1) the first variation
一阶变分
2) first variation systems
一阶变分系统
1.
Firstly we give variation formula for first variation systems of nonlinear singular delay differential control systems, then for the function-controllability of first variation systems of nonlinear singular delay differential control systems, we give some criteria, and finally we give the criteria for the function-controllability of nonlinear singular delay differential control systems.
首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据。
3) first-order difference transformation
一阶差分变换
4) First order differential of state variables
状态变量一阶微分
5) the invariance of differential form of first order
一阶微分的形式不变性
1.
Through the applications in the integration by substitution, finding the value of whole differential equation, differentiate and partial derivative or partial derivative of higher order for multivariate (one variable) function of functions, this paper discusses that the function of the invariance of differential form of first order should be not neglected in calculus.
通过在积分换元、微分方程求解、多(一)元复合函数求全微分、偏导数及高阶偏导数中的应用举例,论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
6) first order differential
一阶差分
1.
The classical moving average technique and first order differential were used for segmentation.
先采用移动平均法(moving average,MA)和一阶差分法确定SEMG信号中对应的每个动作波形的起止点,再利用递归量化分析(recurrence quantifica-tion analysis,RQA)方法提取各种动作波形的非线性特征参量(确定率、递归率等),由两路SEMG信号的这些特征参量构成特征矢量,输入BP(back propagation)神经网络,完成对不同动作的分类。
2.
Combined with the first order differential algorithm, this method has solved the problem successfully.
针对双电位器式传感器检测系统存在的跳区现象,提出了一种新的判区方法,并结合一阶差分算法成功地解决了跳区问题,同时也提高了系统的抗干扰能力。
补充资料:二阶变分
二阶变分
second variation
二”套蕊穿黑磊票暴麟篇粼纂架的变分(variation of a ftmctional),G狱eaux变分(伪teauxvariation)),推广了多元函数的二阶导数的概念.它用于变分法.按一般定义,定义在赋范空间X上泛函f(x)在点x。的二阶变分是 d2 占‘f(“。,”)一~方f(x。+亡h)}:二。·如果一阶变分是零,则二阶变分的非负性是f(x)在x〔、有局部极小值的必要条件,而严格正性 占’f(x。,h))“l}入}1’,“>o是充分条件(在一定的假设下). 在经典变分法的最简单(向量)问题中,在C’类向量函数类上考虑的具有固定边界值x(t。)=x。,x(r,)=义,的泛函 之.z(*)一J:(。,、,*)、:;::【。。,::,xR·xR一R、 ‘o的二阶变分有形式 仁. 。2,(、。,、)一丁(<,(:)、(。),入(。)>+(·) r幻+2+
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