Sentence examples for using the last expression from inspiring English sources

For example, by using the last expression, it is difficult to study composition operators on α-Bloch space.

Using this last expression, we obtain from the assumption (1.2) that I ext ≤ C ∬ R 2 n J ( x, y ) | u ( x ) − u ( y ) | r d x d y. (2.6).

The first expression represents the unconstrained Gaussian channel capacity, the second is an exponential approximation called (Effective Exponential SINR metric) and the last expression uses the mutual information at an SINR, when modulation alphabet size of is used.

We distribute in the last expression, and we use the two formulas (3.18).

Using Zemanian's technique, equation (10) and the Leibnitz-type formula (11), the last expression can be estimated by.

The last expression is the asymptotic variance of the estimator.

From the last expression, we immediately get the following lemma.

By rearranging terms in the last expression, Theorem 2 follows.

The last expression now may be rewritten as (2.22).

The last expression above tends to 0 as R → ∞.

The last expression is just a normalization on quality.