Sentence examples for simpler inequality from inspiring English sources

To address this issue, Darby and Nikolaou (2009) developed a general mathematical framework, that relies on a much simpler inequality as its starting point.

Noticing that Tr(A AH ≤N∥A∥2 and that Tr((A AH p/2)≤N∥A∥ p, we obtain the simpler inequality E 1 N x H Ax − 1 N Tr ( A ) p ≤ C p N p / 2 ∥ A ∥ p E | X 1 | 2 p / 2 + E | X 1 | 2 p. (27).

From this definition we can derive a simpler inequality that can be used to determine the value of the constant k: Proposition 5 (from [ 12]).

Again, from this definition we can derive a simpler inequality that can be used to determine the value of the constant k ′ : Proposition 6 (from [ 12]).

Setting (mathtt{k}=1) in Theorem 2, we get a little simpler inequalities asserted by the following corollary.

Further, choosing (lambda =alpha ), (sigma (0)=1) and (w=0) in Corollary 1, we get simpler inequalities in the following corollary, which are a modification of the Hermite-Hadamard inequalities given in [22].

As the report says, the wealth gap is less a question of fairness between old and young people, and more one of simple inequality.

But, using a simple inequality, he shows that each such pair works exactly once: either as a sum of an odd number of integers with the even integer as the middle, or a sum of an even number of integers with odd/2 as the middle.

A simple inequality characterizes this property: information ≤ data.

So the big data fallacy can be summarized by a simple inequality: insight << information << data.

However, this assertion also teaches us that a simple inequality yields a complicated inequality.