Pseudotwistors

We deal with the Hermitian Hurwitz pairs of signature (, s), + s = 5 + 4, | + 1 – s| = 2 + 4m;, m = 0, 1,.... We introduce the Hurwitz twistors for signature (3, 2) and its dual (1, 4) and we indicate the relationship between Hurwitz and Penrose twistors. The signatures (1, 8) and (7, 6) give rise to pseudotwistors and bitwistors, respectively. For pseudotwistors, we prove a counterpart of the Penrose theorem in the local version, on real analytic solutions of the related spinor equations versus harmonic forms, and in the semiglobal version, on holomorphic solutions of those equations versus Dolbeault cohomology groups. We prove an atomization theorem: There exist complex structures on isometric embeddings for the Hermitian Hurwitz pairs so that the embeddings are real parts of holomorphic mappings.     

Computational studies of the cyclization of thiosemicarbazides

While typically cyclodehydration of thiosemicarbazides in acidic media leads to 1,3,4‐thiadiazoles, we have recently shown that under reflux conditions in anhydrous acetic acid the cyclization yields an imidazolidine derivative. The mechanism of this reaction has been characterized theoretically. Calculations indicate that this direction, facilitated by the presence of the ? CH₂CO₂? moiety in the N4 substituent is favored over the direction leading toward the thiadiazole product. Formation of the C? N bond that closes the five‐member ring appears to be concerted with the departure of ethanol molecule, although the proton transfer from the nitrogen atom to oxygen atom is much more advanced in the transition state. Copyright © 2007 John Wiley & Sons, Ltd.     

Storage Stability of Antioxidant in Milk Products Fermented with Selected Kefir Grain Microflora

The aim of the study was to assess the antioxidant potential of goat’s milk and whey from goat’s milk fermented with selected bacteria strains from kefir grain (L. plantarum, L. fermentum, L. rhamnosus and L. acidophilus) with regard to fermented cow’s milk with the same bacteria strains. The assessment of antioxidant potential was made by ABTS, DPPH, TPC and FRAP methods. The work also assessed metabolic activity of tested lactic acid bacteria using measurement of electrical impedance changes in the growing medium. The highest values describing the antioxidant potential were found for fermented milk by L. acidophilus. It was also found that the time of cooling storage causes significantly increasing the antioxidant potential of most analyzed samples. Metabolic activity of tested lactic acid bacteria was the highest for cow’s milk. The course of curves for goat’s milk and whey from goat’s milk was similar, which confirms the differences between cow and goat milk.     

Michael addition to a chiral non-racemic 2-phosphono-2,3-didehydrothiolane S-oxide

The Michael addition of selected sulfur and nitrogen nucleophiles to a chiral non-racemic 2-phosphono-2,3-didehydrothiolane S-oxide is fully diastereoselective. The enantiomeric excesses of the adducts obtained could be determined by ³¹P NMR spectroscopy using (R)-(+)-tert-butyl(phenyl)phosphinothioic acid as a chiral solvating agent. The addition of thiophenol was monitored by ³¹P NMR spectroscopy which made it possible to observe the formation and evolution of the kinetic and thermodynamic adducts in the reaction mixture. The structures of both enantiomeric thiophenol adducts have been determined by X-ray analysis.     

Determination of microgram amounts of azide by gas chromatography

Azide ions (5–120 μg) are oxidized by cerium(IV) in an acidic medium. The nitrogen evolved is displaced by helium carrier and quantified by gas chromatography with a thermal conductivity detector. The relative standard deviation is <5%. Many sulphur anions, cyanide and some metal ions which form azide complexes do not interfere.     

Brucine and two solvates

The crystal structures of brucine (2,3‐di­methoxy­strychnidin‐10‐one), C₂₃H₂₆N₂O₄, brucine acetone solvate, C₂₃H₂₆N₂O₄·C₃H₆O, and brucine 2‐propanol solvate dihydrate, C₂₃H₂₆N₂O₄·C₃H₇O·2H₂O, have been determined. Crystals of brucine and its 2‐propanol solvate dihydrate exhibit similar monolayer sheet packing, whereas crystals of the acetone solvate adopt a different mode of packing, as brucine pillars. The solvent appears to control the brucine self‐assembly on the basis of common donor–acceptor properties of the surfaces.     

Van der Pauw method on a sample with an isolated hole

Explicit results of the van der Pauw method for a sample containing an isolated hole are presented together with experimental confirmation. Results of measurements and numerical analysis strongly suggest that four probe resistivities obey inequality similar in the form to the famous van der Pauw equation. The inequality seems to be valid for any sample with an isolated hole and contacts located on the same edge, however rigorous proof is not given. The inequality can be used for experimental detection of the sample quality.     

Hyperbolic diffusion in chaotic systems

We consider a deterministic process described by a discrete one-dimensional chaotic map and study its diffusive-like properties. Starting with the corresponding Frobenius-Perron equation we derive an approximate evolution equation for the probability distribution which is a partial differential equation of a hyperbolic type. Consequently, the process is correlated, non-Markovian, non-Gaussian and the information propagates with a finite velocity. This is in clear contrast to conventional diffusion processes described by a standard parabolic diffusion equation with an infinite velocity of information propagation. Our approach allows for a more complete characterisation of diffusion dynamics of deterministic systems.     

Determination of retained austenite in bearing steel

M?ssbauer effect experiments in scattering geometry were performed for gauging plates and bearings in order to measure the retained austenite content. The results, obtained from numerical calculations of Mössbauer spectra are compared with the X-ray diffraction measurements. A simple three point Mössbauer effect technique is applied in order to decrease the time of measurements in the industrial use.