In this work, a formula for the regularized trace of second order differential operator given in a finite interval which has unbounded operator coefficients is found.

Order parameters in physical and biological systems can sometimes become unbounded as the size of an underlying system increases. It is proposed that such a quantity be modeled as a minimizer of the energy functional Iε(u) = − ∫ [ ε2 2 |∇u| − 1 2 log(1 + |u|) ] dx, where u is constrained by a side condition, and ε > 0 is a parameter that is inversely proportional to the linear size of the syste...

We give an asymptotic equivalent at infinity of the unbounded solutions of some boundary layer equations arising in fluid mechanics. Let us consider the following boundary layer differential equation f ′′′ + ff ′′ − βf ′2 = 0 (1) where β < 0. We are interested in non constant solutions (that we will simply call solutions) of (1) defined on some interval [t0,∞) and such that f (∞) := lim t→∞ f (...

in this paper we investigate multi-objective integer linear programming (moilp) problems with unbounded feasible region and introduce recession direction for moilp problems. then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of moilp problems. finally we present some examples with unbounded feasible region and fi...

This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval. The underlying chain-complex is assumed to be unbounded and the results for bounded coalgebras over an operad are deriv...

This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad whose components are projective, finitely generated in each dimension, and satisfy a condition that allows one to take tensor products with a unit interval. The underlying chain-complex is assumed to be unbounded and the results for bounded coalgebras over an operad are deriv...

We consider a free boundary problem with nonlocal diffusion and unbounded initial range, which can be used to model the propagation phenomenon of an invasion species whose habitat is interval $$(-\infty ,h(t))$$ h(t) representing spreading front. Since spatial scale unbounded, different method from existing works about employed obtain well-posedness. Then we prove that always spreads successful...