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 ...

Air pollution has become an essential issue in environmental protection. The Quality Index (AQI) is often used to determine the severity of air pollution. When AQI reaches red level, proportion asthma patients seeking medical treatment will increase by 30% more than usual. If can be predicted advance, benefits early warning achieved. In recent years, a scholar proposed α-Sutte indicator which s...

With any (not necessarily proper) edge k-colouring γ : E(G) −→ {1, . . . , k} of a graph G, one can associate a vertex colouring σγ given by σγ(v) = ∑ e∋v γ(e). A neighbour-sumdistinguishing edge k-colouring is an edge colouring whose associated vertex colouring is proper. The neighbour-sum-distinguishing index of a graph G is then the smallest k for which G admits a neighbour-sum-distinguishin...

and this index is constant on continuous families of such L. Suppose that D is an elliptic operator of order m on sections of a vector bundle E± over a smooth, compact manifold M . Let H (Γ (M,E±)) denote the Sobolev s-norm completion of the space of sections Γ (M,E), with respect to a chosen metric. Then D can be extended to be a bounded linear operator Ds : H s (Γ (M,E)) → Hs−m (Γ (M,E−)) tha...

A Kleinian group Γ is a discrete subgroup of PSL(2, C), the full group of orientation-preserving isometries of 3-dimensional hyperbolic space. In the language of [T1] Q = H3/Γ is a hyperbolic 3-orbifold; that is a metric 3-orbifold in which all sectional curvatures are -1, and for which Γ is the orbifold fundamental group (see [T1] for further details). A Fuchsian group is a discrete subgroup o...

Using the first three and a half years of observations from the Energetic Gamma Ray Telescope (EGRET) on board the Compton Gamma Ray Observatory (CGRO), phase-resolved analyses are performed on the emission from the three brightest highenergy γ-ray pulsars, Crab, Geminga, and Vela. For each pulsar, it is found that there is detectable high-energy γ-ray emission above the galactic diffuse backgr...

(typeset by Robert JS McDonald, UConn1) Lecture 1. Foundational material. The lecture will briefly cover, without proofs, the background in algebra and number theory needed at the beginning of Iwasawa theory. Throughout, p will denote an arbitrary prime number, and Γ a topological group which is isomorphic to the additive group of p-adic integers Zp. Thus, for each n ≥ 0, Γ will have a closed s...