分段函数的分类及分离型分段函数与初等函数之间的关系

将分段函数划分为连结型分段函数 ,分离型分段函数和它们的组合形式三种类型 ,得到了分离型分段函数是初等函数的充分必要条件 ,完整地解决了分离型分段函数与初等函数之间的关系 ,并且给出了初等函数在其任一截取集上的限制函数 (截取函数 )仍然是初等函数的结果     

分段函数的分类及分离型分段函数与初等函数之间的关系

将分段函数划分为连结型分段函数，分离型分段函数和它们的组合形式三种类型，得到了分离型分段函数是初池数的充分必要条件，完整地解决了分离型分段函数与初等函数之间的关系，并且给出了初等函数在其行一截取集上的限制函数（截取函数）仍然是初等函数的结果。     

用初等函数表示一类分段函数的方法

用初等函数表示一类分段函数的方法郑州粮食学院龙洪波，伍毅分段函数作为特珠的函数是建立数学模型时经常遇到的一类函数．在一定的条件下，如果能将分段函数化成初等函数，将有利于研究它们的各种性态．本文将给出只有一个分段点，且在两区间段上的表达式均为多项式函数...     

“谈谈初等函数的定义”一文质疑

《数学通报》90年第三期“谈谈初等函数的定义”一文中主要命题的根据及公式是错误的。该文的主要命题“命题1:一个分段初等函数,如果在它的每个分段之内点都是用一个基本初等函数式表示,称之为分段从初型初等函数,对应于每个分段基初型初等函数,都存在着一个用单一初等函数式表示的函数,除界点之外,它与原来函     

关于初等函数

0引言初等函数是数学中的一个基本概念,但围绕这一概念的讨论始终没有停止过.究其原因就是对初等函数的概念认识还不够.甚至有些人对初等函数不很恰当的理解导致了一些不很恰当的结论.特别是对分段函数、积分上限函数的认识更是参差不齐.     

分段函数的初等性及其初等表达式

本文对两类分段函数的初等性进行了证明,并给出了将其表示成初等表达式的构造公式。     

关于分段函数的初等性

关于分段函数的初等性刘文（河北工学院）按照普通教科书中的定义，初等函数是能用一个解析式表示的函数，而这一解析式是由常数和基本初等函数经过有限次四则运算及有限次函数复合步骤所形成的。由于在这个定义中强调了＂能用一个解析式表示＂这一条件，所以分段表示的函...     

利用分段函数制作的几种反例

为澄清对分段函数的一些误解,给出以下反例;１　驳“分段定义函数一定是非初等函数”事实上,存在着分段定义的初等函数,例如ｆ（ｘ）＝ｘ＋１　ｘ＜０３ｘ＋１　ｘ≥０,（１）这个函数可以用统一的解析式表达为ｆ（ｘ）＝２ｘ＋ｘ２＋１,（２）式（２）是基本初等函数的有限次复合与四则运算,式（２）是初等函数,即（１）是初等函数;２　驳“分段定义函数在界点处必不可导”请看反例：ｆ（ｘ）＝ｘ２＋２　ｘ＜１２ｘ＋１　ｘ≥１,ｆ′（１＋０）＝ｌｉｍΔｘ→０－［２（１＋Δｘ）＋１］－（２×１＋１）／Δｘ＝２,ｆ′（１－…     

分段函数、函数的可积性与原函数存在性

论述了分段函数在数学分析中的作用,并以分段函数为工具,给出了函数的原函数存在和黎曼可积之间的关系,有助于全面掌握原函数和定积分这两个重要概念.     

映射与函数

1 本单元重、难点分析，映射与函数是高中数学的重要内容，映射是揭示两个集合之问的内在联系的一个重要手段，函数刻西的是变量之间的相互关系．本单元的重点是：映射与一一映射的概念，函数的概念．函数的懈析式、定义域、值域及图象。函数的单调性与奇偶性的定义、判断及应用，反函数的概念与求法，函数与其反函数的定义域、值域及图象之间的关系．     

超越整函数半群的游荡域

设G是由一族超越整函数生成的半群,其中半群运算是函数的复合.在满足某些假设下,文中得到G在其游荡域内的极限函数要么是∞,要么属于G中某个函数φ的奇异值集合singφ~(-1)的导集.     

Approximation on attraction domain of Cohen-Grossberg neural networks

In this paper, approximations of attraction domains of the asymptotically stable equilibrium points of some typical Cohen-Grossberg neural networks are achieved. Most Cohen-Grossberg neural networks are highly nonlinear systems which makes it difficult to approximate their attraction domain. Under some weak assumptions, we are allowed to employ the optimal Lyapunov method to obtain a Lyapunov function for asymptotically stable equilibrium points of a given Cohen-Grossberg neural network. With the help of this Lyapunov function, we approximate the corresponding attraction domain by the iterative expansion approach. Numerical simulations also illustrate that the approximation obtained is really part of the attraction domain.     

Bergman kernel on generalized exceptional hua domain

We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near boundary points, based on Appell's multivariable hypergeometric function.     

Sharp Estimates of the Distance from a Fixed Point to the Frontier of a Hele-Shaw Flow

We discuss the global shape of a Hele–Shaw flow which is produced by the injection of fluid into the narrow gap between two parallel planes. We translate the problem into a problem concerning the shape of a quadrature domain of a finite positive measure for subharmonic functions and give sharp estimates of the distance from a fixed point to the frontier of the flow.     

有界域的Bergman核函数显式表示的最新进展

对多维复数空间的有界域，如何求出它的Bergman核函数的显表达式，是多复变研究中的一个重要方向。本文综述了迄今为止的所有重要结果以及方法上的进展，特别对新近引进的华罗域，综述了它们的Bergman核函数的显表达式及其计算方法上的创新。     

Plurisubharmonic polynomials and bumping

We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with ∂Ω, at the site of the bumping, are explicitly realised. Generally, when , the known methods lead to bumpings with high orders of contact—which are not explicitly known either—at the site of the bumping. Precise orders are known for h-extendible/semiregular domains. This paper is motivated by certain families of non-semiregular domains in . These families are identified by the behaviour of the least-weight plurisubharmonic polynomial in the Catlin normal form. Accordingly, we study how to perturb certain homogeneous plurisubharmonic polynomials without destroying plurisubharmonicity. The first-named author is supported by a grant from the UGC under DSA-SAP, Phase IV.     

关于亚纯函数增长级的一个注记

研究了无穷级亚纯函数f与亚纯函数g在某个角域上具有分担集S = {a1,a2,a3}的增长级关系.     

Boundary Values of Harmonic Bloch Functions in Lipschitz Domains: A Martingale Approach

In this paper, the boundary behaviour of a certain class of harmonic functions in Lipschitz domains is studied. It continues the work of N. Makarov on the boudary behaviour of analytic Bloch functions in the unit disk. Certain means associated with the function allow to approximate it by a martingale, and the boudary properties of the function are transferred to the asymptotic behaviour of the martingale.     

Uniqueness theorems of entire functions with shared-set in an angular domain

There have been lots of papers on the uniqueness theory of entire functions concerning shared-sets in the whole complex plane. However, it seems that the uniqueness theory in an angular domain is not widely investigated. In this paper, we study the uniqueness of entire functions concerning shared-sets in an angular domain instead of the whole complex plane, and we supply examples to show that Theorem 1 is sharp.     

Meromorphic functions sharing values in an angular domain

In this paper we study the problems of meromorphic functions sharing values in an angular domain and obtain some uniqueness results which are the improvement of the well-known five-value theorem and four-value theorem given by Nevanlinna.