Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

Magnetic properties of Fe−Mn−Al alloy system in the FCC disordered phase

In this work we report the experimental studies of Fe?Mn?Al alloys in the FCC disordered phase at room temperature by Mössbauer spectroscopy and X-ray diffraction. In this phase the alloys are antiferromagnetic with a constant mean hyperfine field ( \(\bar H\) ) near 26 kOe in the composition range from 0 to 7.5 at.% Al and 50 to 65 at.% Fe. When the Al or Fe concentration increases, the \(\bar H\) value gradually decreases to zero and the alloy becomes paramagnetic. In the same way when the Al concentration increases the lattice parameter increases linearly but when the Fe concentration increases the lattice parameter remains nearly constant for alloys with 5 at.% Al and decreases for alloys with 10 at.% Al.     

Counterion exchange selectivity coefficients at water-in-oil microemulsion interface

The counterion binding at a water/Aerosol-OT (AOT)/heptane microemulsion interface was treated in the context of the pseudo-phase ion exchange formalism. Two approaches were used to determine the selectivity coefficient for copper/sodium counterion binding at the AOT microemulsion interface: measurements of the Cu(II) concentration taken up by the reverse micelle in a Winsor II microemulsion system and steady-state emission quenching measurements of an anionic water-solubilized probe, the tris-(4,4'-dicarboxy-2,2'-bipyridine) ruthenium (II) ion. In addition, the selectivity coefficient for methyl viologen/sodium at the microemulsion surface was determined by the same photophysical technique. The value for copper (II)/sodium exchange (K(Cu/Na)) is 1.1+/-0.3 and that for methyl viologen/sodium (K(MV/Na)) is 0.9+/-0.3. The results show that the pseudo-phase ion exchange model can be used to obtain the selectivity coefficient in a microemulsion system.     

1-Alkyl-2,4-dihydro-1H-pyrazino[2,1-b]quinazoline-3,6-diones as glycine templates. Synthesis of Fiscalin B

An excess of base allows the regio- and diastereoselective alkylation at C(4) of the glycine templates 1-methyl(isopropyl)-2,4-dihydro-1H-pyrazino[2,1-b]quinazoline-3,6-diones 9a and 9b without the need for N(2)-protecting groups. While the alkylation of 9a gave exclusively the 1,4-anti-isomers, the isopropyl derivative 9b required much longer reaction times and occurred with lower diastereoselectivity. Fiscalin B 3 was obtained by alkylation of 9b with N-Boc-3-indolylmethyl bromide followed by indole deprotection.     

Spectrophotometric determination of mercury with thiocyanate and Rhodamine B

Summary Mercury(II) in the presence of a large excess of thiocyanate forms a violet colour with Rhodamine B. The complex formed can be stabilized by addition of poly(vinyl alcohol), and forms the basis for a spectrophotometric method for determination of trace amounts of mercury. The calibration graph for measurement at 610 nm is linear in the range 1–15g of mercury per 25 ml, with a molar absorptivity of 1.1×10⁵l· mole^–1·cm·. The effect of foreign ions has been studied and the method can be applied to the determination of mercury in air with reliable analytical results.

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Spektrophotometrische Bestimmung von Quecksilber mit Rhodanid und Rhodamin B

Zusammenfassung In Gegenwart eines großen Überschusses von Rhodanid bildet Hg(II) mit Rhodamin B eine violette Färbung. Durch Zusatz von Polyvinylalkohol kann dieser Komplex stabilisiert werden und bietet somit die Grundlage für die spektrophotometrische Bestimmung von Hg-Spuren. Die Eichkurve für die Messung bei 610 nm verläuft für 1–15g Hg/25 ml linear. Die molare Absorptivität beträgt 1,1×10⁵ l·mol^–1·cm^–1. Die Fremdionenwirkung wurde untersucht. Das Verfahren kann zur Hg-Bestimmung in Luft verwendet werden.

     

N-Amination of 3-amino-1,2,4-triazole with hydroxylamine-O-sulfonic acid: Synthesis of 1,5-diamino-1,2,4-triazole

N-Amination of the 3(5)-amino-1,2,4-triazolide anion with hydroxylamine-O-sulfonic acid is studied. This method provided an access to the previously unknown 1,5-diamino-1,2,4-triazole.