15 June 2000, Volume 43 Issue 6

    

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  Algebraic Independence of Certain Numbers

  Rao Chen ZHU(1),Yong Gao CHEN(

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 961-964. https://doi.org/10.12386/A2000sxxb0124

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  In this note the algebraic independence of values of the general Mahler series with different parameters at algebraic points is established.
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  Sufficient and Necessary Conditions for Stochastic Comparability of Jump Processes

  Yu Hui ZHANG

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 965-968. https://doi.org/10.12386/A2000sxxb0125

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  This note is devoted to study the stochastic comparability of jump processes. Based on [2] and [3], it is proved that two jump processes are stochastically comparable if and only if their q-pairs are comparable. Meanwhile, the result on the uniqueness given in [6] is also improved.
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  Oseen Coupling Method for the Exterior Flow, I: Oseen Coupling Approximation

  Yin Nian HE,Kai Tai LI

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 969-974. https://doi.org/10.12386/A2000sxxb0126

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  In this paper, we consider the bidimensional exterior unsteady Navier-Stokes equations with the nonhomogeneous boundary conditions and represent an Oseen coupling problem which approximates the Navier-Stokes problem, obtained by coupling the Navier-Stokes equations in the inner region and the Oseen equations in the outer region. Moreover, we prove the existence, uniqueness and the approximate accuracy of the weak solution of the Oseen coupling equations.
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  On the 2k-th Power Mean of the Inversion of Dirichlet L-Functions with the Weight of General Kloostermann Sums

  Yuan YI,Wen Peng ZHANG

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 975-982. https://doi.org/10.12386/A2000sxxb0127

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  The main purpose of this paper is using estimation of the classical Kloostermann sum and the analytic method to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of general Kloostermann sums, and give a sharp asymptotic formula.
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  The Regular Embedded Ends and the Maximum Principle at Infinity

  Zu Huan YU

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 983-996. https://doi.org/10.12386/A2000sxxb0128

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  In this paper,we deal with the CMC-1 surfaces in the hyperbolic 3-space, and give a classification of regular embedded ends of the CMC-1 surfaces, it is called the first Catenoid type end, the second Catenoid type end and the horosphere type end. Moreover, we also discuss the local maximum principle, and establish a maximum principle at infinity.
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  Norm Estimates for Derivations

  Jian Hua ZHANG(1),Zong Ben XU(

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 997-100. https://doi.org/10.12386/A2000sxxb0129

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  In this paper, norm estimates for derivations on nest subalgebras of any factor von Neumann algebra are given. As an application, a distance formulae is obtained. Moreover, it is proved that every nest subalgebra of any factor von Neumann algebra has AIP (r, s) property.
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  Multivalued Order Supermartingale

  Rong Ming WANG

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1001-101. https://doi.org/10.12386/A2000sxxb0130

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  In this paper multivalued order supermartingales with continuous time are studied. First, we show that multivalued order supermartingales have (K-M) Riesz decomposition under some conditions. Then we prove Doob-stopping theorem of setvalued order supermartingales
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  Optimal Recovery of Anisotropic Besov Classes

  Yan Jie JIANG

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1011-101. https://doi.org/10.12386/A2000sxxb0131

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  This paper concerns the problem of optimal recovery of some anisotropic Besov classes SB(Rd) in Lp(Rd) (1 < p < ∞)and in Lq(Rd) (1 < p≤q ≤2). The weak asymptotic behavior is established for the corresponding quantities.
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  Comparison of Some Convergence Rates for Markov Process

  Yong Hua MAO,Shao Yi ZHANG

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1019-102. https://doi.org/10.12386/A2000sxxb0132

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  This paper studies the relations among some convergence rates-spectral gap, various logarithmic Sobolev constants and exponential convergence rate under B-S entropy for Markov process, and then points out their essential difference through some examples.
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  The Blow-up Rate for a System of Heat Equations with Neumann Boundary Conditions

  Zhi Gui LIN(1),Chun Hong XIE(2

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1027-103. https://doi.org/10.12386/A2000sxxb0133

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  This paper deals with the blow-up properties of solutions to a system of heat equations ut = △u,vt =△v in BR ×(0,T) with the Neumann boundary conditions u/ = ev, v/η= eu on SR ×[0, T). The exact blow-up rates are established. It is also proved that the blow-up will occur only at the boundary.
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  A Class of Positive Coefficient Ordinary Differential Operators with Middle Deficiency Indexes

  Zhan Kuan GUO,Jiong SUN

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1031-104. https://doi.org/10.12386/A2000sxxb0134

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  In the paper, we considered a class of ordinary differential expressions as following:=0(-1)kDkeanxDk and =0(-1)kakDkenxDk, proved that their indexes are {n, n + 2,..., 2n- l} or {n, n + 2,..., 2n-2} or a subset of them, and gave some examples of positive coefficient ordinary differential operators with middle deficiency indexes. These examples show that positive coefficient ordinary differential operators needn't to be all limit-point, this is, we give a negative answer to Everitt's conjecture in another way.
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  Hsu-Robbins Type Theorems for Pairwise Products Sums of I.I.D. Random Variables (Ⅱ)

  Chun SU(1),Han Ying LIANG(2),Y

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1041-105. https://doi.org/10.12386/A2000sxxb0135

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  In this part, we replace 1/n quantile an by value bn, which is determined by Levy function (4.1), such that the condition A of Theorem 1 in (I)[1] is eliminated. The necessary and sufficient conditions that can been real called to be Hsu-Robbins type theorem are obtained. As corollary we get the Kolmogorov strong laws of large number for products of corresponding rowwise sums of triangular array of copy lid random variables.
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  The Linearization with Generalized Exponential Dichotomy

  Liang Ping JIANG

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1053-106. https://doi.org/10.12386/A2000sxxb0136

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  In this paper, we extend Hartman's linearization theorem and Palmer's linearization theorem to the system with generalized exponential dichotomy an.d prove that the equivalent function is strongly uniformly continuous. We also give some examples to show the application of the new results in the stability theory.
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  The Chover Law of the Iterated Logarithm for Random Geometric Series of Stable Distribution

  Ping Yan CHEN(1),Li Hu HUANG(2

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1063-107. https://doi.org/10.12386/A2000sxxb0137

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  Let {Xn, n≥0} be mutually indepenent random variables, identically distributed acording to the symmetric stable distribution with exponent α(0 <α < 2). With probability one we have lim supsβ- l(1 -βα)1/α∑∞n=0, exp (1/α).
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  Lwner Partial Order and Singular Values for Compound Matrices of Generalized Schur Complements of a Matrix

  Jian Zhou LIU,Qing Ming XIE

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1071-107. https://doi.org/10.12386/A2000sxxb0138

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  In this paper, combining generalized Schur complements of matrices with compound matrix, we consider the Lowner partial order for compound matrices of the product of generalized Schur complement and its conjugate transpose of an m ×n matrix. We also give an inequality concering singular values of such a compound matrix which generizes some recent results.
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  The Solvability of Cauchy Problem of Non-Newtonian Polytropic Filtration

  Zhong Hai XU

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1077-108. https://doi.org/10.12386/A2000sxxb0139

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  In this paper, we discuss the solvability of Cauchy problem of non-newtonian polytropic filtration when m(p - 1) < 1.
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  On Riesz Basis of Euler-Bernoulli Beam System by Boundary Feedback Controls

  Yao Ting WANG,Guang WANG,Sheng

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1089-109. https://doi.org/10.12386/A2000sxxb0140

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  Using the method of basis perturbation, we show that the generalized eigenfunctions of a flexible Euler-Bernoulli beam system with boundary feedback consisting of velocity and angular velocity form a Riesz basis for the state space H, and give the computational fomula of optimal exponential decay rate of the system.
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  On the Algorithm and Ranks of Embedding Finitely Generated Modules Over a QF-Ring in Free Modules

  Shi Zhong PAN

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1099-110. https://doi.org/10.12386/A2000sxxb0141

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  In the paper it is given an inductive algorithm of the smallest embedding of finitely generated modules over a QF-ring in free modules. And it is also discussed the bound of the ranks of relative free modules.
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  Retakh's Condition (M) and Sequential Retractivity of (LM)-Spaces

  Jing Hui QIU

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1105-111. https://doi.org/10.12386/A2000sxxb0142

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  In this paper, we investigate the connection between Retakh's condition (M) and sequential retractivity of (LM)-spaces (Here, (LM)-spaces denote countable inductive limits of metrizable locally convex spaces). We give a number of characteristic conditions for (LM)-spaces with Retakh's condition (M) to be sequentially retractive.
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  S-Compact Spaces and S-Compact Iocales

  Wei HE

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1111-111. https://doi.org/10.12386/A2000sxxb0143

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  In this paper, we give an internal characterization of S-compactness of locales, as a corollary, an internal characterization of S-compact spaces is obtained.
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  Connecting Orbits of Gradient-Like Systems in R~(n)

  Chang Ming DING

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1115-111. https://doi.org/10.12386/A2000sxxb0144

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  This paper is concerned with the orbits connecting isolated critical points of gradient-like systems in Rn. A criterion to judge the existence of connecting orbits is given, and furthermore, if the two isolated critical points are attractor and repeller respectively, the set composed of connecting orbits is an open and unbounded set.
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  A Class of Lie Algebras with a Symmetric Invariant Non-Degenerate Bilinear Form

  Lin Sheng ZHU(1),Dao Ji MENG(2

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1119-112. https://doi.org/10.12386/A2000sxxb0145

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  In this paper, we give the characteristic properties, structure and realization of a class of Lie algebras with a symmetric, invariant, non-degenerate bilinear Form.
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  Practical Stability of Compensated Lévy Flow

  Bo ZHANG

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1127-113. https://doi.org/10.12386/A2000sxxb0146

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  The objective of this paper is to discuss the practical stability of Compensated Lévy flow. Some random differential inequalities are generalized and by using of Lyapunov function and comprarison theorem, some criteria of practical stability of compensated Levy flow are obtained.
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  A Note on a Semilinear Elliptic Problem at Resonance

  Jia Bao SU(1),Yong Qing LI(2)

  Acta Mathematica Sinica, Chinese Series. 2000, 43(6): 1135-114. https://doi.org/10.12386/A2000sxxb0147

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  In this paper, we study the existence of nontrivial solutions of a semilinear elliptic equation with bounded nonlinear term when the problem is resonant at both infinity and the zero. The methods used here are the well-known Morse theory and a penalization technique.