We introduce new definitions of convergence, based on adding stability criteria to Γ-convergence, that are suitable in many cases for studying convergence of local minimizers.

We study the Γ-convergence of the power-law functionals

Spectral theory of differential operators on metric trees is an interesting branch of such theory on general metric graphs. Among the trees, the so-called regular trees are of particular interest due to their very special geometry. Let Γ be a tree rooted at some vertex o and having infinitely many edges. Below |x| stands for the distance between a point x ∈ Γ and the root o. For a vertex x, its...

We consider Schrödinger operators with a strongly attractive singular interaction supported by a finite curve Γ of lenghth L in R. We show that if Γ is C-smooth and has regular endpoints, the j-th eigenvalue of such an operator has the asymptotic expansion λj(Hα,Γ) = ξα+λj(S)+O(e) as the coupling parameter α → ∞, where ξα = −4 e2(−2πα+ψ(1)) and λj(S) is the j-th eigenvalue of the Schrödinger op...

In this paper, fuzzy h-bi-ideals, fuzzy h-quasi-ideals and fuzzy h-interior ideals of a Γ-hemiring are studied and some related properties are investigated. The notions of h-intra-hemiregularity and h-quasi-hemiregularity of a Γ-hemiring are introduced and studied along with h-hemiregularity and their characterizations in terms of fuzzy h-ideals are also obtained. The concept of fuzzy h-duo Γ-h...

In this paper we study the asymptotic behaviour via Γ-convergence of some integral functionals Fε which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals Fε are defined in particular classes of functions with bounded deformation while the limit problem is set in the usual framework of Sobolev spaces or BD(Ω). We also construct an exam...

We study homogenization by Γ-convergence of functionals of type Z Ω W “ x ε ,∇φ(x) ” dx, where Ω ⊂ RN is a bounded open set, φ ∈ W 1,p(Ω; Rm) and p > 1, when the 1-periodic integrand W : RN ×Mm×N → [0, +∞] is not of p-polynomial growth. Our homogenization technique can be applied when m = N and W has a singular behavior of type W (x, ξ) → +∞ as detξ → 0. However, our technique is not consistent...

We study homogenization by Γ-convergence, with respect to the L1-strong convergence, of periodic multiple integrals in W 1,∞ when the integrand can take infinite values outside of a convex bounded open set of matrices.

The spectral excess theorem for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. A bipartite graph Γ is distance-biregular when it is distance-regular around each vertex and the intersection array only depends on the stable set such a vertex belongs to. In this note we derive a new version of the sp...