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In this paper,the author introduced an approximate augmented Lagrangian function in nonlinear programming,established dual mapping and the related dual problem of this augmented Lagrangian function and obtained the results of approximate strong duality and approximate weak duality of original problems.

介绍了非线性规划中的一种近似增广拉格朗日函数，建立了基于这种增广拉格朗日函数的对偶映射和相应的对偶问题，得到了原问题和对偶问题的强近似对偶和弱近似对偶结果。

A combinatorial identity is obtained:=:~z 2r扟32-rn-iJ As main result of this paper, in section two, the convolution梩ype identities emerge from our discussion about Lagrange formula whom in author 憇 view can be taken as the inherent characteristic of Lagrange formula but have been ignored fOi so long time.

第一章对拉格朗日反演在Riordan群理论中的应用进行了介绍，证明了一个组合等式：第二章通过对拉格朗日反演定理本身的分析，得到一个对任意的形式幂级数都适用的三个拟卷积公式，这些公式体现了任意能在零点解析的函数的内在性质。

Third, the use of Lagrange's theorem proving the points of the study on some conclusions, that the Lagrange theorem in the integral study also has a wide range of applications.

再次，利用拉格朗日定理证明了积分学上的几个结论，说明拉格朗日定理在积分学中也有广泛的应用。

Grantaire had seduced Joly and Bossuet to wine; Bossuet and Joly had conducted Grantaire back towards cheerfulness.

格朗泰尔把若李和博须埃引向了杯中物，博须埃和若李把格朗泰尔引回到欢乐中。

The equation (3) is called the Taylor's formula with Lagrange Remainder term of order based at, and (4) is called the Lagrange Remainder term.

公式（3）称为按的幂展开的带有拉格朗日型余项的阶泰勒公式，的表达式（4）称为拉格朗日型余项。

When, the Taylor's formula with Lagrange Remainder term of order simplifies the Maclaurin's Formula with Lagrange Remainder term of order, which is in form of following

当时，带有拉格朗日型余项的阶泰勒公式简化为带有拉格朗日余项型的阶麦克劳林公式，形式如下

This article is divided into several categories of questions, focus on a typical example of the Lagrange Mean Value Theorem to prove the application of the inequality summarized in the hope that readers can better grasp the Lagrange mean value theorem in the inequality in the application of skills .

本文将题型分成几类，集中典型例题，对拉格朗日中值定理在不等式证明的应用中进行归纳总结，希望读者能够更好的掌握拉格朗日中值定理在不等式中的应用技巧。

We establish a Lagrange multiplier theorem for strict efficiency in convex settings and express strict points as saddle points of an appropriate Lagrangian function.

讨论凸多目标最优化问题的严有效解，建立了拉格朗日乘子定理，并把严有效解表示为一个适当的拉格朗日函数的鞍

This article will write divides into several kinds, the centralism typical sample question, carries on the induction to the Lagrange theorem of mean in the application which the inequality proved to summarize, hoped that the reader can better grasp the Lagrange theorem of mean in the inequality application skill.

本文将题型分成几类，集中典型例题，对拉格朗日中值定理在不等式证明的应用中进行归纳总结，希望读者能够更好的掌握拉格朗日中值定理在不等式中的应用技巧。

The Augmented Lagrangian function defined in this paper guarantees good behavior of the Newton method when minimizing the augmented Lagrangian function.

本章定义的增广拉格朗日函数能保证极小化广义拉格朗日函数时牛顿法的好的表现。

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