On Necessary and Sufficient Conditions for the Asymptotic Stability of Impulsive Systems

We prove that the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are also necessary conditions.     

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.     

Electrochemically induced processes in the formation of phosphorus acid derivatives. 2. The role of polymerization processes in the electrosynthesis of the esters of phosphorus acids from white phosphorus

The mechanism of the electrosynthesis of phosphate esters from white phosphorus was investigated. It was shown that the reaction takes place by two paths, i.e., monomeric (with the participation of dissolved phosphorus) and polymeric (with the participation of phosphorus on the surface of an emulsion drop). It was established that in an alcohol solution of tetraethylammonium iodide the main part of the final product is formed through an intermediate polymeric compound. It was noticed that by studying the dynamics of the accumulation of the dissolved product during electrolysis it is possible to trace the mechanism of reaction of the phosphorus at the individual stages of the process.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan' Scientific Center, Russian Academy of Sciences, 420028 Kazan'. V. I. Ul'yanov-Lenin Kazan' State University, 420028 Kazan'. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 6, pp. 1328–1333, June, 1992.     

Proton Migration in Benzene Complexes of Methyl and Silyl Cations

Quantum-chemical calculations at the B3LYP/6-31G(d,p) level of theory were used to optimize stationary points in the C₆H₆ + H₃X⁺ (X = C, Si) systems. At X = Si, the adduct of the cation with benzene is the most stable isomer, whereas at X = C, the para isomer is more stable than the adduct (ipso isomer). This difference is explained in terms of charge distribution in the benzene ring in toluene and phenylsilane: In the latter, the negative charge on the carbon atom attached to silicon is much higher than on the other carbon atoms, unlike toluene in which the highest negative charge is on the carbon atom para to the methyl group. Proton migration from the ipso to para position requires the lowest (X = C) and highest (X = Si) barriers to be overcome compared with the other barriers to proton migration over the benzene ring. These barriers and relative stabilities of the isomers correlate well with the charge distribution on benzene carbon atoms in toluene and phenylsilane.     

Ion-Molecular Reactions of Diethylsilylium Ions with Alcohols in the Gas Phase

Radiochemistry was used to study reaction of tritium-labeled diethylsilylium ions with alcohols in the gas phase. The reaction involves both rearrangement of the diethylsilylium ions and isomerization of the substituent in the substrate. The hydroxyl hydrogen of the alcohol and the tritium atom of the diethyl-silylium ion undergo exchange which, however, is less vigorous that in the case of the monoethylsilylium ion. A possible reaction mechanism is proposed.     

Anodic synthesis and molecular structure of dodecaethylhexaamidobisphosphonium diperchlorate

The electrochemical oxidation of hexaethyl triamidophosphite in the absence of nucleophiles specially introduced into the electrolyte was studied by anodic voltamperometry and preparative electrolysis. The reversible one-electron oxidation of the triamidophosphite molecule gives an unstable radical-cation, which reacts with a molecule of the starting compound to give a dimeric radical-cation, whose subsequent oxidation leads to dodecaethylhexaamidobisphosphonium diperchlorate. This product is the first example of an acyclic, doubly charged bisphosphonium cation with a . The crystal structure of this compound was obtained by x-ray diffraction structure analysis.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 664–669, March, 1990.     

Electrochemical Reduction of Arylxenon Tetrafluoroborates

Reduction potentials of arylxenon(II) tetrafluoroborates have been measured by cyclic voltammetry method on platinum disc and ultramicro electrodes. The electrochemical properties of the arylxenon(II) tetrafluoroborates are quite different to those of corresponding arylperfluoralkyliodine(III) salts.     

Ideal fluid with the equation of state ε=p in the field of a plane gravitational wave

An exact solution of the equations of relativistic hydrodynamics is obtained for a semiinfinite ideal fluid with the equation of state =p in the field of a plane gravitational wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 99–102, November, 1982.     

Stable and Storable N(CF3)2 Transfer Reagents

Fluorinated groups are essential for drug design, agrochemicals, and materials science. The bis(trifluoromethyl)amino group is an example of a stable group that has a high potential. While the number of molecules containing perfluoroalkyl, perfluoroalkoxy, and other fluorinated groups is steadily increasing, examples with the N(CF₃)₂ group are rare. One reason is that transfer reagents are scarce and metal-based storable reagents are unknown. Herein, a set of Cu^I and Ag^I bis(trifluoromethyl)amido complexes stabilized by N- and P-donor ligands with unprecedented stability are presented. The complexes are stable solids that can even be manipulated in air for a short time. They are bis(trifluoromethyl)amination reagents as shown by nucleophilic substitution and Sandmeyer reactions. In addition to a series of benzylbis(trifluoromethyl)amines, 2-bis(trifluoromethyl)amino acetate was obtained, which, upon hydrolysis, gives the fluorinated amino acid N,N-bis(trifluoromethyl)glycine.