Sentence examples for without derivations from inspiring English sources

Thus they are presented here without derivations.

The error terms will be given without derivation.

The results demonstrated that fatty-acid-based biofuels can be directly determined by GC MS without derivation.

Gerami et al. (2007) applied pseudo-time and pseudo-pressure to dual-porosity reservoirs, and, without derivation, they proposed a pseudo-pressure-based interporosity flow equation for gas.

Cheng et al. ([1999]) have already given (without derivation) the corresponding FMM relations, but in a form ill-suited for computer code.

A result given without derivation by Morse and Bolt [1] pertaining to the reflection of a spherical sound wave from an absorbent surface is investigated.

We have briefly provided the proof of this theorem in [28] without formal derivations.

One of the advantages of the bootstrap methods is that they can be used without analytical derivations.

These results were mostly written up without any derivations.

The variance of the overall strength of the compound member is derived, and can be computed efficiently without requiring derivation of the element strength correlation matrix.

Could Huang et al. use the conditional independence assumption to get such a model without the derivation process of using Bayes' theorem for factorizing the spatial conditional probability distribution function over a neighbourhood?