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Its process mathematical description is illustrated through a typical binary distillation column design. Then the framework and strategy of solving the optimal design and control, which involve the solution of mixed integer dynamic optimization, are presented.

以典型二元精馏塔设计为例阐述了其过程系统的数学描述，给出其最优工艺设计和控制设计的求解框架和求解策略，以及其中混合整数动态优化问题的求解方法。

Then it quotes a sufficient condition, the necessary conditions and necessary and sufficient conditions for integration, including the application of mathematical analysis, Real Variable Function-related content which is useful to sum up the necessary and sufficient conditions of the integrability.

然后引述了积分的充分条件、必要条件及充分必要条件，包括应用数学分析、实变函数相关内容总结的可积的充要条件，并作了翔实扼要的论述和证明，且给出针对性极强的应用例题，以便加深对可积条件的理解及加强应用能力。

The integral calculus is the important content of mathematical analysis in the mathematics, in a very important position, in natural science and social science and technology is widely used in the future.

积分学是数学分析的重要内容，在整个数学领域居于极其重要的地位，在自然科学、社会科学和工程技术中具有广泛应用。

Mathematical morphology is developed from set theory and integral geometry, which is concerned with the shape of a signal waveform completely in the time domain rather than the domain frequency.

数学形态学是从集合论和积分几何学发展起来的，它完全在时域对信号的波形进行分析，不涉足频域分析。

Professor Chen Xingshen achievements in order to affirm and encourage the development of our young mathematicians to contribute to the cause of China's Mathematical What he has in-depth introduction to the mathematics outside the field of theoretical physics to become an important tool G introduced geometric structure of the equivalent problem, a 20th century one of the major developments of mathematics, Integral geometry for the generalized basis, access to basic kinematics formulas.

为了肯定陈省身教授的功绩，激励我国中青年数学工作者对发展我国的数学事业做出贡献他引入的东西已深入到数学之外的领域，成为理论物理的重要工具，引进了G 几何的结构，研究其等价问题，成为20世纪后数学的主要发展之一，为广义的积分几何奠定基础，获得基本运动学公式。

The research achievement are acquired as follows: 1From mathematical models for inverse scattering in two dimensional homogenous media including Dirichlet, Neumann, Robin,all kinds of probable mixed boundaries and cracks, direct and inverse scattering are discussed, and ill-posed integral equation and indicator function method are formulated for the diverse of boundary identification. It is shown that the kernel of the integral equation characters the boundary of scatterer, which is determined by solving it by virtual of regularity method, meanwhile, some numerical tests are given.

本研究取得了如下研究成果： 1）在二维均匀介质逆散射各种边界识别的数学模型（包括Dirichlet，Neumann，Robin，各种可能的混合边界问题，裂纹问题）下，分别考虑了正散射问题和逆散射问题，推导了上述各种边界识别的不适定积分方程以及指示函数方法，由于积分方程的核充分表征了散射物的边界，由此说明只要利用正则化方法求解该积分方程，就可以确定散射物的边界，并给出了一些数值实验。

The theories and methods of complexity science and system science should be applied in the study of the system. The new mode of the innovative development of TCM is established by breaking through the linear thinking and reduction analysis, highly emphasizing mathematical principles and methods from a integral and systematic point of view.

该体系的研究需采用复杂科学和体系科学的理论和方法，突破线性思维和还原分析，强调宏观和系统的有机综合，应用数学科学原理和方法来开辟中药创制的新模式。

This paper discusses the relation of variables and invariames in the course of formationand development of a fold,Using mathematical ways,the elliptical integral relation patternof the arclength .wavelength and amplitude are gained. By using computers,their calculatingprogram is obtained for the purpose of practical application.

讨论了岩层褶皱形成和发展过程中变量与不变量之间的关系，应用数学方法得出了弧长－波长－波幅之间的椭圆积分关系式，且编制了它们的计算机程序以便能进行实际应用，在矿产普查与勘探中具有重要的理论意义。

"In mathematical analysis, an integral transform useful in solving certain types of partial differential equations."

数学分析中的一种积分变换，可用来解决特定类型的偏微分方程式。

In the study, calculation of two types of liner wear types based on the direction of liner wear and wear depth of the changes are studied. Mathematical models in terms of vector integral to calculate the liner wear volume is derived first.

本研究计算两种型式内衬之磨耗体积，依据内衬磨耗方向与磨耗深度的变化建立数学模型，并且使用向量积分计算内衬之磨耗体积。

You can do some assertiveness training.

你可以进行一些自信训练。

We were well on the path to making a rear-wheel-drive global platform," says Mays."

我们正致力于建立一个后轮驱动的平台，"Mays这样说道。"