数学季刊

邓默, 任韩, 董倩

2008, 23(4): 475-479.

摘要 ( 29 )

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In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold:1) Each of such embeddings is minimum genus embedding;2) The facial cycles are precisely the induced nonseparating cycles which implies the uniqueness of such embeddings;3) Every overlap graph O(G,C) is a bipartite graph and G has only one C-bridge H such that CUH is nonplanar provided C is a contractible cycle shorter than every noncontractible cycle containing an edge of C. This extends the results of C Thomassen’s work on LEW-embedded graphs.

一类带有HollingⅡ类功能性反应和相互干扰及脉冲效应的捕食系统

郭红建, 赵中, 宋新宇等

2008, 23(4): 480-490.

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A kind of predator-prey system of Holling typeⅡ and interaction perturbation with impulsive effect is presented. By using Floquet theory and small amplitude perturbations skills, the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively. Finally, the existence of positive periodic solution is investigated by the bifurcation theory.

两类重要p-群及其自同构群的阶

班桂宁, 张新政

2008, 23(4): 491-493.

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In the paper we obtain two infinite classes of p-groups,calculate the orders of their automorphism groups and correct a mistake(perhaps misprinted) of Rodney James’ paper in 1980.

一个包含F Smarandache平方补数的极限

齐琼

2008, 23(4): 494-498.

摘要 ( 17 )

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The main purpose of this paper is using the analytic methods to study a limit problem involving the F Smarandache square complementary number Ssc(n),and obtain its limit value.

非线性比式和问题的全局优化算法

焦红伟, 郭运瑞, 陈永强

2008, 23(4): 499-505.

摘要 ( 22 )

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In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems(P).

一类集值投入产出方程的可解性结果

刘颖范

2008, 23(4): 506-511.

摘要 ( 18 )

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A class of set-valued Leontief input-output equation is introduced and two solvability theorems are obtained,which provide some corresponding existence,surjection as well as continuity results.

一类非稳态热耦合方程组解的存在性和正则性

王会, 李刚, 朱江等

2008, 23(4): 512-524.

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In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers’ theorem and Schander fixed point theorem, where the coupled function sσ(s), k(s) are assumed to be bounded in the C(IR×(0,T)). If σ(s), k(s) are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n≤2 is then analyzed under the assumptions on σ(s)∈W1, ∞(Ω×(0,T)) and the boundedness ofσ′(s) andσ″(s).

有关p-亚正规算子和对数亚正规算子广义Aluthge变换的一个注解

代辉亚, 杨长森

2008, 23(4): 525-532.

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We shall give some results on generalized aluthge transformation for phyponormal and log-hyponormal operators.We shall also discuss the best possibility of these results.

权Herz-Morrey空间上的Marcinkiewicz算子

肖丹, 束立生

2008, 23(4): 533-539.

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In this paper,the weighted Herz-Morrey spaces are introduced and the estimates for Marcinkiewicz Integrals on the weighted Herz-Morrey spaces are studied.

具有六对特殊方向的一类平面齐五次系统的全局拓扑结构

高洁, 籍法俊

2008, 23(4): 540-547.

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In this paper,a class of plane homogeneous fifth system with six special direction is studied,and the global topological classification and coefficient conditions is discussed.

α次β型螺形映照的增长与掩盖定理

刘爱超, 崔志会, 刘浩

2008, 23(4): 548-553.

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In this paper, we consider growth and covering theorem for f(x), where f(x) is spiallike mapping of typeβwith orderαdefined on unit ball B of complex Banach space, and x=0 is zero of order k+1 for f(x)-x. We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper hound for subordinate mapping. This result include some results known.

关于一个积分不等式的一些注记

胡剑骏

2008, 23(4): 554-558.

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Given two positive constantsαandβ,we prove that the integral inequality∫₀¹f^α+β(x)dx≥∫₀¹ f^α(x)x^βdx holds for all non-negative valued continuous functions f satisfying∫_x¹f(t)dt≥∫_x¹tdt for x∈[0,1] if and only if α+β≥1. This solves an open problem proposed recently by Ngo, Thang, Dat, and Tuan.

第三型伯恩斯坦插值过程的双结点修正

常玉宝, 魏平, 袁学刚

2008, 23(4): 559-564.

摘要 ( 15 )

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In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.

Banach空间中关于(H,η)-增生算子的一类新变分包含组问题

刘英, 陈永利, 何震

2008, 23(4): 565-573.

摘要 ( 16 )

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In this paper,we first introduce a new class of generalized accretive operators named(H,η)-accretive in Banach space.By studying the properties of(H,η)-accretive,we extend the concept of resolvent operators associated with m-accretive operators to the new (H,η)-accretive operators.In terms of the new resolvent operator technique,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.

知识的属性扰动与属性扰动定理

张冠宇, 杜英玲

2008, 23(4): 574-581.

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By using the dynamic characteristic of one direction S-rough sets(one direction singular rough sets) and dual of one direction S-rough sets(dual of one direction singular rough sets),the concepts of attribute disturbance of knowledge,the attribute disturbance degree of knowledge,and the disturbance coefficient of knowledge are given.By employing these concepts,the cardinal order theorem of the attribute disturbance knowledge,the unit circle theorem of the attribute disturbance knowledge,and the discernible theorem of the attribute disturbance knowledge are presented.

关于布尔矩阵行空间基数的若干存在区间

钟莉萍, 周剑辉

2008, 23(4): 582-588.

摘要 ( 21 )

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Let B_n be the set of all n×n Boolean Matrices;R(A) denote the row space of A∈B_n,|R(A)| denote the cardinality of R(A),m,n,k,l,t,i,γi be positive integers,Si,λi be non negative integers.In this paper,we prove the following two results: (1)Let n≥13,n-3≥k > S_l,S_i+1> S_i,i = 1,2,…,l-1.if k+l≤n,then for any m=2k+2(S_l) + 2(S_l-1)+…+ 2(S₁),there exists A∈B_n,such that |R(A)|= m. (2)Let n≥13,n-3≥k>S_n-k-1> S_n-k-2>…>S₁>λ_t>λ_t-1>…>λ₁,2≤t≤n-k.If exist γ_i(k+1≤γ_i≤n-1,i=1,2,…,t-1)γ_i<γ_i+1 and λ_t-λ_t-1≤k-S(_n-γ1),λ_t-i-λ_t-i-1≤S(_n-γi)-S(_n-γi+1),i=1,2,…,t-2,then for any m=2^k+2(^SN-K-1)+2(^Sn-k-2)+…+2(^S1)+2(^λt)+2(^λt-1)+…+2(λ1),there exists A∈Bn,as such that |R(A)|=m.

一个四阶收敛的牛顿类方法

王霞, 赵玲玲

2008, 23(4): 589-593.

摘要 ( 17 )

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A fourth-order convergence method of solving roots for nonlinear equation,which is a variant of Newton’s method given.Its convergence properties is proved.It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end,numerical tests are given and compared with other known Newton and Newtontype methods.The results show that the proposed method has some more advantages than others.It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.

关于广义对数平均的一个不等式的加细

石焕南, 吴善和

2008, 23(4): 594-599.

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In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p>2 and strictly Schur-concave function for p<2 on R+2.And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.

主理想环上子群G_r在线性群中的扩群

卫宗礼, 曲贺梅

2008, 23(4): 600-605.

摘要 ( 20 )

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Suppose R is a principal ideal ring, R* is a multiplicative group which is composed of all reversible elements in R, and M_n(R),GL(n,R),SL(n,R) are denoted by, M_n(R)={A=(a_ij)_n×n|a_ij∈R,i,j=1,2,…,n},GL(n,R) = {g|g∈M_n(R),det_g∈R*},SL(n,R) = {g∈GL(n,R)|det_g=1},SL(n,R)≤G≤GL(n,R)(n≥3),respectively, then basing on these facts,this paper mainly focus on discussing all extended groups of Gr={(AB OD)∈G|A∈GL(r,R),(1≤r<n)} in G when R is a principal ideal ring.

多元向量值正交小波包的刻画

华德林, 冯金顺

2008, 23(4): 606-614.

摘要 ( 15 )

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In this paper,the notion of orthogonal vector-valued wavelet packets of space L²(R^s,Cⁿ) is introduced.A procedure for constructing the orthogonal vector-valued wavelet packets is presented.Their properties are characterized by virtue of time-frequency analysis method,matrix theory and finite group theory,and three orthogonality formulas are obtained.Finally,new orthonormal bases of space L²(R^s,Cⁿ) are extracted from these wavelet packets.

极大单调映象的满射定理及其应用

武跃祥, 王拉娣

2008, 23(4): 615-620.

摘要 ( 21 )

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The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory.We prove some new surjectivity theorems under some conditions and give its application in differential equation.

树的Mycielski图的邻点可区别全色染色

谷玉盈, 王淑栋

2008, 23(4): 621-624.

摘要 ( 13 )

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A k-proper total coloring of G is called adjacent distinguishing if for any two adjacent vertices have different color sets.According to the property of trees,the adjacent vertex distinguishing total chromatic number will be determined for the Mycielski graphs of trees using the method of induction.

形式三角矩阵环的特殊性质

范维丽, 王慧

2008, 23(4): 625-632.

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We consider the sufficient and necessary conditions for the formal triangular matrix ring being right minsymmetric,right DS,semicommutative,respectively.

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