Strong Feller properties for distorted Brownian motion with reflecting boundary condition and an application to continuous N-particle systems with singular interactions

Assuming that Ω⊂Rn, n?2, is an open, relatively compact set with boundary ∂Ω of Lebesgue measure zero we prove strong Feller properties for a class of distorted Brownian motions in with reflecting boundary condition. Dirichlet form techniques give the existence of a weak solution to the corresponding stochastic differential equation for quasi all starting points in the sense of the associated martingale problem. Combining this result with the strong Feller properties we can construct a weak solution for specified starting points. If Ω has C²-boundary the construction works for all starting points, where the drift term is not singular, even on the boundary. But also for a certain class of sets with less smooth boundary our approach works for all points in Ω, where the drift term is not singular, and at least some points from ∂Ω. Our techniques allow very singular drift terms. This enables us to construct continuous N-particle gradient stochastic dynamics in cuboids Λ⊂Rd, d∈N, with reflecting boundary condition and singular interactions for dN?2. We can start the stochastic dynamics in all initial configurations having at most one particle in ∂Λ, provided ∂Λ is locally smooth there.     

Biology-oriented synthesis of stereochemically diverse natural-product-derived compound collections by iterative allylations on a solid support

A strategy aiming at the introduction of stereocenters into polymer-bound natural-product-derived and -inspired compound collections is presented. Treatment of immobilized aldehydes with Brown's pinene-derived allylboranes results in the stereoselective formation of homoallylic alcohols with up to 89 % ee (ee=enantiomeric excess). Subsequent iterative ozonolysis-allylation sequences with up to three allylations on a solid support give access to 1,3-polyols with different relative configurations. Esterification with acryloyl chloride and final ring-closing metathesis yields alpha,beta-unsaturated delta-lactones with multiply oxygenated side chains, a substructure found in a group of natural products with a broad range of biological activity. The flexibility of the approach is exemplified by the parallel synthesis of all eight diastereomers of cryptocarya diacetate on a solid support. The individual isomers are obtained in overall yields of 40-60 % over 10 steps and with 63-85 % diastereoselectivity for the major isomer.     

On the Growth of Positive Definite Double Sequences Which Are not Moment Sequences

For every a > 1, there is a function f : N²₀ → R, which is positive semidefinite but not a moment sequence, such that |f(m, n)| ≥ m+ n^a(m+n) for all (m, n). The constant 1 is the best possible.     

Aluminiumorganyle mit pentakoordiniertem Aluminium-Atom: Synthese und Molekülstrukturen von [AlX2{2,6-(NEt2CH2)2C6H3}] (X = Cl,Et, H)

Aluminium Organyls with Pentacoordinate Aluminium: Syntheses and Molecular Structures of [AlX₂{2,6-(NEt₂CH₂)₂C₆H₃}] (X = Cl, Et, H) The reaction of [Li{2,6-(NEt₂CH₂)₂C₆H₃}]₂ with AlCl₃ or Et₂AlCl gives [AlX₂{2,6-(NEt₂CH₂)₂C₆H₃}] [X = Cl ( 1 ), Et ( 2 )] in good yield. 1 reacts with NaH in toluene to give [AlH₂{2,6-(NEt₂CH₂)₂C₆H₃}] ( 3 ). 1–3 were characterised spectroscopically (¹H, ¹³C, ²⁷Al n.m.r., i.r., mass spectroscopy). In solution at room temperature 1–3 exhibit dynamic behaviour. For 1 and 3 this can be frozen out below 278 K (¹H n.m.r.), indicating the presence of monomeric molecules with pentacoordinate Al at low temperature. Such species are also observed in the solid state as shown by an X-ray structure determination on 1 (monoclinic space group P2₁/n, a = 9.7325(14), b = 13.552(5), c = 28.858(7) Å, β = 99.57(2)°, V = 3753(2) ų, Z = 8, at 223(2) K) and 2 (monoclinic space group C2/c, a = 15.0045(12), b = 9.2986(8), c = 14.9955(12) Å, β =99.512(1)°, Z = 4, at 223(2) K).     

Segmentation of Stochastic Images using Stochastic Extensions of the Ambrosio-Tortorelli and the Random Walker Model

We discuss methods based on stochastic PDEs for the segmentation of images with uncertain gray values resulting from measurement errors and noise. Our approach yields a reliable precision estimate for the segmentation result, and it allows us to quantify the robustness of edges in noisy images and under gray value uncertainty. The ansatz space for such images identifies gray values with random variables. For their discretization we utilize generalized polynomial chaos expansions and the generalized spectral decomposition method. This leads to the stochastic generalization of the Ambrosio-Tortorelli approximation of the Mumford-Shah functional. Moreover, we present the extension of the random walker segmentation for our stochastic images, which is based on an identification of the graph weights with random variables. We demonstrate the performance of the methods on a data set obtained from a digital camera as well as real medical ultrasound data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of loading and particle size on the oxygen reaction in CGO impregnated Pt electrodes

Porous platinum electrodes impregnated with Gd _x Ce_1−x O_2−δ (CGO) are investigated to characterise how nano-sized CGO grains affect the oxygen reaction. Impedance measurements were performed at temperatures between 450 and 750 °C and at oxygen partial pressures of 0.2 and 5 × 10⁻⁵ bar for electrodes with various CGO loadings and electrodes annealed at various temperatures. The morphology was characterised by scanning electron microscopy and the CGO grain size was determined from X-ray diffraction peak broadening. The results showed that the polarisation resistance decreased with increasing CGO loading and increasing annealing temperature. CGO facilitates transport of oxygen ions thereby increasing the effective triple-phase boundary.     

2-(2-Methoxyphenyl)-1,3-dimethyl-1H-benzoimidazol-3-ium iodide as a new air-stable n-type dopant for vacuum-processed organic semiconductor thin films

2-(2-Methoxyphenyl)-1,3-dimethyl-1H-benzoimidazol-3-ium iodide (o-MeO-DMBI-I) was synthesized and employed as a strong n-type dopant for fullerene C(60), a well-known n-channel semiconductor. The coevaporated thin films showed a maximum conductivity of 5.5 S/cm at a doping concentration of 8.0 wt% (14 mol%), which is the highest value reported to date for molecular n-type conductors. o-MeO-DMBI-I can be stored and handled in air for extended periods without degradation and is thus promising for various organic electronic devices.     

New luminescence measurement facilities in retrospective dosimetry

This paper gives a review of recent developments in luminescence measurement facilities on the Risø TL/OSL reader including radio-luminescence (RL), exo-electron and violet stimulation attachments, and a method for characterising and if necessary correcting for beta irradiation source non-uniformity.We first describe improvements to the existing RL option to allow near infra-red detection (NIR) during irradiation by the built-in ⁹⁰Sr/⁹⁰Y beta source. The RL optical signal is collected by a liquid light guide through an F34-901 interference filter and detection is based on a dedicated thermoelectrically cooled NIR sensitive PMT (detection window peak at 855 nm, FWHM 27 nm). Software and electronics have been modified to allow standard TL and OSL measurements in the same sequence as RL measurements. Together with a new bleaching source based on a high-power UV LED (395 nm; 700 mW/cm²), this facility has been used to measure natural doses in feldspar using the decaying NIR RL signal.Secondly, we present a method for mapping radiation field of the built-in ⁹⁰Sr/⁹⁰Y β-source and estimating grain-location specific dose-rates. This is important for the accuracy of single grain results, when radiation field is spatially non-uniform across the sample area. We document the effect of this correction method and further investigate on the effect of lifting the source to achieve a better dose-rate uniformity.Finally we summarise two recently-developed novel facilities to help investigate (i) the time scales involved in OSL processes (time-resolved exo-electron detection) and (ii) extending the age range (violet stimulated signals from deep quartz OSL traps).     

Hoeffding's inequalities: A counterexample

A sequence : ₀ satisfiesHoeffding's inequality of order n if wheneverX ₁,...,X _n are independent nonnegative integer-valued elementary random variables and are independent identically distributed nonnegative integer-valued elementary random variables, the common distribution of which is the average of those ofX ₁,...,X _n. We show that for each integerm greater than 2 there exists a sequence satisfying Hoeffding's inequality of every order greater thanm but not that of orderm. This answers a question raised by Berg, Christensen, and Ressel.