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

We study the minimum energy configuration of a uniform distribution of negative charge subject to Coulomb repulsive self-interaction and attractive interaction with a fixed positively charged domain. After having established existence and uniqueness of a minimizing configuration, we prove charge neutrality and the complete screening of the Coulomb potential exerted by the positive charge, and w...

where Ω is an open bounded set of R and W and V are two non-negative continuous functions vanishing at α, β and α, β, respectively. In the previous functional, we fix a = 2 − p and u is a scalar density function, Tu denotes its trace on ∂Ω, d(x, ∂Ω) stands for the distance function to the boundary ∂Ω. We show that the singular limit of the energies Fε leads to a coupled problem of bulk and surf...

1. Liquid–Liquid Phase Transitions Consider a fluid confined into a container Ω ⊂ R . Assume that the total mass of the fluid is m, so that admissible density distributions u : Ω→ R satisfy the constraint ∫ Ω u(x) dx = m. The total energy is given by the functional u 7→ ∫ Ω W (u(x)) dx, where W : R→ [0,∞) is the energy per unit volume. Assume that W supports two phases a < b, that is, W is a do...

BACKGROUND Chronic rhinosinusitis (CRS) with nasal polyps (NPs) in Western populations is associated with TH2 cytokine polarization. IL-25, an IL-17 family cytokine, was recently reported to induce TH2-type immune responses and to contribute to several allergic diseases, such as atopic dermatitis and asthma. However, the role of IL-25 in Asian patients with nasal polyposis remains unclear. OB...

Nano-sized materials have been studied for diverse clinical applications, partly because their size-dependent physical properties and nanometer-scale dimensions have important roles in biological systems. Synergistic combinations of differently nanostructured materials, such as polymer-coated magnetic nanoparticles (NPs), strongly promoted various multifunctional nano-medical platforms for simu...

Reaction of FeCl2 and H4DSBDC (2,5-disulfhydrylbenzene-1,4-dicarboxylic acid) leads to the formation of Fe2(DSBDC), an analogue of M2(DOBDC) (MOF-74, DOBDC(4-) = 2,5-dihydroxybenzene-1,4-dicarboxylate). The bulk electrical conductivity values of both Fe2(DSBDC) and Fe2(DOBDC) are ∼6 orders of magnitude higher than those of the Mn(2+) analogues, Mn2(DEBDC) (E = O, S). Because the metals are of t...

An azadithiolate bridged monocyanide derivative [Fe2(adt)(CO)5(CN)]- of [Fe2(adt)(CO)4(CN)2]2- has been prepared and extensively characterized as a model of the [FeFe]-hydrogenase active site, using a combination of FTIR spectroscopy, electrochemical methods and catalytic assays with chemical reductants. The presence of two basic nitrogen sites opens up multiple protonation pathways, enabling c...