15 July 1995, Volume 38 Issue 4

    

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  On the Problem of Starlikeness of Teichmuller Spaces

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0063

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  Let Γ be a Fuchsian group acting on the unit disk Δ. The Bers embedding repre-sents the Teichmuller space T(Γ)of Γ as a bounded domain in the space of bounded quadraticdifferentials for Γ. Our main result is: There exists a universal constant d_0>0 such that, for anygiven Fuchaian group Γ,suppose that there exists a hyperbolic disk in Δ of radius whichis precisely invariant under the trivial subgroup{1} of Γ, then T(Γ)is not starlike. Particullary,when Γ is a Fuchsian group of the second kind,T(Γ)is not starlike.
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  On the Tensor Products of Operators and the Elementary Operators on C_2

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0064

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  In this paper the necessary and sufficient conditions are given for a tensor productoperator of the form to be selfadjoint,to be in the Schatten p-classwith,to be finite rank or rank-one operator, etc.In particular,as a application, thenecessary and sufficient conditions are abtained for an elementary operator restricted on C_2(H)to be selfadjoint or to be in the Schatten p-class.
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  Construction of Inertial Manifolds by the Hadamard Method

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0067

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  In this paper,the Hadamard method is used to construct inertial manifolds fordissipative dynamic system du/dt + Au + R(u)= 0 with R :D (A)→H. A called“invariantcone property”of the system is thoroughly utilized in the procedure of constructing inertialmanifolds.The spectral gap condition which is crucial to the existence of inertial manifold isthat.
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  Distribution-Free Consistency of Nearest Neighbor Kernel Est imate for the Regres-sion Fuinction

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0068

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  Based on-mixiong or α-mixing samples,we obtain strong consistency, mean andstrong of the integrated absolute error consistency for kernel regression function estimate,ran-dom window kernel estimate and nearest neighbor kernel estimate. The result is true for alldistribution μ of X,the class of applicable kernels includes those having unbounded support andeven not integrable ones.
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  Grobner Basis of Weyl-Algebra

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0066

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  In this paper,we give a definition of Grobner basis of Weyl-algebra and importantproporties of Weyl-algebra with respect to Grobner basis.
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  Decomposition on Weights of weighted Norm for Integral Operatorsand Its Application

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0065

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  Let A decomposition structure onnonnegative functions u(x)and v(x)is given to implyand this structure is both sufficient and necessarycondition for the above inequality. As anapplication, when n=1, we give some sufficient conditions on u(x)and v(x)toimplyand in the most special situation, the condition is the result given in[1].
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  Right Eqtuivalence of Map Germs with Nonisolated Singtilarities

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0072

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  In this article,the author proves firstly a sufficient and necessary condition for twomap germs to be C_J-equivalent,then,by using C-equivalence and R_I-equivalence, he provesseveral sufficient conditions for the M-determinacy of map-germs with nonisolated singularities.
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  A1gebraic Semantics for Quantifed Modal Logic (III)──The Case of Normal Modal Systems without the Barcan Formula

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0071

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  In this paper we acquaint the reader first with the algebraic semantics which is corre-sponding to the Kripke’s semantic having nested domaius. By an application of the completenesstheorem on relational semantics of the quantified normal modal systems with nested domains proved in Hughes and Cresswell’s method to prove a completeness theorem on relational algebraic semantics of those system. Next for normal systems with semantics which admits arbi-trarily variable domains we use Henkin’s method to prove a completeness theorem on relationalsemantics of them which is concerning with Kripke’s special semantic; then through the con-version of relational semantics to algebraic ones we obtained also the completeness theorem onalgebraic semantics of those systems.
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  UniForm Moderate Deviations for Markov Pocesses

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0070

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  In this paper,we prove that the Doeblin recurrence (i.e., Doeblin’s condition andHarris recurrence)is a necessary and sufficient condition for the uniform moderate deviations ofempirical measures of Markov chain.
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  Locally Double-Diagonally Dominant Matrix and Its Applications

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0069

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  In this paper the concept of locally double-diagonally dominant matrices is intro-duced,some properties of these matrices are discussed,are given representations of generalizedstrictly diagonally dominant matrices which are locally double- diagonally dominant matrices,new representations of M-matrices are obtained,corresponding results of[1-12] are generaliZed.
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  The Exact Upper Bounds for Index of Convergence of Doubly Stochastic Matrices

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0073

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  M. Lewin obtained the exact upper bound for the primitive exponent(index ofconvergence)for n × n primitive doubly Stochastic matrices in 1974. In this paper we estimatethe index of convergence for imprimitive and reducible doubly Stochastic matrices, thus provethat Lewin’s upper bound is satisfied by all the doubly Stochastic matrices.
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  On Waring’s Problem for Polynomials(II)

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0074

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  Suppose that f_1(x)is a polynomial of l-th degree with integral coefficients and positivefirst coefficient,and satisfy the condition that there esists no integers d,q>1 such that f_1(x)≡d(modq)identically.Let R_k(n)be the number of solutions of the equation in positive integers x_i Our main result is: For and sufficiently large n wehave R_k(n)>>, which is a generalization for polynomials of a result of Vaughan in Waring’sproblem。
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  Semidirect Product and Wreath Product of Weak Cliffordian Quasi-Regular Semi-groups

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0060

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  This paper gives necessary and sufficient conditions for the semidirect product andthe wreath product of monoids S and T to be weak Cliffordian quasi-regular monoids and thestructure of semidirect product.Furthermore,this paper discusses the relation between theminimum group congruences of the weak Cliffordian quasi-regular monoid and the semidirectproduct.
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  Two Notes about Fourier Coefficients of Modular Forms with Half-Integral Weights

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0058

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  For, H.Iwaniec￣[2]proved that a_n《n￣(k/2-2/7+ε)forany square-free positive integer n.In this paper we shall generalize this result.
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  (C_0,1)-Development Systems of Continuous Linear-operators on Strongly Dual Spacesof Multi-Hilbert Space

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0059

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  It is proved that the development system generated by a family of(C_0,1)-semigroupsis г-stable if the family of gnerators of these(C_0,1)-semigroups is also г-stable, where these(C_0 ,1)-semigroups are defined on a fixed strongly dual space of some multi-Hilbert space. Usingthis result we also get a perturbation theorem of the(C_0,1)-development system.
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  A Compact System(X,j)with A(f)≠M(f)

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0061

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  In this paper, we prove that there is a compact system whose closure of the set ofalmost periodic points is contained genuinely in whose measure centre. Thereby,We concludethat a weakly almost periodic point not only could be not an almost periodic point but alsonot a limit point of almost periodic points and what the set of almost periodic points coincideswith the set of periodic points is only a necessary but not sufficient condition for that a compactsystem has no non-atomic ergodic measure.
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  The Generalization of Moran Fractals and Their Multifractal Decompositfons

  Acta Mathematica Sinica, Chinese Series. 1995, 38(4): . https://doi.org/10.12386/A1995sxxb0062

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  In this paper, the generalization of Moran fractals is given and their multifractaldecompositions are studied.