Barkirov introduced majorization in the research of quadratic form of random variables and got the result as following: If , be independent normal random variables , two positive vectors , then .

• Bakirov首次将控制序概念引入到高斯向量二次型分布的不等式研究，并且证明了下述结论：令 为相互独立的标准正态变量， 和 为两个正的实向量。