求数列极限的三个原则

学习数列极限这部分内容时，除了要牢固掌握极限的定义外，在求数列极限时还要遵循以下三个原则．     

怎样证明数列{(1 1/n)~n}递增且有上界

大家都知道，当n 时，数列的极限是存在的,这个极限记做e=2.71828…。 怎样证明这个极限存在?先证明数列{x_n}递增且有上界,然后根据单调数列极限存在的准则就证明了这个极限存在。     

一道数列极限的多种解法

利用数学分析中关于数列极限的定义、收敛数列的性质及数列极限存在的条件,介绍一道数列极限问题的多种解法.     

数列及函数极限不存在、无界、及有关无穷大问题的讨论

一、数列极限不存在，无界，不是无穷大的分析定义1．数列（Xn）不以A为极限存在ε0＞O，对任意自然数儿都存在从，当N0＞N时使2数列｛xn｝发散对任意数人都存在ε0＞0，对任意自然数N，都有N0＞N，使3．数列无界对任意M＞0，都存在自然数N0，使成立。4数列（Xn）不是无穷大量存在M0＞0，对任何自然数N，都存在N0＞N，使类似地可以出给函数极限不存在，无界，不是无穷大的分析定义。二、证明数列发散的一般方法在同济大学高等数学第四版上册第一章讲数列极限时，给出了一个描述收敛数列与其子数列之间关系的一个定理3，即如果数列｛xn…     

有限集合与数列极限的定义

极限理论是微积分学的理论基础,而数列极限是其中最基础也是最重要的一个部分,准确深入理解数列极限的概念对微积分的学习具有重要作用.本文用集合给出数列极限的另一个定义,它与数列极限的ε-N定义等价,其应用可以使数列极限的验证过程的逻辑关系更为清晰.     

一道数列极限题的注记

用几何方法分析了高等数学中的一道数列求极限的题目,直观地显示了该数列趋向于极限的方式.并把极限的结果从实数域中拓展到复数域中,指出了该数列在复数域趋向于极限的方式是螺旋的,在实数域中趋向于极限的方式是沿直线靠近的.最后类比该数列,构造出相似数列的求极限问题.     

浅谈采用聚点的概念定义多元函数极限的利弊

极限的概念是微积分学的基础，如何合理引入和定义这一概念对于《高等数学》的教学显得较为重要．对于一元函数的极限而言，通常可通过数列的极限问题引入直观的极限的概念，并抽象出数列极限的。“ε-N”语言，进而通过空心邻域的概念导出一元函数的极限的一般概念（ε-δ语言），     

浅谈采用聚点的概念定义多元函数极限的利弊

极限的概念是微积分学的基础，如何合理引入和定义这一概念对于《高等数学》的教学显得较为重要．对于一元函数的极限而言，通常可通过数列的极限问题引入直观的极限的概念，并抽象出数列极限的“ε－Ｎ”语言，进而通过空心邻域的概念导出一元函数的极限的一般概念（ε－...     

数列的极限

数列的极限吴传启，史新房（武汉电大黄陂分校４３２２００）（山东青州八中２６２５００）基本概念１、数列的极限．对于数列｛ａｎ｝，如果存在一个常数Ａ，无论预先指定多么小的正数ε，都能在数列中找到一项ａＮ，使得这一项后面的所有的项与Ａ的差的绝对值都小于ε（...     

借助函数极限判断无限数列的敛散性

本文首先指出了什么是无限数列和无限数列的敛散性的特征,数列的敛散性和连续函数的极限的求值有怎样的关系?数列的敛散性必有其特殊的地方,同时,将连续函数的求极限的方法移植到数列敛散性的判别上,有哪些需要注意的地方.文中作者将针对两者关系进行了详细的论述.无限数列在无穷远处的项具有什么特点呢?或是渐近某一个数,或渐近某几个数,或在某几个数之间来回摇摆等等.当数列渐近某一个数时,无限数列收敛.无限数列敛散性的代数验证方法就是求其在无穷远处的极限.当极限结果为一个有限数时,无穷数列收敛,当极限结果为无穷或不存在时,称其发散.既然数列是一种特殊的函数,那么是否可以借助函数极限来求解数列的极限呢?     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].