We have obtained the analogue of Luecking s result on half spaces R+n+1 for the case 2≤p≤q≤.

Using the properties of SO(n) group and the symmetry of crystal, we study the possible symmetry operation of the super lattice in high dimensional space.

Analyzing the geometry meaning of different structure neurons in high dimensional space, high dimensional geometrical distribution of the sample set in the feature sp.

Geometric inequalities and its applications in higher dimensional space;

A generalization of finite increment theorem in higher dimensional space

Topological properties of higher dimensional spaces are analyzed and a standard graphic method to express such spaces is deduced.

A dynamic KPPCA was developed for process monitoring to eliminate these disadvantages by mapping the compressed data matrix extended by the time series into a high-dimensional space by a kernel function.

In the elements of statistical learning,the nearest-neighbor metbod is a very intuitive and imporant learning method,but the approch and our intuition breaks dowm in high-dimensional space for the″dimension disaster″problem.

A new method to decrease the scale of training data is proposed,which is to find the border of the two categories in the mapped high dimension space.

In this paper a collection of high dimension convex envelope is regarded as the satisfied coverage of the complicated geometrical body formed by characteristics of the same type things in high dimension space,and an effective algorithm of determining whether or not one point is within collection of high dimension convex envelope is given.