Sentence examples for long derivation from inspiring English sources

Due to the very long derivation process, we directly gave the final result in the paper.

It is worth comparing the long filter derivations by Butterweck [24] that exclude border effects at the beginning and ending of the matrices.

Consider some long chain of derivation.

Jeffrey Dukes, of the University of Massachusetts, in Boston, has attempted to do the sums and work out how much photosynthetic effort lies behind the useful energy that people are able to extract from coal, oil and natural gas fossil fuels that ultimately derive from the bodies of long-deceased organisms.That derivation involves many physical and chemical steps.

He showed that for very long filters (M→∞), the derivation does not require the classic IA.

For full explication, see text Fig. 10 Biological-like evolutionary derivation of long bell cornets from short bell cornets.

Musicologists have long squabbled over the derivations of the genre as it emerged in Florence around 1600.

To simplify the derivation, the long-term power constraint is used in this article, which has been commonly used as shown in[15, 16].

Socrates' humour in the Cratylus is at least partly directed at his own uncharacteristic boldness in declaiming long strings of word derivations, contrary to his familiar disavowal of expert knowledge about anything.

To simplify the derivation, the long-term power constraint is also used for the ZF-SI scheme, and the average power at the relay can be presented as E tr ( β B 2 + 1 ) V H H H V H + 1 ρ V V H = β R 2 ( β B 2 + 1 ) E { tr [ ( H H H ) − 1 ] } + β R 2 ρ E { tr [ ( ( H H H ) − 1 ) 2 ] } = β R 2 ( β B 2 + 1 ) M N − M + β R 2 MN [ ( N − M ) 3 − ( N − M ) ] ρ, (30).

Some systems for derivation and long-term in vitro expansion of adult SSCs were inefficient.