The energy of a Von Kármán circular plate is described by a nonlocal nonconvex one-dimensional functional depending on the thickness ε. Here we perform the asymptotic analysis via Γ-convergence as the parameter ε goes to zero.

We show the Γ-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex functional.

The formation of microdomains, also called rafts, in biomembranes can be attributed to the surface tension of the membrane. In order to model this phenomenon, a model involving a coupling between the local composition and the local curvature was proposed by Seul and Andelman in 1995. In addition to the familiar Cahn-Hilliard/Modica-Mortola energy, there are additional ‘forces’ that prevent larg...

In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter ε, representing the interface thickness between the tumorous and non tumorous cells, tends to zero. More in particular, we analyze here a gradient-flow type model arising from a modification of the recently introduced model for tumor growth dynamics in...

Let G be any locally compact metrizable group. The main result of this paper, roughly stated, is that if F < G is any finitely generated free group and Γ < G any lattice, then up to a small perturbation and passing to a finite index subgroup, F is a subgroup of Γ. If G/Γ is noncompact then we require additional hypotheses that include G = SO(n, 1). MSC: 20E07, 20F65, 20F67, 22D40, 20E05.

A group Γ is defined to be cofinitely Hopfian if every homomorphism Γ → Γ whose image is of finite index is an automorphism. Geometrically significant groups enjoying this property include certain relatively hyperbolic groups and many lattices. A knot group is cofinitely Hopfian if and only if the knot is not a torus knot. A free-by-cyclic group is cofinitely Hopfian if and only if it has trivi...

BACKGROUND Our earlier genome-wide expression study revealed up-regulation of a tryptophan-catabolizing enzyme, indoleamine 2,3-dioxygenase (IDO1), in patients with scrub typhus. This gene has been previously reported to have anti-microbial activity in a variety of infectious diseases; therefore, we aimed to prove whether it is also involved in host defense against Orientia tsutsugamushi (OT) i...

The present trial investigated the efficacy of immunotherapy with interferon-gamma (IFN-γ) in the treatment of sulfur mustard (SM)-induced chronic skin complications. Forty subjects who were suffering from chronic skin complications of SM and were diagnosed to have severe atopic dermatitis, were assigned to IFN-γ (50 μg/m(2)) subcutaneously three times per week (n = 20) or betamethasone valerat...

Let K be a field containing a nonsquare γ and F = K (√γ ) a quadratic extension. Let σ denote the unique involutory automorphism of F fixing K pointwise. For every field K such that the nonzero squares of K do not form an index 1 or 2 subgroup of (K ( √ γ )∗)σ+1 = K−, a construction is given which produces large numbers of infinite nearfield and non nearfield flocks of an infinite hyperbolic qu...

In this paper, we prove that in a multigraph whose density Γ exceeds the maximum vertex degree ∆, the collection of minimal clusters (maximally dense sets of vertices) is cycle-free. We also prove that for multigraphs with Γ > ∆ + 1, the size of any cluster is bounded from the above by a function, which depends on ∆ and Γ only. Finally, we show that two well-known lower bounds for the chromatic...