Sentence examples for ranks inequality from inspiring English sources

As long as people have felt that most of the rich earn their wealth on merit, or at least without abuse of power, and that it remains possible for ordinary people to join their ranks, inequality has mattered little.

To make their findings, researchers ranked inequality in the developed world according to the distribution of income.

The two rank inequalities in (2.69) follow from the well-known rank inequality (r(S) geqslant r(PSQ)).

The rank inequality for diagonally magic matrices can be stated as follows.

Then we give a simple proof of the rank inequality for diagonally magic matrices (J. Inequal. Appl. 2015 318, 2015).

Since A ̄ ̃ c ( n ) and A ̄ ̃ d ( n ) are both of full column-rank, we can utilize the rank inequality in [24] to conclude the proof.

Since the dimension of B 1 and T 1 is (N+1)×(N+1), according to the Sylvester's rank inequality [37], we have rank(B 1)+rank(T 1)−(N+1)≤rank(B 1 T 1), then rank(B 1)+rank(T 1)≤N+1.

Using Sylvester's rank inequality (see p. 211 in [39]) on (48) and with the help of (61), we can write following for rank of W n ⋆ : Rank ( W n ⋆ ) ≤ n t + Rank Z n ⋆ W n ⋆ - Rank Z n ⋆ ≤ 1. (62).

They can be regarded as rank inequalities for the independence systems associated with these designs.

The constraint generation is carried out by heuristically solving the separation problem associated with a large class of rank inequalities.

The proposed IRM method aims at solving RCOPs with rank inequalities constrained by upper or lower bounds, as well as rank equality constraints.