数学季刊

龚克, 李伟平.

2008, 23(1): 1-7.

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In this paper, it is shown that: if λ₁,…,λ₈ are nonzero real numbers, not all of the same sign, such that λ₁/λ₂ is irrational, then for any real numberηandε>0 the inequality |λ₁x₁²+λ₂x₂²+λ₃x₃⁴+…+λ₈x₈⁴+η|<ε has infinitely many solutions in positive integers x₁,…,x₈.

L-拓扑空间中的相对强F紧性与相对超F紧性

李尧龙

2008, 23(1): 8-15.

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ctness are defined in L-topological spaces for an arbitrary L-set.Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given.Some examples are illustrated.

一类微分方程亚纯解的增长级

江秀海, 高凌云

2008, 23(1): 16-20.

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By meas of the Nevanlinna theory of the value distribution of meromorphic functions,this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution is determined if the order are sufficiently large.

SU(n,l)/S(U(n) × U(1))上的中心极限定理

连保胜, 胡适耕, 车颖涛

2008, 23(1): 21-27.

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Let G = SU(n,1), K = S(U(n)×U(1)),and for 1∈Z, let {η}_1∈Z be a one- Dimensional K-type and let El be the line bundle over G/K associated to n. In this work we obtain a central limit theorem for the space E_l.

一类具偏差变元的二阶微分方程周期解

杜波, 鲁世平

2008, 23(1): 28-35.

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By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″(t)+f(x′(t))+ h(x(t))x′(t)+g(x(t-τ(t)))=p(t), some sufficient conditions on the existence of periodic solutions are obtained.

有界对称域上的加权Bergman空间

王雄亮, 刘太顺

2008, 23(1): 36-44.

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On bounded symmetric domainΩof Cⁿ, we investigate the properties of functions in weighted Bergman spaces A^p(Ω,dv_s) for 0<p≤+∞ and -1<s<+∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^p(Ω,dv_s) in terms of a class of linear operators D^α,β. Making use of these characterizations, we ex- tend A^p(Ω,dv_s) to the weighted Berg-man spaces A^p_α,β(Ω,dv_s) in a very natural way for 1≤p≤+∞and any real number s, that is, -∞<s<+∞.This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on A^p_α,β(Ω,dv_s) and the dual of A^p_α,β(Ω,dv_s) are given.

一类对角形拟线性双曲型方程组空间周期解的破裂

葛菊

2008, 23(1): 45-55.

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In this paper,we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form,and make the accurate estimate of life-span.These results in this paper extend the conclusion [1～3].

关于Netessine和Rudi库存模型中目标函数的一点注记

李小申, 王仲英, 高克权

2008, 23(1): 56-60.

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Netessine and Rudi(2003) consider a consumer-driven substitution problem with an arbitrary number of products under both centralized management and competition.They obtain analytically tractable solutions,establish concavity of the objective function,i.e.,the expected profit function generated by each product and uniqueness of the equilibrium for the decentralize case.For the centralized case,they indicate that the objective function,i.e., the expected profit function,might not be concave and not even quasiconcave.In this note we show,for the centralize case,that the objective function is submodular,and partially verify Netessine and Rudi’s observation that the objective function be unimodal in each of the decision variables for some case.

奇异三阶两点边值问题解的一个存在定理

姚庆六

2008, 23(1): 61-66.

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By constructing suitable Banach space,an existence theorem is established under a condition of linear growth for the third-order boundary value problem u′′′(t)+f(t,u(t),u′(t),u″(t))=0,0<t<1,u(O)=u′(0)=u′(1)=0, where the nonlinear term contains first and second derivatives of unknown function.In this theorem the nonlinear term f(t,u,v,w) may be singular at t=0 and t=1.The main ingredient is Leray-Schauder nonlinear alternative.

一类具连续分布滞量的非线性中立型偏微分方程解的振动性

罗李平

2008, 23(1): 67-74.

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In this paper,some sufficient conditions are obtained for the oscillation of solu- tions for a class of second order nonlinear neutral partial differential equations with contin- uous distribution delay under Robin and Dirichlet’s boundary value conditions.

广义Kuramoto-Sivashinsky方程强解的全局吸引子的存在性#br#

王素云, 牟录贵, 张艳红

2008, 23(1): 75-82.

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广Using a new method developed in [5],we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in Hper3(Ω) and Hper4(Ω).

具有离散和分布时滞的Lotka-Volterra竞争系统

张嘉防, 张志平

2008, 23(1): 83-88.

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In this paper,the Lotka-Volterra competition system with discrete and distrib- uted time delays is considered.By analyzing the characteristic equation of the linearized system,the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don’t effect the stability of the equilibrium in the delay system.Finally,we can conclude that the positive equilibrium is global asymptotically stable in the delay system.

椭圆方程“△u+K(x)e^2u=0”当K(x)在某些点为正时解的存在性

武三星, 张静

2008, 23(1): 89-95.

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This paper considers the existence problem of an elliptic equation,which is equivalent to the prescribing conformal Gaussian curvature problem on R2.An existence result is proved.In particular,K(x) is allowed to be unbounded above.

一类时滞格种群模型波前解的存在性

孙风兰, 汤燕斌

2008, 23(1): 96-102.

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This paper considers the travelling wave fronts to a delayed lattice differential equation.The existence of the travelling wave solutions is proved by making use of the technique of the upper and lower solutions developed by J Wu and X Zou in [6].This work extends that of [4] in a general class of nonlinear terms.

一类非线性扩散问题解的局部化

周文书, 魏晓丹

2008, 23(1): 103-108.

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This paper concerns with properties of solutions of a nonlinear diffusion problem in non-divergence form.By constructing proper test functions,it is proved that solutions of the problem possess the property of localization.

一类非线性四阶波动方程整体解的存在性

陈勇明, 杨晗

2008, 23(1): 109-114.

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The initial boundary value problem for the fourth-order wave equation u_tt+△²u+u=|u|^p-1u is considered. The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the concept of stable set due to Sattinger.

关于Smarandache LCM序列

薛西峰

2008, 23(1): 115-119.

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For any positive integer n,let L(n) = [1,2,...,n] be the least common multiple of the integers from 1 to n.Let k be any positive integer.The main purpose of this paper is to study the asymptotic property of L(n^k), and give some interesting relevant results.

A><_TH上的辫子Monoidal范畴

王永忠, 刘瑞华

2008, 23(1): 120-126.

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Let A and H be Hopf algebra,T-smash product A><_TH generalizes twisted smash product A * H.This paper shows a necessary and sufficient condition for T-smash product module category_A><THM to be braided monoidal category.

Sobolev型方程高次Wison元逼近及超收敛分析

石东洋, 郝晓斌

2008, 23(1): 127-134.

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In this paper,a new higher order Wilson element is presented,and the conver- gence is proved.Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.

关于logA≥logB的一个注记

高福根, 杨长森

2008, 23(1): 135-139.

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In this paper,firstly we shall show some equivalent conditions of A>B>0; secondly by using the results of ours we shah show some characterizations of the chaotic order(i.e.,logA≥log B) by norm inequalities.

半线性热传导方程的解关于边值的连续依赖性

曹殿立, 王建平

2008, 23(1): 140-143.

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Reference [1] deals with the uniqueness of solution to problem (A) and solution of problem (A) is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of problem (A) is continuously dependent on boundary value on the basis of references [2] and [3].

价格时间序列及其应用

耿显民

2008, 23(1): 144-155.

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This paper tries to utilize the methods of stochastic analysis and matrix analysis to research the existential problem of price series.By using the means of time series analysis, the input-output,Markov processes and the modern matrix analysis,the limiting problem of price balance and vibration in stochastic economic environment has been researched,and surprising conclusions obtained are as following:the probability that the economic collapse time is equal∞is 0.

单位圆内亚纯函数的T点

张洪奎, 肖泽昌

2008, 23(1): 156-158.

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In this paper,the T points of meromorphic functions are defined and existence of the T points is showed in the Unit disk,we also prove T point must be J point.

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