The compaction process is then modelled as a self-similar contraction of unit (average) cells, in contrast to commonly used phenomenological assumptions, yielding a simple but rigorous relation between the densification density and centre-to-centre approach of adjacent powder particles.
The rigorous relation (hbar langle f|textbf {P}|i rangle = im (E_{f}-E_{i}) langle f|textbf {r}|i rangle ) [18] has been utilized to express the momentum matrix elements in terms of the position matrix elements, which are readily calculable.
Within the class of such bodies, one can obtain through a rigorous approximation, constitutive relations for the linearized strain as a nonlinear function of the stress.
In this study, we report a rigorous derivation of the relation between the spatially averaged consumption speed and the absolute flame speed for spherically expanding flame configurations.
Due to the difficulties in gaining a rigorous assessment of migraine in relation to menstruation timing, these group distinctions are lost in large cohort studies.
The motivation for the Kullback-Leibler work was to provide a rigorous definition of information in relation to Fisher's sufficient statistics.
The resulting MCES-clusters are typically small in size and the members are in a rigorous, medicinal chemistry based structural relation with each other.
Consequently, it is necessary a rigorous analysis directed to establish relations between food properties and physico-chemical changes in the product along the process.
Despite its strengths—hefty investment in research, a rigorous approach to manufacturing and good relations with its local community Kodak had become a complacent monopolist.
A rigorous assessment for possible nonlinearities in such a relation would require a pooled analysis of the original data, not an ecologic analysis of the summary results across studies (Lanphear et al. 1998).
The "elastic" force has been estimated by employing a rigorous approach which needs not resort to equilibrium-based relations.
