Chinese Quarterly Journal of Mathematics

The Covering Theorems for Normalized Holomorphic Mappings on Bounded Starlike Circular Domains in Cⁿ

LIU Tai-shun, FENG Shu-xia

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.

Compact Space-like Submanifolds in Pseudo-Riemann Manifold

SUN He-jun, WU Bao-qiang

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.

Global Bounded Solutions for Reaction-diffusion Systems with a Full Matrix of Diffusion Coefficients and a Balance Law

CHEN Xue-hong, JIANG Cheng-shun

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.

The Bergman Kernels on W_Ⅲ

L U Ke-ping, ZHAO Xiao-xia

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.

Oscillation of Second-order Delay Differential Equation

YIN Fu-qi, LI Yong-kun

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.

Extensions and Refinements of Adamovic's Inequality

SHI Huan-nan, LI Da-mao

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.

On Kendall's Conjecture for an Extended Birth-death Q-processes with Instantaneous State and Catastrophes

WU Qun-ying

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.

Restricted Edge Connectivity of Binary Undirected Kautz Graphs

OU Jian-ping

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.

Regularity of Continuous Linear Operators on Banach Function Spaces

JIANG Nian-sheng, Chen Zi-li

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.

On the Spectral Radius of Trees with the Given Diameter d

TAN Shang-wang, GUO Ji-ming, QI Jian

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

A Conjecture on Veronese Generating Submanifolds

SONG Hong-zao, SONG Xiao-xin a

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.

Some Identities Involving Square of Fibonacci Numbers and Lucas Numbers

LIU Duan-sen, LI Chao, YANG Cun-dinn

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.

Iterative Solutions for a Non-monotone Binary Operator Equations and Operator System of Equations

ZHANG Fei-ran, ZHOU Xiao-zhong

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.

On the Distribution Property of Lehmer DH Number

GAO Li

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.

Hamilton Graph Based on DNA Computing

ZHANG Jia-xiu

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.

On the Lucas Base and Computation of Counting Function Mean Value

LI Hai-long, LIU Hua-ke

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.

Edge-face Chromatic Number of 2-connected 1-tree with △(G) = 5

DONG Gui-xiang, CHEN Dong-ling, XU Zhen-yu

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.

Induced Matching Number of the Plane Grid Graph

LU Xiao-xu, PEI Ming, YAO Wei-li, ZHOU Ju

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

On the Existence of Positive Solutions of Singular Second Order Boundary Value Problems

LI He-cheng

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.

Set Valued Vitali-Hahn-Saks-Nikodym Theorem

LU Tong-fu, Cho Minhyung

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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