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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。

Thirdly, the problems of institution investor'optimal liquidation strategy and optimal liquidation time were investigated with the conditions that the price of risky asset followed arithmetic Brown motion and liquidation velocity was limited. The problems involved the following scenes: price impact function was linear expression of liquidation velocity which was boundary closed set with an isolated point; price impact function was stochastic; price impact function was nonlinear.

接着，当风险资产的价格服从算术布朗运动，且对投资者的变现速度做出限制时，研究机构投资者的最优变现策略和最优变现时间问题，其中包括：价格冲击函数为变现速度的线性函数，变现速度是一带有孤立点的有界闭集；价格冲击是随机形式；价格冲击是变现速度的非线性函数。

Many will continue to choose to live in duality and in conflict.

许多人将继续选择活在二元对立性和冲突中。

I find that students of the University of Physical Education all wear sportswear at first sight.

我发现：体育大学的学生乍一看，都是穿运动衣，大家都一样