查询词典 integral of a differential equation

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

This curriculum primary coverage includes: Function and limit, a circular function derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral, definite integral application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral, curvilinear integral and surface integral, infinite series, differential equation.

该课程的主要内容有：函数与极限，一元函数的导数与微分，中值定理与导数的应用，不定积分，定积分，定积分的应用，空间解析几何和向量代数，多元函数微分法及其应用，重积分，曲线积分与曲面积分，无穷级数，微分方程。

By changing differential equations into nonlinear integral equation,we study the existence of positive solution of a class of second order differential equations problems by the fixed point theorem of cone expansion and compression,and the fixed point index theorem,then we obtain two multiple positive .

通过将常微分方程转化为非线性积分方程，利用锥拉伸和锥压缩不动点定理和不动点指数讨论了一类二阶常微分方程的正解存在性问题，在一定条件下，得到了几个多重正解定理，同时证明了与此相关的主要引理

Properties are discussed for a class of exponential sum function on recurrence relationship,integral formula,it has been proved that its curve configuration is single peak and it is a probability density,the application of this function is showed in proving equalities and a differential equation model of substance transform reaction.

对一类指数和函数的递推关系、积分公式、曲线的单峰形态等性质进行了讨论，证明了该函数为概率密度函数，并给出了该函数在等式证明、物质转化反应的微分方程模型等方面的应用。

The integral inequality is a useful tool when we study the stability theory of differential equation, especially when we study the stability, the estimate of solution and the boundedness of differential equation.

在研究微分方程稳定性理论中，尤其在探讨微分方程的稳定性，解的估计及有界性的过程中，积分不等式是一强有力的工具。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation. In part I, a group of sufficient conditions is given on continuation of solutions and three groups of sufficient conditions are given on boundedness of solutuicns of equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

In Chapter Five, we compare numerical integration of the reproducing kernel with the integral equation of complexified trapezoid through a detailed solution to the initial-value problem of ordinary differential equation to exemplify that the method of interpolation spline integrating and the reproducing kernel is not only feasible in theory but also significant in pratice.

在第五章，我们通过具体的求解一个常微分方程的初值问题，把再生核方法的数值积分和复化梯形积分公式相比较，说明样条插值和再生核相结合的方法不仅是理论上可行的，而且还具有重要的实际意义。

Because the workpiece is in dynamic balance, the resultant moment acting on it should be zero. Introducing the moment from lapping tool and press head a moving differential equation is built. In this equation only workpiece rotating speed is unknown. It means that workpiece rotating speed can be got by this equation. Since there is a transcendental function in integral function of the equation an analytic result can not be got, only digital result can be got by a computer. Thus a change rule of workpiece rotating speed with lapping parameters is known, e.g. the radius of press disc ball socket, radius of press head ball, the distance between the workpiece rotating axis and lapping tool rotating axis, workpiece radius, modulus of elasticity of the press head and press disc, friction coefficients between the lapping tool and workpiece, and between the head and disc, pressure between the lapping tool and workpiece and pressure between the press head and press disc.

因工件处于动态平衡状态，其上所受到的来自于磨具和压头的力矩应相等，将二力矩表达式联立，建立工件运动微分方程，该方程中只有工件的旋转角速度是未知量，因此可以求出工件旋转角速度，但该方程积分式中含有超越函数，得不出解析解，只能通过计算机求出数值解，得出工件旋转角速度随各研磨参数的变化规律，如压盖球座半径、压头的球头半径、工件回转中心相对磨具回转中心的偏心距、工件半径、压头和压盖材料的弹性模量、磨具与工件间的摩擦系数、压头压盖间的摩擦系数、磨具与工件间的压强、压头压盖间的压力等。

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

Then, it studies the supply chain management system as a complex system to confirm the state existing during operating of the system. After that, it conducts a probability analysis on the state which the system located by applying supplement variable method, and establishes the model of distributed parameter system in a form of partial differential equations. Combining C0 ? semigroup theory in the functional analysis, it conducts a dynamic analysis on the established mathematical model. Using this method, it obtains the mathematical expression of the dynamic solution and the steady state solution, and proves the uniqueness, non-negativity and the asymptotic stability of the system solution. This dissertation applies the Matlab tool and uses two-step, three-step Simpson integral equation to imitate the condition of system solution. Then, it adds possible mode of failure and the optimization adjustment state to the system, based on which it has established the distributed parameter system model which is described by partial differential system of equations. Combining the functional analysis C0 ? semigroup theory, it studies the established mathematical model, and obtains the mathematical expression of the dynamic solution system and the steady state solution. It has proven the existing of uniqueness of the system solution, the asymptotic stability of system solution and the system solution. In addition, it has lying the theory rationale for further analysis and the research on the optimization of system.

本文首先简要综述了供应链理论、可靠性研究、鲁棒性研究以及供应链鲁棒性研究的现状；然后，将供应链系统作为一个复杂系统来分析，确定了系统运行过程中所经历的状态，通过引入补充变量的方法，建立了用偏微分方程组描述的分布参数系统模型，用泛函分析中的C_0 -半群理论得到了系统动态解和稳态解的数学表达式，证明了系统解存在的唯一性、非负性和指数阶渐近稳定性；并借助Matlab工具，利用二阶、三阶辛普森积分方程模拟系统解的性态，并给出系统动态解的仿真图；本文又对上述系统增加了系统可能失效状态和优化调整状态，并在此基础上建立了用偏微分方程组描述的分布参数系统模型，同样用泛函分析中的C_0 -半群理论对所建立的数学模型进行了研究，得到系统动态解和稳态解的数学表达式，证明了系统动态解存在的唯一性、非负性及渐近稳定性，为进一步分析和研究供应链优化奠定了理论基础。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。