多项式

The exact modedling methods include: representation and construction of control mesh of some special minimal surface; exploration and properties of polynomial parametric minimal surfaces with isothermal parameter.

精确造型方法主要包括两个部分：某些特殊极小曲面的控制网格表示与构造；等温参数多项式极小曲面的挖掘与性质。

The test for the independent testing dataset and the jackknife test were both carried out.

本研究使用了6种长度的局部序列，并采用了具有不同参数d的多项式核函数。

At first, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the vertical vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient Cv versus the dimensionless frequency is derived, and the program is compiled.

首先，采用Fourier积分变换解析求解了Biot方程，得到了该动力控制方程在Fourier变换域上的一组通解，然后由混合边值条件建立了地基上基础竖向振动的对偶积分方程，并应用Jacobi正交多项式将其转化为一组线性代数方程组，通过求解得到了不同无量纲频率下基础振动的动力柔度系数Cv，编制了相应的计算程序。

The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the correspo

借助非定常时间分裂法和无波动无自由参数的NND耗散格式，建立直接求解微观分子速度分布函数的有限差分数值格式；研究并发展可用于离散速度坐标点选取和离散速度空间宏观取矩的高斯─埃尔米特无穷积分方法、等均间隔的牛顿─柯斯复合积分法、以勒让德多项式的根为积分结点的高斯─勒让德数值积分法，并应用于不同马赫数绕流模拟；通过对不同流域一维激波管问题、二维圆柱绕流问题和三维球体绕流的计算研究，并将计算结果与其他途径得到的研究结果诸如DSMC模拟值、N-S解及有关实验数据进行比较分析，创建了一套能有效模拟稀薄流到连续流不同流域气体流动问题简化的统一数值算法研究框架

In this paper, the Lagrange interpolation formula asked a class function expression question, the determination function to the higher mathematics in the elementary mathematics in some value scope question, the equality proof question, the multinomial factorisation question, to ask to have the Finite series to pass the formula question, the certificate any n function at will n+1 different spots function value maximum value minimal problem and so on six aspects should serve as the simple introduction, and has separately made the comparison with these six aspects elementary mathematics method, thus solved some operation problems in elementary mathematics.

摘要本文对高等数学中Lagrange插值公式在初等数学中的求一类函数表达式问题、确定函数在某点的取值范围问题、恒等式的证明问题、多项式的因式分解问题、求有穷数列的通项公式问题、证明任一n次函数的随意的n+1个两两不同点的函数值的最大值的最小值问题等六个方面的应用作了简单介绍，并与这六个方面的初等数学方法分别作了比较，从而解决一些初等数学中的运算问题。

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。

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。

Meanwhile,by analyzing the calculation results of NL Method,and using Least Squares Method or Lagrange's Interpolation Polynomial Curves to simulate the relationship between horizontal force and deformation of both Steel-pile Cluster and Rubber Fender separately,the energy allocation rate of Steel-pile Cluster and Rubber Fender can be determined.

采用NL法来计算桩身内力和变形，同时，对NL法计算出的多个结果进行分析，并采用最小二乘法或Lagrange插值多项式曲线分别模拟钢簇桩和橡胶护舷承受的水平力和相应的变形之间的关系来求解钢簇桩和橡胶护舷能量分配比例。

Here pis 1 or 2.In chapter 8. we extend the Runge-Kutta methods to variable delay differentialalgebraic system. It is proved that if the Runge-Kutta method which is algebraicallystable and diagonally stable is consistent with order p , the extended Runge-Kuttamethod with Lagrange interpolation procedure is D_A-convergence with order M. HereM=min{p, u + q + 1 }, and u + q is the degree of Lagrange interpolation polynomial.

第八章将求解常微分方程的Runge-Kutta方法改造后用于求解变延迟微分代数系统，并且证明如果代数稳定且对角稳定的Runge-Kutta方法对于常微分方程初值问题在经典意义下是p阶相容的，那么具有Lagrange插值过程的该方法是M阶D_A-收敛的，M=min{p，u+q+1}，u+q为Lagrange插值多项式的次数。

Most threshold schemes are based on Lagrange interpolation or Chinese Remainder Theorem.

大多数门限方案都基于Lagrange插值多项式或者是同余理论。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。