Any Coxeter group Γ, with string diagram, is the symmetry group of a (possibly infinite) regular polytope P. When Γ is crystallographic, we may reduce its standard real representation modulo an odd prime p, thereby obtaining a finite representation in some orthogonal space over Zp. In many cases, the latter group will be the symmetry group of a finite regular polytope. In this paper, we investi...

We study splitting densities of primitive elements of a discrete subgroup Γ̃ of a connected non-compact semisimple Lie group G of real rank one with finite center in another larger such Γ. When the corresponding cover of such locally symmetric negative curved spaces is regular, the densities can be easily obtained from the results of [Sa] or [Su]. Our main interest is a case where the covering i...

We present a simple example of toughening mechanism in the homogenization of composites with soft inclusions, produced by crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack process. Because of that it cannot be detected through the standard homogenization tool of the Γ-convergence.

We prove the Γ-convergence of the one-dimensional Allen-Cahn action functional in the sharp-interface limit. In previous work, a good lower bound was developed under the assumption of single multiplicity, but the bound deteriorated in the case of higher multiplicity interfaces. We develop an improved bound by working directly with the limiting energy measures.

We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice with twoand three-point atomic interactions, using Γ-convergence.

We prove that the family of functionals (Iδ) defined by Iδ(g) = ∫∫ RN×RN |g(x)−g(y)|>δ δ |x− y|N+p dx dy, ∀ g ∈ L(R ), for p ≥ 1 and δ > 0, Γ-converges in L(R ), as δ goes to 0, when p ≥ 1. Hereafter | | denotes the Euclidean norm of R . We also introduce a characterization for BV functions which has some advantages in comparison with the classic one based on the notion of essential variation o...

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.

We consider a sequence of linear Dirichlet problems as follows

In this paper, we introduce a modified epidemic model on regular and scale-free networks respectively. We consider the birth rate δ, cure rate γ, infection rate λ, α from the infectious disease, and death rate β from other factors. Through meanfield analysis, we find that on regular network there is an epidemic threshold λc dependent on the parameters δ, γ, α, and β; while for power law degree ...

We examine the action of the fundamental group Γ of an mpunctured Riemann surface on the middle dimensional homology of a regular fiber in a Lefschetz fibration, and describe to what extent this action can be recovered from the intersection numbers of vanishing cycles. Basis changes for the vanishing cycles result in a nonlinear action of the framed braid group B̃ on m strings on a suitable spac...