Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

Nonlinear magneto-optical diffraction by two-dimensional magnetic superstructures

Nonlinear (at the second-harmonic frequency of the incident light) optical reflection by two-dimensional magnetic superstructures is theoretically studied. A square lattice of magnetic dots and a hexagonal lattice of magnetic bubbles (cylindrical magnetic domains) are considered. Because the periods of these structures are comparable with the wavelengths of the fundamental and the second-harmonic radiation, it would be possible to observe diffraction at the second-harmonic frequency. A polarization analysis of nonlinearly diffracted radiation is performed and the numbers of observable diffraction orders for the above structures are estimated. Received: 10 January 2002 / Published online: 11 June 2002     

Liquid chromatographic analysis of mexiletine in serum, with alternate application to tocainide, procainamide, and N-acetylprocainamide.

A simple and precise high performance liquid chromatographic method for the determination of mexiletine in human serum or plasma is described. Following addition of N-propionylprocainamide as internal standard the specimens are extracted, under basic conditions, into methylene chloride. After removal of the aqueous layer the drug is back-extracted into dilute acid, which is then injected directly for analysis. The extraction efficiency is 79% for both mexiletine and internal standard, and the assay is linear to 4 mg/L (twice upper therapeutic concentration). Inter-run coefficients of variation are 3.0% or less. The relative retention time of mexiletine to internal standard averages 1.3. An adaptation of this method is described for an alternate application to the analysis of tocainide, procainamide and N-acetylprocainamide.     

Oscillatory kinetics and mechanism of the chromate catalyzed decomposition of hydrogen peroxide

Oscillatory change of pH occurs during the chromate-catalyzed decomposition of hydrogen peroxide in a weakly acidic medium at elevated temperature and at high initial concentration of hydrogen peroxide. In a closed system, there are only two or three periods, but sustained oscillation occurs in a CSTR. In a CSTR bistability is also found. In closed systems the temperature exhibits a great maximum (up to 15°C increase), in a CSTR sustained oscillation occurs at a constant stationary temperature.     

Investigations of potassium-cerium phosphates rich in P2O5

In the ternary system Ce₂O₃-K₂O-P₂O₅, the partial system Ce(PO₃)₃-KPO₃-P₂O₅ was examined by means of differential thermal analysis and powder X-ray diffraction. The phase compositions of the products obtained on various thermal treatments were investigated. The phase diagram of the system Ce(PO₃)₃-KPO₃-P₂O₅ is suggested.

---

Zusammenfassung Mittels DTA und Röntgendiffraktion wurde im ternären System Ce₂O₃-K₂O-P₂O₅ das Teilsystem Ce(PO₃)₃-KPO₃-P₂O₅ untersucht. Die Phasenzusammensetzungen der durch verschiedene Erhitzungsvorgänge erhaltenen Produkte wurden untersucht und ein Phasendiagramm für das System Ce(PO₃)₃-KPO₃-P₂O₅ erstellt.

     

Glass transitions in hydrogen-bonded polymer complexes

Mutual precipitates of poly (N, N-dimethyl acrylamide) and poly (4-hydroxystyrene) were collected from dioxane, methanol, or acetone. The glass transition (T_g) temperatures of the precipitates are higher than the weight-average values. Clear films cast from dimethylformamide solutions have lower T_g values. Complexation also occurred between poly (ethyl oxazoline) and poly (4-hydroxystyrene) in dioxane and between poly (vinyl pyrrolidone) and poly (4-hydroxystyrene) in methanol. Again, the glass transition temperatures of the precipitates are higher than the values for the blend films. The ΔC_p values associated with the glass transitions of the complexes are smaller than those of the blends having the same compositions. Negative excess heat capacities of mixing have been observed for several precipitates.     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

Structural and optical characterization of the propolis films

We have performed structural and optical characterizations of the propolis (an organic entity of biological nature) films grown on various non-organic substrates. The films were grown from a propolis melt or a propolis alcohol solution. The crystal structure has been observed in the films precipitated from the solution onto substrates such as an amorphous glass and sapphire or semiconductor indium monoselenide. For any growth method, the propolis film is a semiconductor with the bandgap of 3.07 eV at 300 K that is confirmed by a maximum in photoluminescence spectra at 2.86 eV. We argue that propolis films might be used in various optoelectronic device applications.     

Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.