Studies on terbium activated yttrium based tantalate phosphors

Terbium activated yttrium niobium tantalate phosphors were prepared by solid-state reaction and were characterized by photoluminescence measurements, X-ray diffraction and scanning electron microscopy. Photoluminescence (PL) of Y_0.95Tb_0.05Ta_1?xNb_xO₄ phosphors (x = 0–1) are influenced by the host-lattice composition, degree of crystalline order and particle morphology and size. The effect of the morpho-structural properties on PL characteristics of Y(Ta,Nb)O₄:Tb powders is reported.     

Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces

We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain ${\Omega}$ , with boundary data in the Besov space ${B_{s}^{p,p} (\partial\Omega).}$ The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p < 1. This is accomplished by using a Besov-based nontangential maximal function in place of the classical one. This builds on the works of Jerison and Kenig [14], where the case p > 1 was treated.     

Occurrence of rotation domains in heteroepitaxy

Heteroepitaxy can involve materials with a misfit of crystal structure. Rotation domains in the epilayer are a fundamental consequence. We derive a general expression for their (minimum) number which is determined by the mismatch of the rotational symmetries of the substrate and epilayer. In the case of a mismatch of rotational symmetry, the number of rotation domains of material A on material B is different from that of B on A. A larger number of rotation domains can occur due to domain structure or nearly fulfilled additional symmetries of the substrate surface.     

Iterated exponential inequalities: a classroom-tailored approach

We explore the connection between the notion of critical point for a function of one variable and various inequalities for iterated exponentials defined on the positive semiline of real numbers.     

Global analysis of the shadow Gierer-Meinhardt system with general linear boundary conditions in a random environment

The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on \emph{a priori} estimates of solutions.     

Boundary value problems for the Laplacian in convex and semiconvex domains

We study the fully inhomogeneous Dirichlet problem for the Laplacian in bounded convex domains in Rn, when the size/smoothness of both the data and the solution are measured on scales of Besov and Triebel-Lizorkin spaces. As a preamble, we deal with the Dirichlet and Regularity problems for harmonic functions in convex domains, with optimal nontangential maximal function estimates. As a corollary, sharp estimates for the Green potential are obtained in a variety of contexts, including local Hardy spaces. A substantial part of this analysis applies to bounded semiconvex domains (i.e., Lipschitz domains satisfying a uniform exterior ball condition).     

The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients

We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the unit normal of the boundary belong to the space VMO.     

Spectral theory for perturbed Krein Laplacians in nonsmooth domains

We study spectral properties for HK,Ω, the Krein-von Neumann extension of the perturbed Laplacian −Δ+V defined on , where V is measurable, bounded and nonnegative, in a bounded open set Ω⊂Rn belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class C1,r, r>1/2. In particular, in the aforementioned context we establish the Weyl asymptotic formula

     

Saturated models in institutions

Saturated models constitute one of the powerful methods of conventional model theory, with many applications. Here we develop a categorical abstract model theoretic approach to saturated models within the theory of institutions. The most important consequence is that the method of saturated models becomes thus available to a multitude of logical systems from logic or from computing science. In this paper we define the concept of saturated model at an abstract institution-independent level and develop the fundamental existence and uniqueness theorems. As an application we prove a general institution-independent version of the Keisler–Shelah isomorphism theorem “any two elementarily equivalent models have isomorphic ultrapowers” (assuming Generalized Continuum Hypothesis).     

Maximal regularity for the Lamé system in certain classes of non-smooth domains

The aim of this article is twofold. On the one hand, we study the well-posedness of the Lamé system ${-\mu\Delta-\mu'\nabla{\rm div} }The aim of this article is twofold. On the one hand, we study the well-posedness of the Lamé system -mD-m￠?div{-\mu\Delta-\mu'\nabla{\rm div} } in L ^q (Ω), where Ω is an open subset of \mathbbRⁿ{{\mathbb{R}}^n} satisfying mild regularity assumptions and the Lamé moduli μ, μ′ are such that μ > 0 and μ + μ′ > 0. On the other hand, we prove the analyticity of the semigroup generated by the Lamé operator as well as the maximal regularity property for the time-dependent Lamé system equipped with a homogeneous Dirichlet boundary condition based on off-diagonal estimates.