The behavior of a thin curved hyperelastic film bonded to a fixed substrate is described by an energy composed of a nonlinearly hyperelastic energy term and a debonding interfacial energy term. We compute the Γ-limit of this energy under a noninterpenetration constraint that prohibits penetration of the film into the substrate without excluding contact between them.

We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the problem solution. For the main convergence results of this paper, we use the notion of two-scale convergence. A two-scale homogenized system is obtained as th...

We compute the large-body and the small-particle Gamma-limit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and incompressible materials. In the large-body asymptotics, even if we describe the local orientation of the liquid crystal molecules according to the model of perfect order (Frank ...

We show that for a sufficiently simple surface S, if a right-angled Artin group A(Γ) embeds into Mod(S) then Γ embeds into the curve graph C(S) as an induced subgraph. When S is sufficiently complicated, there exists an embedding A(Γ) → Mod(S) such that Γ is not contained in C(S) as an induced subgraph.

A graph Γ is said to be locally (G, 2)-arc transitive for G a subgroup of Aut(Γ) if, for any vertex α of Γ, G is transitive on the 2-arcs of Γ starting at α. In this talk, we will discuss general results involving locally (G, 2)-arc transitive graphs and recent progress toward the classification of the locally (G, 2)-arc transitive graphs, where Sz(q) ≤ G ≤ Aut(Sz(q)), q = 2 for some k ∈ N. In ...

This paper examines the effect of five major pretreatments on the surface coverage Γ(m) of dodecanethiol self-assembled monolayer on polycrystalline gold electrode (C(12)SH-SAMs-Au). It is based on the electrochemical reductive desorption in the alkaline solution by cyclic voltammetry (CV). The five different pretreatment methods include: aqua regia pretreatment, reductive annealed pretreatment...

We consider linear Hamiltonian equations in R2n of the following typedγdt(t)=J2nA(t)γ(t),γ(0)∈Sp(2n,R), where J=J2n=def[0Idn−Idn0] and A:t↦A(t) is a C1 curve space 2n×2n real matrices which are symmetric. Then, t↦γ(t) C2 (real) symplectic matrices. obtain second order asymptotics for eigenvalues bifurcated from non-real Krein indefinite with algebraic multiplicity two geometric one. As corollar...

Let γ(G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that γ(G)γ(H) ≤ 2γ(G H) for all simple graphs G and H. 2000 Mathematics Subject Classifications: Primary 05C69, Secondary 05C35 We use V (G), E(G), γ(G), respectively, to denote the vertex set, edge set and domination number of the (simple) graph G. For a pair of graphs G and ...

Given a simple graph Γ, we describe a “lifting” to a 3-uniform hypergraph φ(Γ) that sends the complement of Γ to the complement of φ(Γ). We consider the effects of this lifting on cycles, complete subhypergraphs, and complete subhypergraphs missing a single hyperedge. Our results lead to natural lower bounds for some hypergraph Ramsey numbers.

Ni2+ supported on hydroxyapatite-core@shell γ-Fe2O3 nanoparticles (γ-Fe2O3@HAp-Ni2+) was found to be a useful catalyst for the synthesis of benzimidazole derivatives from o-phenylenediamine and aldehydes under solvent and solvent-free conditions at 80 °C. This reaction affords the corresponding benzimidazole derivatives compared with the classical reactions this method consistently gives a high...