Chinese Quarterly Journal of Mathematics

Periodic Solution of Weakly Damped 3D Schrödinger-Boussinesq Equations

GUAN Mei-jiao, LI Yong-sheng

2003, 18(4): 331-337.

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In this paper the authors consider a model of the interaction of a nonlinear complex
Schrödinger field and a real Boussinesq field in a 3D domain with the weakly damping which arises in
the laser and plasma physics and prove the existence of the periodic solution．

A General Representation of Hankel Matrix about Bell Numbers

LIU Mai-xue , ZHANG Hai-mo

2003, 18(4): 338-342.

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The purpose of this note is to establish a general representation of Hankel matrices of Bell numbers and the convoluted Bell numbers．As a special case ,the results of Aigner are extended .

A Strong Limit Theorem on Generalized Random Selection for m-valued Random Sequences

WANG Zhong-zhi , XU Fu-xia

2003, 18(4): 343-348.

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In this paper ,a strong limit theorem on gambling strategy for binary Bernoulli sequence ,i．e . irregularity theorem ,is extended to random selection for dependent m -valued random variables ,via us- ing a new method-differentiability on net．Furthermore ,by allowing the selection function to take value in finite interval［－ M ,M］,the conception of random selection is generalized .

Oscillation Criteria Related to Integral Averaging Technique for Quasilinear Elliptic Equations

XU Zhi-ting , MA Dong-kui

2003, 18(4): 349-357.

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Sufficient conditions are obtained for oscillation of certain quasilinear elliptic equations ... ,where Ωis an exterior domain ,m ＞1,and p（x）is an alternating function． The integral averaging technique is employed to establish our results .

The Properties of Transitive Bipartite Tournaments

TAN Shang-wang , ZHANG De-long

2003, 18(4): 358-363.

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Let Γ ,n denote all m × n strongly connected bipartite tournaments and α（ m ,n）the maxi- mal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament．Let t（ m ,n ,k ,l）＝ max｛t（ T _{m ,n} ,k ,l）：T _{m ,n} ∈ Γ ,n ｝,where t（ T _{m ,n} ,k ,l）is the
number of k× l（ k ≥2,l ≥2）transitive bipartite subtournaments contained in T _{m ,n} ∈ Γ ,n ．We ob-
tain a method of graph theory for solving some integral programmings,investigate the upper bounds of α（ m ,n）and obtain t（ m ,n ,k ,l）.

The Markov Chain Analysis of Premature Convergence of Genetic Algorithms

ZHAO Xiao-yan, NIE Zan-kan

2003, 18(4): 364-368.

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This paper discussed CGA population Markov chain with mutation probability．For premature convergence of this algorithm ,one concerned,we give its analysis of Markov chain.

The Orders of Automorphism Group of p⁶ Rank Groups

ZHAO Xiao-yan, NIE Zan-kan

2003, 18(4): 369-377.

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In this paper ,we determine the order of automorphism group of p-groups in the third family ( Φ₃）and the fourth family ( Φ₄）in［1］,whose order is p⁶（ p ≥3）．Here p denotes an odd prime .

The Existence of Multiple Solutions for Second Order Differential Equations with Infinite Delay

SUN Xing-wang , DAI Xin-li

2003, 18(4): 378-387.

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This paper discusses the existence of multiple solutions for second order differential equations with infinite delay .

On the Borel Radius of K-quasimeromophic Mappings in the Unit Disk

LI Shu-yun , LIU Ming-sheng

2003, 18(4): 388-394.

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K-quasimeromorhpic mappings in the unit disk ,the filling disks and the existence theorem of the Borel radius are derived .

Unique of Meromorphic Functions

XIONG We-ling

2003, 18(4): 395-399.

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In this paper the Gross uniqueness question is studied ,and the unique range sets of two classed entire functions are obtained .

Convergence Rate of E ·B Estimation for Location Parameter Function of One-side Truncated Family Under NA Samples

LING Neng-xiang

2003, 18(4): 400-405.

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In this paper ,we construct the E ·B estimation for parameter function of one-side truncated distribution under NA samples．Also ,we obtain its convergence rate at O（ n－q ）,where q is approach- ing 1／2.

Divisible Semiring Congruences on Distributive Semiring

LI Shan-hai , LI Shi-zheng

2003, 18(4): 406-409.

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In this paper ,we describe all the divisible semiring congruences on a distributive semiring S and also establish a one-to-one ,inclusion-preserving mapping from the set of full ,closed ,self-conja- gate ,ideal subsemirings of S to the set of all divisible semiring congruences on S .

On Hochschild Homology of Endomorphism Algebras of Exceptional Sequences

YAO Hai-lou , PING Yan-ru , PING Da-wen

2003, 18(4): 410-413.

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In this note,we studied the Hochschild Homology of endomorphism algebras of exceptional sequences over any hereditary algebras．

Comparison Theorem for General Volterra-Stieltjes Integro-differential Equations

LOU Mei-zhi

2003, 18(4): 414-418.

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In this paper ,A．B．Mingarelli s result is generalized to General Volterra-Stieltjes Integro-dif- ferential Equations ．Comparison theorem and equivalence condition of non-oscillation are obtained . Classical Sturm comparison theorem and some conclusions are generalized .

On the Coefficients Problem of Quasi-convex Mappings and Starlike Mapppings in Cⁿ

LIU Wei-xian , WANG Yu-min

2003, 18(4): 419-424.

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Let Bⁿ be the unit ball in Cⁿ ,we study quasi-convex mappings and starlike mappings on Bⁿ . The upper bounds of second order item coefficients of r quasi-convex mappings and starlike mappings are obtained .

Several Research Results of π（x＋y）≤ π（x）＋ π（y）

WANG Guo-fu, ZHANG Chang-chun

2003, 18(4): 425-428.

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The famous conjecture in distribution of prime numbers remains unsolved whether there exists a constant inequality of“ π（x ＋ y）≤ π（x）＋ π（y）”for all integers such as x ,y ≥2．The present article argues that when x ＞11,y ≤30,there always is a constant tenable inequality．

A Boundary Integral Equation Approach for Boundary Problem of Laplace Equation

SUN Jian-she , YE Liu-qing

2003, 18(4): 429-434.

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Using the second Green formula ,the boundary problem of Laplace equation satisfied by po- tential function of static electric field is transformed to the problem of the boundary integral equation , and then a boundary integral equation approach is established by partitioning boundary using linear boundary element .

Involutions Fixing the Lens Spaces L¹（p）

LIU Xi-bo , YAO Li , WANG Yu-su

2003, 18(4): 435-440.

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Let（M^3＋k ,T）be an involution on a closed manifold such that its fixed point set is L ¹（p）. In this paper ,we determine the existence of（M^3＋k,T）and give the equivariant bordism classification of such involutions .

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