Chinese Quarterly Journal of Mathematics

Asymptotically Optimal and Admissible Empirical Bayes Estimation of Normal Parameter

LIU Huan-xiang, SHI Yi-min, ZHANG Su-mei, ZHOU Bing-chang

2007, 22(1): 1-6.

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Under square loss,this paper constructs the empirical Bayes(EB) estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover,the convergence rate of the EB estimation obtained is proved to be O(n-1).

The Minimal Cycle Basis of Circular Graphs

WEI Er-ling, HE Wei-li, LIU Yan-pei

2007, 22(1): 7-11.

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For most of circular graph the length of the minimum cycle basis is given.For the others a bound of the length of the minimum cycle basis is given and the given bound is reached.

Ramsey Number of K_2,s+1VS, K_1,n

QIN Da-wei, SHEN Da-peng

2007, 22(1): 12-15.

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It is shown that the Ramsey number r(K_2,s+1,K_1,n)<n+sn1/2+(s+3)/2+o(1) for large n,and ... and q is a prime power such that s|(q-1).

Small Excess and the Topology of Open Manifolds with Ricci Curvature Negatively Lower Bounded

XU Sen-lin HU Zi-sheng

2007, 22(1): 16-21.

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In this paper,we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry.We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius,which improves some results in [4].

A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of Order α

LIU Xiao-song, FENG Shu-xia

2007, 22(1): 22-28.

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Suppose f is an almost starlike function of orderαon the unit disk D.In this paper,we will prove that ... preserves almost starlikeness of order α on …, where … are real numbers.

Dynamic Behavior of a Predator-prey System with Stage-structure for Prey

2007, 22(1): 29-37.

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In this paper,we considered the predator-prey system with stage-structure for prey,where the predators predate immature preys only.The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed,and then uniformly persistent sufficient conditions of populations were found.

The Spectral Representation of a Class of m-KP Equation and Its Quasi-periodic Solution

WU Yong-qi

2007, 22(1): 38-42.

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This paper gives the spectral representation of a class of (2+1)-dimensional mod- ified Kadomtsev-Petviashvili(m-KP) equation with a constant parameter.Its quasi-periodic solution is obtained in terms of Riemann theta functions.

Analysis of Linear Triangular Elements for Convection-diffusion Problems by Streamline Diffusion Finite Element Methods

ZHOU Jun-ming, JIN Da-yong, ZHANG Shu-hua

2007, 22(1): 43-51.

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The Spectrum of Positive Operators on Hilbert Lattices

DENG Chun-yuan, DU Hong-ke

2007, 22(1): 52-56.

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Some spectral characterizations of positive operators on Hilbert lattices are pre- sented.The application of these results can yield some equivalent relations of an irreducible positive operator.Some related results for positive operators on Hilbert lattice are also obtained.

The Joint Distribution of the Maximum Excursion and the Minimum Excursion for Brownian Motion with Drift

LLÜ Yu-hua, XU Run

2007, 22(1): 57-62.

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In this paper,we discuss the problem of extreme value for Brownian motion with positive drift.We obtain the joint distribution of the maximum excursion and the minimum excursion.

Criteria Conditions for Generalized Diagonally Dominant Matrices

TIAN Su-xia

2007, 22(1): 63-67.

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In this paper,some new sufficient conditions for generalized dominant matrices are given,and some results in [1] are generalized and improved.

An Improvement of the Hardy-Hilbert Type Integral Inequalities and an Application

HE Le-ping, CHEN Xiao-yu, SHANG Xiao-zhou

2007, 22(1): 68-74.

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In this paper,it is shown that Hardy-Hilbert’s integral inequality with parameter is improved by means of a sharpening of Holder’s inequality.A new inequality is established as follows: ... , where R=(S_p(F, h)-S_q(G, h))²,m=min{1/p,1/q}.As application;an extension of Hardy-Littlewood’s inequality is given.

A Generalized Form of Whitney's Theorem

CEN Yan-ming, CEN Li-hui

2007, 22(1): 75-78.

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Whitney’s theorem is a famous theorem in the local singularity theory.In this paper,as an application of Malgrange preparation theorem,a generalized form of Whitney’s theorem will be derived.

Some Results on Minimum Aberration Mixed-level (2^r)2ⁿ Factorial Designs

SHI Cheng-tang, ZHANG Dan, CHEN Bao-ting, LI Yu-kai

2007, 22(1): 79-86.

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Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2^r)2ⁿ factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2^r)2ⁿ factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001).

A Dirac Type Condition for Heavy Cycles in Weighted Graphs

LI Ping

2007, 22(1): 87-93.

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In this paper we give a Dirac type condition for heavy cycles in a 3-connected weighted graph,reading that if d^w(v)≥d for all v∈V(G)\{x} and w(uz)=w(vz),when uz,vz∈E(G) and uvE(G).Then G contains either an (x,y)-cycle of weight at least 2d or a Hamilton cycle.

On an Extension and a Refinement of Van der Corput's Inequality

YANG Bi-cheng

2007, 22(1): 94-98.

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By introducing a parameter a,we give an extension of Van der Corput's inequal- ity.Also a new strengthened version of it is considered.

Generalizations of Some Formulas of the Reciprocal Sum and Alternating Sum for Generalized Lucas Numbers

YE Xiao-li, LIU Mai-xue

2007, 22(1): 99-103.

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The purpose of this article is to provide the inversion relationships between the reciprocal sum S(1,2,…,m) and the alternating sum T(1,2,…,m) for generalized Lucas numbers which generalizes the Melham’s results.

Some Characterizations of GV-semigroups

ZHANG Jian-gang, SHEN Ran

2007, 22(1): 104-108.

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GV-semigroups are the generalizations of completely regular semigroups in the range ofπ-regular semigroups.In this paper,Green*-relations on GV-semigroups and some congruences on it are studied.

The Optimal Weighted Combinational Forecasting with Constant Terms

ZHANG Jian-guo

2007, 22(1): 109-113.

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We propose a model based on the optimal weighted combinational forecasting with constant terms,give formulae of the weights and the average errors as well as a rela- tion of the model and the corresponding model without constant terms,and compare these models.Finally an example was given,which showed that the fitting precision has been enhanced.

Multiplicity Results for Second-order Generalized Sturm-Liouville Boundary Value Problems with Dependence on the First Order Derivative

SHEN Chun-fang, YANG Liu, LIU Xi-ping

2007, 22(1): 114-125.

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By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term explicitly.We show the existence of multiple positive solutions for the problems.Example is given to illustrate the main results of the article.

The Borel Point of Infinite Order K-quasimeromorphic Mappings in the Unit Disk

ZHANG Hong-shen, HE Yi-nong

2007, 22(1): 126-130.

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In this paper,the existence of the Borel point of infinite order K- quasimeromorphic mappings in the unit disk is showed.

The Convergence of the Steepest Descent Algorithm for D.C.Optimization

SONG Chun-ling, XIA Zun-quan

2007, 22(1): 131-136.

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Some properties of a class of quasi-differentiable functions(the difference of two finite convex functions) are considered in this paper.And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.

On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings

CHEN Xing-di, HUANG Xin-zhong

2007, 22(1): 137-142.

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The distortion property of hyperbolic area of planar quasiconformal mappings is studied in this paper.In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings their hyperbolic area distortions are estimated quite sharply.The result can be applied to judge whether the hyperbolic area of a planar subset is explodable.

Quasilinear Hyperbolic Conservation Laws with Relaxation

LIU Fa-gui, ZHANG Yuan-zhang

2007, 22(1): 143-154.

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In this paper,we investigate the relaxation phenomenon for quasilinear hyper- bolic conservation laws,and obtain global smooth solutions and the life span of classical solutions to its Canchy problem.These results shows that the relaxation admits the effects of dissipation.

Further Extension on a Theorem of the Value Distribution of f′fⁿ

DOU Pan-ying, WU Chang-qun

2007, 22(1): 155-158.

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By using small function method,the following result is obtained.If f(z) is transcendental meromorphic and that Ψ(z) is non-zero meromorphic and that T(r,Ψ)= S(r,f), then ...

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