15 May 1997, Volume 40 Issue 3

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  Derivations on Nest Subalgebras of Von Neunxann Algebras (II)

  JianHua Zhang,HongKe Du

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0058

  Abstract ( 3257 ) Download PDF ( 885 )   Knowledge map   Save

  In this paper derivations on nest subalgebras of factor Von Neumann alge- bras are discussed. It is proved that every derivation from nest subalgebras of factors Von Neumann algebras into Compact operators is inner,
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  A Proposition of the Convergent Power Series Ring

  LiHuang Tu

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0059

  Abstract ( 2522 ) Download PDF ( 909 )   Knowledge map   Save

  We proved that the tensor product of convergent power series rings is not noetherian and raised a unsolved problem.
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  ^StochastictMethod for Quasilinear Partial Differential Equations

  ShaoZhong Chen

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0041

  Abstract ( 2812 ) Download PDF ( 800 )   Knowledge map   Save

  lt is proved by stochastic analysis method that if u0 is bounded and mea- surable and f> 0 then the solution of Cauchy problem of the quasilinear parabolic partial differential equation u0+f(u)ux+=0 , u(0,x) =u0 (x) xonverges to the entropy solution of the quasilinear partial differential equation u0 +f (u)ux=0 , u(0,x) = u0(x), as - 0, that is the validity of " vanishing viscosity" method for the equation. This is the well known result due to Oleinik by using difference method in 1975. The result of this paper suggests the importance of probabilistic method for solving nonlinear partial differeatial equations.
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  Some Propertiea of Noaliear Operator and Poaitive Solutioas of a Clasa of lntegral Equation

  ZhanDong Liang

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0042

  Abstract ( 6530 ) Download PDF ( 783 )   Knowledge map   Save

  ln this paper sorae properties of nonliaear operator are given , aad using these properties, the existence and uniqueness of the positive solutions of a class of iategral equatioo are discussed .
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  Comment of the Paper "A Theorem on the Dimensions of Self-similar Sets

  Jing Wang

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0050

  Abstract ( 3041 ) Download PDF ( 785 )   Knowledge map   Save

  In this note, we point out some problems in tbe paper " A Theorem on the Dimensions of Self-similar Sets" , and give a couater example to show that the conclusion of this paper is incorrect .
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  Limits in the Category of Molecular Lattices

  Bin Zhao

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0051

  Abstract ( 3090 ) Download PDF ( 766 )   Knowledge map   Save

  By the .analysis of the relation on complete lattices, we introduced the concepts of -coraplete lattice and -lower set , discussed some properties of -lower set, and proved that the set of all -lower sets of a -coraplete lattice forms a molecular lattice. Using the above results and the category theory, we coastructed the limit structures in the category of molecular lattices, and solved one of the difficult problems in tbe research field of the categorical properties of molecular lattices ,
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  Weighted Hardy Space and Weighted Norm Inequalities of the Area Integral

  XingMin Li(1),LiZhong Peng(2)

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0052

  Abstract ( 3146 ) Download PDF ( 921 )   Knowledge map   Save

  In this paper, we establish a weighted atomic Hardy space that has high order vanishing moments, and tbe two-sided weighted norm inequalities of the Area Integral are given.
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  A New Regularization Method for the Operator Equation of the First Kind

  HongQi Yang,ZongYi Hou

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0053

  Abstract ( 3264 ) Download PDF ( 733 )   Knowledge map   Save

  In this paper, we present a new regularization method for solving t he operator equation of the first kind with approximate operator and the right-hand side. By applying the generalized Arcangeli's criterion to choose the regularization parameter, we obtain the convegence of the regularized solution, and as compared with Tikhonov regularization , the asymptotic order of tbe regularized solution is improved .
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  The Isomorpbism Problems for Incidence Riags of Partially Ordered Sets

  Bin Zhu

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0046

  Abstract ( 2657 ) Download PDF ( 794 )   Knowledge map   Save

  Let . be a locally finite partially ordered set, R is an ring with identity 1, I(x, R) is the incidence ring of X over R, the isomorphism problems about incideace riags are discussed in the present paper. The following results are obtained : If R is an unique idempotent ring, the. ordered sets) : If R,S. are commutative iadecomposable riogs, then
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  Linear Maps of μ-preserving Kerael into Range on Jacobson Radical of Nest Algebras

  Jun Zhu,ChangPing Xiong

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0047

  Abstract ( 3016 ) Download PDF ( 773 )   Knowledge map   Save

  Let A be an operator algebra in B(H) , and letμ(A) denote the set of all partial isometric operators in A. We say that a linear map . : A→ B(H) is a map of μ-preserving kernel into range if .(U)(kerU) C ran (U) for any . Cμ(A). In this paper, we show that a norm continuous linear map of μ-preserving kernel into range on Jacobson radical of nest algebras is a generalized inner derivatio., i.e , ip(T) =TA+BT for Some A,B G B(H).
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  The Exis tenceof Unique Almost Periodic Solutionon a Neutral Volterra Integro-DifferentialEquation with InfiniteDelay

  XiTao Yang(1),ChunHua Feng(2)

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0048

  Abstract ( 3542 ) Download PDF ( 850 )   Knowledge map   Save

  Westrdy the boundedness,uniformly asympotic stability ofsolutions and the existence ofunique almost periodicsolution ona neutral Volterraintegrodifferentialequation as (1) byusing anewLiapunov function .
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  A Family Analytic Functions ofLinearHomeomorphic and Starlike Functions

  YeXi Zhao

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0049

  Abstract ( 2357 ) Download PDF ( 898 )   Knowledge map   Save

  This paper defines a family analyticfunctions A( ,α)of linear homeomorphicandstarlike functions。We deduce the integral expressionof functions in A( ,α);with the hilpof operatortheory study contain relation of family A(,α)andprove convolution theorem ,determine its close convexhull ,extreme points of close convex hull and its supportpoints;making use of differential subordination prove on ainequalityof realpart ,Lastly ,we also showthat the distortiontheoremof functions in A(,α)。
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  On the Three Dimeasioinal Revised Vortex Patches Prnblem of .. Incompressible Euler Equations

  Ping Zhang,QingJiu Qiu

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0045

  Abstract ( 2653 ) Download PDF ( 693 )   Knowledge map   Save

  In this paper, we will introduce the revised vorticity space C, ,.,c . In this frame, we prove that the initial value problem of incompressible Euler equations with divergence free deta (E) exists a unique local Lipschitz solution., and the solution remains propagation of regularity of the initial subznanifold and the initial vorticity,
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  On the Divisibility of the Primitive Root and Its Inverse Modulo N .

  Hui Wang(1),ZhiXing Hu(2),Li G

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0055

  Abstract ( 3290 ) Download PDF ( 799 )   Knowledge map   Save

  In this paper, we study the divisibility of the primitive roots and its inversen modulo n, and give a asymptotic formula for min(|a - a| ,|n+a_a|). a=1 a A d|a=a
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  Persistence for Nonautonomous Predator-Prey Systems with lafinite Delay

  Ke Wang

  Acta Mathematica Sinica, Chinese Series. 1997, 40(3): . https://doi.org/10.12386/A1997sxxb0061

  Abstract ( 2589 ) Download PDF ( 715 )   Knowledge map   Save

  In this paper , using new approachs, we study the persistence of no au- tonomous, nonconclutipn predator-prey systems with infinite delay. New and interest- ing results are obtained , which are a extention of the known results.