Nonstandard extensions of uniform algebraic systems

Important applications of nonstandard analysis to the theory of Banach spaces are based on the construction of the nonstandard hull of a normed linear space [1,2]. By making use of the iterated nonstandard enlargements [3], in the present article we propose a universal construction for arbitrary uniform algebraic systems which allows one to study the nonstandard hulls and completions of such systems.In Section 1 we give necessary information about nonstandard enlargements and prove a number of important results in the general theory of monads. In Section 2 we present basic facts on nonstandard topologies and uniform algebraic systems. In Section 3 we describe a general algebraic construction with the help of which we study the question of completing uniform algebraic systems. Conditions for existence of nonstandard hulls for such systems are obtained in Section 4.Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 1094–1105, September–October, 1994.     

Effect of solvent on the adsorption of benzene vapors by dicyclohexane-18-crown-6 thin films

The solvent effect on the stability of the zero signal of resonators with a dicyclohexane-18-crown-6 film was studied. The adsorption capacity and sensitivity of the film coatings to benzene vapors was estimated. The performance characteristics of the microweighing of benzene vapors were calculated. A model was proposed for benzene adsorption from the gas phase on thin films of crown ether.     

Catalysts based on filamentous carbon in the hydrogenation of aromatic compounds

In order to extend the area of application of the base catalytic system metal-filamentous carbon, the catalytic properties of Ni-filamentous carbon catalysts have been tested in the hydrogenation of aromatic compounds (benzene, benzyl cyanide, benzophenone, and nitrobenzene). The selectivity of the catalysts depends on the outer faceting of the active metal particles. The benzene ring is hydrogenated on the (111) face of the metal nanoparticles, whereas the selective hydrogenation of functional groups in substituted aromatic compounds occurs on the surface of active component nanoparticles in which the (111) face is blocked.     

Synthesis of hybrid photochromes containing fulgimide and salicylidenaniline fragments and study of their properties

Fulgimide salicylidenaniline derivatives were synthesized and studied in solutions and solid-phase films. It was found that the compounds obtained exhibit photochromic properties in different aggregate states. Comparative studies showed that the nature of substituents in the aldehyde moiety of the fulgimide azomethine fragments has little effect on the photochromic properties of the compounds obtained.     

Regioselective addition of cyclic nitrones to Feist��s acid dimethyl ester

Cyclic nitrones, viz., tetrahydropyridine 1-oxide, 3,4-dihydroisoquinoline 2-oxide, and 2-methoxycarbonyl-4,5-dihydro-3H-pyrrole 1-oxide, regioselectively add to dimethyl 3-methylidenecyclopropane-1,2-dicarboxylate to form 5-spirocyclopropaneisoxazolidines. The latter undergo isomerization upon heating to give the corresponding tetrahydropyridin-4-ols and enaminones.     

A universal planar automaton is determined by its semigroup of input symbols

Universal planar automata are universally attracted objects in the category of automata, for which the set of states and the set of output symbols are equipped with structures of planes. We investigate the problem of determinability of these automata by their semigroups of input symbols.     

Structure of neutral molecules and monoanions of selected oxopurines in aqueous solutions as studied by NMR spectroscopy and theoretical calculations

A methodology enabling investigation of a multicomponent tautomeric and acid-base equilibria by (13)C NMR spectroscopy supported by theoretical calculations has been proposed. The effectiveness of this method has been illustrated in a study of 2-oxopurine, 6-oxopurine (hypoxanthine), 8-oxopurine, and 2,6-dioxopurine (xanthine) in neutral and alkaline aqueous solutions. For each compound a series of (13)C NMR spectra were recorded at pH ranges in which neutral molecules, monoanions and/or dianions occurred in dynamic equilibrium. The carbon chemical shifts for these three forms of the investigated compounds were retrieved from the analysis of pH-dependence of the measured, dynamically averaged values of these parameters. The structures of several stable tautomers of the neutral and monoanionic oxopurine forms were predicted from theoretical calculations and nuclear magnetic shielding constants for (13)C nuclei in these tautomers were calculated. At both calculation steps (molecular geometry optimization and calculation of NMR parameters) the PBE1PBE/6-311++G(2d,p) level of theory was used. The populations of the most stable tautomers were determined from the experimental data analysis exploiting the fact that they were population-weighted averages of the chemical shifts of particular tautomers. It has been shown that only the oxo forms of the investigated oxopurines are present in aqueous solutions and that the determined populations in most cases remain in a qualitative agreement with the calculated free energies of the appropriate tautomers. The obtained results are in general agreement with other literature reports on oxopurine tautomerism and confirm importance of the hydration phenomena for the investigated systems. The data analysis has shown that the best compliance between theory and experiment is obtained when the hydration phenomenon is modeled by discrete hydration augmented by PCM (polarizable continuum solvation model).     

Spectral and polarization analysis of optical images by means of acousto-optics

This paper presents results of a theoretical and experimental study of Bragg anisotropic diffraction. The diffraction may be used for filtration of optical radiation and processing of images. Special attention is devoted to the investigation of diffraction, which provides spectral filtration simultaneously with polarization analysis of divergent optical beams. A tunable tellurium dioxide acousto-optical filter for processing of optical images is described in the paper. Some experimental results of the image analysis in visible light and in the near-infrared region of the spectrum are discussed.     

Application of the Wavelet Transform for Detecting Signals of Nuclear Quadrupole Resonance

In the present study, the wavelet transform is used to increase the signal-to-noise ratio of nuclear quadrupole resonance (NQR) signals in the direct pulse method. The efficiency of the wavelet and Fourier transforms used for detecting the NQR signal component is compared. The signal consists of noise, magnetoacoustic and piezoelectric signals, noise from external sources, and NQR signal. Signals from ¹⁴ N nuclei in hexahydro-1,3,5-trinitro-s-triazine C₃H₆N₆O₆ (RDX) are investigated at a temperature of 298 K.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 47–50, January, 2005.     

Composite mechanism of the catalytic hydrogenation of unsaturated hydrocarbons on hydrided magnesium intermetallides

Two temperature ranges are distinguished in the catalytic hydrogenation of unsaturated hydrocarbons on magnesium intermetallide hydrides. In the lower temperature range, the reaction proceeds by a composite mechanism, as is indicated by the fact that the rate of the catalytic hydrogenation of ethylene, n-butenes, and butadiene is equal to the rate of the reduction of these hydrocarbons with hydride hydrogen. It is assumed that, at higher temperatures, the reaction proceeds by a heterogeneous-homogeneous mechanism.