Austauschreaktionen der Cellulose im wasserfremden Medium

Zusammenfassung Es wird das Verhalten der Kristallviolettbase in absol.-benzol. Lösung gegenüber benzolgequollener Cellulose mit neutralisierten (versalzten bzw. veresterten) COOH-Gruppen unter-sucht.Der Einfluß des Kations auf die Umsetzung wird einer ersten Prüfung unterzogen.Herrn Prof. Dr.A. Zinke zum 70. Geburtstag gewidmet.     

On the Best Constants in Some Non-Commutative Martingale Inequalities

The optimal orders are determined for the best constants inthe non-commutative Burkholder–Gundy, Doob and Stein inequalitiesobtained recently in non-commutative martingale theory. 2000Mathematics Subject Classification 46L53, 46L51.     

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).