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Table of Content

    30 June 2005, Volume 20 Issue 2
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    On the Cauchy Problem for a Class of Nonlinear Wave Equations with Damping Term
    SONG Chang-ming, KONG De-xing
    2005, 20(2):  111-120. 
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    The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the above-mentioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.

    On the Decay Number of a Graph
    LI De-ming
    2005, 20(2):  121-127. 
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    The decay number of a connected graph is defined to be the minimum number of the components of the cotree of the graph. Upper bounds of the decay numbers of graphs are obtained according to their edge connectivities. All the bounds in this paper are tight. Moreover, for each integer k between one and the upper bound, there are infinitely many graphs with the decay number k.

    Another Simple and Elementary Proof of the Classical Isoperimetric Inequality
    PAN Sheng-liang, YANG Juan-na
    2005, 20(2):  128-130. 
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    In this short note we will give another simple and elementary proof of the classical isoperimetric inequality in the Euclidean plane.

    On Semiring Semigroups
    LI Shi-zheng, CHENG Tao
    2005, 20(2):  131-136. 
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    This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.

    The Non-countable Summation Type Hahn-Schur Theorems
    LÜ Tong-fu , HUJian-hua, CHOMin-hyung
    2005, 20(2):  137-140. 
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    The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.

    A Decomposition Theorem on Herz Spaces over Locally Compact Vilenkin Groups
    LAN Sen-hua, LI Rui
    2005, 20(2):  141-146. 
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    In this paper, by applying a vector-valued inequality we obtained a decomposition theorem on Herz spaces over locally compact Vilenkin groups with new range 0 < q≤1.

    Inequalities in Connection with Post-Widder Operators
    SONG Zhan-jie
    2005, 20(2):  147-150. 
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    The purpose of this paper is to derive the inequalities in connection with Post-Widder operators, the result is corresponding to Wickeren in connection with Bernstein polynomials.

    Harmonic Bergman Metric
    ZHAO Zhen-gang
    2005, 20(2):  151-157. 
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    We have constructed the positive definite metric matrixes for the bounded domains of Rn and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of Rn and the metric matrix of the same bounded domain.

    The Estimation of the Number of Zeros of the Abelian Integrals for a Class of Hamiltonian Systems
    SONG Yan
    2005, 20(2):  158-162. 
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    In this paper,we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n.The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.

    On σ-images of Metric Spaces
    2005, 20(2):  163-166. 
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    In this paper the relation between the σ-images of metrical spaces and spaces with σ-locally finite cs-network, or spaces with σ-locally finite cs*-network, or spaces with σ-locally finite sequence neighborhood network, or spaces with σ-locally finite sequence open network are established by use of σ-mapping.

    Avoidance of Blow-up by Moving Medium
    YAO Li, LIU Yun-xian, YANG Peng-fei
    2005, 20(2):  167-177. 
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    This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions. 
    Hyperreflexivity of Operator Algebras of the Banach Space
    YUAN Guo-chang, QIN Li-ming
    2005, 20(2):  178-184. 
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    In this paper, we introduced the hyperreflexivity of operator algebra A on’Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.

    Asymptotic of the Solutions to the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors
    WANG Wen-bin, LIU Shu-mei
    2005, 20(2):  185-191. 
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    In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.

    Category of Generalized Intuitionistic Fuzzy Sets
    YANG Wan-cai, LI Xiao-shen
    2005, 20(2):  192-199. 
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    In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.

    The First Eigenvalue of a Compact Manifold
    ZHAO Di, YANG Jian-an
    2005, 20(2):  200-205. 
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    This paper discusses the first eigenvalue on a compact Riemann manifold with the negative lower bound Ricci curvature. Let M be a compact Riemann manifold with the Ricci curvature≥-R, R=const.≥0 and d is the diameter of M. Our main result is that the first eigenvalue λ1 of M satisfies λ1≥π2/d2-0.518.R.
    Deduction Theorem and Hypothetical Syllogism Rule on Fuzzy Logic System
    YANG Xiao-bin, DENG Shu-xian
    2005, 20(2):  206-213. 
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    Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-Rand LG, respectively. In LG-R we proved that neither the deduction theorem nor the hypothetical syllogism (HS) rule held but a deduction theorem and an HS rule are obtained in a weak sense. We also proved that both the deduction theorem and the hypothetical syllogism(HS) rule hold in LG.

    Complete Kaehler Submanifolds in CPn
    SONG Xiao-xin, HU Cong-e
    2005, 20(2):  214-220. 
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    In this paper we mainly investigate projectively flat complete Kaehler sub-manifolds, in CPn. We give the pinching constants and the local structure.
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