共查询到19条相似文献,搜索用时 62 毫秒
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将调和级数分别去掉那些分母是奇数的项、分母是偶数的项、分母是质数的项、分母是合数的项,所得无穷级数仍发散.利用欧拉常数的概念可证明调和级数发散. 相似文献
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无穷级数是高等数学中的一部分重要内容.在判断无穷级数收敛或发散时,比较原理(比较审敛法或比较判别法)是一个有效的判别法,其基本原理是: 相似文献
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本文从调和级数前n项和的欧拉估计出发,定义正项发散级数发散速度序列,给出判别正项级数发散速度快慢法则.并依据此法构造出发散速度无限降低的正项级数序列,其比调和级数发散速度更慢. 相似文献
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探讨积分上限函数的周期性.得到积分上限函数是周期函数的两个充分必要条件.并得到当被积甬数是周期函数时.无穷限的反常积分发散性的一个结论. 相似文献
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本文主要结果如下: 1.合理地用无穷小量的方法定义了极限。 2.证明了无穷小说法与ε-δ说法的极限定义是完全相当的。 3.能确定无穷发散积分的值。 例1 例2 由下式可以算出经典电子半径 η=2.818×10~(13)cm(c,光速,…) 相似文献
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调和级数的一个有趣性质 总被引:1,自引:0,他引:1
对于调和级数sum from n=1 to ∞(1/n),它是一个发散的无穷级数,但笔者对其稍作变形,发现它有一个很有趣的性质.即性质:调和级数sum from n=1 to ∞(1/n),如果在调和级数中删去分母中含有数字1,2,3,…9 中任一个的所有项,则所得无穷级数将都收敛,且其和小于30. 相似文献
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本文研究了圆球在半无穷长圆管入口处的蠕动流。得到了速度分布,压力分布和流函数的无穷级数形式的分析解.采用配置法将无穷级数截断并确定出级数中各项系数.求出了均匀入口流绕静止圆球以及圆球以瞬时速度在管内静止流体中运动这两种情形下圆球的阻力系数以及圆球表面上的应力分布.结果表明,当圆球在入口处运动时会遭受到较无穷圆管内为大的阻力.本文还对配置法的收敛性进行了数值实验.试验证明,该法具有好的收敛性. 相似文献
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The dual representation formula of the divergence between two distributions in a parametric model is presented. Resulting estimators do not make use of any grouping or smoothing. For smooth divergences they all coincide with the MLE on any regular exponential family. 相似文献
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Recent investigations by Castillo and Grone have led to a new method for constructing mimetic discretizations of divergence and gradient operators. Their technique, which employs a matrix formulation to incorporate mimetic constraints, is capable of producing approximations whose order at a grid boundary is equal to that in the grids interior. In this paper, we construct a second-order mimetic discretization using Castillo and Grones approach and compare it to other second-order discretizations by applying them to an elliptic boundary value problem in one dimension. A detailed perturbation analysis is provided to offer some insight into the two discretizations yielding the best numerical results in the study.Mathematics Subject Classifications (2000) 65D25, 65M06, 65G99.This paper is an expanded version of the article [2] presented at the International Conference on Parallel and Distributed Processing Techniques and Applications held in Las Vegas, Nevada in June of 2003. 相似文献
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A. Albouy 《Regular and Chaotic Dynamics》2008,13(6):525-542
We show that there exists a projective dynamics of a particle. It underlies intrinsically the classical particle dynamics
as projective geometry underlies Euclidean geometry. In classical particle dynamics a particle moves in the Euclidean space
subjected to a potential. In projective dynamics the position space has only the local structure of the real projective space.
The particle is subjected to a field of projective forces. A projective force is not an element of the tangent bundle to the position space, but of some fibre bundle isomorphic to
the tangent bundle.
These statements are direct consequences of Appell’s remarks on the homography in mechanics, and are compatible with similar
statements due to Tabachnikov concerning projective billiards. When we study Euclidean geometry we meet some particular properties
that we recognize as projective properties. The same is true for the dynamics of a particle. We show that two properties in
classical particle dynamics are projective properties. The fact that the Keplerian orbits close after one turn is a consequence
of a more general projective statement. The fact that the fields of gravitational forces are divergence free is a projective
property of these fields.
相似文献
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In general, divergences and measures of information are defined for probability vectors. However, in some cases, divergences are ‘informally’ used to measure the discrepancy between vectors, which are not necessarily probability vectors. In this paper we examine whether divergences with nonprobability vectors in their arguments share the properties of probabilistic or information theoretic divergences. The results indicate that divergences with nonprobability vectors share, under some conditions, some of the properties of probabilistic or information theoretic divergences and therefore can be considered and used as information measures. We then use these divergences in the problem of actuarial graduation of mortality rates. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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运用了Moser迭代技巧,先择适当的检验函数,讨论了散度形式的椭圆型偏微分方程弱解的Hlder连续性. 相似文献
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Pengwen Chen Yunmei Chen Murali Rao 《Journal of Mathematical Analysis and Applications》2008,342(2):915-930
We present a novel classifier for a collection of nonnegative L1 functions. Given two sets of data, one set coming from “similar” distributions labeled as normal, and the other unspecified labeled as abnormal. To understand the structure of normality, and further to classify new data with minimal errors, we propose to find the smallest CKL spheres (based on Csiszar divergences) including as many normal data as possible and excluding as many abnormal data as possible. We prove the existence and uniqueness of such a classifier. 相似文献
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指出江泽坚等合编教材《实变函数论》[2-3]中的一处瑕疵.这个瑕疵起始于第二版,在第三版时又没更正,时间已有22年(1994-2016).鉴于此教材影响大,使用面广,我们特写此注记将此瑕疵指出,与作者和读者商榷. 相似文献
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