一类二元有理分式函数极限的存在性探析

本文为一类二元有理分式函数极限的存在性建立了一个幂指数判定定理,其结果与文[3,4]中的结论保持一致.通过总结本文曲线路径的构造经验,给出了一个证明二元函数极限不存在的常用的曲线路径的构造方法.     

广义齐次有理分式函数极限的存在判别法

本文给出一个二元广义齐次有理分式函数极限的存在性判别准则.     

一类多元函数极限不存在性判别法

为一类二元及三元广义齐次有理分式函数极限的不存在性建立一个判别准则.     

泰勒公式在判定二元函数极限存在性中的应用

本主要探索利用Taylor公式对无穷小量的阶进行估计，从而有效地判断出二元函数极限的存在性。     

二重极限不存在的一种证明方法

给出一类常见的二元有理分式函数极限不存在的一种证明方法,并举例说明.     

Mathematica数学软件的图形功能在微积分中的应用问题

讨论如何正确使用Math.的图形功能,对微积分中二元函数在一点极限不存在的情形及二元函数在点不连续但偏导数存在的情形给出几何解释。     

求二元函数的极限两例

求二元函数的极限两例王婕，金钟（本溪高等职业专科学校）（蚌埠市职工大学）求二元函数的极限，不可简化为求一元函数的极限。若极限不存在，则简化出现许多花样。今就两例说之。因沿各条直线趋于原点，极限都存在，但不相等。若沿通过原点的抛物线ｙ＝ａｘ２趋于原点，...     

一类幂指函数的二重极限的存在性

通过选取极坐标系下的不同路径,证明了几类"0~0"型未定式的二重极限的不存在性;通过两边夹准则获得了一些"0~0"型未定式的二重极限的存在性,进而给出了研究底数和指数都是二元多项式函数的"0~0"型未定式的二重极限的一般方法.     

二元函数极限不存在的几何解释

本文通过几何方法更为直观的解释二元函数极限不存在.     

关于导数极限定理的几个应用及其推广

本文首先利用导数极限定理,总结了一些导函数分析性质,并举例说明各种类型间断点在导函数中出现的可能性,最后将导函数极限定理推广到二元函数情形.     

CONVERGENCE OF THE CLIPPED SAMPLE AUTOCORRELATION AND AUTOCOVARIANCE

1.IntroductionClassicalmethodstoestimatetheautocorrelationandautocovarianceofastationarylineartimeseriesworkwellforgoodobservations,buttheyaresensitivetotheexistenceofoutliers.[1]gayeamethodofestimatinganARprocessbycountingthenumberofcertainrunsintheassociatedclippedbinaryseries.Althoughinsodoingsomeefficiencyislost,theproceduregivesgoodestimatesagainstoutliers.LetX.,n=0,11,12,'1beareallinearGaussiansequencewithzeromeanandautocorrelationspj~EXoXj/EXI,j=0,1,'landXu,n~0,11,',theclipped…     

Existence of a limiting distribution for the binary GCD algorithm

In this article, we prove the existence and uniqueness of a certain distribution function on the unit interval. This distribution appears in Brent's model of the analysis of the binary gcd algorithm. The existence and uniqueness of such a function was conjectured by Richard Brent in his original paper [R.P. Brent, Analysis of the binary Euclidean algorithm, in: J.F. Traub (Ed.), New Directions and Recent Results in Algorithms and Complexity, Academic Press, New York, 1976, pp. 321–355]. Donald Knuth also supposes its existence in [D.E. Knuth, The Art of Computer Programming, vol. 2, Seminumerical Algorithms, third ed., Addison-Wesley, Reading, MA, 1997] where developments of its properties lead to very good estimates in relation to the algorithm. We settle here the question of existence, giving a basis to these results, and study the relationship between this limiting function and the binary Euclidean operator B₂, proving rigorously that its derivative is a fixed point of B₂.     

二元函数梯度存在的一个充要条件

本文首先拓展了二元函数方向导数的计算公式,并给出了该公式成立的充分必要条件,在此基础上也给出了二元函数梯度存在的一个充要条件.     

一个特殊的二元函数

欧拉常数γ是以极限形式给出的,本文由此得到一个特殊的二元函数γ(x,y),并给出它的一些性质,最后给出它在求数列极限与数项级数和方面的应用.     

一个特殊的二元函数

欧拉常数γ是以极限形式给出的，本文由此得到一个特殊的二元函数γ（x，y），并给出它的一些性质，最后给出它在求数列极限与数项级数和方面的应用．     

Cycle control functions and the number of limit cycles

The cycle control function is defined and used to estimate the number of limit cycles for some planar autonomous systems. Some sufficient conditions for the existence of no or at most one limit cycle are given.     

关于求解极限的若干思考

无穷小等价替换是计算极限一种常用且好用的方法,但要求替换项在极限点的某个邻域内没有零点,文章证明了函数在极限点的任意邻域都出现零点时,满足一定条件,等价替换仍可实施.另外利用极坐标计算二元函数极限时有诸多的限制,文章针对一类特殊函数给出了应用极坐标便于计算应用的若干结论.     

Periodic orbits for perturbations of piecewise linear systems

We consider the existence of periodic orbits in a class of three-dimensional piecewise linear systems. Firstly, we describe the dynamical behavior of a non-generic piecewise linear system which has two equilibria and one two-dimensional invariant manifold foliated by periodic orbits. The aim of this work is to study the periodic orbits of the continuum that persist under a piecewise linear perturbation of the system. In order to analyze this situation, we build a real function of real variable whose zeros are related to the limit cycles that remain after the perturbation. By using this function, we state some results of existence and stability of limit cycles in the perturbed system, as well as results of bifurcations of limit cycles. The techniques presented are similar to the Melnikov theory for smooth systems and the method of averaging.     

Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs

We prove the existence of absolutely continuous spectrum for a class of discrete Schrödinger operators on tree like graphs. We consider potentials whose radial behaviour is subject only to an ?^∞ bound. In the transverse direction the potential must satisfy a condition such as periodicity. The graphs we consider include binary trees and graphs obtained from a binary tree by adding edges, possibly with weights. Our methods are motivated by the one-dimensional transfer matrix method, interpreted as a discrete dynamical system on the hyperbolic plane. This is extended to more general graphs, leading to a formula for the Green's function. Bounds on the Green's function then follow from the contraction properties of the transformations that arise in this generalization. The bounds imply the existence of absolutely continuous spectrum.