查询词典 continuously differentiable function

The growth of functions in these spaces depends on a weighted function ρ. We investigate the relation between growth and boundary values of the functions, and prove that a function or its radial derivative is in one of the spaces if and only if the p'integral average of the difference of its boundary value function is integrable or bounded.

研究这些函数空间中函数的增长性与边界值的关系，得到了函数或其径向导数属于相应空间的充分必要条件是其边界值差分的p次积分平均应具备一定的可积性或有界性。

A method of construction of Liapu-nov function is given. This Liapunov function has form of x plus an integral of a nonlinear function ?

提出一种处理"二次型加非线性函数的积分"形式的函数的方法，并得到一个新的绝对稳定准则。

When computing the diagonal elements of the Galerkin matrix, one will encounter the integral of Hankel function, the Green's function of 2-dimensional Helmholtz equation and the cosine weighting function, whose integrand is singular in the integration range. A new approach is proposed to deal with this kind of singular integrals, which is pivotal but have not been reported so far.

首先建立了透镜边缘上任一点的电场满足的边界积分方程，然后选择适当的正交模式函数展开端口上的电场分布，采用边界元法的思路及Galerkin法将该积分方程离散化为—矩阵方程求解即可得到透镜的多模式散射参数。

This system has the space and time different interpellation, characteristic and so on relative stability, multiplicity and dynamic characteristic, but also has the production function, protects and restores the function, the expense and the destruction function.

该系统具有时空异质询性、相对稳定性、多样性和动态特征等特性，还具有生产功能、保护和恢复功能、消费和破坏功能。

To create a Perlin noise function, you will need two things, a Noise Function, and an Interpolation Function.

为了创建一个柏林噪声函数，我们需要两个东西，一个噪声函数和一个插值函数。

If there is a possibility of the existence of its inverse function, it will be easier to integrate the function by using its inverse function than by using normal integral way.

表面上看，这里边似乎有一定的规律性，实则需要大量的特殊灵活的技巧，显然，求一个积分往往不止一种方法。

The inverse function of that restricted sine function is called the arcsine function.

被限定的正弦函数之反函数叫做反正弦函数。

Three common mathematic models are always employed to predict the growth of regional or urban population,including exponential function,inverse hyperbolic function,and logistic function.

预测人口增长的数学模型通常采用3种函数，即指数函数、Logistic函数和双曲函数。3种模型的数学根源都在于二阶Bernoulli式微分方程，它们是不同的生长条件下的Logistic方程的特解。

The course content links up always background mathematics course for nine years, have eight chapter in all, include the set, real number, multinomial, dividing into type and irrational expression, function, figure, trigonometric function, against such chapters as trigonometric function and complex number, etc..

课程内容衔接九年一贯基础数学课程，共有八章，包含集合与实数、多项式、分式与无理式、函数及图形、三角函数、反三角函数及复数等章节。

According to invalidate transform between non-linear constraining function and linear constraining function, and the disable partial differential coefficient of first order for objective function, GA has been chosen for the built mathematic mode, also, the conception of GA, its computing process, features, and operating parameters are introduced irrespectively in this article, meantime, a managerial software for oil pipeline's optimization is programmed.

根据优化模型中的非线性约束函数无法化为线性约束函数，目标函数无法求一阶偏导数的特点，本文从众多优化方法中选择遗传算法对所建立的数学模型进行求解，并对遗传算法的概念、计算步骤、特点、运行参数等逐一进行介绍，并编写了输油管道优化运行管理的软件。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。