复合函数

Within this framework we develop a theoretical approach to interpret photoelectron angular distributions in terms of a generalized phase Bessel function which can determine the principal features of the distribution and its variation with laser frequency and intensity.

文章作者及其合作者发展了光电子角分布的处理方法，利用复合相位Bessel函数来表征光电子的跃迁几率幅，将光电子的角分布与复合相位Bessel函数直接联系起来。

There are mainly four innovations made in this thesis: By introducing the notion"collectively compact operator sequence"into the study of composition operators, we give a sufficient and necessary condition on generalized Nevanlinna counting functions of the inducing maps for {C〓} to be collectively compact, extend some previous results and enrich the content of the study of composition operators.

本文主要在以下几个方面有所创新：第一，把逼近论中的算子序列总体紧性的概念引入到复合算子理论的研究中来，并通过值分布理论中的广义Nevanlinna计数函数给出了Hardy空间与加权Bergman空间之间的复合算子序列的总体紧性的刻画，从而推广了Shapiro的结果，丰富了复合算子理论的内容。

Iii By using the well-known properties of the dela vallee-poussin summability kernels and the pass principle of weakly compact operator, we study the weak compactness of C〓 on vector-valued analytic function spaces H〓, B〓, N and N〓, establish some connections between the weak compactness of composition operators and the structure properties of Banach spaces. These generalize and unify the corresponding results in the scalar-valued setting and enrich the content of the study of composition operator in another way.

第三，利用著名的de la Vallee-poussin可和核及有关算子的弱紧性的传递原理给出了向量值解析函数空间H〓、B〓、N及N〓上的复合算子的弱紧性的刻画，建立了复合算子的弱紧性与Banach空间的结构性质之间的联系，统一和推广了对应的数量值解析函数空间上的复合算子的弱紧性，这从另一种途径极大地丰富了复合算子的研究内容。

The polar form is used as the representation for one of the composite functions, whereas the Bernstein representation is used for another function. At the last part of this chapter, we consider the problem about generalized Bezier surface, which is defined in arbitrary convex polygon.

我们利用函数复合的思想去处理这个问题，被复合的两个函数一个用Polar形式表示，另外一个用Bernstein基形式表示，这样就可以充分利用Polar形式的多元仿射性，直接生成新的控制顶点，简化了证明过程。

And proved equivalent relation of characteristic functions with asymptotically of two composite entire functions under given conditions.

证明了在一定条件下两个复合整函数的特征函数具有渐近等价的关系；并给出了复合亚纯函数的特征函数的一个上界。

This paper discusses such problems which are easily solved incorrectly in limitedteaching as, segment function is uncertain not to be elementary function, elementary function is un-certain to be continuous in its field of definition, unlimited variable is uncertain to be infinity, theinfinitely many infinitesimal is uncertain to be infinitesimal, the multiplication of two non- infinitesi-mal is uncertain not to be infinitesimal.

1分段函数不一定不是初等函数我们知道初等函数的定义是：常数和基本初等函数经过有限次的四则运算或复合，用一个解析式表示的函数叫初等函数。教材中的定义强调的"有限次"和"一个解析式"，使很多同学产生"非有限次"和"非一个解析式"的函数就不是初等函数的误解。例1f=ceox，s xx！0为分段函数，但也可以表示为f=e12(x-x2")+cos12(x+x2#"$)-1，故为初等函数。

This paper is committed to expatiate on the attribute of the functions profoundly from several aspects such as the mapping, inverse functions, compound function and etc and discuss the attributes of mapping and several special functions energetically.

本文着重从几个方面如映射、函数的复合、反函数等深刻阐述了函数的性质，且重点讨论了映射、几种特殊函数的性质和应用。

The main goal is to use some results and methods from classical analytic-function theory to determine some of the most basic questions you can ask about linear operators and functional space. At the same time using functional space theory and operator theory as a tool to study the classical questions in function theory.

解析复合算子的研究是解析函数论和算子理论结合的产物，其目的是利用经典解析函数论中的方法与结论探讨泛函空间与算子理论中的一些最基本的问题，同时也以泛函空间与算子理论为工具研究函数论中的经典问题。

However, the study, as a part of linear operator theory, of operators induced by composition with a fixed function has a relatively short history.

但是一个固定的函数与某个函数空间上的函数复合作为该空间上的线性算子进行研究则是不久的事情，这可追溯到二十世纪60年代末E。

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。