2) saddle point theorem
鞍点定理
1.
By using the least action principle and the saddle point theorem in Critical Point theory,the existence theorems for periodic solutions of a class of nonautomomous second-order systems are obtained.
分别利用极小作用原理及鞍点定理在势泛函为一次线性泛函和次二次泛函之和的条件下讨论了一类非自治二阶Hamilton系统周期解的存在性。
2.
Two saddle point theorems were proven in according to the H α conjugate map and its properties.
借助一类非闭非凸的 α-较多锥 ,对多目标规划问题引进 Hα- Lagrange映射及其鞍点的概念 ,利用 Hα-共轭映射及其性质得到了两个鞍点定理 ,并对含有不等式约束的多目标规划问题建立了鞍点定
3.
The existence of periodic solutions for second order systems (M(t)u′)′+Au+F(t, u)=h(t), u(0)-u(T)=u′(0)-u′(T)=0, is dicussed with sublinear nonlinearity, by using the saddle point theorem, the problem has at least one periodic solution.
讨论了一类二阶系统(M(t)u′)′+Au(t)+ F(t,u(t)=h(t),u(0)-u(T)=u′(0)-u′(T)=0,在非线性项满足次线性条件下周期解的存在性,利用鞍点定理得到该问题至少存在一个周期解。
3) Node theorem
节点定理
4) theorem of zero point
零点定理
1.
Furthermore,it also discusses the application of theorem of zero point in our life,to achieve the goal of combining theory and practice in mathematical education.
高等数学中的零点定理是闭区间上连续函数的一个重要性质,利用它既可以证明方程根的存在性或求根的近似值,即解“等式”问题,又可以解“不等式”问题,本文从生活中谈谈零点定理的几个应用,以达到在数学教育教学中理论与实践相结合的作用。
5) Zero-Point Theorem
零点定理
1.
Through some examples the author enumerates three kinds of problems testifying the existence of formula root and further proves it by using Zero-Point Theorem, Rolle Theorem , Lagrange Middle Theorem , reduction ad absurdum proof,etc.
通过例题列举了利用零点定理、罗尔定理、拉格朗日中值定理,反证法等证明方程根存在的三类问题。
2.
This article extends the zero-point theorem for continuous functions from a closed interval to other types of intervals,and a series of zero-point theorems for continuous functions on relevant intervals are obtained,so that the theory on the zero-point theorem can be applied in more general cases.
将闭区间上连续函数的零点定理扩展到其它区间上,得到若干个相应区间上连续函数的零点定理,从而使零点定理理论更完善、应用更广泛。
6) Zero point theorem
零点定理
1.
In this paper ,the inferences and their proof about the property for continuous function of closed interval -Zero point theorem, Intermediate value theorem and the mean value theorem for derivatives-Rolle theorem ,Lagrange mean value theorem are given.
本文给出了闭区间上连续函数的性质定理———零点定理,介值定理,微分中值定理———罗尔定理,拉格朗日中值定理的推论及其证明,将函数在闭区间上连续的条件改为在开区间内连续且极限存在(或为∞)的条件,从而拓宽了定理的应用范围。
2.
In this paper we summarize several kinds of identification methods of the Zero point theorem,and discusse the way of exploring the zero point of function.
总结了零点定理的几种证明方法,并讨论了函数零点的求解方法。
补充资料：Borel不动点定理
Borel不动点定理
Borel fixed - point theorem
B吮l不动点定理{B.限l五xe小州nt价e僻m二匆卿，T侧邓吧，f.01”聊叉B“狱班滋n卜.王j 设F为代数闭域kl二非空完全代数簇，正则地作用于犷上的连通可解代数群G(见变换的代数群扭1罗-braic goup of transformat一ons))在卜中有不动点.由这个定理可以推出代数群的B.耽l子群(Borel sub-grouP)是共扼的(Bore卜MOI洲)叉)B定理(Borel一Moro-zov theorem))，不动点定理是A.Borel([lj)证明的.Borel定理可以推广到任意域k(不一定代数封闭卜设F为在域k上定义的完全簇若连通可解k分裂群(人一sPlit grouP)G正则地作用在F上，则有理人点集V(k)或者为空集，或者它包含G的一个不动点.因此推广的Bore]子群共扼性定理是:若域k是完满的，则一个连通人定义的代数群H的极大连通可解北可裂子群，在H的k点构成的群中元素作用下互相共辘(f21)，
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