查询词典 Euclidean algorithm

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

The innovation points of this paper are:(1) The traditional FCM algorithm uses the Euclidean distance for calculating the distance of two data points, but in the visual principle FCM clustering algorithm we used the number of edges of average shortest route instead.

本文的创新点在于：(1)传统的FCM算法中计算两点之间的距离采用的是欧氏距离，而本文提出的视觉原理的FCM聚类算法采用的是复杂网络中常用的两点之间的最短距离。

Extraneous roots are found during the process to obtain the other 3 variables by using Euclidean algorithm.

首先使用结式对四个多项式方程直接消元，得到一个一元52次的多项式方程，用辗转相除法求其他三个变量的过程中发现了6个增根。

You can probably skip the detailed calculations of the running times of raising to powers and of the euclidean algorithm; just say what the final estimate is.

比如你可以把计算时间的估计这些内容删掉，只讲最后的结果。

A modified Euclidean algorithm was proposed by the generalization of synthetic division. It didn't judge the degree of polynomial and could decrease the complexity of decoding and hardware circuit and improve the decoding speed.

通过对综合除法进行推广，提出了一种改进型欧几里德算法，它不需要进行多项式次数的判断，能够降低译码的复杂度，减少硬件电路的复杂性，提高译码速度。

After that a 40 degree univariate polynomial equation can be obtained. Other variables can be computed by Euclidean algorithm and Gaussian elimination.

使用辗转相除法和高斯消去法可以直接快速的求出其他3个变元。

According to the complexity of decoding circuit in digital TV and the moderate speed of decoding,a modified Euclidean algorithm is proposed based on the related deduction of division with reminder of polynomials.

针对数字电视译码电路复杂，译码速度不高的特点，基于多项式带余除法的相关推论，提出一种改进型欧几里德算法。

algebra ; general solution ; matrix solution ; program ; Euclidean algorithm ; MATLAB

1通解与算法数域F}多项式环厂刘上多元一次不定方程组的一般形式为

This paper first replaces the Euclidean distance in Otsu's thresholding segmentation method with the generalized harmonic mean distance and obtains a kind of new robust image segmentation algorithm,then the method of choosing its optimal parameter in new segmentation algorithm is brought forward.

首先将Otsu图像分割法中的欧式距离用广义调和均值距离代替并得到一种具有鲁棒性的图像分割新算法，其次给出该算法中参数选取办法。

A generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance is proposed,which incorporates geodesic distance and generalized Gaussian function into the original Laplacian eigenmap algorithm.GGLE algorithm can adjust the similarities between nodes of neighborhood graph,and can preserve the different degrees of local properties by using super-Gaussian function,Gaussian function or sub-Gaussian function.Moreover,GGLE can avoid the deficiency of Euclidean distance by using geodesic distance when neighborhoods of data points are enlarged for preserving more neighborhood relations.Experimental results show that the global low-dimensional coordinates obtained by GGLE have different clustering properties and different degrees of preserving local neighborhood structures when different generalized Gaussian functions are used to measuring the similarities between high-dimensional data points.(3) An ensemble-based discriminant algorithm based on GGLE is proposed.

该算法将测地线距离和广义高斯函数融合到传统的拉普拉斯特征映射算法中，可以调整近邻图结点间的相似度，通过选择超高斯、高斯或者次高斯函数来实现不同程度的近邻局部特性的保持；而且当需要保持更多的近邻关系使得数据点邻域增大时，采用测地线距离可以避免欧氏距离度量不合理的缺陷；实验结果表明在用不同的广义高斯函数度量高维数据点间的相似度时，局部近邻结构保持的程度是不同的，GGLE获得的全局低维坐标也呈现出不同的聚类特性。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。