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2005年 第20卷 第2期    刊出日期：2005-06-30

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关于一类具阻尼项的非线性波方程的 Cauchy问题

宋长明, 孔德兴

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.



图的分散数

李德明

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.



经典等周不等式的又一简单初等的证明

潘生亮, 杨娟娜

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.



关于半环半群

李师正, 程涛

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.



不可数求和型Hahn-Schur定理

吕同富, 胡建华, 赵玫亨

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.



局部紧Vilenkin群上Herz空间的一个分解定理

蓝森华, 李锐

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.



关于Post-Widder算子的不等式

宋占杰

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.



调和Bergman度量

赵振刚

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.



一类Hamiltonian系统的Abel积分的零点个数估计

宋燕

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.



关于度量空间的σ-映象

梁洪亮, 杨巍纳

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.



通过移动媒质避免爆破

姚俐, 刘蕴贤, 杨鹏飞

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. 


Banach空间上算子代数的超自反性

袁国常, 覃黎明

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.



半导体中扩散方程初始边界问题的解的渐近性

王文彬, 刘淑梅

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.



广义直觉模糊集的范畴

杨万才, 李小申

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.





紧流形上的第一特征值

赵迪, 杨建安

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.



模糊逻辑系统中的演绎定理和HS规则

杨晓斌, 邓书显

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.



复射影空间的完备Kaehler子流形

宋晓新, 胡聪娥

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.