第一积分

本文不仅证明了下面的第一积分中值定理：定理设1）函数f（x）在[a，b]上连续；

In this paper the following result is proved : Theorem Let 1 ) f ( x ) be Continuous over Closed interal [ a , b ] ;

利用相对论性自治Birkhoff系统的第一积分求非等时变分方程的特解

Solving nonsimultaneous variational equations of relativistic autonomous birkhoff systems by using its first integral

文章在第一积分中值定理的条件下，证明了介值点ξ必可在开区间（a，b）内取得，并且给出以上结果的一些应用。

This paper proves that the point ζ must be in the open interval ( a , b ) under the conditions same as in the first mean value theorem of integrals , and gives some applications of the above results .

首先，由这种相对运动的Routh方程给出系统的第一积分；

Firstly , based on the Routh equation of the relative motion of nonlinear nonholonomic system gives the first integral of the system .

非惯性系动力学的第一积分

The First Integrals of Dynamic in Non-inertia Coordinate System

经典的第一积分能否作为约束是一个存在争议和令人困扰的问题，至今仍没有定论。

There exists dispute whether the classical first integrals can be treated as constraints or not .

再次，建立这类系统运动的正则方程和变分方程，并由第一积分构造系统的积分不变量；

Thirdly , derives canonical equation and variation equation and by using the first integral constructs integral invariant .

首先给出非完整相对运动动力学系统的非等时变分方程，然后研究它们的解，并证明在一定条件下可利用第一积分来得到非等时变分方程的特解。

This paper presents the nonsimultaneous variational equations of relative motion for nonholonomic systems , and studies the solutions of the equations .

给出了拉格朗日微分中值定理和第一积分中值定理中值点的渐进性的更一般性的结果及其简洁证明。

Gives more general results on the gradualness of the median point of Lagranges median theorem and first median theorem for integrals and its succinct proof .

在求解动力学系统的方程中，动力学系统的第一积分与积分不变量是求解运动方程积分理论的重要内容之一。

The first integration and integrated invariant of dynamic system belongs to important contents of solving equations of motion integrated theory during solving equations in dynamic system .

利用函数连续模分别给出了第一积分中值定理和第二积分中值定理的中间点收敛速度的一个估计。

By using modulus of functional continuity . A estimates of the asymptotic rate of convergence for " intermediate point " of the first integral mean value theorem and the second integral mean value theorem are given .

给出了广义经典力学的正则方程，研究了其非等时变分方程，讨论了它们的解，并证明可由第一积分构造相应的积分不变量。

The author gives the canonical equation of generalized classical mechanics , and then studies its nonsimultaneous variational equations and their solutions , and proves that integral invariant of the system can be constructed by using the first integral .

通过Helmholtz方程外Dirichlet问题产生的第一类积分方程的核具有对数奇性。

The kernel in the first kind integral equation arising from exterior Dirichlet problem of Helmholtz equation has a logarithmic singularity .

POISSON方程边界值问题边界元法所应用的边界积分方程，其类型，关于未知位势导数是第一类积分方程，关于未知位势是第二类积分方程。

The ordinary boundary integral equation for poisson equation is of the second kind for the unknown potential , but is of the first kind for the unknown exterior normal derivative .

这些桩的分析问题归结为一Fredholm第一种积分方程并用数值法求解。

Both problems of rigid and compressible pile are reduced to a Fredholm integral equation of the first kind and is solved by numerical method .

本文则采用线性基函数，详细推导了在线性单元上二重积分第一重积分的解析公式，第二重积分使用Gauss数值积分。

For calculation of the double integration on the boundary , the analytical formula of the first integral is deduced in detail with linear basic function , and a Gauss integration formula is used in the second integral .

本文给出一种三维Helmholtz方程Neumann问题的新的数值解法。首先利用双层位势推得问题解的积分表达式并导出了一个Fredholm第一类积分方程。

This paper presents a new numerical solution for Neumann problem of Helmholtz equation in R ~ 3 . The expression of the solution for this problem is obtained by use of a double layer potential and it leads to a Fredholm boundary integral equation of the first kind .

径向基函数在求解第一类积分方程中的应用

Solving Integral Equation of the First Kind Using Radial Basis Functions

第二个积分比第一个积分更易于接近。

The second integral is easier to approximate than the first one .

第一类积分方程的小波函数解

On wavelet function solutions for first-kind integral equations

求解第一类积分方程的正则化-小波方法及其数值试验

Regularization-wavelet method for solving the integral equation of the first kind and its numerical experiments

解第一类积分方程与代数方程组的一种投影迭代算法

A projection iterative method for solving integral equations of the first kind and algebraic systems

本文推出了第一重积分的解析计算公式，对外层积分则采用高斯数值积分。

The paper presents the analytical formula to calculate the inner integration and the Gaussian quadrature is used for the outer integration .

荷兰车手在上一站撒丁岛拉力赛上退赛了，下周的比赛中他的目标就是完赛，甚至是自己本赛季的第一个积分。

The Dutch driver retired on the last round in Sardinia and will be targeting a finish next week , if not his first points of2011 .

考虑一类垂直断层效应反演问题，其数学模型是具有解析核的第一类积分方程。

A class of inverse problems of perpendicular fault effect are discussed , which are modeled by a first kind integral equation with an analytic kernel .

将动载荷识别问题完全归结为求解Voterra第一类积分方程的正解问题，进而获得了比例阻尼系统和一般粘性阻尼系统动态载荷的识别计算模式。

It transforms the problem of load identification into that of solving a first kind Volterra integral equation . The computational formulations for identification of dynamical loads on system with either proportional damping or general viscous damping characters are presented .

第一类Volterra积分方程的CAS小波解法

CAS Wavelet Solution to Volterra Integral Equation of the First Kind

为了得到第一类Fredholm积分方程稳定的数值解，对p个不同的光滑因子，分别利用光滑化方法求解，可得到p组带有光滑因子的稳定解。

To obtain the stable solutions of the Fredholm integral equation of the first kind , the smooth method with p smooth factors is used .

第一类Dirichlet积分的公式解

Formula solutions to the first dirichlet 's integral

稳定求解第一类Fredholm积分方程的一个方法

A Stable Method for Calculating Fredholm Integral Equation of First Kind