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.     

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.     

Lipophilicity Evaluation of the Products Obtained in the Reaction of N3-Substituted Amidrazones with cis-1,2-Cyclohexanedicarboxylic Anhydride

The lipophilicity of the novel 12 products of the reaction of N³-substituted amidrazones with cis-1,2-cyclohexanedicarboxylic anhydride (4 linear, 4 triazole-like and 4 isoindole ones) with potential pharmacologic activity was evaluated by thin layer and liquid chromatography. Using organic-aqueous eluent systems (with methanol or acetonitrile) on RP18 plates and C18 column, a linear relationship between the volume fraction of modifiers and the retention indices was obtained. The retention values, log k or R _M were extrapolated to zero organic modifier content to obtain the log k _w or R _MW values. 12 compounds with known literature lipophilicity were used as a calibration dataset. The results were compared in a multivariate way with in silico methods (ALOGPs, AC_logP, AB/LogP, COSMOFrag, miLogP, ALOGP, MLOGP, KOWWIN, XLOGP3).

     

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.     

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.     

Spectroscopic and theoretical study on peramine and some pyrrolopyrazinone compounds

The comparative analysis of IR and Raman spectra of peramine and its four derivatives in solid state was carried out. The harmonic vibrational frequencies, infrared intensities, and Raman scattering activities were calculated at density functional B3LYP methods with 6-311++G(d,p) basis set. For the predicted spectra, a potential energy distribution of normal modes was also calculated. For peramine derivatives the conjugation effect of pyrrole with pyrazinone ring was observed as a result of introduction of double bond. Moreover, ¹H NMR analysis indicated that pyrrole protons are deshielded in comparison with the pyrrolopyrazinone model ring system.     

1,4-dialkoxy-2,5-bis[2-(thien-2-yl)ethenyl]benzenes as promising materials for laser optical limiters

A new promising organic chromophore for two-photon laser absorption at 1064 nm with 1,4-diethoxy-2,5-bis[2-(5-methylthien-2-yl)ethenyl]benzene (A-C) was synthesized. We have performed evaluations of the two-photon absorption for these chromophores incorporated into the polymer matrices. Following the obtained quantum chemical data, we have performed quantum chemical simulations of the third-order susceptibilities for the investigated chrompophore incorporated into the PMMA matrices. The calculations were done within the three-level model. We have established that the experimentally calculated data are a bit less than theoretically calculated; however, the general tendency of their changes shows a good coincidence. The maximally achieved value of the TPA is equal to about 59.2 cm/GW at wavelength 1064 nm, which, together with their high photothermal stabilities, make them good candidates for optical-limiting processes.