数学季刊

徐森林, 宋冰玉

2006, 21(4): 475-481.

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In this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature,large volume growth has finite topological type provided that ... for some constant ε＞0.We also prove that a complete Riemannian manifold with nonnegative kth-Ricci curvature and under some pinching conditions is diffeomorphic to Rⁿ.

三变量中的一类坐标多项式

龚胜军, 李尚志

2006, 21(4): 482-487.

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In this paper,we introduce a polynomial sequence in K[x],in which two neigh- bor polynomials satisfy a wonderful property.Using that,we give partial answer of an open problem: if φ(x,y,z)=(f(x,y),g(x,y,z),z),which sends every linear coordinate to a coor-dinate,thenφis an automorphism of K[x,y,z].As a byproduct,we give an easy proof of the welt-known Jung’s Theorem.

一类螺旋映射的增长与掩盖定理

刘浩, 崔宏宇, 刘爱超

2006, 21(4): 488-492.

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In this paper,we deduce growth and covering theorem for f(x) by the other means,where f(x) is strongly spiral-like mapping of typeβwith orderαdefined on Unit Ball B of complex Banach space,and still give growth upper bound and distortion upper bound for subordinate mapping.

Fuzzy幂群与Fuzzy商群的相互关系

闫广霞, 米洪海, 施雅婷

2006, 21(4): 493-496.

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In this paper,we extend the concept of fuzzy quotient groups.The structures of fuzzy power groups and fuzzy quotient groups are discussed.The relationship between fuzzy power groups and fuzzy quotient groups are considered.

Cuccia定理的一个推广

徐颖吾, 李世荣

2006, 21(4): 497-502.

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For a finite group G,let S(G)be the set of minimal subgroups of odd order of G which are complemented in G.It is proved that if every minimal subgroup X of odd order of G which does not belong to S(G),CG(X)is either subnormal or abnormal in G.Then G solvable.

具有连续变量的非线性偏差分方程的振动性

杨军, 王春艳, 关新平

2006, 21(4): 503-510.

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This paper is concerned with the oscillation of nonlinear partial difference equa- tions with continuous variables and the corresponding dual equations.Several sufficient conditions are obtained for the oscillation of these equations.

关于含临界指数的p-平均曲率算子

傅红卓, 沈尧天, 杨俊

2006, 21(4): 511-521.

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This paper is concerned with the existence of positive solutions of the following Dirichlet problem for p-mean curvature operator with critical exponent: ... is a bounded domain in R^N(N＞p＞1)with smooth boundary Ω,2＜=p＜=q＜=P*,P*=(Np)/(N-p),λ,P＞0.It reaches the conclusions that this problem has at least one positive solution in the different cases.It is discussed the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with critical exponent by using Nehari-type duality property firstly.As p=2,q=p,the result is correspond to that of Laplace operator.

一般变系数耗散长水波方程的精确解

张令元, 张金良, 王明亮

2006, 21(4): 522-528.

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By using the homogeneous balance principle(HBP),we derive a Backlund trans- formation(BT)to the generalized dispersive long wave equation with variable coefficients. Based on the BT,we give many kinds of the exact solutions of the equatioh,such as,single solitary solutions,multi-soliton solutions and generalized exact solutions.

一个时滞微分方程模型的全局吸引性

李林, 王炳顺

2006, 21(4): 529-537.

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This paper considers the scalar differential delay equation x(t)=-μx(t)-f(x(t-τ)),where f(x)is a decreasing continuous function.By proving that all solutions will be ultimately in some interval,we give the conditions under which the unique equilibrium point of the differential delay equation is globally attractive.

一类广义长短波方程的整体适定性

张瑞凤, 梁宏伟

2006, 21(4): 538-544.

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In the present paper,we investigate the well-posedness of the global solution for the Cauchy problem of generalized long-short wave equations.Applying Kato’s method for abstract quasi-linear evolution equations and a priori estimates of solution,we get the existence of globally smooth solution.

一类带有种痘年龄的流行病模型

郭淑利, 丁凤霞

2006, 21(4): 545-552.

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A simple SI epidemic model with age of vaccination is discussed in this paper. Both varing birth rate,the mortality rate caused by disease and vaccine waning rate are considered in this model.We prove that the global dynamics is completely determined by the basic reproductive number R(Ψ)(Ψdenotes per capita vaccination rate).If R(0)＜1, the disease-free equilibrium is a global attractor;If R(Ψ)＜1,the disease-free equilibrium is locally asymptotically stable;If R(Ψ)＞1,an unique endemic equilibrium exists and is locally asymptotically stable under certain condition.

带有约束线性分式规划问题的最优性条件

孙建设, 叶留青

2006, 21(4): 553-556.

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In this article,the authors discuss the optimal conditions of the linear fractional programming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution with constraint condition.

各向异性网格下具有数值积分的非协调有限元逼近

杨乔, 石东洋

2006, 21(4): 557-560.

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In this paper we mainly discuss the nonconforming finite element method for second order elliptic boundary value problems on anisotropic meshes.By changing the discretization form(i.e.,by use of numerical quadrature in the procedure of computing the left load),we obtain the optimal estimate O(h),which is as same as in the traditional finite element analysis when the load f∈H¹(Ω)∩C⁰(Ω)which is weaker than the previous studies.The results obtained in this paper are also valid to the conforming triangular element and nonconforming Carey’s element.

非自治时滞微分方程的正周期解

彭世国

2006, 21(4): 561-566.

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By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.

Mahler型函数值的代数无关度量

王天芹, 刘华珂

2006, 21(4): 567-576.

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In this paper,we give the algebraic independence measures for the values of Mahler type functions in complex number field and p-adic number field,respectively.

亚纯函数的一个正规定则

章文华

2006, 21(4): 577-580.

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We proved:Let F be a family of meromorphic functions in a domain D and a≠0,b∈C.If f′(z)-a(f(z))2≠b,f≠0 and the poles of f(z) are of multiplicity＞=3 for each f(z)∈F, then F is normal in D.

关于Smarandache伪数序列问题

刘燕妮

2006, 21(4): 581-584.

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The main purpose of this paper is to study the mean value properties of the second Smarandache pseudo-odd number sequence and pseudo-even number sequence,and give some interesting asymptotic formula for them.

关于规范型拉丁方个数的上界

段炼

2006, 21(4): 585-589.

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In this note,the author find an upper bound formula for the number of the p×p normalized Latin Square,the first row and column of which are both standard order 1,2,...,p.

漂移-扩散型半导体方程解的整体有界性

郭秀兰, 张玉兰, 李功胜

2006, 21(4): 590-596.

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This paper is devoted to the mixed initial-boundary value problem for the semi- conductor equations.Using Stampacchia recurrence method,we prove that the solutions are globally bounded and positive.

两组算子单调函数序列与严格Chaotic序

张蕾, 姜健飞

2006, 21(4): 597-607.

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In this paper we introduce two sequences of operator functions and their dual functions: ... defined on (0,+∞). We find that they are all operator monotone functions with respect to the strictly chaotic order and some ordinary orders among positive invertible operators. Indeed, we extend the results of the operator monotone function (tlog t -t+1)/(log²t) which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics [1].

一类紧支撑矩阵值正交小波的构造

陈清江, 程传蕊, 程正兴

2006, 21(4): 608-616.

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In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.

部分线性自回归模型中误差方差伪最小二乘估计的渐近正态性

武新乾, 田铮, 句彦伟

2006, 21(4): 617-622.

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Consider the model Y_t=βY_t-1+g(Y_t-2)+ε_tfor 3＜=t＜=T. Here g is an unknown function,βis an unknown parameter, vε_t are i.i.d,random errors with mean 0 and varianceσ2 and the fourth moment α_4,andεt are independent of Y_s for all t＞=3 and s=1,2. Pseudo-LS estimators ... distribution to N(0,1). The result can be used to establish large sample interval estimates of σ² or to make large sample tests for σ².

关于一个级数的计算公式

杨倩丽, 李海龙

2006, 21(4): 623-628.

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It is one of the most interesting problems in number theory to compute some especial series by using Zeta and Gamma functions,and results have been obtained for some especial series.In this paper,we give an important formula which is proved also by using Zeta and Gamma functions.

两类拟共形映射的掩盖定理

廖茂新, 高纯一, 王智刚

2006, 21(4): 629-632.

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In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.

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