微分

Chapter 5 is to study the group classification and the classification of conservation law for the nonlinear differential equations.

第五章主要研究非线性微分方程的群分类和守恒律分类。

Nonlinear hyperbolic conservation law is one of the core problems in nonlinear PDEs, it has very important physics background.

非线性双曲型守恒律是非线性偏微分方程中的核心问题之一，它有很强的物理背景。

Firstly, the development of the spherical robot is introduced and according to the knowledge of the research forepassed, the nonholonomy and the nonlinear controllability for a spherical robot based on the principle of angular momentum conservation are discussed with the differential geometric control theory.

首先介绍了球形机器人的发展状况，在了解前人研究领域的基础上，应用微分几何控制理论，对此角动量守恒的球形机器人的非完整性和非线性可控性进行了研究。

We also show their conservation properties of mass and energy and set up the corresponding erroe estimates in terms of the L〓-norm.

这样的离散化模型含有原连续模型的几何与物理特征，用它能够更好的模拟发展型微分方程的长时间的和全局的动力行为。

According to the principle of mass conservation, the kinetic model of SCFE is set up founded on differential extraction, and the mass transfer in SCFE is analyzed.

根据质量衡算原理，建立了基于微分床萃取的超临界流体萃取的动力学数学模型，从理论上分析了超临界流体萃取的传质过程。

According to the principle of mass conservation, the dynamic model of SCF-CO_2 is set up on differential extraction base on determining the extracted conditions.

在确定了最佳工艺条件的基础上，根据质量守恒原理，建立了基于微分床萃取的超临界流体萃取动力学模型，从理论上分析了超临界流体萃取过程中各因素对提取率的影响情况，并对模型中的主要参数进行了讨论。

By the law of conservation of mass and the principle of effective stress as well as the equilibrium differential equation, an anisotropic coupled model for the analysis of groundwater seepage and stress is developed.

根据质量守恒定律、有效应力原理、以及土的平衡微分方程建立了各向异性渗流场与应力场的耦合分析的数学模型。

With the modernization of scientific and technological progress and industrial development, physics, chemistry, biology, engineering, aerospace, medical, economic and financial areas of the many principles and laws can be described as an appropriate ordinary differential equations, such as Newton's laws of motion, gravity law, law of conservation of mechanical energy, energy conservation law, the law of population development, ecological population competition, disease transmission, genetic variation, the trend of the stock's up V, the floating interest rates, the market equilibrium price changes.

随着科技进步和工业现代化的发展，物理、化学、生物、工程、航空航天、医学、经济和金融领域中的许多原理和规律都可以描述成适当的常微分方程，如牛顿的运动定律、万有引力定律、机械能守恒定律，能量守恒定律、人口发展规律、生态种群竞争、疾病传染、遗传基因变异、股票的涨伏趋势、利率的浮动、市场均衡价格的变化等。

From equations eliminated some unknown function and its derivative, are contained only one unknown function with constant coefficient of linear differential equations.

从方程组中消去一些未知函数及其各阶导数，得到只含有一个未知函数的高阶常系数线性微分方程 9。

The observer is adaptive one because an adaptation law which can adjust the Lipschitz constant of Lipschitz term is introduced. For this reason, the Lipschitz constant can be unknown in our design.

通过引进一项对Lipschitz非线性项的Lipschitz常数自适应调节的微分调节项，使得观测器具有自适应性，从而设计具有不必知道Lipschitz常数之大小的优点。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。