A class of quasi-variational inequalities for adaptive image denoising and decomposition

We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives rise to a class of quasi-variational inequalities. We provide sufficient conditions for the existence of fixed points as solutions, and an algorithm based on solving a sequence of variational problems. Denoising experiments with spatial and spatio-temporal image data and an adaptive total variation regularizer illustrate our approach.     

Mechanism of multi‐metal(loid) methylation and hydride generation by methylcobalamin and cob(I)alamin: a side reaction of methanogenesis

Metal(loid)s are subject to many transformation processes in the environment, such as oxidation, reduction, methylation and hydride generation, predominantly accomplished by prokaryotes. Since these widespread processes affect the bioavailability and toxicity of metal(loid)s to a large extent, the investigation of their formation is of high relevance. Methanogenic Archaea are capable of methylating and hydrogenating Group 15 and 16 metal(loid)s arsenic, selenium, antimony, tellurium, and bismuth due to side reactions between central methanogenic cofactors, methylcobalamin (CH₃Cob(III)) and cob(I)alamin (Cob(I)). Here, we present systematic mechanistic studies on methylation and hydride generation of Group 15 and 16 metal(loid)s by CH₃Cob(III) and Cob(I). Pentavalent arsenical species showed neither methylation nor reduction as determined by using a newly developed oxidation state specific hydride generation technique, which allows direct determination of tri‐ and pentavalent arsenic species in a single batch. In contrast, efficient methylation of trivalent species without a change in oxidation state indicated that the methyl transfer does not proceed via a Challenger‐like oxidative methylation, but via a non‐oxidative methylation. Our findings also point towards a similar mechanism for antimony, bismuth, selenium, and tellurium. Overall, we suggest that the transfer of a methyl group does not involve a free reactive species, such as a radical, but instead is transferred either in a concerted nucleophilic substitution or in a caged radical mechanism. For hydride generation, we propose the intermediate formation of hydridocobalamin, transferring a hydride ion to the metal(loid)s. Copyright © 2012 John Wiley & Sons, Ltd.     

Pseudospark switches for the power supply circuits of pulsed lasers

A family of sealed-off low-pressure spark gap switches developed at the Institute of High Current Electronics (Tomsk) and at the Plasma Scientific Research Institute (Ryazan) with participation of researchers from the Physical Institute of the University of Erlangen (Germany) is described. The devices are of cermet construction, are capable of switching pulsed currents over wide ranges of amplitudes and durations, and have a number of unique characteristics. The principle of operation of the spark gap switches is described and their designs are given. The triggering circuits of the switches are considered. Institute of High-Current Electronics, Siberian Division of the Russian Academy of Sciences. Plazma Scientific Research Institute of Gas-Discharge Devices. Physical Institute of the University of Erlangen. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 97–105, April, 2000.     

Isoperimetric balls in cones over tori

In the cone over a cubic three-torus T ³, balls about the vertex are isoperimetric if the volume of T ³ is less than π/16 times the volume of the unit three-sphere. The conjectured optimal constant is 1.     

On representations,inversions, and approximations of laplace transforms in banach spaces

The paper extend's some of the basic results of classical Laplace transform theory to the Laplace transform of bounded Bochner integrable functions and the Laplace-Stieltjes transform of Lipschitz continuous functions with values in a Banach space.