超球面 meaning in Chinese
hypersphere
Examples
- Theorem 1 . 4 let m be a hypersurface with non - zero constant scalar curvature in rn + l spanning a sphere sn - 1 ( r ) . if its gauss image lies in the semisphere , then m is a hypersphere cap
)为边界的紧致常纯量曲率(非零)超曲面，如果其高斯映照像落在一个以s ~ ( n - 1 ) ( r )为边界的半球面内，则m只有超球面盖。 - This paper proposes weighted support vector machine algorithms based on the analysis of the cause of such problem , and this algorithm overcomes the drawback which standard support vector machine algorithm ca n ' t deal with each sample flexibly and compensates for the unfavorable impact caused by this bias
通过比较它们各自的优缺点等情况，为提出新的支持向量机算法做了理论准备。 ( 2 )介绍了超球面支持向量机算法的思想，以及超球面和超平面的区别。 - Normal behavior and anomaly are distinguished on the basis of observed datum such as network flows and audit records of host . when a training sample set is unlabelled and unbalanced , attack detection is treated as outlier detection or density estimation of samples and one - class svm of hypersphere can be utilized to solve it . when a training sample set is labelled and unbalanced so that the class with small size will reach a much high error rate of classification , a weighted svm algorithm , i
针对训练样本是未标定的不均衡数据集的情况,把攻击检测问题视为一个孤立点发现或样本密度估计问题,采用了超球面上的one - classsvm算法来处理这类问题;针对有标定的不均衡数据集对于数目较少的那类样本分类错误率较高的情况,引入了加权svm算法-双v - svm算法来进行异常检测;进一步,基于1998darpa入侵检测评估数据源,把两分类svm算法推广至多分类svm算法,并做了多分类svm算法性能比较实验。 - In the second part , we investigate the compact submanifolds m with the parallel isoperimetric section in the real space forms rm ( c ) and prove that if there exists a parallel isoperimetric section on m , and the sectional curvature of m is always greater than zero , then m is contained in a hyper - sphere ; and get that the gauss curvature of the compact surfaces m with constant mean curvature in constant curvature space r4 ( c ) is always greater than zero , then m is a totally geodesic surface or a sphere , where an isoperimetric on m means a unit normal vector field defined globally on m with m1 ( ) = constant
( 2 )研究了实空间形式r ~ m ( c )中具有平行等参截面的紧致子流形m ，证明了具有一平行等参截面的子流形m ，如果m的截面曲率恒正，则m包含在r ~ m ( c )的一个超球面内；对于常曲率空间及r ~ 4 ( c )中具有常平均曲率的紧致曲面m ，如果m的高斯曲率处处大于零，则m或为r ~ m ( c )中的全测地曲面或为一球面。这里m上的等参截面是m上整体定义的单位法向量场，使得m关于它的平均曲率m _ 1 ( )是常数。