Suppose that Γ is a connected graph and G is a subgroup of the automorphism group Aut(Γ) of Γ. Then Γ is G-symmetric if G acts transitively on the arcs (and so the vertices) of Γ and Γ is G-semisymmetric if G acts edge transitively but not vertex transitively on Γ. If Γ is Aut(Γ)symmetric, respectively, Aut(Γ)-semisymmetric, then we say that Γ is symmetric, respectively, semisymmetric. If Γ is ...

The thermodynamic behaviour of a relativistic perfect simple fluid obeying the equation of state p = (γ − 1)ρ, where 0 ≤ γ ≤ 2 is a constant, has been investigated. Particular cases include: vacuum(p = −ρ, γ = 0), a randomly oriented distribution of cosmic strings (p = −13ρ, γ = 2/3), blackbody radiation (p = 1 3ρ, γ = 4/3) and stiff matter (p = ρ, γ = 2). Fluids with γ < 1 become hotter when t...

By using combinatorial properties of stationary sets, we give a simple proof of some generalization of Silver’s Theorem i.e. if κ is an uncountable regular cardinal such that אκ is a singular strong limit cardinal, then the following hold. (1). If {α < κ : א<κ α ≤ אα·2} is stationary, then 2אκ ≤ אκ·2. (2). If {α < κ : א<κ α ≤ אα+γ}, where 0 < γ < κ, is stationary, then 2אκ ≤ אκ+γ.

We construct a closed Jordan curve γ ⊂ R so that γ∩S is uncountable whenever S is a line segment whose endpoints are contained in different connected components of R \ γ. We say that a Jordan arc σ ⊂ R crosses a compact set K ⊂ R if the two endpoints of σ are in different connected components of R \ K. Clearly any arc crossing K must intersect K in at least one point of K. If the intersection c...

We show a rigidity result for subfactors that are normalized by representation of lattice Γ in higher rank simple Lie group with trivial center into finite factor. This implies every subfactor LΓ which is the natural copy or index.

We define and study a family of partitions of the wonderful compactification G of a semi-simple algebraic group G of adjoint type. The partitions are obtained from subgroups of G × G associated to triples (A1, A2, a), where A1 and A2 are subgraphs of the Dynkin graph Γ of G and a : A1 → A2 is an isomorphism. The partitions of G of Springer and Lusztig correspond respectively to the triples (∅, ...

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Γ-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.

This paper is devoted to prove new relaxation and Γ-convergence theorems on BV(Ω) for a class of integral functionals, whose integrands have a product type structure, but they do not satisfy any assumptions of coerciveness or continuity with respect to the spatial variable.

A variational model for the epitaxial deposition of a film on a rigid substrate in the presence of a crystallographic misfit is studied. The scaling behavior of the minimal energy in terms of the volume of the film and the amplitude of the misfit is considered, and reduced models in the various regimes are derived by Γ-convergence methods. Depending on the relation between the thickness of the ...

This paper is devoted to prove a continuity theorem for integral functional defined on BV(Ω). This result is applied in order to obtain new relaxation and Γ-convergence theorems on BV(Ω) without any coerciveness and any continuity assumption of the integrand with respect to the spatial variable.