15 February 1999, Volume 42 Issue 2

    

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  Congruence Extensions on Orthodox Semigroups (2)

  Xilin TANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0036

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  It is very importent in algebraic semigroup theory to characterize congruencesand congruence extensions on semigroups (see [1-5]). In this paper, we describe theclass of orthogroups by virtue of ways in [6] that investigating the normality and thevariance for the congruences oil bands and congruence extension (Theorem 2.6), andobtain the sufficient and necessary conditions for the class of orthodox semigroups thatall congruences on whose idempotent bands extend to these orthodox semigroups.
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  Periodic Solutions To a Class of Neutral Higher Dimensional Periodic Differential System

  Ming Ke HE

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0037

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  In this paper, we cosider the neutral higher dimensional periodic system:Where (t, x) ∈ R ×Rn, the n×n matrix A(t, x) is continuous, xt ∈C([-r, 0], Rn),xt(9) = x(t + θ), 0 E [-r, 0], denote C = C([-r, 0], Rn), f. R ×C→ Rn is continuous,furthermore A(t + T, x) = A(t, x)∈(t,x) E R ×Rn, f(t + T, ) = f(t,),(t，) ER × C, T, r ＞ 0, c ∈R. Using fixed point method, we get some sufficient conditionsto guarantee the existence and uniqueness of T-periodic solutions for the system. Thecorresponding results in [1-3] are extended and improved.
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  Some Large Sample Results for a Class of Functionals of Kaplan-Meter Estimator

  Qi Hua WANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0038

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  In this paper, a class of functionals of Kaplan-Meter estimator are investigated. Counting process martingale methods are used to show the asymptotic normality, and establish a mean square error inequality and a probability inequality ofthem without the assumption that F, G are continuous, where F, G are survival timedistribution and censoring time distribution respectively.
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  Conformal Deformations for Prescribing Scalar Curvature on Riemanaian Manifolds with Negative Curvature

  Ze Jun HU

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0035

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  We study the conformal deformation for prescribing scalar curvature function S on Cartan-Hadamard manifold Mm (n 3) with strongly negative curvature.By employing the super-subsolution method and a careful construction for the supersolution, we obtain the best possible asymptotic behavior for S near infinity so thatthe problem of complete conformal deformal is solvable. In the more general cases,we prove an asymptotic estimation oil the solutions of the conformal scalar curvatureequation.
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  Distribution of Borel Rabid of Meromorphic Functions in the Unit Disc

  Qing De ZHANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0030

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  For any nonempty closed set E in the unit circle, any positive number A andany real number μ (0 ≤μ≤λ), we construct a meromorphic function f(z) of orderA in the unit disc, which takes the set {L(θ)|θ∈E} as its Borel radii set and the set{L(θ)|θ| E} as its non-Julia radii set. And the order of its counting function N(r, f)Is μ.
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  On the Uniqueness of the Limit Cycle of the Quadratic System with a 2nd-Order Weak Focus

  Ping Guang ZHANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0031

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  In this paper,we prove that the plane quadratic system has at most one limitcycle surrounding a 2nd-order weak focus, and that if the product of the second andthird focus value of the weak focus is positive definite, then the system has no limitcycle surrounding the 2nd-order weak focus.
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  The Weighted Kernel Estimators of Nonparametric Regression Function with Censored Data

  Shan Chao YANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0033

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  We discuss the consistency of the weighted kernel estimators of nonparametric regression function with censored data.Some more weakly sufficient conditions forstrong consistency are given. These results greatly improve the current ones.
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  Global Stability for Uniformly Stable Cooperative Systems

  Cai Feng TU

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0032

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  In this paper, the convergence of solutions of cooperative systems is studied.The basic assumption is that the Jacobian matrices are uniformly stable in Withthis assumption, we provide the complete classification on the global behavior of suchsystems. The main results are the following. If the system has a positive steadystate then it is globally asymptotically stable in Int A sufficient and necessarycondition for a nonnegative steady state of the system to be globally asymptoticallystable is presented.
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  On Structure of Ordered Fields Satisfying the Infinite-dimensional Real Nullstellensatz Ⅱ

  Guang Xing Zeng

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0034

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  In the second part of this paper, we investigate the structure of ordered fieldssatisfying the infinite-dimensional real Nullstellensatz. By embedding these fields intothe associated fields of power series, we prove that an ordered field satisfies the infinitedimensional real Nullstellensatz if and only if its real closure is isomorphic to somesubfield of , which has the infinite-dimensional approximation property, where is a divisible ordered group without gap, and is the field of power series withcoefficients in the field of real numbers and exponents in .
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  The Schwarzian Derivative in Several Complex Variables (Ⅴ)

  Sheng GONG(1),Xue An ZHENG(2),

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0052

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  From point view of Thurston we define and discuss the Schwarzian derivativeand Schwarzian derivative of high order of holomorphic mappings on domains of thematrix space Cm×n (m n) by using the approximation of second order. We provethat if the Schwarzian derivatives exist,then they are the invariant up to similarityunder the group of holomorphic auomophism of the compact dual space of RI(m,n)Also we prove that the Schwarzian in this paper is same as the Schwarzian in [1-4]Schwarzian of holomorphic mappings on domains of Cn
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  Fixed Point Theorems of Some Decreasing Operators and Applications

  Fu Yi LI(1),Jin Feng FENG(2),P

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0048

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  In this paper, the decreasing operator with convexity or concavity is studied,and existence, uniqueness and iteration of the fixed point on decreasing operator areobtained. Finaly, some applications to various equations are also done.
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  Existence and Nonexistence of Global Solutions for a Class of Semilinear Heat Equations

  Ya Cheng LIU,Hai Ou YANG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0049

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  This paper studes the existence and nonexistence of nonnegative global LPsolutions for the initial value problem of semilinear heat equations ut -△u = uγ + cu,(γ＞ l), u(x, 0) = (x). First proves that if c ＞0 then there are no nonnegative globalsolutions. Next for the case c＜0 gives the sufficient conditions of global existence andnonexistence of solutions, in particular proves that if or ,then when is sufficiently small there exist nonnegative global LP solutions. Finallyobtains ifinit threshold results for the coefficient c and the initial data (x).
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  Idempotent Completions of Operator Partial Matrices

  Jin Chuan HOU(1),Heydar RADJAV

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0050

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  Necessary and sufficient conditions are obtained for operator partial 2 × 2matrices to have an idempotent completion and all such completions are parametricallyrepresented.
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  A Sufficient Condition for a Smash Product as a Transfinite Left Free Normaling Extension and Its Applications

  Fang LI(1),Zhong Kui LIU(2)

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0051

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  In this paper, a sufficient condition is given under which the smash productA#H is a transfinite left free normalizing extension of the algebra A. Moreover, theresult is applied to a skew semigroup ring, a skew group ring and the quantum groupUq(sl(2)) such that some properties are shown.
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  The Commutators of Convolution Operators

  Guo En HU(1),Shan Zhen LU(2),B

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0043

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  By reducing the problem to a local one and using the Fourier transformestimates, we establish the LP boundedness results for some operators related to thecommutators of a class of convolution operators. We also give some applications of ourresults.
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  Generalized Inverses of Morphisms with Universal-Factorzation

  Sheng Yuan JIANG(1),Xiao Ji LI

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0044

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  In this paper we research generalized inverse of product f = pgq in categories.Suppose these exist morphism p' and q' such p'pg = g = gqq', we characterize theexistance of the Moors-Penrose inverse f+ and the Drazin inverse fD in terms of g+and g# respactively, and establish the expression of f+ and fD.
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  D-determination of Bifurcation Problems with Respect to C~0 ContactEquivalence from the Weighted Point of View

  Jian Cheng ZOU,Fu Wei SUN,Rui

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0045

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  In this paper, singularity theory is used to study the topological propertiesof bifurcation problems under a kind of singular Riemannian metric. A criterion isgiven to judge the d-determination of bifurcation problems with respect to Co contactequivalence. Some results in [1-3] are generalized.
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  The Besov and Triebel-Lizorkin Spaces on Lipschitz Surfaces

  Li Xin YAN,Dong Gao DENG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0046

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  Besov spaces and Triebel-Lizorkin spaces on Lipschitz surfaces are introducedby using Clifford analysis. Characterization of these spaces is given also.
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  On Stability of a Class of Singular Integral and Cauchy Type Integral with Respect to Path of Integration

  Xiao Lin WANG,Ya Fang GONG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0047

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  Given f(, t) being Holder continuous with respect to T, t in a region E C.For the Cauchy principal integral operator where C E is a close or open smooth curve, We discuss the stability of I(f) when the smoothperturbation of r occurs, and give the corresponding error estimates. Furthermore,when is a close contour and W E H(E), the stability and error estimate of Cauchytype integral . are also given.
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  An Embedding Theorem for Space of Distributions on Locally Convex Space

  Fu Zhou GONG,Zhao DONG

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0039

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  Let Y be a locally convex vector space with a Gaussian Radon measureγ denote by A(Y) and (y), two spaces of test functions on Y, and denote byμ(Y) and με(y), two spaces of distributions on Y. We prove that A(Y) (or(the symbol "*" means the complex conjugate operation). Using this embedding theorem we give a direct formula forFourier transform of h∈L2(Y, γ) as a distributions on Y. Moreover, by this embeddingtheorem we prove that infinite dimensional pseudodifferential operator A on A(Y) (orε(Y)) is continuous ω.r.t the norm of L2(Y, γ) if and only if for the adjoint operatorA' of A, we have A'(L'(Y, γ)) L2(Y, γ).
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  Quantales and Process Semantics of Bisimulation

  Yong Ming LI(1),Zhi Hui LI(2)

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0040

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  The bisimulation quantale QB is constructed by taking certain observationsas its generators, the modules over QB are constructed by formalizing process actions astheir constitutions, general completness criteria about process semantics of bisimulationare stated. One 'tantalizing' open problem about the quantale semantics of bisimulationposed by Abramsky S. and Vickers S. is answered, the uniform algebraic frameworkfor the studying of various notations of observing,testing process and the epuivalencethey induced is completed.
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  Approximation of Multivarite Periodic Function and Degree of Approximation

  Chuan Hai JIANG(1),He Bing WU(

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0041

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  In this paper, we consider a kind of approximation of multivariate periodicfunction and obtain a necessary and sufficient condition for denseness. We also givestructive approximate functions and exactly estimation of approximate order.
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  The Compact-covering s-mappings on Metric Spaces

  Peng Fei YAN(1),Shou LIN(2)

  Acta Mathematica Sinica, Chinese Series. 1999, 42(2): . https://doi.org/10.12386/A1999sxxb0042

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  In this paper, the authors introduce the concept of compact-finite-partitionnetworks and give the characterization of the compact-covering s-images of metricspaces, many well-known results about s-mappings on metric spaces are direct corolcorollaries by the characterization, and the Michael-Nagamis problem has been partially answered.