1) auxiliary function
辅助泛函
1.
In this paper,we consider the following second order nonhomogeneous delay differential equation (r(t)x′(t))′+p(t)x′(t)+q1(t)x(t)+q2(t)x(h(t))=f(t,x(t)) with the aid of auxiliary functions and inequalities.
借助于辅助泛函,得到了二阶非齐次非线性时滞微分方程(r(t)x′(t))′+p(t)x′(t)+q1(t)x(t)+q2(t)x(h(t))=f(t,x(t))所有解均平方可积及所有解都有界的判定准
2) auxiliary floodlight
辅助泛光灯
3) auxiliary function
辅助函数
1.
Parameter alternating method to construct the auxiliary function;
利用参数变导法构造辅助函数
2.
Several ways of establishing auxiliary function to testi fy median proposition;
中值命题证明中构造辅助函数的几种方法
3.
On the construction of auxiliary function when using the calculous intermediate value theorem;
谈微分中值定理运用中辅助函数的构建
4) supplementary function
辅助函数
1.
A supplementary function can be given.
通过给出关于凹凸函数的一个性质定理及其推论,对一些特定类型的三角不等式通过构造辅助函数,求出函数的二阶导数;再结合其凹凸性利用定理的推论给予简捷的证明。
2.
This paper, by means of Rolle theorem, introduces constant method to demonstrate mean value theorem for differential calculus and attains the corresponding supplementary function of the demonstrating method.
借助于Rolle定理,用待定常数法证明了微分中值定理,得到了该证明方法的辅助函数簇,这种证明方法对解决同类问题有很好的推广应用价值。
3.
In this paper,a new structural method of supplementary function is introduced, and the method is used to prove differential identical equation or integral inequality.
本文给出辅助函数新的构造方法 ,并将它运用于微分恒等式和积分不等式的证
5) auxiliary functions
辅助函数
1.
By constructing auxiliary functions and ordinary differential equations, we have obtained some new exact traveling wave solutions of the nonlinear coupled KdV equations which include soliton wave solutions and periodic solutions.
利用构造辅助函数和辅助常微分方程组的方法,给出了非线性耦合KdV方程的某些新的精确行波解,其中包括孤波解和周期解。
2.
By constructing auxiliary functions,some new exact traveling wave solutions of the nonlinear coupled VB equations are obtained,which include solitary wave solutions,trigonometric function solutions,Jacobian elliptic function solutions and rational solutions,and some solutions are complex linear solutions.
利用构造辅助函数的方法,给出了非线性耦合VB方程组的某些新的精确行波解,包括孤子解、三角函数解、椭圆函数解和幂函数解,其中某些解还是复线型的。
3.
By constructing auxiliary functions, we have obtained some new exact traveling wave solutions of the nonlinear coupled KdV equations which include solitary wave solutions, trigonometric function solutions,Jacobian elliptic function solutions and rational solutions.
利用构造辅助函数的方法,给出了非线性耦合KdV方程的某些新的精确行波解,其中包括孤子解,三角函数解,椭圆函数解和幂函数解。
6) assistant function
辅助函数
1.
Constructing assistant functions in Proofing the Mean-Value Theorem;
中值定理证明中辅助函数的构造
2.
For example,when teaching the construction of Assistant Function in Differential Mean-value Theorem,we can introduce them the idea of inversion thought;when teaching the Series,we can lead them to establish the relation between Series and Limit by use of inversion thought.
结合高等数学中部分典型知识点,介绍在平时教学中如何培养和训练学生的逆向思维能力,如在讲授微分中值定理时,通过辅助函数的构造向学生介绍逆推法;在级数的教学中,引导学生利用逆推法建立级数和极限间的关系。
3.
How to cultivate students creative thinking during the process of proving the Lagrange Value Theorem is briefly described,this can be achieved with the help of imagination and guess,and should be based on the combination of the condition and conclusion of the theorem,as well as the construction of the assistant function.
结合拉格朗日中值定理的教学,简述了定理证明过程中如何利用想象和猜想,联系定理的条件和结论构造定理的辅助函数,对学生进行创造性思维的培养。
补充资料：Марков过程的泛函
Марков过程的泛函
functional of a Markov process
M仰助“过程的泛函【加犯份班司健a扮如d如vpr以犯岛;中y业，o.a月oT Map二招e.o np()朋eCea] 一个以可测方式依赖于MaPKo.过程轨道的随机变量或随机函数，其可测性条件随具体情况而定.在MaP盆oB过程的一般理论中，采用以下的泛函定义.假设给定一个具有时间推移算子氏的非停止齐次M叩-Ko。过程(M田玉ov plx兀启弥)X二(xr，风，氏)，其相空间为可测空间(In纷s幽 blespaCe)LE，少)，设才是基本事件空间中包含每个形如{。:x，“B}(t)0，B任分)的事件的最小。代数，/’是对于所有可能的测度Px(x‘E)关于/’的完全化的交.如果对于每个t)O，7，关于。代数才门不是可测的，那么，称随机函数叭(‘)0)为Ma伴oB尽捍X的攀甲(丘功d沁n目of此MaJ改ov Pnx君邓)· 人们特别关心的是M川阵..过程的乘性和加性泛函.它们分别润足条件下，十:，下;疏凡和，，十，，，，+氏大，s，亡》0.这里假定，，在【0，co)上是右连续的(代替这些条件，有时只假定对所有固定的s，t)O，这些条件关于P:几乎处处成立).在停止和非齐次过程的情形下，采用类似的方式来定义.MaPI..过程x‘(x，，心，不，P)的加性泛函的例子可以通过以下方式得到:设对于t<‘，，，等于f(x，)一f(x。)，或北f(气)d:，或随机函数f(x，)在:。10，，]中跳跃值的和，这里f(x)是有界并且关于岁可侧的函数(第二和第三个例子只在某些附加限制下有效).从任意加性泛函，.，可以得到乘性泛函以py，.在标准MaP-血过程的情况下，设t
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