超球面

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。

A novel approach of binary component discriminant function is proposed by generalizing the original quadratic-form distance metric.

针对现有基于核函数的相关反馈方法处理样本不对称性时的缺陷，提出了基于超球面的支持向量分类方法。

How many equal three-dimensional spaces would a hypersphere be cut into by hyperplanes at right angles to each other?

一个超球面被切割成相互垂直的超平面会产生多少三维空间？

The fuzzy hypersphere support vector machine is proposed for shallow buried target discrimination, and its two aspects, hyperparameter optimization and kernel function selection, are comprehensively studied.

提出了模糊超球面支持向量机浅埋目标鉴别算法，并对FHS-SVM的超参数优化和核函数选择两个问题进行了深入研究。

According to the above characteristics of shallow buried target discrimination, the hyperplane SVM, which has achieved the best classification results for many classification problems in different fields by now, has been modified to yield the FHS-SVM, which uses the hypersphere in the kernel space to separate shallow buried target and clutter.

根据浅埋目标鉴别的特点，对在许多领域的分类问题中取得迄今为止最好分类结果的超平面SVM进行了改进，得到利用核特征空间的超球面区分浅埋目标和杂波的FHS-SVM。

This a obtains method maximum separation ratio to separate two classes instances via a single hypersphere and also provides the facility to control the upper bounds of two classes error rates respectively with two parameters. As such, the performance of classification and prediction of imbalanced data sets can be improved, and the range of selection of parameters can be greatly narrowed.

该方法通过一个超球面将两类数据以最大分离比率分离，并且引入两个参数来分别控制两类错分率的上界，不仅提高了不平衡数据集的分类和预测的性能，而且大大缩小了参数的选择范围。

Mainly in a method of the lattice vector quantifying coding and decoding, a new basic code book is selected out and directly or indirectly comprises all points whose value is less than or equal to 3 of any dimension in a RE point set, and points on a fourth grade hypersphere in the basic code book are all odd points so that part of nearest adjoint point values can be comprised in the basic code book only via corresponding odd number processing.

一种格矢量量化编解码的实现方法及装置，其主要是在格矢量量化编码方案中，选定新的基础码本，在该基础码本中直接或间接地包含了RE 8 点集中任意维的数值小于等于3的所有点，且该基础码本中的第4级超球面上的点全部为奇数点，以使得部分的最近邻点数值仅经过相应的奇数化处理便可以包含于基础码本中。

By considering the color randomicity of foreigns and the color difference between the regular materials and the foreigns in fast foreign real-time recognition,the specialities of an One-class Support Vertor Machine for foreign recognition are studied,and an approach to real-time recognition based on hypersphere OC-SVM is presented.

针对高速异物在线识别中正常物料与异物颜色差异及异物颜色随机性的特点，研究了一类支持向量机在异物识别中的特性，提出了一种基于一类超球面支持向量机的在线识别算法。

The FHS-SVM based on the structural risk minimization criterion can solve the small sample learning problem, which can get a good shallow buried target and clutter classification performance with only shallow buried target training samples to obtain the parameters of hypersphere. Furthermore, the factors of misclassification risk and bury environment diversity are combined into the discriminator study procedure using the fuzzy membership of training samples, which improve the practical value of the FHS-SVM in shallow buried target discrimination.

FHS-SVM基于结构风险最小原理，在有效解决小样本学习问题的同时，只需要浅埋目标训练样本就能优化超球面参数，获得较好的浅埋目标和杂波分类性能；并且利用训练样本的隶属度将误判风险和埋设环境多样性等因素融入鉴别器学习过程，提高了FHS-SVM浅埋目标鉴别算法的实用性。

There is a sort of new lens effect in hyperspherical universe, and it should result in some periodicity in observation.

在超球面宇宙中存在一种新的透镜效应，其结果导致观测上的某种周期性。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。