共查询到18条相似文献,搜索用时 156 毫秒
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关于勒贝格可测函数的再认识 总被引:4,自引:4,他引:0
戚民驹 《上海电机学院学报》2007,10(1):74-77
由[a,b]上的勒贝格可测函数与几乎处处连续的函数几乎处处相等,给出勒贝格可测函数的等价定义及几个勒贝格可测函数的性质,提出一些关于勒贝格可测函数进入工科数学教学的设想。 相似文献
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拉格朗日中值定理证明的辅助函数 总被引:1,自引:0,他引:1
郁美玲 《上海电机学院学报》2004,7(1):30-32
讨论了拉格朗日中值定理证明中采用的各种辅助函数及其适用的教学对象,并为了使辅助函数的几 何意义更加明确,对其中的几何学角度出发建立的辅助函数作了改进。 相似文献
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本文借助于连续函数的多项式逼近与 L-可积函数的光滑化来处理有界可测函数的多项式逼近。特别是,它给出一系列有用的估计,按照这种估计,对这种函数,在几乎所有点处能给出一系列有用的估计,而这是以前不曾有过的。 相似文献
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积分学基本公式是计算定积分的一个重要公式,但它的使用条件较为苛刻,本文利用勒贝格测度,将定理的条件进行了改进,得到了定理3,并说明了定理3已不能再推广。 相似文献
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关于本性函数积分定义的注 总被引:2,自引:1,他引:1
戚民驹 《上海电机学院学报》2008,11(2):147-150
对照几乎处处连续的本性函数的积分定义,给出几乎处处连续的本性函数绝对可积的充要条件,证明几乎处处连续的本性函数积分是非绝对可积的,将无穷区间上几乎处处连续的本性函数的积分问题化为有穷区间的积分。 相似文献
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Zhang Xuedong 《电工标准与质量》1994,(3)
线性赋范空间理论中的Helly定理的证明一般都是借助于深刻的开映射定理和线性泛函的Hahn—Banach扩张定理(几何形式),而且,任意>0的意义是不明确的.文中给出Helly定理一个简单、初等的证明(仅用到商空间的概念).它具有显明的几何特征而且澄清了任意>0的几何意义. 相似文献
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Irwin W. Sandberg 《International Journal of Circuit Theory and Applications》2006,34(5):547-558
An expression is given for the most general continuous causal linear input–output map that takes the space of (Lebesgue) integrable functions into itself. This expression is a function‐space limit of an integral. As an application, a representation result is given for an important family of linear maps that take the space of bounded measurable functions into itself and satisfy a certain continuity condition. Some related material concerning engineering education is also given. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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《Education, IEEE Transactions on》1966,9(1):29-32
In this paper, the convolution theorem is used as a fundamental tool to solve problems associated with frequency translation, amplitude modulation, sampling, and transformation of random variables. The four basic steps involved in the convolution of two functions are explained in detail using graphic techniques. It is concluded that the approach used makes possible the covering of a class of important problems at high level and in a short period of time. 相似文献
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《Education, IEEE Transactions on》1965,8(4):136-139
The Onsager theorem pertains to symmetries inherent in two-dimensional current flow, through either a conducting or a semiconducting medium in the presence of an externally applied magnetic field oriented perpendicular to the current-carrying plane. Although the theorem can be derived on a statistical basis, as done originally by Onsager, in many courses dealing with thermoelectricity, it is necessary to state the theorem without proof, rather than take the time to develop the background properly. Therefore, it is of considerable pedagogical interest to have a derivation of the theorem based upon thermodynamics only. To that end, the following discussion has been found useful. 相似文献
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《Education, IEEE Transactions on》1971,14(2):71-72
The compensation theorem relates the change in current when an impedance is added in a loop to the current that existed originally. It is shown that the voltage scattering variables may be defined in terms of the current change and the original current. The compensation theorem may then be used to determine the scattering matrix. 相似文献
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《Education, IEEE Transactions on》1970,13(2):87-88
It has been found that, for linear networks, both Thevenin's and Norton's theorems are special cases of the compensation theorem. To illustrate the interdependence of these network theorems, Thevenin's theorem is proved using the compensation theorem. Norton's theorem can be derived by using a dual form of the compensation theorem. 相似文献
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《Education, IEEE Transactions on》1985,28(2):92-93
Miller's theorem is an important analysis tool. Its presentation in many introductory electronic circuits texts often leads to student misunderstandings with regard to its applicability. An alternative presentation that may improve students' understanding is suggested. 相似文献
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《Education, IEEE Transactions on》2005,48(3):559-561
Conventional application of Miller's theorem in amplifiers often leaves a student with an erroneous impression that the approximation provides an incorrect estimate for the nondominant pole. The present paper clarifies that not only can a reasonable estimate for both dominant and nondominant poles be obtained through Miller's theorem but additional insight is offered into pole splitting, not afforded by conventional analysis. 相似文献