Sentence examples for relation together with from inspiring English sources

If fn is a function defined on the positive integers, then a relation that expresses fn + k as a linear combination of function values of integer index less than n + k, in which a fixed constant in the linear combination is written ai, is called a recurrence relation The relation together with the initial values f0, f1,…, fk − 1 determines fn for all n.

This relation, together with (3.32) yields (3.34).

This relation, together with statement yields (3.8).

This relation together with (4.6) implies (4.3).

Based on this relation together with the conditional extremum method, we theoretically derive an optimization equation group.

The Gutenberg-Richter frequency-magnitude relation, together with other analyses, gives that the completeness of this catalogue for the Japan islands region is above Mw 5.2, satisfying the requirement of AMR analysis for the cutoff magnitude.

She sources and executes deals involving SMEs, managing an investment portfolio and investor relations together with driving strategy for the businesses Dina Behrman is a PR coach.

A discussion is given for various dispersion relations, together with theoretical justification and practical implementation.

Therefore, it is of great importance to understand the phase relations together with the knowledge of the degree of melting at relevant pressures and temperatures.

Use of the new relations, together with an iterative procedure to obtain polynomials with the specified ripples from the Parks McClellan algorithm, are shown to give simulated slice profiles that have the desired ripple amplitudes.

This paper analyses discrete dispersion relations together with numerical propagation accuracy to determine the effect of tetrahedral shape on the phase accuracy of standard 3-D edge-element approximations in comparison to other methods.