引理

Secondly, we consider of the representation of the inverse Vandermonde matrix with multiple knots.

这两个引理对解决本文的问题是十分重要的。

By the delta matrix inverse lemma, the delta operator recursive least squares algorithm is derived, and convergence about DRLS is also proved.

基于Delta算子矩阵求逆引理，导出Delta算子最小二乘估计的递推算法，证明了DRLS的收敛性。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

Finally,by applying a ran-dom version of Kifer's large deviation theorem and the volume lemma,we prove thelevel-1 LDT for randomly perturbed Axiom A attractors of diffeomorphisms withrespect to the Lebesgue measure.

最后，利用Kifer的大偏差定理的随机版本和体积引理，我们证明了微分同胚的公理A吸引子的随机扰动系统相对Lebesgue测度的level-1 LDT。

According to differentiable manifolds theory, the paper discusses tile Legendre transformation of the Pfaffian form, introdues the operator of the Legendre transformation, derives the relation between the Legendre transformation and the partial differentiation and proves three law s.

从微分流形理论出发，讨论了Pfaff形式的勒让德变换；引入了勒让德变换算子；给出了勒让德变换与偏微商的关系；证明了两个定理和一个引理。

From the proof of Lemma 2 we know that (6) Therefore, if

从证明 引理2我们知道，（ 6 ）因此，如果

Also note that Lemma 2 still holds with this new definition of relevant subproblems.

还注意到，引理2仍持有这一新定义的有关子。

Note that Lemma 2 does not imply that xi will converge to -x for all i.

请注意，引理2 ，并不意味着席将衔接到X的所有一。

To solve this problem, upper and lower method and comparison lemma are introduced.

这里涉及到两个非常重要的引理，上下解原理和半线性椭圆型方程的比较原理。

It is given a geometrical proof of an essential combinatorial lemma of Liao.

给出廖山涛一个关键的组合引理一个几何式的证明。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新