查询词典 explicit differential equation

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。

This data visualization system in this thesis has an extensive function, including calculus operation, solving the algebraic equation and differential equation, the operation of series and the transform of integral and so on.

本设计开发的数据可视化系统具有强大的运算功能，包括微积分运算、代数方程与微分方程的求解、级数运算、积分变换等。

Specifically, there are three kinds:(1) constant variation method to track two-body problem the root number of variables to establish perturbed equation;(2) coordinate perturbation method in order to track objects in real position and the location of an intermediate orbit perturbation differential equation as a variable to establish;(3) transformation theory, through a series of canonical transformation to reduce the order of the equations of motion to make it a more simple form.

具体做法有三种：（1）常数变异法，以二体问题轨道根数为变量建立摄动方程；（2）坐标摄动法，以天体在实际轨道上的位置与某一中间轨道上的位置差作为变量建立摄动方程；（3）变换理论，通过一系列正则变换，降低运动方程的阶数，使其具有更简单的形式。

This is the learning algorithm "Adams steps with four bands interpolation formula correction" of their times calculated for the numerical solution of differential equations procedures, they can modify the equation for the solution and the other equation, Hi!

这个算法是在学习"用Adams三步四阶内插公式校正"时自己遍的计算这个微分方程数值解的程序，可以修改里面的方程而用于求解其他的方程，请指正！

Firstly, several kinds of schemes were proposed according to the design demand. The best scheme was chosen after analyzing and comparing the schemes. The robot's structure was designed with Pro/Engineer and AutoCAD software. Secondly, the kinematics analysis conducted, coordinate transformation matrix using D-H method was set up, and the kinematics equation direct solution and inverse solution was deduced. The manipulative interface about the kinematics equation direct solution and inverse solution was completed with VC++ and the velocity Jacobian of displacement matrix was constructed using differential transform method. In the process of the trajectory planning based on robot's kinematics analysis, I propone a method by which we can get middle nodal point with normalizing factor in order to simplify our searching for these middle nodal points. In addition, I give these middle nodal points with actual physics signification. For eliminating contradiction between real-time and accuracy, I bring forward separately limit of error and reversal interpolation method. For decreasing calculation quantity, we resort to tri-spline interpolation in the articulation space.We analyse the work range of the robot by resorting to graphic means.

首先，作者针对机器人的设计要求提出了多个方案，对其进行分析比较后，选择其中最优的方案后用Pro/Engineer和AutoCAD软件进行了机器人模型结构设计；其次，进行了运动学分析，用D-H方法建立了坐标变换矩阵，推算了运动方程的正、逆解，运用VC++制作了正、逆运动学求解的求解界面；并且用微分变换法推导了速度雅可比矩阵；在基于机器人的运动学的轨迹规划中，通过在操作空间的规划，提出了归一化因子来求解中间结点，通过它可以使求解中间结点变得更简单，并且赋予这些中间结点实际的物理含义，对于规划中精确性和实时性的矛盾，提出了以误差极限法和反向插值法来解决的方法；为了减少规划过程中计算量，在关节空间进行三次样条插值；然后借助图解法进行工作空间分析，作出了实际工作空间的轴剖图。

Lyapunov second method is applied to analysis of partial stability of equilibrium of linear ordinary differential equation with constant coefficients, the problems on partial stable matrix, partial positive definite matrix and Lyapunov matrix equation are studied.

将Lyapunov第二方法用于研究常系数线性系统零解的部分变元渐近稳定性，可引出相关的一些特殊矩阵问题，包括部分稳定矩阵、部分位正定矩阵、矩阵方程的可解性等。

After a linear differential equation showing the pressure variation has been derived, the theoretical equation of the spraying time is...

建立了存储压力与时间的变量分离型一阶微分方程，进而得出喷射时间的理论公式。

This volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner.

这卷涉及在一个数学物理学的线的第2 命令的偏微分方程的对称性之间的关系，坐标系统，方程式通过变量分离和如此出现的特殊函数的特性承认解决办法。

After a linear differential equation showing the pressure variation has been derived, the theoretical equation of the spraying time is then obtain...

建立了存储压力与时间的变量分离型一阶微分方程，进而得出喷射时间的理论公式。

Yet, Edith says, there was always money in the bank.

但是Edith说，她的银行户口里面总是有钱。

We have created a series of files that resolve this problem--one for each day of the 40 days of purpose.

我们制作一系列的档案去解决这问题---一个为标竿40天中的每一天。