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.     

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.     

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

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

     

Über Diazomethan

Ohne ZusammenfassungFür eine zur Ausführung dieser Untersuchungen gewährte Subvention sagen wir der kaiserlichen Akademie der Wissenschaften in Wien ergebenen Dank.     

Preconcentration methods for the determination of trace elements in water by x-ray fluorescence spectrometry: Part 2. Interference studies

Seven methods for the preconcentration of fifteen elements for their subsequent measurement by x-ray fluorescence spectrometry have been evaluated for their susceptibility to interferences. A two-level factorial experimental design has been used, enabling an economical and meaningful comparison of the seven methods to be made. A scheme for rating the methods on the basis of the effect of several interfering species is proposed. Use of such a scheme has enabled an objective comparison of the methods considered to yield their relative ranks. It is also shown that spectral and chemical interferences can be discerned to some extent. Combination of the response rating proposed earlier and the interference rating schemes reported here gives rise to an overall comparison and rank for the methods, allowing an objective choice of the optimal method(s) to be made.     

Photochemische Reaktionen 115. Mitteilung [1]. Zur Photochemie konjugierter γ,δ-Epoxyenone: Der Einfluss eines Hydroxylsubstituenten in ϵ-Stellung

Photochemistry of Conjugated γ,δ-Epoxyenones: The Influence of a Hydroxy Substituent in ?-Position On ¹n, π*- or ¹π,π*-excitation (λ ≥ 347 or λ=254 nm), the ?-hydroxy-γ;,δ-epoxyenone 8 undergoes fission of the C(γ)? O bond followed by the cleavage of the C(δ)-C(?) bond. This hitherto unknown sequence of reactions is evidenced by the structure determination of the new type products 10–17 and 25 , including a synthetic proof for 12 and the X-ray analysis of 11 (X-ray data: triclinic P1; a=7,386(2), b=8,904(4), c=9,684(5)Å; α=82,29(4)°, β=74,46(3)°, γ=82,29(3)°; Z=2). The selective ¹π,π*-excitation also induces competitive C(γ)-C(δ) bond cleavage to yield the bicyclic acetal 18 and a ketonium-ylide intermediate a , which photochemically forms a carbene b giving the allene 19 and the cyclopropene 20 . On ¹n,π*-excitation of the acetate 9 the initial C(γ)-O bond fission is, in contrast to the behaviour of the corresponding alcohol 8 , followed by a 1,2-methyl shift affording (E/Z)- 28 or by a cyclization-autoxidation process yielding the lactone 29 .     

Curved two-dimensional electron gases

A method is introduced which makes it possible to fabricate non-planar two-dimensional electron gases. Making use of the “epitaxial lift-off” process, patterned, gated and contacted heterostructures are transferred from their crystalline substrate onto small glass tubes with diameters of a few millimeters. The transport properties of two-dimensional electron gases inside these curved semiconductor films are characterized by low-temperature magnetoresistance measurements. In the longitudinal resistance we find weak Shubnikov–de Haas oscillations, which are periodic in B⁻¹. The transverse resistance exhibits well-developed quantum Hall plateaus at low magnetic fields. At high fields, we observe a pronounced breakdown of the Hall effect. The experimental results are compared with simple theoretical models.     

Fractal structure of high-temperature graphs of O(N) models in two dimensions

The critical behavior of the two-dimensional O(N) model close to criticality is shown to be encoded in the fractal structure of the high-temperature graphs of the model. Based on Monte Carlo simulations and with the help of percolation theory, de Gennes' results for polymer rings, corresponding to the limit N-->0, are generalized to random loops for arbitrary -2相似文献   

Photochemische Reaktionen. 112. Mitteilung [1] Zur Photochemie α, β-ungesättigter γ, δ-Epoxyester. III. Ergänzende Untersuchungen zur Triplettreaktivität

On triplet sensitization (E)- 5 gives (Z)- 5 and isomerizes via C(δ), O-bond cleavage to the cyclobutanone 6 and the conjugated γ-ketoester 7 . - On singulet excitation 6 undergoes decarbonylation and yields the bicyclo [4.1.0]heptane 8 . However, on triplet sensitization 6 is converted to the isomeric tricyclononane 9 by a stereospecific oxa-di-π-methane rearrangement. The structure of 9 is determined by X-ray analysis of the p-nitrobenzoate 15: a = 10.573, b = 14.707, c = 13.494 Å, β = 112.40°, P2₁/n, Z, = 4.     

Continuity of eigenvalues for Schrödinger operators, $L^p$-properties of Kato type integral operators

Given an arbitrary relatively compact (finely) open subset of -eigenvalues of are studied where is the Dirichlet Laplacian on D and are measures on such that is continuous and is bounded for every ball X in being Green's function for X). Moreover, it is shown that these eigenvalues depend continuously on D and . The results are based on very general compactness and convergence properties of integral operators of Kato type which are developed before. Received: 9 November 2000 / Published online: 24 September 2001