函数

It can also be used as a powerful tool in data base systems. A kind of Mini-LISP language used on VAX/VMS 11-780 and PDP11/45 under the support of RSX-11M operating system is presented with an introduction of the LISP language structure, composition and its programming ...

全文分三部分连载：第一部分介绍Mini-LISP的基本成份、简单原语和基本函数，是LISP程序设计的基础；第二部分介绍λ函数、递归函数及过程函数的表示法，并列举Mini-LISP的常用函数；第三部分介绍LISP语言在符号处理、人工智能和数据库系统设计中的应用实例。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

In mathematics the smoothing of a function is often measured with the continuity, or nth deriv-ation, of the function, and the more precise measurement is the Lipschitz exponent of afunction.

函数在某点的光滑程度可用其在这点的连续性和各阶导数描述，但更细致的描述是用函数在这点的Lipschitz指数来刻划的，而函数在一个区间上的光滑性则可以用函数的一致连续和导函数来考察，更精确的是用一致Lipschitz指数来考虑。

The process of our study links some of the most basic questions about C〓 with beautiful classical results from analyticfunction theory. For instance, it is essential Littlewood subordination theorem that assures that composition operators act boundedly on many analytic function spaces. And there are close connections between the compactness of C〓 and the existence of angular derivatives of ψ at points of 〓D. It involves the classical Julia-Careatheodory theorem, Denjoy-Wolff theorem and Nevanlinna counting functions and so on. It makes many old theorems in analytic-function theory getting some new meanings, and bestows upon functional analysis an interesting class of linear operators. This thesis consists of six chapters as follows: Chapter 1 is a preparatory in nature.

从而建立了C〓的算子性质与解析函数论中许多漂亮的经典结果之间的联系，如许多解析函数空间上复合算子的有界性本质上往往是著名的Littlewood从属原理，复合算子的紧性与其诱导映射在边界〓D上的角导数之间有着紧密的联系等等，这样自然而然地涉及到经典函数论中的Julia-Caratheodory定理，Denjoy-Wolff定理及Nevanlinna计数函数等等一些结果，并以此赋予函数论中许多古老问题以新意，同时也为泛函分析提供了一类十分具体的线性算子。

The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

Deduced the analytical structure of the Mamdani fuzzy system whose input sets were with generalized linear membership function and manifested that the output of the fuzzy systems were monotonical, decreasing, continuous and bounded.

设计了一种将三角形和梯形隶属函数作为特例的广义线性隶属函数，推导了输入采用广义线性隶属函数的典型Mamdani模糊系统的解析结构，证明了典型模糊系统是单调、递减的有界连续函数；在此基础上证明了该类模糊系统能以任意精度逼近任意连续实函数，最后仿真实例证明了本设计的有效性。

Address the characteristics of non-uniform speed transmission, position function control and transmission ratio function control were presented to realize electronic gearbox. The differences between position function curve interpolation and general NC interpolation were analyzed. Considering the effect of uncontrollable continuous principal motion, interpolation slope and position function precompensation interpolation were presented. The relationship among interpolation, servo dynamic response and transmission precision was studied. The coordinate linkage relationship and electronic gearbox scheme in noncirclar gear hobbing were studied.

对电子齿轮箱实现非匀速比传动进行了研究，提出了位置函数控制与传动比函数控制两种非匀速比传动关系的实现方法；对位置函数控制方式，分析了位置函数曲线的插补与普通数控插补方法的区别，提出了插补斜率的概念与位置函数曲线的预补偿插补方法；对非匀速比电子齿轮箱传动精度进行研究，得出了插补精度、伺服系统动态性能指标与传动精度之间的关系；研究了非圆滚齿加工坐标联动的非匀速比传动关系，列出了多种可以满足要求的电子齿轮箱传动方案。4。

The investigations in this thesis focus on several aspects as follows: We investigate the method that how to produce permutation matrix by using chaotic map, and get the method of image permutation based on chaotic map. This method can make original image to unorderly image to protect the true content of image. We investigate gray level mix function, and put forward a gray level mix function based on chaotic map. Because this function has chaotic characteristics, the image dealed with this function has very uniform histogram. Aiming at the contradiction between error robust and security on image encryption, we put forward a kind of gray level mix function including diffusion mechanism.

本文的研究工作主要集中在以下几方面：研究了如何利用混沌映射产生置乱矩阵的方法，给出了基于混沌的数字图像置乱方法，该方法能够将原始图像变成面目全非的杂乱图像，从而保护了数字图像的真实内容；研究了灰级混合函数，提出了基于混沌的灰级混合函数，由于该函数具有混沌特性，所以经过该函数处理后的图像具有非常均衡的灰级直方图；针对图像加密的错误鲁棒性与安全性之间的矛盾，提出了一种含有扩散机制的灰级混合函数。

This is a vast collection of computational algorithms ranging from elementary functions like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.

MATLAB 的工具箱函数库收集了大量的数学函数，从求和，正弦，余弦以及复杂的算术运算等基本函数，到矩阵求逆，矩阵求特征值，贝塞尔函数和快速傅里叶变换等复杂函数。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。