格朗

With a rational dynamic model established on basis of the structural features and constraining conditions of the annular plate installation and through Duhamel＇s integral solution of Lagrange motion equation, the impact load and dynamic response of surface casing cementing unit induced from the cementing operation have been analyzed.

根据表层固井环板装置的结构特点和约束条件，建立了合理的力学模型，应用杜哈默积分求解拉格朗日运动方程的方法，对固并碰压状态下承受冲击载荷及其动力响应问题进行了分析。

With a rational dynamic model established on basis of the structural features and constraining conditions of the annular plate installation and through Duhamel's integral solution of Lagrange motion equation,the impact load and dynamic response of surface casing cementing unit induc.

根据表层固井环板装置的结构特点和约束条件，建立了合理的力学模型，应用杜哈默积分求解拉格朗日运动方程的方法，对固井碰压状态下承受冲击载荷及其动力响应问题进行了分析。

Leastsquare method and Lagrange's interpolation formula see their applicationsfor fitting fore-and-aft lines-whose aim is to calculate the intersection point ofequivalent inclined waterline-and differences. In order to replace theinconvenient alternate conduct of drawing and calculating, improvement hasbeen introduced into the paper which means all work can be done bycomputer. Capacity calculation cannot be done without boundary layer build-up. Fit every area curve and area moment curve is necessary because ofinterpolation.

在第二章中，给出了B样条函数的数学表达形式，推导了B样条曲线下所围面积、面积矩公式；讨论了最小二乘法和拉格朗日插值法的数学形式，并在拟合船体型线上给出首、尾轮廓线的具体实例，对比不同方法进行拟合的差异，其目的是为了求得与等体积倾斜水线的交点；而水线的确定改变了以往人工作图与计算交替进行的不足，尝试用计算机完全代替人工作图，以求有所改进；在舱容计算中，在至少包括舱室前、后壁的范围内拟合横剖面积、面积矩曲线，插值求得任一纵向位置处的剖面，以解决舱室边界条件。

There are some mature curve fitting methods in the reverse engineering, such as Lagrange interpolation, piecewise polynomial interpolation, least square method and spline interpolation.

成熟的曲线拟合方法有拉格朗日插值法、分段多项式插值法、最小二乘法和样条曲线插值法等，本文在分析各自优缺点的基础上，提出选用三次样条曲线拟合法。

Based on the elliptic curve cryptosystem, a multi-key sharing scheme in which the Lagrange interpolation polynomial is used and the cheaters can be detected is presented.

文章利用拉格朗日插值的思想，提出了一种基于椭圆曲线的可防欺诈的动态多密钥共享方案；方案中每个参与者的子密钥可以不受限制的重复使用，因此在更新主密钥的时候，无需更改参与者的子密钥，从而减少了可信中心与参与者之间的通信量；方案可灵活地增删参与者，且安全性是基于椭圆曲线离散对数问题的难解性，因而其安全性比在有限域上更高；方案实现过程中解决了检验子密钥真伪的问题。

The main results are as follow:(1) Systematically discussed the methods that built up the DEM by the contour line, we put forward new algorithms of auto-adding characteristic points that eliminated the "plane triangle" in constructing TIN and approximating important characteristic points by Lagrange interpolation polynomial.

主要成果有：(1)系统地论述了基于等高线建立DEM的方法，提出新的消除TIN构造中出现"平三角形"的算法——自动增加特征点和利用拉格朗日插值多项式拟合重要地形特征点，并验证算法对TIN结构的优化。

There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory.

这门课程也包括了对最适化条件，拉格朗日乘数理论，和对偶理论的综合论述。

For special vector optimization problems, namely abstract optimization problems, a generalized multiplier rule of Lagrange is given.

对特殊的向量最优化问题，即抽象最优化问题，给出了一个一般的拉格朗日乘子法则。

Lagrange multiplier method has been the research object by people.

拉格朗日乘数法一直都是人们研究很多的数学对象。

This article tries to present a proof to Lagrange multiplier in the condition of n functions with m additional conditions.

本文就n元函数在m个附加条件下，给出拉格朗日乘数法的一个证明。

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