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函数振幅是微积分中最基本的概念之一,它的性态决定了函数许多解析性质.本文中扩充了函数振幅的定义.并利用它定义了函数振动性强弱的概念.作为这一概念的应用,建立起判定函数连续性、一致连续性、可积性、有界变差性的比较判别法,并给出了一些应用实例. 相似文献
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给出了一元函数在区间上一致连续的一个充分必要条件,举例说明了使用它来讨论函数在区间上的一致连续性将更为简单. 相似文献
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对二元函数连续性判定条件给出了详细分析,强调有关问题的关键点,纠正了常见的模糊认识,得到一系列连续性充分条件及其推广形式. 相似文献
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分段函数在分界点处不连续时所得的不定积分在分界点处的连续性问题,可根据分段函数在分界点的连续性或间断类型来判定,并由此解决分段函数求不定积分时各段所带常数之间的关系问题. 相似文献
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讨论了函数项级数∑(-1)n 1在[0,1]上的一致收敛性判定的两个方法,同时对[1]中的判别方法作了一些补充. 相似文献
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本文进一步讨论多元分布的连续性与它的边缘分布函数的连续性之间的关系,从而指出文献[2]与[5]中关于多元分布函数序列一致收敛性的两个定理之间的等价性,并且进一步改进多元分布序列一致收敛性的条件。 相似文献
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在给出了实Clifford分析中双正则函数列内闭一致有界和内闭一致连续的定义的基础上,讨论了内闭一致有界双正则函数列的内闭一致连续性、完备性、列紧性和收敛性. 相似文献
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Smail Djebali 《International Journal of Mathematical Education in Science & Technology》2013,44(5):677-689
The purpose of this paper is to understand whether there exists any link between the uniform continuity of a real function defined on an unbounded interval and its growth at infinity. The primary objective is to present some results from teaching experience which help in the comprehension of this notion and yield some classroom techniques. It is well known that a uniformly continuous function has a monomial growth; it will be proved that there does not exist another growth of positive order. After introducing three kinds of growth, some results are recalled in connection with the behaviour near infinity of a uniformly continuous function. Using a series of counterexamples, it is shown that the uniform continuity of a function cannot be described by its asymptotic behaviour near infinity. Finally, some useful properties of the averaging convergence are reviewed, and how this is related to uniform continuity is investigated. 相似文献
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关于函数一致连续的研究性教学 总被引:1,自引:0,他引:1
详细介绍函数一致连续的教学模式:先通过几何直观,使学生理解这一概念,随之引导学生认真学习一致连续在积分计算、函数项级数以及含参变量积分问题中的应用,使学生加深对这一概念的认识.同时就这一内容设置一系列探索性问题,进行研究性教学,以培养学生独立思考和解决问题的能力. 相似文献
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J. Ewert 《Periodica Mathematica Hungarica》1993,26(1):77-84
The almost uniform convergence is between uniform and quasi-uniform one. We give some necessary and sufficient conditions under which the almost uniform convergence coincides on compact sets with uniform, quasi-uniform or uniform convergence, respectively. In the second section continuity of almost uniform limits is considered. Finally we characterize the set of all points at which a net of functions is almost uniformly convergent to a given function. 相似文献
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A. Chojnowska-Michalik T. E. Duncan B. Pasik-Duncan 《Applied Mathematics and Optimization》1992,25(2):171-187
In this paper the continuity in the uniform operator topology of the solution of the stationary Riccati equation in Hilbert space as a function of parameters is verified. The assumptions for this verification are the uniform operator continuity of the uncontrolled semigroup with respect to parameters, the uniform finiteness of the infimum of the quadratic cost functionals over the admissible controls, and uniform detectability. Some families of semigroups are described that satisfy the condition of continuity in the uniform operator topology with respect to parameters. The uniform operator continuity of the solution of the stationary Riccati equation with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.This research was partially supported by NSF Grant ECS-8718026. 相似文献
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Rodrigo López Pouso 《International Journal of Mathematical Education in Science & Technology》2013,44(4):551-557
We present a teaching approach to uniform continuity on unbounded intervals which, hopefully, may help to meet the following pedagogical objectives:
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To provide students with efficient and simple criteria to decide whether a continuous function is also uniformly continuous;
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To provide students with skill to recognize graphically significant classes of both uniformly and nonuniformly continuous functions.
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We extend a notion of effective continuity due to Mori, Tsujii and Yasugi to real-valued functions on effective topological spaces. Under reasonable assumptions, Type-2 computability of these functions is characterized as sequential computability and the effective continuity. We investigate effective uniform topological spaces with a separating set, and adapt the above result under some assumptions. It is also proved that effective local uniform continuity implies effective continuity under the same assumptions. 相似文献
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Estimates from above for the uniform deviation of the mean value of a periodic function and the best approximation by constants are obtained on some classes of functions defined by moduli of continuity of even order. Similar results are established for approximations in the space L
2 and for the error of rectangular formula. Bibliography: 10 titles. 相似文献
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《Historia Mathematica》2005,32(3):303-311
It has often been thought that the distinction between pointwise and uniform continuity was a relatively late arrival to real analysis, due to the mathematicians associated with Weierstrass. In this note, it is argued that Bolzano, in his work on real function theory dating from the 1830s, had grasped the distinction and stated two key theorems concerning uniform continuity. 相似文献
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In the theory of function spaces it is an important problem to describe the differential properties for the convolution u = G * f in terms of the behavior of kernel near the origin, and at the infinity. In our paper the differential properties of convolution are characterized by their modulus of continuity of order k ∈ N in the uniform norm. The kernels of convolution generalize the classical kernels determining the Bessel and Riesz potential. They admit non-power behavior near the origin. The order-sharp estimates are obtained for moduli of continuity of the convolution in the uniform norm as well as for continuity envelope function of generalized Bessel potentials. Such estimates admit sharp embedding theorems into a Calderon space and imply estimates for the approximation numbers of the embedding operator. 相似文献