Sentence examples for this last relation from inspiring English sources

We prove this last relation.

This last relation is the well-known and extensively studied Hadamard fractional integral [21 23].

Defining the quality factor (Q) of attenuation as (7) Eq. (5) yields (8) This last relation implies that (9) which restricts the value of β for any attenuating wave with a given value of Q.

Following the most relevant literature on the topic and to investigate this last relation, we decided to perform a correspondence test to our sample such as in Riach and Rich (2002) and Drydakis (2009) among others.

Now applying for this last relation the Shakalikov multiray Tauberian theorem (see [6]), we get N ( tau ) simsum_{k=1}^{v} N_{k} ( tau ), quad taurightarrowinfty, where (N_{k} ( tau ) sim c_{k} tau^{frac{1}{2}}) with (c_{k}) as before.

Since both (c - a + 1) and (C - A + 1) are congruent modulo 3, we know by definition that (c - a - C + A mod3 = 0. We used this last relation to test whether permuted repeats were frame preserving given that natural repeats are frame-preserving, without knowing the length or coordinates of the introns.

This together with the last relation implies that (lim_{krightarrowinfty}h_{r}(t^{k})=0).

Using again the fact that and have no common roots and, it follows that the coefficients in the last relation are zero and this implies (2.33) and (2.34).

With the help of the last relation, we have (2.19).

Since is monotone, we obtain from the last relation (3.18).

Choosing for now T ≤ 1 2 J ∥ α ∥ R, the last relation yields: ∥ σ ∥ ≤ ∥ σ 0 ∥ + 1.