1) higher order integrals
高次积分
1.
Construction theorems of second and third order ordinary differential equations which admit higher order integrals are formulated by use of the method of determining higher order integral factors and higher order integrals for ordinary differential equations,and by use of the characteristic set method as well.
本文利用确定高次积分因子的引理与确定对应的高次积分的公式以及微分特征列集(吴)方法,给出了拥有高次积分的二阶三阶常微分方程结构定理。
2.
The higher order integrals of general ordinary differential equations (ODEs) and their determination by Characteristic set method (Wu s method) are considered.
考虑了一般微分方程(组)高次积分和其微分特征列集(吴方法)机械化确定算法。
2) higher order integral factors
高次积分因子
1.
Construction theorems of second and third order ordinary differential equations which admit higher order integrals are formulated by use of the method of determining higher order integral factors and higher order integrals for ordinary differential equations,and by use of the characteristic set method as well.
本文利用确定高次积分因子的引理与确定对应的高次积分的公式以及微分特征列集(吴)方法,给出了拥有高次积分的二阶三阶常微分方程结构定理。
2.
Firstly,the concepts of higher order integral factors and the corresponding higher or- der integrals of ODEs,which are generalization of the concepts of usual integral factors and first integral of ODEs,are put forward.
首先提出微分方程的积分因子和首次积分的推广高次积分因子与其对应的高次积分的概念。
3) first integral
首次积分
1.
Let x~2+y~2+z~2=h(>0) be the first integral of the perturbed system,then the existence of limit cycles on the spherical surface was discussed by using averaging method and center manifold theory.
对球面族上的平行流进行了一般的2n+1次齐次扰动,在x2+y2+z2=h(>0)是扰动系统的首次积分的情况下,运用平均方法及中心流形定理,给出了扰动系统在球面上出现极限环的一般情况。
2.
Under general conditions, a method for solving first integrals of the 3-rd order autonomous system is given based on the generators of two admitted single-parameter Lie groups.
在较一般的条件下,对3阶自治系统给出利用系统所接受的两个单参数李群的生成元计算首次积分的方法。
4) successive integral
逐次积分
1.
Throush the interlace series type linear differential equation,coefficient containing three negative number of times,power function and arrangement number can be changed into the linear differential equation of successive integral.
通过把系数含有负三次幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程,找出了求这类方程通解的方法与理论,把所得定理给出了严格的证明,并将其推广,同时通过实例介绍了它的应用。
2.
Pass linear differential equation xy~((n))+ny~((n-1))=f(x) change into the linear differential equation of successive integral has been found witty the form that untied,have gicen strict proof,and to popularize it gets to know xy~((n))+(x+n)y~((n-1))+(n-1)y~((n)-2)=f(x) to untie.
通过把线性微分方程xy(n)+ny(n-1)=f(x)化为可逐次积分的线性微分方程,找出了它通解的形式,给出了严格的证明,并将它推广,得到xy(n)+(x+n)y(n-1)+(n-1)y(n-2)=f(x)的通解。
3.
By transforming the interlace series type linear differential equation with coefficients containing negative second order power function and arrangement number into the linear differential equation of successive integral,the theory and method for the general solution of this kind of equation are determined.
通过把系数含有负二次幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程,找出了求这类方程通解的方法与理论,所得定理给出了严格的证明,并通过实例介绍了它的应用。
5) quadratic integral
二次积分
1.
A preliminary probe into the method of exchanging the order of quadratic integral;
交换二次积分次序方法初探
6) repeated integral
累次积分
1.
Nowadays,almost all the general mathematic softwares can t directly calculate double integral,they only can be used to calculate repeated integral,the softwares can t recognize and deal with complicated domain of integration.
目前常用数学软件包无法直接进行二重积分的运算,只能处理累次积分,难以处理复杂的积分区域,文章基于有关数学定理提出一种新型算法,通过对积分区域和边界条件进行判断和处理,实现二重积分与累次积分之间的转换,使常用数学软件包能够直接计算二重积分,从而简化运算过程,提高计算效率。
2.
The solution for the equation is deduced by making repeated integral and substitution of variables.
给出奇异积分方程阿贝尔方程的一种技巧解法,作累次积分及变量替换推出此方程的解式,提出一个注记,拓展了求解积分方程的思路。
3.
This paper using several instances, analyses that the multiple integral and repeated integral are two independent concepts and there is no certain implication between them.
本文通过若干实例说明重积分与累次积分是两个独立的概念,它们的存在性没有必然的蕴含关系,并指出只有在一定条件下它们之间才存在相等关系。
补充资料：电力牵引高次谐波
电力牵引高次谐波
harmonics of electric traction
d Ionl一qlony旧gooe}x{ebo电j]牵引高次谐波(harmonies of eleetrietraction)整流式交流电力机车在整流过程中将引起交流侧电流、电压波形畸变，按傅立叶级数分析该畸变波形可分解成频率为基波频率整数倍的一系列高次谐波分量的叠加。 高次谐波电流、电压可引起下列不良影响: (1)对通信线产生杂音干扰影响; (2)引起电力系统中其他电力电容器设备的过负荷; (3)当电气化铁路负荷某次谐波电流频率与电力系统自身谐振频率相近时，可产生电流谐振，使该次谐波电流在电力系统中放大，危及电力系统安全运行; (4)使旋转电机、变压器、电力电缆的出力减少并产生过热，影响电气设备寿命; (5)造成继电保护误动或仪表读数误差; (6)使半导体开关元件换相失灵。 为限制谙波的危害，各国都规定了允许谐波含量的标准(见供电质童)。 为降低电力牵引负荷产生的谐波，在电力牵引变电所和电力机车中可装设由电容、电感组成的谐波吸收装置。交流一直流一交流电力机车利用电力电子技术，可实现低谐波分量的负荷特性，使谐波含量降低。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条