球面

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。

In this paper, we mainly study the gap of the second fundamental form of hypersurface with constant mean curvature in the unit sphere.

本文主要研究了单位球面内常平均曲率超曲面的第二基本形式模长平方的间隙性。

For Lorentzian hypersurfaces in the Lorentzian sphere, the situation is different from in, the hypersurface may has complex eigenvalues.

对洛伦兹球面S(上标 n+1 下标 1)中的洛伦兹等参超曲面，情况有所不同，可能会有复的特征值。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simon\'s nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simons nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐