15 September 1997, Volume 40 Issue 5

    

• Select all
  |

论文
• Select
  Extending Questions of Localization Functions

  Peng Ding,WenHuai Shen,ZaiSi Z

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0083

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this note, we consider whether the maximal extension and minimal extension of p -localization of nilpotent or 1-connected spaces in sone categories admit a localization functor.Here p is a prime or zero.
• Select
  Left Free Normalizing Extensions and Quasi-ExcellentExtensions of Rings

  Fang Li

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0084

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  The left free normalizing extension andquasi-excellent extension of a ring are introduced. Some properties ofexcellent extension of a ring are generalized to left free normalizingextension and quasi-excellent extension. The main results are about thealmost Noetherian property, regularity, coherent property andsemiheredity.
• Select
  On Spectrum of the sub Laplacian on Two Step Nilpotent Lie Group

  XueBo Luo,PengCheng Niu

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0085

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper we consider the spectrum of a class of generalized homogeneous linear partial differential operators including Greiner's operator and the sub Laplacian L on the two step nilpotent Lie group, then give the spectral structure of L by using the unitary representation theory. The related result of K. Furutani et al for Laplacian is deepened.
• Select
  The Existence of Nilpotent Hall π Subgroups

  HuiWen Deng

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0086

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper the Hall's theorem is first generalized as follows: Let N be a normal subgroup of a finite group G . If N is an E n π group and G/N is a D π group, then G is a D π group. On the basis of this, we show that a finite group G is an E n π group if and only if (1) there exists a normal subgroup N of G such that N and G/N are E n π groups; and (2) for any p∈π, any q∈π-{p} , and any p element x,C G(x) contains a Sylow q subgroup of G . At the same time we have some discussions for nonabelian simple groups.
• Select
  A Further Discussion on The Covergence Rates of The Strong Law for Non Stationary φ mixing Squences

  XiaoMing Wang

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0090

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper we further investigate the strong law for non stationary Φ mixing sequences. Firstly, without any mixing rates, we obtain the sufficient and necessary condition of the complete convergence. Secondly, under the weak condition of mixing rates, we discuss the necessary condition of the Marcinkiewicz Zygmund strong law and obtain the strong law for Φ mixing sequences. The main results are simular to those of independent sequences.
• Select
  Boundary Values of the Poisson Semigroup

  JingQi Yao

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0091

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  The Poisson semigroup e --△ z on L p(R n) , 1≤p<∞ , is an analytic semigroup on the righ thalf plane Re z>0 . We consider its boundary values, and prove that the closed densely defined operator i △ generates an exponentially bounded (I+ △) α semigroup for some α≥0 .
• Select
  A Class of Rough Singular Integral Operators on Product Domains

  Yong Ding

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0089

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper we give the L p boundedness for a class of singular integral operators with the atomic Hardy space H 1(S n-1 ×S m-1 ) function and the radial function space l ∞(L q)(R +×R +) function kernels on the product domains R n×R m.
• Select
  Properties of Locality and Fredholm of Toeplitz Operators on the Bergman Space

  YuFeng Lu,ShanLi Sun

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0087

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper we discuss the relationship of local spectra of Toeplitz operators on the Bergman space. A sufficient condition is found for the quasicommutator to be compact. Sufficient conditions are given for a class of Toeplitz operators to be Fredholm operators.
• Select
  On the Linear Independence over a Number Field

  YaoChen Zhu

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0088

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper a criterion for the linear independence of a set of complex numbers over a number field is proved. And its application to transcendental number theory is also given.
• Select
  On Sderlind Conjectures on Nonlinear Lipschitz Operators

  JiGen Peng,ZongBen Xu

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0101

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let f:D C m C m be a nonlinear Lipschitz operator with the 1.u.b. Lipschitz constant L(f) , the radius of Gerschgorim region r(f) and the radius of spectral region ρ(f) . In this paper it is justified the Sderlind's conjecture that there is an equivalent norm ‖·‖ * such that L *(f)=r *(f) , and disproved his another conjecture “there is an equivalent norm ‖·‖ * such that L *(f)r(f) ”. The counterexample presented disproved also the conjecture “For any ε >0, there is an equivalent norm ‖·‖ ε so that L ε(f)ρ(f)+ε ” proposed by Wang and Xu (this journal, 38:5 (1995), 628-631). As an applications of the confirmed Soderlind's conjecture,some fundamental identities on Daugavent equation related to a linear operator are generalized to the nonlinear case.
• Select
  On the Cauchy Problem for a Reaction Diffusion Systemof Fujita Type

  KaiJun Zhang(1),LiangTao Wang(

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0102

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper is concerned with the L p global solutions and blow up problem in a finite time for the reaction diffusion system of Fujita typeu t-Δu=α 1|u| q1-1 u+β 1 |v| p1-1 v, v t-Δ v=α 2 |u| q2-1 u+β 2 |v| p2-1 v,(x∈R N, t>0), u(x,0)=u 0 (x)0, v(x,0) =v 0 (x) 0, (x∈R N)where q i>1 , p i>1 ( i=1,2) , α 1 0 , α 2>0 , β 1>0 , β 2 0 , 1 p+∞ .
• Select
  Extension of Pickands type Estimator

  ZuoXiang Peng

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0103

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this note, Pickands type estimator was extended,its consistency and rate of strong convergence was proved.
• Select
  The Problem of Weak Solution for Navier Stokes Equation

  XiaoDing Shi(1),YongGeng Gu(2)

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0099

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this article we discuss solvability of the solutions for Navier Stokes system. We obtained more general existence, uniqueness and regularity results. We also apply these results into description of motion of viscous incompressible fluids.
• Select
  Beltrami Systems with Double Characteristic Matrices and Quasiregular Mappings

  ShenZhou Zheng

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0100

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let Ω be an open subset of R n (n2) and f∈ W 1,n loc (Ω, R n) . Assume that G(x), H(x)∈C k,α (Ω, R n× n ) for k1 and 0<α<1 ;One will obtain that f∈C k+1,δ loc (Ω, R n) (0<δ<1) for the weak solutions of Beltrami systems (1.4).
• Select
  Bounded Composition Operators on Hardy Spaces

  GuangFu Cao

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0096

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, the boundedness of composition operators induced by analytic maps from B n to B m be discussed. In particular, some properties of composition operators induced by preserve measure maps be studied. As a consequence, we given an answer of a problem of W. Rudin .
• Select
  Some Convergence Theorems for the Ishikawa Iterative Sequences of Certain Nonlinear Operators in Uniformly Smooth Banach Spaces

  HaiYun Zhou

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0093

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, by a new technique, we have obtained some strong convergence theorems for the Ishikawa iterative sequences of strongly accrective mappings. Our results generalize and/or improve the recent coresponding those obtained by others.
• Select
  On the Non existence of Closed Orbits for Generalized Liénard System with Several Singularities

  QiMin He

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0094

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  By using a different technique of constructing the auxiliary functions, we give some non existence criteria of closed orbits for generalized Liénard system with several singularities. They include the classical Bendixson and Poincaré criteria of (E) as their special examples. Moreover, we also give the examples of cubic system ect.
• Select
  Some Studies for the Problem of Multiple Positive Solutions

  ShuLang Yang

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0095

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In the paper, under several suitable transformations, the problem of multiple positive solutions for set valued mapping equation in an ordered (B) space is studied by the fp homotopy method. And some properties of quasi derivative of set valued mapping are used in the related works of the paper.
• Select
  The Local Cauchy Problem of Singular Semilinear Evalution Equations in Banach Spaces

  SuWen Jian

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0097

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we study the following cauchy problem  dudt + 1t σ Au =J(u), 01), E=L p, E J=L pγ , we have the similar results with the results of Fed B. Weissler in .
• Select
  The Number of Solutions to the Symmetric Matrix Equation over a Finite Field of Ch.≠2 and Representation of Itsq hypergeometric Series

  HongZeng Wei,YiBin Zhang

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0098

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let F q be a finite field with q elements,where q is a power of an odd prime. In this paper, using singular orthogonal goemetry over F q, we have given the number of solutions X of rank k and solutions X to the equation XAX′=B over F q, when A and B are symmetric matrices of order n, rank 2ν+δ and order m, rank 2s+γ, respectively. Finally, we have obtained simple representation of enumerational formulas using q hypergeometric series.
• Select
  Grothendieck Rings and Their Applications

  HuanYin Chen

  Acta Mathematica Sinica, Chinese Series. 1997, 40(5): . https://doi.org/10.12386/A1997sxxb0104

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  By virtue of K 0 ring, we describe Grothendieck groups from related rings, and obtain some important characterizations of conected properties and stably free properties. Finally, we give some applications to group rings.