Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Self-Interactions of Strands and Sheets

Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology, and engineering. Often the physical interpretation dictates that self-avoidance should be enforced in the continuum model, i.e., finite energy configurations should not self-intersect. Current continuum models with self-avoidance frequently employ pairwise repulsive potentials, which are of necessity singular. Moreover the potentials do not have an intrinsic length scale appropriate for modelling the finite thickness of the physical systems. Here we develop a framework for modelling self-avoiding strands and sheets which avoids singularities, and which provides a way to introduce a thickness length scale. In our approach pairwise interaction potentials are replaced by many-body potentials involving three or more points, and the radii of certain associated circles or spheres. Self-interaction energies based on these many-body potentials can be used to describe the statistical mechanics of self-interacting strands and sheets of finite thickness.     

The influence of glass coating on the single domain wall potential in amorphous glass-coated Fe-based microwires

The effect of the glass coating on the single domain wall potential in amorphous glass-coated Fe-based microwire has been studied by the switching field distribution technique. The thermoactivated mechanism model is used to describe the thermally activated switching through the complex energy barrier in amorphous FeSiB microwires. Glass removal leads to the increase of the probability of the thermally activated switching pointing to the decrease of the energy barrier.     

Alkane oxygenation with H2O2 catalysed by FeCl3 and 2,2′-bipyridine

The H₂O₂-FeCl₃-bipy system in acetonitrile efficiently oxidises alkanes predominantly to alkyl hydroperoxides. Turnover numbers attain 400 after 1 h at 60 °C. It has been assumed that bipy facilitates proton abstraction from a H₂O₂ molecule coordinated to the iron ion (these reactions are stages in the catalytic cycle generating hydroxyl radicals from the hydrogen peroxide). Hydroxyl radicals then attack alkane molecules finally yielding the alkyl hydroperoxide.     

Relaxation processes in room temperature ionic liquids: the case of 1-butyl-3-methyl imidazolium hexafluorophosphate

A detailed investigation on the nature of the relaxation processes occurring in a typical room temperature ionic liquid (RTIL), namely, 1-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF(6)]), is reported. The study was conducted using both elastic and inelastic neutron scattering over a wide temperature range from 10 to 400 K, accessing the dynamic features of both the liquid and glassy amorphous states. In this study, the inelastic fixed energy scan technique has been applied for the first time to this class of materials. Using this technique, the existence of two relaxation processes below the glass transition and a further diffusive process occurring above the glass-liquid transition are observed. The low temperature processes are associated with methyl group rotation and butyl chain relaxation in the glassy state and have been modeled in terms of two Debye-like, Arrhenius activated processes. The high temperature process has been modeled in terms of a Kohlraush-Williams-Watts relaxation, with a distinct Vogel-Fulcher-Tamman temperature dependence. These results provide novel information that will be useful in rationalizing the observed structural and dynamical behavior of RTILs in the amorphous state.     

A new technique for the identification of chloride ions by the formation of chromyl chloride

Summary A new technique is described for the identification of the chloride ion through the formation of chromyl chloride, based on the extraction of the latter with carbon tetrachloride. The identification limit is 2g of chloride. It is possible to carry out the test in the presence of many other anions, including fluoride, which cannot be present when the traditional distillation technique is employed.

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Zusammenfassung Vorgeschlagen wird eine neue Technik zum Chloridnachweis durch Bildung von Chromylchlorid. Dieser Nachweis beruht auf der Extraktion des Chromylchlorids mit Tetrachlorkohlenstoff. Die Nachweisgrenze liegt bei 2g Chlorid, wobei die Möglichkeit besteht, den Test auch in Gegenwart von Fluorid durchzuführen, das bei Anwendung der üblichen Destillationsmethoden nicht anwesend sein darf.

     

Abnormally mild synthesis of bis(dithiolo)pyrroles from 2,5-dimethylpyrroles

[chemical reaction: see text]. Treatment of N-substituted 2,5-dimethylpyrroles 2 with an equilibrated mixture of disulfur dichloride and DABCO in chloroform at 0 degrees C gives pentathiepinopyrroles 3 in moderate yields; further reaction of 3 with the same mixture at room temperature leads, in an extensive reaction cascade, to bis(dithiolo)pyrroles 4 in high yield; 2 can be converted into 4 in a one-pot operation under unusually mild conditions.     

Terpenoids of the red alga laurenciapinnatifida

The structures of three brominated terpenoids which are natural products from the red alga Laurencia pinnatifida (Gmal. Lamour) are described. The structures of the sesquiterpenes $\text{4}$ and $\text{5}$ were determined by spectral comparison and chemical interconversion. The structure of the squalene-derived terpenoid $\text{8}$ was secured by chemical transformation into thyrsiferol, a brominated triterpene previously isolated from the red alga Laurencia thyrsifera.