共查询到20条相似文献,搜索用时 250 毫秒
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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。 相似文献
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示性函数在实分析等课程中很基本且应用广泛,但在初等概率论教材里应用不多.本文举例说明示性函数可以帮助学生理解初等概率论中一些基本概念、结论并精简其中一些计算. 相似文献
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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,所以分段表示的函数是否为初等函数就另需加以判定了.本文的目的就是要讨论这一问题.引理三函数都是初等函数.证明因为g1(x),g2(x),g3(X)分别可表示为放它们都是初等函数.引理2函数都是初等函数.证明因为分别可表示为放它们都是初等函数,引理3若分别是和(a,b)上的初等函数,均为常数,则都是初等函数,它们分别… 相似文献
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<正> 关于初等函数的连续性问题,通常教材上有两种叙述方式,一种是“一切初等函数在其定义域内都连续”,另一种是“一切初等函数在其定义区间内连续”.这些都是关于初等函数连续性的结论.有了上述初等函数连续性的结论,似乎有关初等函数连续性问题就没有讨论的必要了,但是要问:(i)初等函数有无不连续函数,或者初等函数在定义域内有无不连续点?(ii)初等函数的定义域是否都是区间或区间的并集?那应怎样回答呢?利用初等函数连续性己知的结论,(i)的答案应是“无”;那(ii)的答案呢?似乎就不太好回答.这两个问题,我们只要看一个反例,就很好回答了.看函数y=(sinx-1)/(1/2)它可以看成是由y=u/(1/2),u=sinx-1复合而成的,又y=u/(1/2),u=sinx-1都是基本初等函数,所以由初等函数的定义可知y=(sinx-1)/(1/2)是初等函数,它的定义域是 相似文献
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The mean value form is a well‐known interval arithmetic means to compute tight range bounds for real functions. In this paper, the mean value form is extended for the computation of range bounds for complex analytic functions, both for rectangular and for circular complex intervals. Quadratic convergence and inclusion isotonicity of the complex mean value forms are discussed. 相似文献
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In this paper, firstly, we obtain the variable separation solutions of (2 + 1)-dimensional KdV equation by the extended tanh-function method (ETM) based on mapping method. Novel localized coherent structures about multi-valued functions, i.e. special dromion, special peakon and foldon, and the interactions among them, are discussed. The interactions between two special dromions and between two special peakons possess novel property, that is, there exists a multi-valued foldon in the process of their collision, which is different from the reported cases in previous literature. Moreover, the explicit phase shifts for all the local excitations offered by the quantity u have been given, and are applied to these novel interactions in detail. 相似文献
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根据Nevanlinna理论讨论了一族亚纯函数中每个函数与其k(k为任一正整数)阶导数单向分担3个有限复值时的正规性,并举例说明这一结果是精确的. 相似文献
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Michiel Hazewinkel 《Acta Appl Math》2003,75(1-3):55-83
This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric functions. The focus is on the incredibly rich structure of the Hopf algebra of symmetric functions and the question of which structures and properties have good analogues for the noncommutative symmetric functions and/or the quasisymmetric functions. This paper attempts to survey the ongoing investigations in this topic as dictated by the knowledge and interests of its author. There are many open questions that are discussed. 相似文献
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D. Yu. Panin 《Moscow University Mathematics Bulletin》2013,68(3):173-176
Systems of unary monotone functions of multi-valued logic are considered. These functions are monotone with respect to partial orders of special form. Criteria for the completeness of these functional systems are obtained. 相似文献
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运用复分析方法,首次给出了一类由三角函数、指数函数与幂函数乘积的线性组合产生的函数在某个区间上恒为零的充分必要条件证明,建立了此类函数积分计算的理论基础,结合微分和线性代数思想,系统讨论了待定系数法在一类含有三角函数的积分计算中的应用. 相似文献
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B. C. Dhage 《Applicable analysis》2013,92(9):953-970
This article studies the existence of solutions to boundary-value problems for second order multi-valued perturbed differential inclusions under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions and the weaker nonconvexity conditions for multi-valued functions. 相似文献
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首先给出了复$k$-hypergenic函数的几个等价条件,其中包括广义的Cauchy-Riemann方程.其次给出了复$k$-hypergenic调和函数的几个等价条件.
最后讨论了复$k$-hypergenic函数和复$k$-hypergenic调和函数的关系.例如,已知一个复$k$-hypergenic调和函数$u(z)$,则局部存在复$k$-hypergenic
函数$f(z)$, 使得$P_0f(z)=u(z)$. 相似文献