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They are presented in need of special curves and surfaces in engineering applications. In order to prove that the uniform C-B-spline basis is normalized totally positive, we compute the matrix which transforms the C-Bézier basis into the uniform C-B-spline and decompose this matrix into a product of. bidiagonal and stochastic factors. Furthermore, we give a normalized B-basis by inserting knots.

本文用递推的方法,计算出代数三角空间中的n次C-Bézier基与n次均匀C-B-spline基之间的转换矩阵,并把该矩阵分解为一系列二对角阵的乘积,从而证明出n次均匀C-B-spline基是一个标准全正基,进一步用插入节点的方法,把它扩充为一组标准B基,从而我们可以利用B基的很多优良性质,在工程应用中对这两组基进行开发利用。

Motivated by Baker\'s result, we introduce a functional index‖E‖_∞to prove that if a mapping f which is from a normed space to a normed algebra satisfying‖ab‖=‖a‖‖b‖satisfies that‖E‖_∞is bounded,then either f is bounded or f is exponential.

受到Baker的结论启发,通过引入一个泛函指标‖E‖∞,证明了从赋范空间到满足范数可乘性的赋范代数的映射f,只要满足‖E‖∞是有界的,则f要么是有界的,要么是指数的。

In the front of this chapter,using operator inner-outer faetorization,we reduce the estimation problem to a distance minimization between a certain operator and the nest algebra in question.

本章第一节,利用算子中的内外分解理论以及Banach空间的对偶理论,将估计问题约化为某个算子与讨论的套代数之间的一个距离问题。

Projective transformation of curved surface and plane intersecting line are completed based on vector algebra,adopting space coordinate transforming method.

方法基于向量代数,采用空间坐标变换方法,建立了圆锥面与平面相交中截交曲线的形成特点,讨论了二次曲线的构成的数学原理。

Nonsingular H-matrix; generalized H-matrix; eigenvalue; numerical radius; matrix splitting; saddle point problem; Krylov subspace method; preconditioning technique

基础科学,数学,代数、数论、组合理论非奇H-矩阵;广义H-矩阵;特征值;数值半径;矩阵分裂;鞍点问题; Krylov子空间法;预处理技术

There are three main methods in face localization: localization according to face outline, localization according to complexion and localization according to templates constructed by some standard sample images. As to feature extraction, it can be divided into two parts because face features can be divided into geometrical features and algebraic features. While extracting geometrical features, the features of eyes, nose, mouth, eyebrows can be gained by some image processes: binary, sharpen, smooth, projection, calculating gradient and so on. In order to extract algebraic features, we can do some mathematical transformation for the digital images such as singular value decomposition, K-L transformation.

在人脸检测部分,目前存在的方法有利用人脸的几何轮廓进行检测、利用人脸的肤色信息进行检测、构造标准人脸模板进行匹配检测等等;在人脸特征提取部分,可以用一些图像处理的方法如投影、二值化、求梯度图像等提取人脸中各特征器官如眼睛、鼻子、嘴巴等的几何特征,另外也可以借助于数学变换,求取人脸图像的一些代数特征,如对图像进行奇异值分解,以奇异值代表图象的特征,或对图像进行K-L变换,以图像在构造的特征空间上的投影系数作为图像的特征等;在识别部分,可以通过距离度量或相似度来判断输入图像与样本图像的匹配程度,还可以通过神经网络方法进行人脸的识别。

SVD can reflect the algebra character of the image effectively, and then through SVD operation on vehicle image matrix which includes singular value dimensionality reduction and singular value vector compositor, the feature subspace for recognition is established.

奇异值分解是基于代数特征的特征提取,经过对车辆图像矩阵的奇异值分解,再经过奇异值降维压缩和奇异值矢量排序,最后建立了用于识别的特征子空间。

Methods A new basis, to be called H-Bézier basis, is constructed for the space Γ=span{1, t, t^2,…t(superscript n-2), sinh t , cosh t}(n≥2) by an integral approach.

在代数双曲混合函数空间Γ=span{1,t,t^2,…,t(上标 n-2),sinh t,cosh t}(n≥2)中构造一组规范基,基于该规范基函数定义曲线。

Next,similar to the studies of Friedland-Hersonsky inequalities in norm form and Martininequalities for discrete groups of 〓,we establish 〓 type inequalitiesfor subgroups of unitary transformation group U(1,n,C)in complex hyperbolicspace 〓 and we also give several 〓 type inequalities in the form of fgfg〓for the norm algebra 〓 in C.

其次,我们对复双曲空间〓上的酉变换群U(1,n,C)的子群建立了〓型不等式,推广了Martin的相应结果。最后,我们对复数域C上的范数代数〓建立了形如〓的〓型不等式,推广了Friedland-Hersonsky不等式。

This article analyses the Vector Space Model based on Algebra, and expands the model: expresses the index terms with minterm in order to reflect the relationship between terms, uses singular value decomposition to present the semantic structure of documents.

本文分析了代数理论的向量空间模型,并对该模型进行了扩展:用最小项标引词以反映词与词之间的关系,用奇异值分解来捕捉文献的语义结构;最后对这三种模型进行了比较。

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推荐网络例句

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应,而且减少跟风的可能性。

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