Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

Solvent Effects in the Electrophilic Amination of Mesitylene with the System NaN3-AlCl3-HCl

Russian Journal of Organic Chemistry -     

Nonisothermal deoxygenation of cobalt complexes in free form and attached to aerosil

Thermal deoxygenation under vacuum has been examined for free oxygenated cobalt complexes formed with phenanthroline, histidine, and histamine and also for those attached to aerosil; mass spectrometry has been applied to the products. The free compounds are deoxygenated in accordance with the Roginskii equation f() = (1–)^2/3 in a certain range. Deoxygenation for the grafted complexes is described by an equation for nucleation and one-dimensional growth f() = 1–. The kinetic parameters have been determined.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 3, pp. 311–317, May–June, 1987.     

Selective hydrodechlorination of fluorinated arylamines

Chlorine-containing polyfluorinated anilines and meta-phenylenediamines undergo selective hydrodechlorination easily upon reduction by zinc in aqueous ammonia. A new approach is thus provided to synthetically valuable, partially fluorinated arylamines based on utilizing polyfluorochloroarenes, which are available as intermediates of perfluoroarene production from perchloroarenes. When chlorine atoms are present in positions both ortho and para to the amino group, para chlorine is initially eliminated. Based on this reaction, a one-pot synthesis of partially fluorinated 4-aminopyridines from 3,5-dichlorotrifluoro- and 3-chlorotetrafluoropyridine has been realized.     

Explicitly solvable model of Mössbauer scattering

An explicitly solvable model of Mössbauer scattering of rays by a nucleus bound in a harmonic-oscillator potential is constructed. The probability of elastic scattering, which is proportional to the Debye—Waller factor, is calculated in the framework of the explicitly solvable scattering problem. It is assumed that the rms deviation x of the nucleus and the photon wave numberk satisfykxE /E , whereE andE are typical energy levels of the photon and the oscillator states.St Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 3, pp. 439–430, June, 1993.     

The effect of nanosized titania-silica film composition on the photostability of adsorbed methylene blue dye

The effect of nanosized porous films (average density 10 g/m²) of TiO₂. TiO₂/SiO₂, and SiO₂ on the photostability of adsorbed methylene blue (MB) dye during UV irradiation in air was investigated by optical spectroscopy and laser-induced mass spectrometry. The effectiveness of the photodecomposition of MB decreases in the order TiO₂ > TiO₂/SiO₂ > SiO₂ with rate constants 1E-2, 0.6E-2, and 0.3E-2 min⁻¹ respectively. A mechanism including the participation of both excited states of the dye molecules and photoexcited titanium dioxide is proposed for the photodecolorization of MB adsorbed on the surface of the investigated films. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 4, pp. 220–225, July–August, 2007.     

Replacement of an oxygen atom by chlorine atoms in the reaction of pentafluorobenzaldehyde with CCl3-substituted compounds in the presence of AlCl3

The interaction of pentafluorobenzaldehyde with RCCl₃ (R = Cl, Ph, C₆F₅) in the presence of threefold molar excess of AlCl₃ proceeds with replacing the oxygen atom of the aldehyde group by two chlorine atoms from the CCl₃ group and results in the formation of pentafluorobenzylidene chloride. The electrophilic mechanism of the reaction is proposed.     

Dissociation and rearrangements of the molecular ions of sulfides,sulfoxides, and sulfones generated by a strong electric field

The field mass spectra of 18 sulfides, sulfoxides, and sulfones were investigated, and the principles of charge localization in the dissociation and rearrangements of the molecular ions of these compounds were established. A new type of fragmentation leading to the elimination of S^+., SO^+., and SO₂. was observed. A new mechanism, according to which cleavage of two C-S bonds and the formation of one new C-C bond due to radical recombination cocur in the cyclic transition complex, is proposed. Prior migration of alkyl radicals from sulfur to oxygen with subsequent cleavage of the S-O and C-S bonds via the above-mentioned mechanism may also occur in the molecular ions of sulfoxides and sulfones.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 2, pp. 172–181, March–April, 1987.     

Efficient control of the molecular weight of modified epoxy resins in the course of their synthesis

Epoxy resin modified with sebacic acid was synthesized. It exhibits improved elastic properties and impact resistance.     

Torsional strain of TaS3 whiskers on the charge-density wave depinning

We find that an electric current I exceeding the threshold value results in torsional strain of o-TaS3 samples with one contact freely suspended. The rotation angle deltavarphi of the free end achieves several degrees and exhibits hysteresis as a function of I. The sign of deltavarphi depends on the I polarity; a polar axis along the conducting chains (the c axis) is pointed out. We associate the effect with surface shear of the charge-density wave (CDW) coupled to the crystal shear. The current-induced torsional strain could be treated in terms of enormous piezoelectric coefficients (>10(-4) cm/V) corresponding to shear. In essence, TaS3 appears to be a ready torsional actuator based on the unique intrinsic property of the CDW.