Sentence examples for derivation of results from inspiring English sources

The tools link together transparently and automatically the processes of spectral ''browsing", feature identification, measurement, and computation and derivation of results.

As an application we obtain a shorter derivation of results due to Ray Singer [RS], Cheeger [Ch], Müller [Mu1, 2] which, in increasing generality, concern the equality for odd dimensional manifolds of the analytic torsion with the average of the Reidemeister torsion corresponding to the triangulation T=(h, g) and the dual triangulation TD=(d−h, g).

Most importantly, the composition of both stimulated and unstimulated saliva may be altered by genetic predisposition factors and physiological, pathological and environmental factors [14, 15, 17, 18], all these factors may hinder the correct derivation of results for best care outcomes.

Here we give the precise theorem we used in the derivation of Result 1.

The choice of the l1 is motivated by its calculation convenience (see the derivation of Result 1 and Appendix 1).

For completeness, we present an alternative derivation of these results that helps interpret the more general results presented below.

Although the derivation of the results is mathematically tough for untrained readers, we have tried to extract widely understandable conclusions from our mathematical results and we believe this paper brings novel elements to the debate about the role and mechanisms of learning in large scale networks.

In particular, Jensen's and Wirtinger based integral inequalities are employed to simplify the integral terms which appeared in the derivation of stabilization results.

HL conducted earlier derivation of the results.

In response to numerous requests by students, material is presented with an unprecedented level of detail in both derivation of technical results and discussion of their physical significance.

For the purpose of clarity, however, we have chosen to present a short derivation of these results.