Intrinsic Hölder Continuity of Harmonic Functions

We consider the stochastic differential equation (SDE) of the form

$$\begin{array}{@{}rcl@{}} \left\{\begin{array}{rcl} dX^ x(t) &=& \sigma(X(t-)) dL(t) \\ X^ x(0)&=&x,\quad x\in{\mathbb{R}}^ d, \end{array}\right. \end{array} $$

where \(\sigma :{\mathbb {R}}^ d\to {\mathbb {R}}^ d\) is globally Lipschitz continuous and L={L(t):t≥0} is a Lévy process. Under this condition on σ it is well known that the above problem has a unique solution X. Let \((\mathcal {P}_{t})_{t\ge 0}\) be the Markovian semigroup associated to X defined by \(\left ({\mathcal {P}}_{t} f\right ) (x) := \mathbb {E} \left [ f(X^ x(t))\right ]\), t≥0, \(x\in {\mathbb {R}}^{d}\), \(f\in \mathcal {B}_{b}({\mathbb {R}}^{d})\). Let B be a pseudo–differential operator characterized by its symbol q. Fix \(\rho \in \mathbb {R}\). In this article we investigate under which conditions on σ, L and q there exist two constants γ>0 and C>0 such that

$$\left| B {\mathcal{P}}_{t} u \right|_{H^{\rho}_{2}} \le C \, t^{-\gamma} \,\left| u \right|_{H^{\rho}_{2}}, \quad \forall u \in {H^{\rho}_{2}}(\mathbb{R}^{d} ),\, t>0. $$

     

Periodic Mg distribution in GaN:δ-Mg and the effect of annealing on structural and optical properties

High p-type conductivity of GaN - commonly achieved via doping with Mg - is a challenge to be faced on the way to the realization of a GaN-based diluted magnetic semiconductor showing ferromagnetism at room temperature. In this work we present a study of GaN:Mg films grown in a metalorganic vapor phase epitaxy process where the Mg atoms are incorporated in a δ-doping fashion. The effect of a post-growth annealing step on the diffusivity of magnesium is studied by means of atomic force microscopy and photoluminescence measurements in the ultraviolet regime. A comparison of the presented results with transmission electron microscopy studies leads to the conclusion that a considerable amount of Mg is transported towards the surface where it is thermally removed during the annealing step.     

Influence of spin on the activation energies at

The activation energy Δ of the fractional quantum Hall state at constant filling factor and also at and has been measured as a function of the perpendicular magnetic field B while modulating the electron density via a top gate. At small magnetic fields we observe a linear increase of Δ with the magnetic field. The slope of Δ vs. B allows us to directly extract the composite fermion g-factor.     

Local investigation of the energy gap within the incompressible strip in the quantum Hall regime

We experimentally study the energy gap within the incompressible strip at local filling factor ν _c = 1 at the quantum Hall edge for samples of very different mobilities. The obtained results indicate strong enhancement of the energy gap in comparison to the single-particle Zeeman splitting. We identify the measured gap as a mobility gap, so a pronounced experimental in-plane magnetic field dependence can both be attributed to the spin effects as well as to the change in the energy levels broadening.     

Comparability and compatibility of proficiency testing results in schemes with a limited number of participants

Comparability and compatibility of proficiency testing (PT) results are discussed for schemes with a limited number of participants (less than 20–30) based on the use of reference materials (RMs) as test items. Since PT results are a kind of measurement/analysis/test result, their comparability is a property conditioned by traceability to measurement standards applied in the measurement process. At the same time, metrological traceability of the certified value of the RM (sent to PT participants as test items) is also important, since the PT results are compared with the RM certified value. The RM position in the calibration hierarchy of measurement standards sets the degree of comparability for PT results, which can be assessed in the scheme. However, this assessment is influenced by commutability (adequacy or match) of the matrix RM used for PT and routine samples. Compatibility of PT results is a characteristic of the collective (group) performance of the laboratories participating in PT that can be expressed as closeness of the distribution of the PT results to the distribution of the RM data. Achieving quality-of-measurement/analysis/test results in the framework of the concept “tested once, accepted everywhere” requires both comparability and compatibility of the test results.     

Probing a Kondo-correlated quantum dot with spin spectroscopy

We investigate the Kondo effect and spin blockade observed in a many-electron quantum dot and study the magnetic field dependence. At lower fields, a pronounced Kondo effect is found, which is replaced by the spin blockade at higher fields. In an intermediate regime, both effects are visible. We make use of this combined effect to gain information about the internal spin configuration of our quantum dot. We find that the data cannot be explained assuming regular filling of electronic orbitals. Instead, spin polarized filling seems to be probable.     

Über Hemipinsäureäthyläther

Ohne Zusammenfassung     

Eine Verunreinigung des k?uflichen Baryumcarbonats

Ohne Zusammenfassung     

Global comparison of perturbed Green functions

Given a Green function G (e.g. with respect to (−Δ)^α/2, 0<α≤2) on a region X where G has a generalized triangle property and given a (G-bounded) signed measure μ on X, necessary and sufficient conditions are given for the existence of a perturbed Green function which is comparable with G. This is done in the general setting of measurable spaces. Applications to C^1,1-regions in R^d and, for the classical case α=2, to finitely connected regions in ℝ² are given.