Sentence examples for without derivation from inspiring English sources
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.
Thus they are presented here without 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?
For the design of compliant mechanisms, the designer can advantageously use the bifurcation diagrams to evaluate the relevance of the selected mechanism, then to identify a configuration in order to obtain desired kinematic properties without the derivation of the inverse kinematic model (IKM) or the direct kinematic model (DKM).
However, the finite-size effect with a cut-off value at system size has been assumed without analytical derivation (though, see the companion paper to this article [24], as described below) and the questions of how a finite critical system behaves and what types of dynamics are possible for such a system remain open in the field.
Importantly, this approximation preserves gene specificity and progression character, in order to make gene pair identification without systematic derivation.
