That a set of sentences is consistent in Hilbert's sense is a matter that's entirely independent of what its geometric terms mean, and this consistency is immediately implied by the satisfiability of the relation defined by those sentences when their geometric terms are treated as place-holders.
In the former setting, a standard Gaussian graphical model (as implied by the multivariate normal) describing the relations between the genes is fitted.
In cohesive fracture mechanics (CFM), fundamental nondimensional parameters are the ratios of spacetime domain geometries and loadings to corresponding intrinsic scales implied by the cohesive fracture traction separation relations (TSRs).
Finally, reminding ourselves that the tissue order relation implied by the lineage-tissue map, is one of dominance if and only if there is an individual lineage L i such that for all r* in the Euclidean Space ℝ n, if for the lineages r i * > r i, then for the tissue r*Pr.
What we have shown in Figure 4 and 5 is that with respect to r*, the tissue order relation implied by the lineage-tissue mapping must lead to one of two rankings - one in which lineage 1 dominates (with assumption that region II is more feasible than r*) or one in which lineage 2 dominates (if we had assumed that region II is less feasible than r*).
The basic lessons of competition colonization models for deforestation stand, but the ensured extinction implied by the extinction debt concept is further ameliorated as more realistic pattern process relations are theorized.
Seeing such power relations as a contributory factor, does not amount to some kind of "anti-business conspiracy theory" – as expediently implied by the Science Media Centre.
This effect supports of the finding from previous studies that social support is important in the development and maintenance of PTSD [ 22, 46], but implies that the relation could be moderated by the environmental factors and changes.
