Sentence examples for a useful relation from inspiring English sources

The following lemma gives a useful relation between the directional STFT and the Fourier transform of the function f.

Also a useful relation between fluorine photoelectron energy vs. polymer composition expressed through the atomic ratio fluorine/carbon (F/C) was found.

In Section 2.2 we observed a useful relation between and for the APQ: A feature pair with a higher would approximately also obtain a higher detection rate for APQ.

A few useful relations are derived for the cavitation pressure which reveal the coupled effect of plastic pressure sensitivity and material inertia.

Following Zhang [19], in the next definition, we define a useful binary relation between an ordered vector space Y and the set of all subsets of Y.

The useful relation between the Riemann Liouville operator and Caputo operator is given by the following expression: bigl( I^{alpha} D_^{alpha} f bigr) ( x ) = f ( x ) - sum_{k = 0}^{n - 1} f^{ ( k )} bigl( 0^ bigr)frac{x^{k}}{k!},quad x > 0, n - 1 < alpha le n, (5) where n is an integer, (x > 0), and (f in C_{1}^{n}).

We note that only the first equality seems to be available in the literature, and the interesting and useful relation to the Gini coefficient has not yet been observed.

It has been a useful public relations exercise for a president who is expected to reveal much more of herself on the international stage if she is re-elected to a second term in office.

For clinics and private practices the event might also be an incentive to attract future patients and therefore be a useful public relations event; in case of a clinical uncertainty this might also contribute to recommend a clinical follow up rather than a reassurance.

One derived useful relations and used simulated examples to illustrate how this method can be applied.

Thus, the objective of this study was to develop useful relations for a more general class of reactions with power-law kinetics, which may be accompanied by either exponential, hyperbolic or reciprocal catalyst decay forms for both PFR and CSTR systems in the presence of pore-diffusional limitations.