15 March 1999, Volume 42 Issue 3

    

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  The Inverse Abel Transforms of some Bounded Symmetric Domains of Type D Ill

  Fu Liu ZHU

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0071

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  By using three shift operators Di (1 i 3) of the bc2 root system, wegive in the present paper the explicit expressions of elementary shperical functions andof the inverse Abel transforms for the bounded symmetric domains SO*(8)/U(4) andso* (1o)l/u(5).
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  The Existence and Uniqueness of Almost Periodic Solutions forNonlinear Differential Equations with Time Lag

  Quan Yi WANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0069

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  This paper deals with the problems on the existence and uniqueness ofbounded solntions and almost periodic sofutions for a class of nonlinear differentialequations with time lag. Using the change of variable and fixed point method andmethod of approximation, we obtain some interesting and new results on the existenceand uniqueness of bounded solutions and almost periodic solutions of these equations.Our results improve and extend greatly the main results of [2].
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  Several Theorems of Random Semiclosed 1-Set-Contractive Operator

  Chuan Xi ZHU

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0070

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  in this paper, we generalize Rothe's theorem, Petryshyn's theorem and Alt-man's theorem. Meanwhile, we obtain some new results.
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  Tke Weak Compactness of the Sets of L1 ( Ω,F,μ) and Applications

  Xin Jian YANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0072

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  Let ( Ω,F,μ) be any complete measurable space, may be infinite measure.In this paper, a sufficient and necessary condition about the weak compactness of thesets of L1 ( Ω,F,μ) is obtained. Furtherimore, when be infinite measure, we considerthe sets by sets convergence for finite generalized measures defined on the measurablespace ( Ω,F) which are absolutely continuous with and obtained some interestingresults which generalize the Vitali-Hahn-Saks theorem.
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  On Reciprocal Sums of a Class of Additive Functions

  Wen Guang ZHAI

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0073

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  Suppose g(n) > 0 is any real-valued function, the additive function G(n) isdefined by G(1) = 0, G(n) = is a fixed integer constant.The sum is studied and an asymptotic formula is obtained.
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  The Existence and Uniqueness of the Solution ofNonlinear Singular Diffusivity Equation

  Jia Qing PAN

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0074

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  This paper is concerned with the Cauchy problem with singular diffusivity,the existence and uniqueness of the solution are discussed, the main results is thatthere exists only one classical solution.
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  Existence Theorems of Maximal Elements in NoncompactH-Spaces with Applications

  Zi Fei Shen

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0075

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  in this paper, we establish some new existence theorems for maximal elementin a kind of noncompact H-spaces. As applications, we study existence of solutions forvariational inequalities and Ky Fan's minimax inequality and obtain some new results.
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  On Core Compactness of Scott Open Fliter Topology

  Lin XIE

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0076

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  This note is devoted to the discussion of the following problem: characterizethose DCPO's (i.e. directed complete poset), for which the open-set lattices withrespect to the Scott open filter topology are continuous. The problem is also one ofthose open problems which were posed by Lawson J.D. and Mislove M.
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  A Note on Cosine Operator Functions

  Jing Qi YAO

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0077

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  Suppose A is a closed linear operator in Banach space X, A isinjective for all In this paper, Banach space () is defined, Z X, andnorm on Z majorizing the norm on X. We show that, Az i the part of operator Ain Z, generates a cosine operator function in space Z, and space Z is maximal-uniquein a suitable sense.
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  The -limit Sets of a Flow

  Wen Cheng CHEN

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0058

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  Some properties of the -limit sets of a flow on a locally compact metricspace are investigated. Some results of Conley C. in [1] are generalized.
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  On the Braided Monoidal Categories of Twisted Smash Products andthe Twisted Smash Products over Braided Monoidal Categories

  Shuan Hong WANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0059

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  A necessary and sufficient condition for the twisted Smash product modulecategories A H to be a braided monoidal category is given; Furthermore, a classof category which is equivalent to category A HM is studied. A generalized yetter-Drinfeld category HMC is introduced. Finally, a necessary and sufficient condition forthe twisted Smash product over the braided monoidal categories to be Hopf algebra isfound.
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  On the Rate of Growth of Meromoaphic Solutions ofHigher Order Linear Differential Equations

  Zong Xuan CHEN

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0060

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  In this paper, we investigate the properties of growth of meromorphic solu-tions of two type of higher order linear homogeneous differential equations with mero-inorphic coefficients, we obtain precise estimate of the rate of growth of meromorphicsolutions of the equations when there is some coefficient that is main dominating tothe properties of the solutions of the equations.
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  The Existence on Periodic Solutions and Almost PeriodicSolutions of Forced Lienard-type Equations

  Jin ZHOU

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0061

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  Using the exponential dichotomy theory, we give the sufficient conditions ofthe existence on periodic solutions and almost periodic solutions for forced Lie'nard-type equation These conditions are the naturalextension and generalization of the results already obtained by Fink A.M., Lin Faxingin 11, 2] associated with the same problems for Lie'nard equations.
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  Closeness of Product and Coprodnct Operation in Several Kinds ofthe Category of Lattice-valued Topofogical Spaces

  Jian Gang TANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0062

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  This paper introduces four kinds of the category of lattice-valued topologicalspaces, and discusses the product and the coproduct operation among it respectively,and the problems of its relevant structureness, uniqueness and existenceness. Throughdiscussion, this paper gives more satisfactory product space of lattice-valued topologicalspaces, points out that commonly-used the product space of lattice-valued topologicalspaces at present has definite limitation, and morphism of the category is Zadeh's typemapping, these type of mapping keeps the height of fuzzy point unchangeable, andimplys metric unchangeable.
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  Fixed Point Theorems for Stable Banach Space

  Chang Song HU

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0063

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  The aim of this paper is to give that stable Banach space X which has anunconditional basis which is unconditionally monotone has f.p.p.
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  Bond Percolation on Lattice Sierapinski Carpet and lts Critical Phenomena

  Jian Sheng LV

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0064

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  This paper will discuss a bond percolation and its critical phenomena on onekind of lattices without translation invariability-lattice fractals.
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  ^Some Properties of *-module

  Lin XIN

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0065

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  The main aim of this paper is to give some necessary and sufficient conditionsthat RP is a *-module and to show that if f : R S is a ring homomorphism and Rpis P-projective, if RP is a *-module, a Tilting module, a quasi-Tilting module then sois S R P, respectively
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  A New Limit Theorem of Bartle Integration

  Huan Guang ZHAO

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0066

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  in this paper, we gave a new limit theorem for Bartle integration, and solvedmain problem in limit theory of Bartle integration.
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  Compact Ragular Reflections of Locales

  Wei HE

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0067

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  The problem of how to give an explicit description of the compast regularreflections of focales is raised by Banaschewski B. and Mulvey C. J. in 1980, but it hasnot been made any progress for the past years. In this paper, we give a constructivedescription of the compact regular reflection of a locale by introducing a two-elementsrelation on locales.
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  Oscillation Criteria of Partial Difference Eqnations with Continuons Variables

  Bing Gen ZHANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0068

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  In this paper we consider the partial difference equation with continuousvariables of the form A(z + a, g) + A(x, y + a) - A(x, g) + P(x, y)A(x - r, y - ) = 0,where P C(R+ x R+, R+\{0}), a, r, are positive. Some sufficient conditions for allsolutions of this eqnation to be osciliatory are obtained.
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  On the Main Conjecture of Geometric MDS Codes Arising from Plane Curves

  Hao CHEN,Li Qing XU

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0054

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  By the using of a classical theorem of Lang S. and Weil A., we prove thatfor the geometric MDS codes from plane curves, the main conjecture is true when thedimensions of codes are restricted in certain range and the ground field is sufficientlylarge.
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  The Mean Convergence Properties of Extended Hermite-Fejer Interpolation Operators

  Cheng Lin WEN,Shu Ling ZHANG(2

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0053

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  Weighted L mean convergence of Extended Hermite-Fejer operators basedon the zeros of orthogonal polynomials with respect to the Jacobi weight is investigated.First, we obtain the conditions of convergence, further we get the order of convergence.
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  Denseness of Superposition of One Function with Its Translationand Dilation in Soboley Space W2m(Rn)

  Chuan Hai JIANG(1),Tian Ping C

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0055

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  In this paper, we investigate denseness of superposition of one functionwith its translation and dilation in Sobolev space W2m(Rn), and give a necessary andsufficient condition for denseness. Furthermore, we obtain a strong aproximate resultto the functions in any compact set of W2m(Rn).
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  The Gamma Functions on Nonselfdnal Cones of the Third Type

  Wei Ping YIN,Ping LIN,Bing Xin

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0056

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  In this paper, we generalize the Gamma function and Siegel integral tononselfdual cones of third type. As the applications, the Cauchy-Szego kernels andformal Poisson kernels on the tube domains (or Siegel domains of the first type) oversuch nonselfdual cones are given in the explicit forms.
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  Qualitative Stndies on Nonlinear Lipschitz Operators ( )-the glb-Lipschitz Constant

  Li Sheng WANG,Zong Ben XU,Bai

  Acta Mathematica Sinica, Chinese Series. 1999, 42(3): . https://doi.org/10.12386/A1999sxxb0057

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  in this paper, the glb-Lipschitz constant l(T) of nonlinear Lipschitz oper-ator T is introduced. It is shown that the constant l(T) qualitatively characterizesthe biggest perturbation radius at which the nonlinear invertible operator T maintainsits invertibility in the semi-norm operator space composed of all Lipschitzian contin-uous operators. The obtained results are used to establish a “Nonlinear PerturbationLemma”, to define nonlinear condition number and to extend linear operator approx-imation theory. We apply also the obtained results to construct an inclusion regionof spectrum of nonlinear Lipschitz operator which is a generalization of the famousGerschgorin theorem.