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2007年 第22卷 第1期    刊出日期：2007-03-30

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正态分布参数的渐近最优与可容许的经验 Bayes估计

刘焕香, 师义民, 张素梅, 周丙常

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).



循环图圈空间的最小基

魏二玲, 何卫力, 刘彦佩

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.



关于K_2,s+1VS, K_1,n的Ramsey数

秦大伟, 沈大鹏

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).



小Excess与具负下界Ricci曲率开流行的拓扑

徐森林, 胡自胜

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].



关于α次的殆星映射推广的Roper-Suffridge算子的一个注记

刘小松, 冯淑霞

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. 


食饵具有阶段结构的捕食-食饵系统的动力学行为

张嘉防, 张志平

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.



一类m-KP方程的谱表示及其拟周期解

吴勇旗

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.



对流占优扩散问题流线扩散法的最优误差估计--线性三角元

周俊明, 金大永, 张书华

2007, 22(1):  43-51. 

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This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems.In [8], under the condition that ε≤h2 the optimal finite element error estimate was obtained in L2-norm.In the present paper,however,the same error estimate result is gained under the weaker condition that ε≤h.



Hilbert格上正算子的谱

邓春源, 杜鸿科

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.



带漂移的布朗运动的极大游程与极小游程的联合分布

吕玉华, 徐润

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.



广义对角占优矩阵的判定准则

田素霞

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.



Hardy-Hilbert型积分不等式的一个改进及其应用 

贺乐平, 陈小雨, 尚小舟

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. 



Whitney定理的一个推广形式

岑燕明, 岑丽辉

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.



最小低阶混杂混合水平(2^r)2ⁿ因子设计的一些结果

史成堂, 张丹, 陈宝亭, 李玉凯

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). 


赋权图中重圈的Dirac型条件

李萍

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.





关于Van der Corput不等式的一个推广及改进

杨必成

2007, 22(1):  94-98. 

摘要 ( 7 )   PDF (156KB) ( 7 )  

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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.



广义Lucas数的倒数和及交错和若干公式的拓广

叶小丽, 刘麦学

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.





GV-半群的若干刻画

张建刚, 申冉

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.


带常数项的最优加权组合预测

张建国

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.



非线性项含一阶导数广义Sturm-Liouville边值问题的多个正解

沈春芳, 杨柳, 刘锡平

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.



单位圆内无限极拟亚纯映射的Borel点

张洪申, 何一农

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.



D.C.优化的最速下降法的收敛性

宋春玲, 夏尊铨

2007, 22(1):  131-136. 

摘要 ( 8 )   PDF (215KB) ( 2 )  

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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.



拟共形映照的双曲面积偏差估计

陈行堤, 黄心中

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.



具张弛的拟线性双曲守恒律方程组

刘法贵, 张愿章

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.



关于 f′fⁿ值分布一定理的再推广

窦盼英, 吴昌群

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 ...