数学季刊

刘太顺, 冯淑霞

2004, 19(1): 1-5.

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In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cⁿ.

伪黎曼流形中的紧致类空子流形

孙和军, 吴报强

2004, 19(1): 6-15.

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We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds N_p^n+p. Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in N_p^n+p and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.

具有扩散系数完全矩阵和平衡律的反应扩散方程组的整体有界性

陈雪鸿, 江成顺

2004, 19(1): 16-23.

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This paper deals with an initial boundary value problem for the strongly coupled reaction-diffusion systems with a full matrix of diffusion coefficients. The global existence of solutions is proved by using the techniques based on invariant regions, Lyapunov functional methods, and local Lp prior estimates independent of time.

W_Ⅲ上的Bergman核

卢克平, 赵晓霞

2004, 19(1): 24-29.

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In this paper, we compute the Bergman kernel function on W_III.and RIII(q) denote the Cartan domain of the third class. Because domain W_IIIis neither homogeneous domain nor Reinhardt domain, we will use a new way to solve this problem. First, we give a holomorphic automorphism group, such that for any Zo, there exists an element of this group, which maps (W, Zo) into (W,O). Second, introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.

二阶时滞微分方程的振动性

尹福其, 李永昆

2004, 19(1): 30-34.

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By using some differential inequality, a second-order delay differential equation(r(t)x’(t))’+p(t)x(q(t)) = 0has been investigated and some necessary condition for this equation has a nonoscillatory solution and some sufficient condition which ensures that all of the solutions of the above equation are oscillatory are obtained.

Adamovic's不等式的推广与加细

石焕南, 李大矛

2004, 19(1): 35-40.

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In this article, by means of the theory of majorization, Adamovic’s inequality is extended to the cases of the general elementary symmetric functions and its duals, and the refined and reversed forms are also given. As applications, some new inequalities for simplex are established.

广义单瞬时生-灭过程的Kendall猜想

吴群英

2004, 19(1): 41-46.

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A new structure with the special property that instantaneous state and catastrophes is imposed to ordinary birth-death processes is considered. Kendall’s conjecture for the processes is proved to be right.

元向二元Kautz图的限制性边连通度

欧见平

2004, 19(1): 47-50.

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A restricted edge cut is an edge cut of a connected graph whose removal results in a disconnected graph without isolated vertices. The size of a minimum restricted edge cut of a graph G is called its restricted edge connectivity, and is denoted by λ(G). Let ξ(G) be the minimum edge degree of graph G. It is known that λ(G)≤ξ(G) if G contains restricted edge cuts. Graph G is called maximal restricted edge connected if the equality holds in the the preceding inequality. In this paper, undirected Kautz graph UK(2, n) is proved to be maximal restricted edge connected if n ≥ 2.

Banach函数空间上连续线性算子的正则性

蒋念生, 陈滋利

2004, 19(1): 51-56.

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In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.

直径石d的树的谱半径

谭尚旺, 郭纪明, 亓健

2004, 19(1): 57-62.

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Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1

关于Veronese生成子流形的一个猜想

宋鸿藻, 宋晓新

2004, 19(1): 63-66.

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In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L₁^m+2, it is proved that in the higher dimentional Lorentz Space L₁^m+2, the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S₁^m+1 in L₁^m+2 and is of 1-type in L₁^m+2.

关于裴波那契数和鲁卡数的平方的一些恒等式

刘瑞森, 李超, 杨存典

2004, 19(1): 67-68.

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By studying the properties of Chebyshev polynomials, some specific and meaningful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbers and Lucas numbers are obtained.

一类非单调二元算子方程及方程组的迭代解法

张斐然, 周晓中

2004, 19(1): 69-74.

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By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A₁+A₂, B=B₁+B₂, A₁ and B₁ are mixed monotone, A₂ and B₂ are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.

关于Lehmer DH数的分布性质

高丽

2004, 19(1): 75-78.

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This paper is to study the distribution property of Lehmer DH number by use the estimation of general Kloostermann sum and the estimation of trigonometric sum.

基于DNA计算的Hamilton图

张家秀

2004, 19(1): 79-83.

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DNA computing is a novel method for solving a class of intractable computational problem, in which the computing can grow exponentially with problem size. Up to now, many accomplishments have been achieved to improve its performance and increase its reliability. Hamilton Graph Problem has been solved by means of molecular biology techniques. A small graph was encoded in molecules of DNA, and the "operations" of the computation were performed with standard protocols and enzymes. This work represents further evidence for the ability of DNA computing to solve NP-complete search problems.

关于LUCAS基和一个计数函数均值的计算

李海龙, 刘华珂

2004, 19(1): 84-89.

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In this paper, we introduce a new counting function a(m) related to the Lucas number, then use conjecture and induction methods to give an exact formula Ar(N)=α(n), (r=1,2,3) and prove them.

最大度等于5的2-连通的1-树图的边面色数

董桂香, 陈东灵, 许振宇

2004, 19(1): 90-94.

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Wang Wei-fan[1] proved that the edge-face chromatic number of a 2-connected 1-tree with the maximum degree is not less than 6 is its maximum degree, and he conjectured that it is true when the maximum degree is 5. This paper proves the conjecture.

平面格子图的导出匹配数

鲁晓旭, 裴明, 要卫丽, 周菊

2004, 19(1): 95-100.

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An induced matching M in a graph G is a matching such that V(M) induces a 1-regular subgraph of G. The induced matching number of a graph G, denoted by I M(G), is the maximum number r such that G has an induced matching of r edges. Induced matching number of Pm×Pn is investigated in this paper. The main results are as follows:(1) If at least one of m and n is even, then IM(Pm×Pn=[(mn)/4].(2) If m is odd, then

奇异二阶边值问题正解的存在性

李和成

2004, 19(1): 101-106.

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This paper deals with the existence of positive solutions of the equation u"+f(t, u)=0 with linear boundary conditions. We show the existence of at least one positive solution if / is neither superlinear nor sublinear on u by a simple application of a fixed point Theorem in cones.

多值Vitali-Hahn-Saks-Nikodym定理

吕同富, 赵玟亨

2004, 19(1): 107-110.

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In this paper, we establish the set valued Vitali-Hahn-Saks-Nikodym Theorem.

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