Sentence examples for ordering of majorization from inspiring English sources

We consider a partial ordering of majorization.

The Schur-convexity described the ordering of majorization, the order-preserving functions were first comprehensively studied by Issai Schur in 1923.

To continue our discussion, we need definitions of some stochastic orders and the concept of majorization which is given in Section 2.

For the concept of majorization, the order-preserving functions were first systematically studied by Schur (see [1, 2], p.79).

In order to tackle this new descriptor, we extend prior results of majorization into the realm of weighted majorization [23], and then we express the descriptor as an appropriate p-Schur-convex function to which the new technique can be applied.

This new order opened a path for the study to generalize the theory of majorization of Hardy et al. [18].

Firstly, we recall the definitions of majorization and weak majorization.

Considering a weighted relation of majorization, Sherman obtained a useful generalization of the classical majorization inequality.

Other notions of majorization are examined in these C⁎-algebras.

Some kinds of majorization such as multivariate or matrix majorization were motivated by the concepts of vector majorization and were introduced in [3].

Let us now give the most general definition of majorization.