continued fractions with elements anx (n≥0) at algebraic and transcendental points is proved, where an (n ≥ 1) are positive algebraic numbers. Especially, some results about algebraic independence of simple continued fractions are extended to more wide cases.
  • Qi Ye ZHANG,Lei FAN,Chong You
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 823-828. https://doi.org/10.12386/A2001sxxb0105
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    In this paper, we constructed a new category of domains-the category AlgD of algebraic domains and Scott continuous functions of approximation-order- preserving (or way-below-relation-preserving); and its full subcategory AlgD, the category of pointed algebraic domains and Scott continuous functions of approximation- order-preserving. We showed that these categories are not Cartesian closed in general, and then determined the maximal Cartesian closed full subcategories of these cate-gories.
  • Guo Jun WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 829-836. https://doi.org/10.12386/A2001sxxb0106
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    The concept of component and width of element of complete lattices are introduced.It is proved therefrom that the set of components of any element is closed under the operation of finite unions and the set of components with finite width of any element is directed.Elements without proper component are called granules.A complete lattice is called a granule representable lattice if every non-zero element is the union of all its granular components.It is proved that a topological space is locally connected if and if the lattice consisting of all its open sets is a granule representable lattice.
  • Shi Jin WU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 837-842. https://doi.org/10.12386/A2001sxxb0107
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    This paper gives differently a necessary and sufficient condition of existence of the solutions and Cramer formulas of linear equations, the related property of vector, opposite and rank of matrix, and characteristic root and characteristic vector of linear transformation etc by setting up a weakly exchangaeble law of quaternion product, and obtain a effective solution of the problems.
  • Li Shan LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 843-848. https://doi.org/10.12386/A2001sxxb0108
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    In this paper, we will prove that Ky Fan's Theorem[1] is true for 1-set- contractive maps defined on a bounded closed convex subset K in a Banach space with int K ≠0. This class of 1-set-contractive map includes condensing maps, non- expansive maps, semicontractive maps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations and improvements the recent results obtained by many authors.
  • Peng Nian CHEN(1),Jian Xun HE(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 849-856. https://doi.org/10.12386/A2001sxxb0109
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    Let f ∈ C1(R2, R2), f(0) = 0. The Jacobian Conjecture says that if for any x ∈R2, the eignvalues of the Jacobian matrix Df(x) have negative real parts, then the zero solution of the differential equation x = f(x) is globally asymptotically stable. In the paper, we prove that the conjecture is true.
  • Xian Yuan WU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 857-860. https://doi.org/10.12386/A2001sxxb0110
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    We prove the uniqueness of infinite open cluster for high-density bond per- colation on lattice Sierpinski Carpet, forthermore, an alternative proof of the existence of phase transition of the model is given. A rescaling technique is developed and used as the main tool of our proofs.
  • Lin TANG,Da Chun YANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 861-868. https://doi.org/10.12386/A2001sxxb0111
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    This paper, the authors prove that the multilinear operators of finite sums of products of singular integrals on Rn are bounded from HK q1α1,p1 (Rn) ×…× HKqkαk,pk(Rn) into HK qα,p(Rn) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments satisfying by the multilinear operators are also necessary when αj 0 and the singular integrals considered here include the Calderon-Zygmund singular integrals and the fractional integrals of any orders.
  • Shu Xiang HUANG(1),Chun Hong X
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 869-880. https://doi.org/10.12386/A2001sxxb0112
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    In this article, we advance a model arising in modeling the chemical in- terficial reaction problem. This model is described by a couple of reactiondiffusion equations with nonlinear boundary conditions. By constructing and solving some class of differential inequalities of solution, we obtain the rate of convergence for the solution.
  • Kun Hui LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 881-890. https://doi.org/10.12386/A2001sxxb0113
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    This paper proves the existence of solution of a class of variaational equations with applying of the conclusion in (I) (see Vol.44, No.4, p.727-736), presents the special method in analysis of this paper and points out that this class of variational equations will have important applying on studying of some kind of new stochanstic control models under quite wide condition.
  • Qi Qi WU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 891-898. https://doi.org/10.12386/A2001sxxb0114
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    Let P(n, k) be the number of unordered partitions of an integer n into k parts where each part ≥1, set by master Euler (1707-1783). It is one of most important numbers in Combinatorics, Graph theory and Number theory.However, it is rather difficult to find the values of P(n, k) and to construct a large table of P(n, k). In this paper, from this formula P(n, k) = P(n - 1, k - 1) + P(n - k, k) we define the "number of left shoulder" of P(n, k) and the "acute number" of P(n, k), by which we get at the "law of left shoulder" to find P(n, k) (First law), also the "law of oblique line" to find P(n, k) (Second law) on the basis of some important theorems of the paper Wu Qiqi [5]. By using these laws we obtaine an ioteresting principle for constructing a large table of P(n, k). For the sake of convenience, we use the only first law to design the proceeding of calculator, by which we can quickly construct an arbitrary large table of P(n, k).
  • An Min MAO(1),Mei XUE(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 899-908. https://doi.org/10.12386/A2001sxxb0115
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    Several existence theorems on positive solutions of superlinear (and sublinear) BVPs are proved by utilying the theory of fixed point index. Applying these results to nonlinear eigenvalue problems yields some new conclusions.
  • Jun CHEN,Jian Long CHEN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 909-916. https://doi.org/10.12386/A2001sxxb0116
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    In this paper, we define generalized factorization of morphisms in the preaddi- tive category and give existential conditions and expressions for the {i}-inverses, {1, i}- inverses, Moore-Penrose inverses, Drazin inverses and group inverses of morphisms with generalized factorization. In the meantime, we generalize the corresponding results of morphisms with universal factorization.
  • Chun Hua FENG(1),Chang Xiang Y
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 917-922. https://doi.org/10.12386/A2001sxxb0117
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    By using Liapunov functional, this paper investigated the existence and uniqueness of almost periodic solutions of some second order nonlinear retarded sys-tems.
  • Chang Yong PENG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 923-928. https://doi.org/10.12386/A2001sxxb0118
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    Kloosterman sum over the finite field Fq(q odd )is the sum of two conjugate the angle of the corresponding Kloosterman sum. In this paper, we give some results on the angles of Kloosterman sums, and improve some of N. Katz N.[1] result, improve and genaralize Conrey J. and Iwanie' H. [2] result.
  • Xiang Yi GENG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 929-932. https://doi.org/10.12386/A2001sxxb0119
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    In the paper, a sufficient and necessary condition for maps to be chaotic in the sense of Li-Yorke is given.
  • Guo Dong LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 933-946. https://doi.org/10.12386/A2001sxxb0120
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    In this paper, properties of the generalized central factorial numbers arediscussed. The relations between the generalized central factorial numbers and higherorder Euler-Bernoulli polynomials are expounded, some identities involving NorlundEuler-Bernoulli polynomials have been established, extends the results of Dilcher K.[1],Zhang Wenpeng[2] and Zeitlin David[3].
  • Deng Feng LI(1),Si Long PENG(2
    Acta Mathematica Sinica, Chinese Series. 2001, 44(5): 947-960. https://doi.org/10.12386/A2001sxxb0121
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    IN the paper [1], Chen H. L., Xiao S. J. the authors construted a class of periodic wavelets which possess good properties. In this paper, we study do some investigation on this class of periodic wavelets, and obtain that these periodic wavelets are well localized in one period.