Junction of ferromagnetic thin films

In this paper, starting from the classical 3D micromagnetic energy, we determine, via an asymptotic analysis, the free energy of two joined ferromagnetic thin films. We distinguish different regimes depending on the limit of the ratio between the small thicknesses of the two films.     

On the long time behavior of non-autonomous Lotka-Volterra models with diffusion via the sub-supertrajectory method

In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under some conditions on the parameters, we prove the existence of a unique nondegenerate global solution for these models, which attracts any other complete bounded trajectory. Thus, we generalize the existence of a unique strictly positive stable (stationary) solution from the autonomous case and we extend to Lotka-Volterra systems the result for scalar logistic equations. To this end we present the sub-supertrajectory tool as a generalization of the now classical sub-supersolution method. In particular, we also conclude pullback and forwards permanence for the above models.     

A fast solver for linear systems with displacement structure

We describe a fast solver for linear systems with reconstructible Cauchy-like structure, which requires O(rn ²) floating point operations and O(rn) memory locations, where n is the size of the matrix and r its displacement rank. The solver is based on the application of the generalized Schur algorithm to a suitable augmented matrix, under some assumptions on the knots of the Cauchy-like matrix. It includes various pivoting strategies, already discussed in the literature, and a new algorithm, which only requires reconstructibility. We have developed a software package, written in Matlab and C-MEX, which provides a robust implementation of the above method. Our package also includes solvers for Toeplitz(+Hankel)-like and Vandermonde-like linear systems, as these structures can be reduced to Cauchy-like by fast and stable transforms. Numerical experiments demonstrate the effectiveness of the software.     

Representation of MV-algebras by regular ultrapowers of [0, 1]

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable way, thus providing a sort of “canonical” set of values for the functional representation.     

Outer approximation algorithms for canonical DC problems

The paper discusses a general framework for outer approximation type algorithms for the canonical DC optimization problem. The algorithms rely on a polar reformulation of the problem and exploit an approximated oracle in order to check global optimality. Consequently, approximate optimality conditions are introduced and bounds on the quality of the approximate global optimal solution are obtained. A thorough analysis of properties which guarantee convergence is carried out; two families of conditions are introduced which lead to design six implementable algorithms, whose convergence can be proved within a unified framework.     

Absolutely Continuous Embeddings of Rearrangement-Invariant Spaces

Compactness of embeddings between rearrangement invariant spaces is closely related to absolute continuity of these embeddings. We study absolutely continuous embeddings between rearrangement invariant spaces. In particular it is shown that an absolutely continuous embedding is never optimal. We give sufficient (and under additional hypotheses necessary) conditions for absolute continuity of these embeddings. We also provide quantitative estimates of absolutely continuous embeddings.     

Manifolds with S 1-category 2 have cyclic fundamental groups

A closed topological n-manifold M ⁿ is of S ¹-category 2 if it can be covered by two open subsets W ₁, W ₂ such that the inclusions W _i → M ⁿ factor homotopically through maps W _i → S ¹. We show that for n > 3 the fundamental group of such an n-manifold is either trivial or infinite cyclic.     

12-Laplacian problems with exponential nonlinearity

By exploiting a suitable Trudinger–Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential growth.