查询词典 analytical differential

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

二阶线性齐次微分方程在微分方程理论中占有重要位置，但二阶变系数微分方程却没有一般的求解方法，大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式，并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

Content: By learning this course, students should grasp the elementary solution of first order differential equation, the structure theory of linear differential equation or system of linear differential equations and the solution of constant coefficient differential equation or system of constant coefficient differential equations.

主要内容：通过对本课程学习，使学生掌握一阶微分方程的初等解法、线性微分方程的结构理论和常系数方程的解法，对微分方程初值问题的一些基础理论有一定的了解，对

Limited slip differential is improved according to common differential. Not having the common differentials disadvantage of dividing the torque into two equal parts, limited slip differential can give most torque or even all torque to another driving wheel which is not revolving in order to make use of the friction of this driving wheel to produce enough traction. This will greatly increase the dynamical capability, the passing capability, the stability and the safety of automobiles on different friction roads. So limited slip differential is substitute for common differential.

防滑差速器是对普通差速器的革新与改进，它克服了普通差速器只能平均分配扭矩的缺点，可以使大部分甚至全部扭矩传给另外一个不滑转的驱动轮，以充分利用这一驱动轮的附着力而产生足够的牵引力，大大提高了汽车在双附着系数路面上的动力性和通过性，显著改善了汽车操纵稳定性，有效地提高了汽车行驶安全性，是普通差速器的理想替代产品。

In this paper, the investment planning of wireless network monitor system can provide a basis for decision-making for this technology industrializationIn this paper, according to advanced mature Payoff ability analytical method; rePay ability analytical method; sensitivity analytical method; Profit and loss balance analytical method, etc.

本文利用盈利能力分析法、偿债能力分析法、敏感性分析法、盈亏平衡分析法等相关方法，根据项目特点，结合调查分析资料，对目标顾客群进行细分，确定了该产品的目标市场及其营销模式；对原材料供应商进行地域和功能分析，结合国家产业导向，确定了该产品的生产组织模式；对投资规模、财务状况以及预期的投资风险进行预测，确定了该项目预期的收益和现金流，并为潜在风险提供了可行的规避办法。

An explicit analytical solution of the threshold pump power of the laser has been derived based on rate equations which contain the attenuation coefficients of the pump and laser radiations as well as the major contribution of the re-emission of the upper level atoms to the pump wave by using the analytical solutions. An analytical solution of the minimum fiber length required for the onset of the oscillation is presented. In addition, the analytical solutions describing the variations of the density of the pump radiation and upper laser level population along the fiber length have also been given.

从速率方程组出发，在不忽略光纤损耗系数和保留再发射项主导部分的近似条件下推导出了双包层光纤激光器阈值泵浦功率的显函数解析表达式，得到了光纤激光器产生振荡所需的最小光纤长度的显函数解析解；还给出了泵浦光子数密度和上能级粒子数密度沿光纤方向随光纤长度变化的显函数解析解。

By the natural and harmonious relationship between differential forms and differential equations and between differential forms and vector analysis, we discuss the properties, which are covariant under the transformation of coordinates in the framework of differential forms, of particle motion in a central force field .

通过微分形式与微分方程和向量分析之间存在的自然而协调的关系，在微分形式框架下讨论了质点在有心力场中运动的特性并得出在坐标变换下其均是协变的

This article use the improved integral inequalities with the deviate variable and some skills of inequalities as well as related knowledge about second-order differential equation,to obtain the following results: the classification of limit point case or limit circle case and boundedness for second order differential or difference equation with deviative variable,discussed the classification for certain n-order differential equations,Criteria for the classification of second order differential equation with deviative variable.

本文利用推广的具有偏差变元的积分不等式，结合不等式的一些技巧以及常微分方程的相关知识对一类二阶具有偏差变元的微分方程及一类二阶差分方程极限圆型的分类问题作了相关的研究工作，并且讨论了一类n阶具有偏差变元的常微分方程解的平方可积性与有界性和一类二阶非线性具有偏差变元的微分方程解的有界性。

Anna: No, I've got a hangover.

不是，我昨晚宿醉了。

We head into the mountains in Su's new Land Cruiser, stop for lunch at a scenic restaurant and then hang around drinking beer and eating fruit as two of his employees attempt to lure the birds with a tape recording of the fowl's mating call.

我们坐上苏的巡逻车向山顶出发，在一家风景优美的餐馆吃了中饭。然后我们喝着啤酒吃着水果四处逛。