Sentence examples for since this inequality from inspiring English sources

and since, this inequality reduces to (3.7).

Since, this inequality together with (b) yields (3.6).

Since this inequality is homogeneous in and, and also in and, we may set and.

Since this inequality holds for all ε > 0, it follows that, for any x ∈ V, f(x) = 0.

Since this inequality is homogeneous in and, and also in and, without loss of generality, assume that and.

Since this inequality is true for every (ninmathbb{N}), from (8) and by passing to the limit as (nrightarrow+infty ), we obtain (14).

Since, dividing this inequality by, we obtain that is a solution to (GVI) on.

On the other hand, since, dividing this inequality by, we get (4.39).

Mordell and Barrow [2] first proved it in 1937, and since then this inequality is known as the Erdös-Mordell inequality and has attracted the attention of many mathematicians who offered various new proofs, generalizations, variations, sharpness, and conjectures (see [3 33] and the references therein).

Since then, this inequality has been of concern for more and more authors (e.g., Chow [8] and Gan [9] for martingales, Liu et al. [10] for negatively associated random variables and Kim et al. [11] for asymptotically almost negatively associated random variables).

Yet public spending does not make up for this inequality, since Whitehall's Barnett formula gives more per head to Scotland than to Wales.