查询词典 interpolation polynomial

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

The conventional linear and circular interpolation in Cartesian coordinates were supplemented by polar coordinates and helical interpolation.

传统的笛卡尔的线形和环形内插法结合被极坐标和螺旋插补所补充。

When the determinant is expanded, it produces a polynomial, called the characteristic polynomial

当行列式展开后，得到一个多项式，叫它为特征多项式。

The differential characteristic set for differential polynomial system maintains the essential character of original differential polynomial system.

微分多项式系统的微分特征列集保留了原微分多项式组的本质特征，具有三角化良序结构等优点，能够克服不同领域问题中的一些困难。

In this paper, We firstly present a nonuniform sampling DCT method based on the relationship of Chebyshev polynomial interpolation and DCT, in which, the sampling points are chosen as zeros of Nth degree Chebyshev polynomials of the first kind.

文章首先利用Chebyshev多项式插值与DCT变换之间的相互关系，提出了基于第一类Chebyshev多项式的第N次多项式的零点作为非均匀取样点的DCT变换方法。

Based on the examples analyzed,this paper mainly discusses the impacts of the polynomial degree,fit time span and interval of the fitting points when using chebyshev polynomial to fit the satellite orbit,the situation using more orbital elements and the area and choosing of the orbital elements are also discussed at last.

以实例分析为基础，主要讨论了利用切比雪夫多项式拟合GPS卫星轨道时多项式阶数、时段长度、拟合点间隔等因素的设置问题；并对使用多组轨道参数进行轨道拟合的情况进行了分析；最后讨论了轨道参数的使用范围和选择问题；得出了有用的结论。

This paper provides an algorithm of constructing self adaptive partial least sqaures regression model based on Chebyshev's polynomial.It automatically builds a multinomial model based on Chebyshev's polynomial with less predicting error.

引 言偏最小二乘法[1 ] 是一种多元统计数据分析方法，它克服了自变量之间的多重相关性，既是一类模型式的方法，又是一类认识性的方法，在统计应用中起着重要的作用。

Due to the coupling of every Zernike circular polynomial in the annular field, the SEIDEL coefficients solved by wavefront fitting with circular polynomial for annular pupils with big central obscuration would have larger errors.

由于Zernike圆多项式各项在环域上的交叉耦合，对于具有大中心遮拦的环孔径波面采用圆多项式拟合求解SEIDEL像差系数存在较大误差。

And certain q-polynomial coalgebras arisesnaturally,which is a q-deformation of classical polynomial coalgebra.

并且我们自然地引出了一类q-多项式余代数，它是经典多项式余代数的变形。

The polynomial greatest common divisor is one of the most important polynomial contents, as which is not only the basic summary in the whole Higher Mathematics and Number Theory .

多项式最大公因式是多项式众多内容中十分重要的一项，它在整个高等代数、抽象代数、数论等科目当中，既是基础性的内容，也是很多其它项目研究中要求具有的储备知识。

He's a pretty westernised kind of guy.

他是一个非常西化的人。

National spirit is the moral kingpin for a nation to realize common ideal and goal.

一、中华民族精神的基本内涵党的十六大报告指出：在五千多年的发展中，中华民族形成了以爱国主义为核心的团结统一、爱好和平、勤劳勇敢、自强不息的伟大民族精神。