Sentence examples for useful equivalent from inspiring English sources

The next section is devoted to the (simple) proof of Theorem 1.2 based on Lemma 1.3 and to a useful equivalent formulation (Corollary 2.1).

Further, on yearly basis useful thermal energy, useful electrical energy, useful equivalent thermal energy, thermal exergy and overall thermal efficiency have been calculated.

According to the Von Neumann-Theobald inequality, the complementarity condition (Lambda{mathcal {A}}(x)=0 ) has the following two useful equivalent forms: begin{aligned}& operatorname{Tr}bigl(Lambda{mathcal {A}}(x bigr)=0, & lambda_{j}(Lambda)lambda_{j}bigl({mathcal {A}}(x) bigr)=0,quad forall jin{ 1,2,ldots,m}.

Abraham Lincoln's killer was a member of a prominent theatrical family, so imagine Jake Gyllenhaal killing Barack Obama you've got yourself a useful equivalent.

While erythema is difficult to observe in the mouse, the MED can be quantified largely by its edema component or the acute inflammatory response to UV radiation which causes an increase in the dorsal skinfold thickness and is a useful equivalent to the minimal erythemal dose measurement in humans (Ibuki et al., 2007).

A useful approach is to use equivalent current dipoles to model coherent electrical activity arising in small cortical areas (de Munck et al. 1988).

In thinking about mobility, migration or poverty reduction, it is useful to do the analysis using equivalent cohorts.

"You was" had, in fact, taken the place of both "thou wast" and "thou wert" as a useful singular equivalent of the accepted plural "you were".

Impedance spectroscopy enables label-free detection and is nondestructive and useful in equivalent circuit models for interpretation on an electrode surface, whereas from the ligation reaction, the specificity is derived by the allele-specific oligonucleotide of the capture probe on immobilized gold electrode.

The electric field was formally defined as the force exerted per unit charge, but the concept of potential allows for a more useful and equivalent definition: the electric field is the local gradient of the electric potential.

42 Botulinum toxin was reported as useful with equivalent success to some surgical case series.