Sentence examples for minimum of functional from inspiring English sources

Therefore, the non- standard problem formulated in this study consists of finding the global minimum of functional (1) among species trees S that have the set of leaves V0 and a set of clades belonging to a fixed set P. Thus, P is a parameter of the problem and of the solving algorithm.

Reference [ 7] contains a 15-pages proof of the theorem that asserts for a class of algorithms (including the discussed algorithm of supertree construction): if only duplications and losses are the allowed evolutionary events, and condition is true, then any algorithm of this class exactly finds the global constrained minimum of functional (1).

Thus, promotion of survival apparently requires on one hand a certain minimum level of functional ADM and on the other hand the reduction of excessively high concentrations of ADM.

However, the variables do provide information on the existence of social ties and frequency of meeting/seeing friends and relatives, as they presuppose a minimum level of functional capacity.

Comparison of the R i, values of a series of inactivated and minimally active splice sites revealed the minimum strength of functional splice sites (R i,min) to be at least 2.4 bits for the original donor and acceptor models of Stephens and Schneider (1992) (based on 103 mutations with functional validation, including 57 natural and 46 cryptic site activating mutations).

The local regularity results for minima of functionals and solutions of elliptic equations have been obtained in [8].

In the case of minima of functionals of the form ∫ΩA x, u)|Du|2dx, Jost-Meier [8] established full regularity in a neighborhood of the boundary.

Jost-Meier [11] established full regularity in a neighborhood of boundary for minima of functionals with the form ∫ Ω A ( x, u ) | D u | 2 d x.

In the case of minima of functionals of the form ∫ Ω A ( x, u ) | D u | 2 d x, Jost-Meier [7] established full regularity in a neighborhood of the boundary.

The optimal regression function is given by the minimum of the functional, ϕ w, ξ, ξ * = 1 2 w 2 + C ∑ i = 1 l ξ i + ∑ i = 1 l ξ i ∗ Open image in new window (5).

We define an extensive set of elementary evolutionary events and suggest an original definition of mapping β of tree G into tree S. We introduce the cost functional c(G, S, f ) and define the mapping β as the global minimum of this functional with respect to the variable f, in which sense it is a generalization of classical mapping α.