Sentence examples for the distinct solutions from inspiring English sources

This average network model highlights the interactions with high Wij values if shared by the majority of the distinct solutions.

The contrast between plant and animal mtDNA behaviour might therefore reflect the two distinct solutions they implement to cope with repeated element threats: either avoiding them, at the cost of a high point mutation rate (animals), or repairing the damage they cause by selecting for efficient DNA repair activity (plants).

It was of interest to examine how their sampled initial concentrations correlated with the eight distinct solutions found.

In this case, one of the given circles is itself a solution to the Apollonius problem, and the number of distinct solutions is reduced by one.

Taking in Theorem 3.1, we can obtain the existence of three distinct solutions for the Duffing-type equation without perturbation (1.2) as following.

Using the variational principle of Ricceri and a local mountain pass lemma, we study the existence of three distinct solutions for the following resonant Duffing-type equations with damping and perturbed term, a.e., and without perturbed term, a.e.,.

Out of these 1000 initial values, the number of distinct solutions of (32)–(33) that satisfy (34) is recorded, and their stability is determined as described above.

The theory of such functions (see Knopp [378] or Simon [613, Section 3.5]) implies there is a discrete set of points (S subset Omega ) (i.e. with no limit points in (Omega )) so that all solutions of (2.5) are multivalued analytic functions on (Omega {setminus } S) and so that the number of distinct solutions and their multiplicities are constant on (Omega {setminus } S).

By applying a generalized linking theorem for the strongly indefinite functionals developed recently by Bartsch and Ding [31] (also see [32, 33]), the authors obtained the infinitely many geometrically distinct solutions under different assumptions.

To overcome the existence of multiple near-optimal solutions, in the present work the ILP solver furnishes 100 distinct solutions within a 10% difference in the objective value.

Under the assumption that (A x,u)) (which is generalized from the nonlocal term (a(s))) is bounded, there are some results on the existence of positive solutions and the existence of n distinct solutions; see [4, 5].