查询词典 affine space

Linear constraint particle swarm optimization algorithm is a global optimization dealing with constraints of non-negative and affine real space.

粒子群算法虽有全局优化性能，但也会陷于局部极小，且缺少约束处理机制。

The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples.

全书共分七章，前三章是基础知识部分；后四章是本书的核心部分，总结了近年来代数几何码的最新研究成果，并且包含了作者的一些尚未发表的结果。

Keywords: Hecke algebra; quantum affine algebra; Fock space

中文关键词：黑克代数；量子仿射代数； Fock空间

Local invariant feature ; object recognition ; image matching ; image classification ; scale space ; affine invariant moment ; detector ; descriptor

吉林大学；刘萍萍局部不变性特征；物体识别；图像匹配；图像分类；尺度空间；仿射不变矩；检测子算法；描述子算法

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

3D reconstruction is one of the most challenging problems in computer vision. This project uses CAD model to increase the accuracy,robustness and speed of 3D reconstruction and five different works are conducted: 1 research on space curve 3D reconstruction method based on high curvature point nad turning point; 2 free-form curve 3D reconstruction based on B-spline and BURBS; 3 Active surface affine reconstruction based on single frame; 4 Matching and reconstruction of 3D sparse points; Data fitting method based on the iteration of nearest point.

三维重建是计算机视觉中公认的难题，本项目使用CAD模型来提高三维重建的精度、稳健性和速度的思路，围绕着空间曲线和曲面的三维重建和匹配开展了以下五个方面的研究：1）基于高曲率点和拐点分割的空间曲线三维重建方法研究；2）基于B样条和NURBS表示的空间自由曲线三维重建方法研究；3）基于单帧图像的有源曲面仿射重建；4）三维离散数据的匹配与重建；5）基于迭代最近点的数据拟合方法。

A method for estimating 3D space face pose was proposed based on affine transformation and linear regression.

提出了一种由仿射变换关系到线性回归的3D人脸空间姿态估计方法。

Using the substitution-elimination method affine algebraic variety can be resolved to pure d-dimensional subvariety and expressed by an algebraic hypersurface on d+1-dimensional space with a sequence of elimination-polynomial systems. All 0-dimensional solution can be found, too.

利用变换消元法可以把代数簇分解成纯d维的子簇，并把代数簇表示为d+1维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用。

Affine transformations are transformations that preserve collinearity and relative distancing in a transformed coordinate space.

仿射型变是在一个转变坐标空间内保持共线性和相对距离的型变。

In this paper we define the concept of Projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. We prved that if M be a complete projective Blaschke n-sphere and its universal covering manifold is isometric to a complete (n+1) dimensional parabolic, elliptic or hyperbolic affine hypersphere, then M is a quotient space of E^n, S^n or D^n by a isometric subgroup of its corresponding spaces.

在这篇文章中我们定义了射影Blaschke流形的概念，将等仿射微分几何的理论推广到了射影Blaschke流形，并证明：如果n维完备射影Blaschke 超球面 M 的通用覆盖流形分别是完备的抛物型、椭圆型或双曲型仿射球，则M分别是n维欧氏空间、n维超球面或n维单位圆盘关于各自空间的一个等距离散子群的商，从而对完备射影Blaschke 超球面进行了分类。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。