1) 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。
2) 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。
3) accumulation factor in analytic hierarchy process
层次分析积因子法
1.
This paper discusses that sequence of agricultural separated rice mill is arranged according to comprehensive properties by using accumulation factor in analytic hierarchy process,which avoids deviation of subjective judgment and makes evaluation result objective.
为此,利用层次分析积因子法,对农用分离式碾米机综合性能排序,避免了主观评判的偏差,评价结果客观,并通过应用取得了与实际情况完全一致的结果。
4) integrating factor
积分因子
1.
Two special integrating factors of a non-complete differential equation;
一个非恰当方程的两类特殊积分因子
2.
The existence condition for some types of integrating factor;
关于某些积分因子的存在条件
3.
The application of th integrating factor of first order differential equation;
一阶微分方程积分因子的应用
5) integral factor
积分因子
1.
On integral factor approach for first derivative differential equation;
关于一阶方程的积分因子法
2.
The solution of first order ordinary differential equation with the integral factor of a product form
一阶常微分方程具有一种乘积形式积分因子的求解
3.
A new method is suggested to derive the Duhamel integral in the linear vibration systems of singledegreeof freedom for the response to arbitrary excitations by the depression of order of integral factor.
利用积分因子降阶法，给出了确定单自由度线性振动系统对任意激励响应的杜哈梅积分的一种新的推导方法。
补充资料：积分因子
积分因子
integrating factor
积分因子【勿峡卿山稽血ctor;“二印“pylo哪益M.二-犯JU.] 一阶常微分方程 P(x，夕)dx+Q(x，夕)d夕二0(l)的积分因子是具有下述性质的函数拜二拜(x，y)举。它使得 拜(x，y)p(戈，夕)dx+拼(x，夕)Q(x，夕)d夕”0是全微分方程(d正rerenhal eqUation withto词d迁re化n-tial).例如，对于线性微分方程y’十a(x)y二f(x)或者方程(a(x)y一f(幻)dx+dy=o，函数#=expf。(x) dx是一个积分因子.如果方程(1)在区域D(使得尸’十仓并0)中有光滑通积分(邵理ml访沈梦d)U(x，夕)“C，则它有无穷多个积分因子.如果p(x，夕)和Q(x，夕)在区域刀(使得p’+Q’护0)中具有连续偏导数，则偏微分方程 八刁。_日;.「日O口尸1。 O亡士生一P止匕上立+，，lwe兰公乙一止三一}二O “日x一日y尸!刁x ay} ‘一“(2)的任一非平凡特解都可取作积分因子，见【11.然而，不存在求(2)的解的一般方法，因此只在例外情形才对具体的方程(1)成功地求出积分因子，见【ZJ.
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