查询词典 existence theorem of implicit function

In this paper,pose representation by quaternions are researched.With the basic quaternion algebra,the "quaternion based rotations combination theorem" is introduced and proved theoretically.On the basis of this theorem,a method for compute of pose nonliear state transfer function and its linearization is purposed.Then,the computing of the measurement function and the linearization is studied.With the Extended Kalman Filter,the pose is tracked and estimated.

研究用四元数表示物体的姿态，在四元数基本运算法则基础上提出并证明了"基于四元数的多个旋转运动合成规则"，然后将此规则为依据，推导出一种用来计算姿态非线性状态方程系数的方法，对非线性状态转移函数进行线性化，并且研究了测量方程函数的确定及线性化，借助扩展Kalman滤波实现了对姿态的跟踪。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对&中间点&的渐近性进行了研究，得出了一系列&中间点&的渐近性的结果，概括了有关文献对微分中值公式的&中间点&的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

Each of us has a superior function, which we prefer and which is best developed in us, a secondary function, which we are aware of and use in support of our superior function, a tertiary function, which is only slightly less developed but not terribly conscious, and an inferior function, which is poorly developed and so unconscious that we might deny its existence in ourselves.

每个人都有自己第一优先的方法，这是我们最喜欢或做的最好的方法；第二优先的方法，是我们知道或使用来辅助第一优先方法；第三顺位方法，是我们仅仅使用一点点但不太了解的方法；而最后考虑的方法，是做的不好而不了解，以致於我们自己可能会否定它的存在。

Due to the sensitivity analysis plays an important role in the parameter method, arbitrary order sensitivity formula is derived on basis of an obtained corollary of an implicit function theorem of Several Variables Theory.

由于灵敏度分析是参数型模型修正中的一个重要环节，本文运用多元函数论，得到一个隐函数定理的推论，在此基础上导出了任意阶灵敏度的计算公式。

A complete analysis must build on the implicit function theorem.

完整的分析必须建立在隐函数定理的基础上。

But the implicit function theorem cant satisfy the requirement of the controllability.

但常用隐函数存在性定理不满足能控性分析的需要。

The anti-integrable limit theory is much simpler than the KAM theory since it is just obtained as a variation of the standard implicit function theorem.

近年来提出的反可积极限理论是研究完全混沌系统的扰动。

By the implicit function theorem,the continuation of the eigenvalues depending on the parameters of the system can be established,except...

依据多元向量值函数连续性，建立对特征值的排列算法，给出系统特征根轨迹的正确曲线，再输出V-g和V-f图数据，从而避免"窜支"现象。

Then,the system is linearized by variational approach,the local null controllability is proved by applying a generalized implicit function theorem and combining the property of the solution mapping.

首先得到了系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后给出系统零能控的结论。

In this project, we intend to combine the above mathematical ideas. First, we consider a wild family of dynamical systems which can be derived into a family of difference equations. Then using a generalized version of the implicit function theorem which we will establish, we want to show that for any dynamical systems near 「singular limit」, there exists a horseshoe structure and hence chaotic phenomena occur.

在此研究计画中，我们打算结合上述的数学结论与想法，进一步考虑一类能够转化成差分方程的动态系统函数族，使用即将建立的推广性隐函数定理，我们希望证明当参数接近奇异极限时，动态函数会具有马蹄结构所以有混沌现象。

For the head-teacher of the class said that I had seriously broken the school rules,which led me to a three-day suspend class.

为什么呢？因为我的班主任说我严重的违反了校规，于是让我停课三天。

Many of them believe that the conversion of thousands of working-class folk in England spared that nation from the mass carnage and the tyranny that came with the revolution in France.

他们之中有许多人相信，在英国数以千计的劳工阶级之悔改信主使英国免於遭受如法国大革命所造成的大屠杀和专制暴政。