1.1. Definition. It is traditional to say that a group Γ virtually has a property if some finite-index subgroup of Γ has the property. It is convenient to extend this terminology to group isomorphisms. • A virtual isomorphism from G1 to G2 is an isomorphism Λ: G ′ 1 → G ′ 2, where G ′ i is a finite-index, open subgroup of Gi. • A virtual automorphism of G is a virtual isomorphism from G to G. •...

The automorphic A-chromatic index of a graph Γ is the minimum integer m for which Γ has a proper edge-coloring with m colors which is preserved by a given subgroup A of the full automorphism group of Γ. We compute the automorphic A-chromatic index of each generalized Petersen graph when A is the full automorphism group.

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.

Pair-interaction atomistic energies may give rise, in the framework of the passage from discrete systems to continuous variational problems, to nonlinear energies with genuinely quasiconvex integrands. This phenomenon takes place even for simple harmonic interactions as shown by an example by Friesecke and Theil [19]. On the other hand, a rigorous derivation of linearly elastic energies from en...

If Γ 1 and Γ 2 are limit groups and S ⊂ Γ 1 × Γ 2 is of type FP 2 then S has a subgroup of finite index that is a product of at most two limit groups.

We consider a Hamiltonian setup (M, ω,H,L,Γ,P), where (M, ω) is a symplectic manifold, L is a distribution of Lagrangian subspaces in M, P a Lagrangian submanifold of M, H is a smooth time dependent Hamiltonian function on M and Γ : [a, b] 7→ M is an integral curve of the Hamiltonian flow ~ H starting at P . We do not require any convexity property of the Hamiltonian function H . Under the assu...

We prove an extension of the Index Theorem for Morse–Sturm systems of the form −V ′′ + RV = 0, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint. The result is then applied to the case of a Jacobi equation along a geodesic in a Lorentzian manifold, obtaining an extension of the Morse Index Theorem ...