The twisted SU(N) group. On the C *-algebra C(S μ U(N))

It is proved that C(S U(N)) is a type I C ^*-algebra.     

Quantum field theories of vortices and anyons

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be anyons, i.e. particles with arbitrary real spin and intermediate () statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of HighT _csuperconductors.     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

Emulsion stability and potassium leakage in emulsion liquid membrane systems

Potassium leakage was studied in liquid membrane systems containing various emulsifiers and compared with emulsion, stability in the storage test. The effects of various parameters upon emulsion stability and the leakage of standard traces are discussed. The transfer of cations can be caused by emulsion breaking, by transport with the specific carrier and/or with surfactants used as emulsifiers. The latter case becomes especially important when hydrophilic surfactants, e.g. ones containing polyoxyethylene chains, are present in liquid membranes. In systems containing hydrophobic emulsifiers the transfer of potassium is relatively low. In each case considered the effect of emulsifiers upon the transfer of the standard tracer should be checked prior to using the leakage test to characterize emulsion stability.     

DTA determination of the anhydrite content in rock salts

The DTA method was used to determine the phase diagram of the NaCl-CaSO₄ system over the range 0.55 wt.% of CaSO₄ in air atmosphere. The effects of SiO₂, CaCO₃ and Fe₂O₃ on the melting temperatures of pure NaCl and the eutectic were determined. On the basis of the above temperatures, a method of quantitative determination of the anhydrite content in rock salts has been developed.

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Zusammenfassung DTA wurde benutzt, um in Luft im Bereich 0 bis 55,0 Gew.% CaSO₄ das Phasendiagramm des Systemes NaCl-CaSO₄ zu bestimmen. Es wurde auch der Einfluß von SiO₂, CaCO₃ und Fe₂O₃ auf die Schmelztemperatur von reinem NaCl bzw. des Eutektikums bestimmt. Auf der Grundlage obiger Temperaturen wurde eine Methode zur quantitativen Bestimmung des Anhydritgehaltes in Steinsalzen entwickelt.

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- 0–55,0 . , . , ( ) .

     

Extension of the measuring range of balances

The basic principle of comparing the sample mass with the mass of a reference body in equilibrium gives the equal-armed beam balance a unique accuracy. Main parameters characterising the suitability of the instrument are measuring range, resolution and relative sensitivity (resolution/maximum load). The historical development of the values of these parameters achieved depended strongly on the practical need in those times. Technically unfavourable scales of the oldest Egyptian dynasties (~3000 BC) could resolve mass differences of 1 g and had a relative sensitivity of at least 10^–3. More sophisticated instruments from the 18^th Dynasty (~1567–1320 BC) achieved a relative sensitivity of 10^–4 independent of the size of the instrument. In 350 BC Aristotle clarified the theory of the lever and at about 250 BC Archimedes used the balance for density determinations of solids. The masterpiece of a hydrological balance was Al Chazini’s 'Balance of Wisdom’ built about 1120. Its relative sensitivity was 2⋅10^–5. Real progress took place when scientists like Lavoisier (1743–1794) founded modern chemistry. At the end of the 19^th century metrological balances reached a relative sensitivity of 10^–9 with a maximum load of several kilogrammes. That seems to be the high end of sensitivity of the classical mechanical beam balance with knife edges. Improvements took place by electrodynamic compensation (Emich, Gast). In 1909 Ehrenhaft and Millikan could weigh particles of 10^–15 g by means of electrostatic suspension. In 1957 Sauerbrey invented the oscillating quartz crystal balance. By observing the frequency shift of oscillating carbon nanotubes or of silica nanorods, masses or mass changes in the attogram or zeptogram have been observed recently.     

Enzymatic synthesis of neopentylpolyol esters in organic media

Utilization of lipases for synthesis of esters of hydrophilic polyols has been investigated. The choice of a suitable solvent is crucial in this type of reaction. An interesting case is fatty acid esters from neopentylpolyols, such as trimethylolpropane, which are of great interest as high temperature lubricants. Enzymatic synthesis of trimethylolpropane tricaprylate was studied as an alternative to chemical manufacturing. Triester production occurred only if the water produced by esterification was continuously removed from the medium. In these condition, kinetics of appearance and transformation of mono-, di- and triesters were determined in order to define optimal conditions.     

New example of a non-heme mononuclear iron(IV) oxo complex. Spectroscopic data and oxidation activity

The green complex S=1 [(TPEN)FeO]2+ [TPEN=N,N,N',N'-tetrakis(2-pyridylmethyl)ethane-1,2-diamine] has been obtained by treating the [(TPEN)Fe]2+ precursor with meta-chloroperoxybenzoic acid (m-CPBA). This high-valent complex belongs to the emerging family of synthetic models of Fe(IV)=O intermediates invoked during the catalytic cycle of biological systems. This complex exhibits spectroscopic characteristics that are similar to those of other models reported recently with a similar amine/pyridine environment. Thanks to its relative stability, vibrational data in solution have been obtained by Fourier transform infrared. A comparison of the Fe=O and Fe=(18)O wavenumbers reveals that the Fe-oxo vibration is not a pure one. The ability of the green complex to oxidize small organic molecules has been studied. Mixtures of oxygenated products derived from two- or four-electron oxidations are obtained. The reactivity of this [FeO]2+ complex is then not straightforward, and different mechanisms may be involved.     

A 1,8-naphthalenediol-based unsymmetrical dinucleating ligand

A facile synthesis of 2-formyl-1,8-naphthalenediol is reported. Its potential as a general precursor for the preparation of unsymmetrical multidentate chelating ligand systems based on 1,8-naphthalenediol is demonstrated by the synthesis of the dinucleating ligand L(4-)(H(4)L=N,N'-bis(2-(1,8-naphthalenediol)methylidene)propylenediamine). Reaction of H(4) L with copper acetate results in the formation of the unsymmetrical dinuclear Cu(II) complex [LCu(2)](3), which has been structurally characterized by single-crystal X-ray diffraction. One Cu(II) ion is coordinated by a N(2)O(2) compartment of L(4-) and the other Cu(II) ion is coordinated by an O(4) compartment of L(4-) while they are bridged by two aryloxide functions of L(4-). A dimerization of two molecules of 3 to a tetranuclear entity 3(2) occurs through formation of weak apical Cu--O interactions. Analysis of the temperature dependent magnetic susceptibility measurements (2--290 K) established a strong intradimer exchange coupling J(12)=-371 cm(-1). This strong superexchange interaction fits nicely in a magneto-structural correlation which has been established for dinuclear bis(phenoxide)-bridged Cu(II) complexes demonstrating the electronic equivalence of the aryloxides of a phenol and 1,8-naphthalenediol.