3 citations · 10 across the 12 of their papers we have counts for
4 papers · 1 filter
The weighted difference substitutions and Nonnegativity Decision of Forms
Xiaorong Hou, Song Xu, Junwei Shao
In this paper, we study the weighted difference substitutions from geometrical views. First, we give the geometric meanings of the weighted difference substitutions, and introduce…
Simplex Subdivisions and Nonnegativity Decision of Forms
Xiaorong Hou, Song Xu
This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to s…
Completeness of the WDS method in Checking Positivity of Integral Forms
Xiaorong Hou, Junwei Shao
Examples show that integral forms can be efficiently proved positive semidefinite by the WDS method, but it was unknown that how many steps of substitutions are needed, or furtherm…
Spherical Distribution of 5 Points with Maximal Distance Sum
Xiaorong Hou, Junwei Shao
In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how to configure 5 points on a sphere such that the mutual distance sum attains the ma…