Sentence examples for proof of relation from inspiring English sources

Analogously to the proof of relation (14), we obtain the relation f(theta -f(0)=sum^{inftheta -f}D_{n} cosbiggl(n-frac{beta}{2}biggr)theta -sum^{infty}_{n=1}D_{n}. (19) The convergence of numerical series (sum^{infty}_{n=0}D_{n}) is proved analogously to the proof of the convergence of series (sum^{infty}_{n=sum^{infty

This completes the proof of recurrence relation.

As further proof of the relation between HyLIMPs and LIMPs, a HyLIMP decanucleotide-like sequence was found just left of LIMP #11 (see Fig.  2a), and the loop of HyLIMP #3 resembled that of the LIMPs (see Fig.  5).

This initial screening constitutes proof-of-concept in relation to bloodstream infections and, although this is not a full validation of the oCelloScope system, the results are compared to commercially available systems.

Finally, a proof of the intrinsic relation between the ion current at the cathode and the deposition rate has been shown, finding a linear relation between these two quantities.

First, we give an alternative proof of the limit relation (1.4) including the existence of the limit in (1.3).

So as long as the proof of the equiconvergence relation is carried out by means of the contour integration, we obtain the uniform convergence of the series (2.20).

On differentiating (mu_{n,m}(x)) with respect to x, the proof of the recurrence relation easily follows; hence the details are omitted.

We prove that the Segal Bargmann transform of those L-invariant polynomials are, under the spherical transform on D, multi-variable Wilson-type polynomials and we give a simple alternative proof of their orthogonality relation.

Specifically, we demonstrated that LM1 signalling and biomimetic extracellular elasticity are clearly necessary for functional differentiation of MECs; these cells in turn exhibit a strong correlation with biomimetic cellular elasticity, although the proof of a mechanistic relation between the latter and β-casein expression remains to be elucidated.

The proof of the equivalent relations of, and can be found in [3].