System of cryostating wide-aperture nonlinear crystals for generating the fifth harmonic of neodymium-laser radiation

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 5, pp. 867–870, November, 1989.     

Electrochemical reduction of sodium metavanadate in an equimolar KCl-NaCl melt

Electrochemical reduction of sodium metavanadate in an equimolar KCl-NaCl melt and the effect of acid-base properties of environment on this process are studied by a voltammetry method on a stationary platinum electrode. It is established that the limiting current of the NaVO₃ electroreduction process has a kinetic nature. The process proceeds via an autoinhibition scheme and its rate is limited by an acid-base reaction conjugated with an irreversible charge transfer reaction. A substantial role of cationic composition of the melt is revealed experimentally. Following acidification of the KCl-NaCl-NaVO₃ melt by Mg²⁺ (from MgCl₂), the process passes from an irreversible kinetic regime into a reversible diffusion (quasi-diffusion) process. Values of stability constants for vanadates produced with the aid of acid-base titration of vanadium pentoxide by oxygen ions in experimental conditions are presented. These values are taken into account when calculating kinetic parameters of the NaVO₃ electroreduction.     

Primary dependence of 7-aryl-2,5-di-t-butyl-1,3,5-cycloheptatriene valence tautomerism on the π-acceptor strength of the 7-aryl substituent

¹³C NMR studies showed that the population of the norcaradiene form of the title systems containing p-CH₃O, H, and p-CF₃ on the 7-aryl group increases in this order. The result is consistent with the prediction from the π-acceptor strength of the aryl group estimated by INDO calculations.     

Modulation of Particle Concentrations in the Interference Laser Radiation Field

Spatial redistribution of microparticles in a suspension on exposure to the interference laser field depending on the parameters of the particles and the field characteristics has been analyzed theoretically. Results of experimental investigations are presented that illustrate the capture of an ensemble of polymeric small spheres and also of the lymphocytes of human blood and other microparticles in a liquid in the interference radiation bands of the He–Ne laser.     

The limit distribution of the maximal deviation of a spline estimate of a probability density

One finds the limit distribution of the maximum absolute value of the normalized deviation of a spline estimate from an unknown probability density.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 447–467, 1986.     

Electrochemical reduction of 1,1-dihalo-2,2-disubstituted cyclopropanes

The electrochemical reduction of 1,1-dihalo-2-R-2-methylcyclopropanes was studied by polarography and preparative electrolysis. A mixture of stereoisomeric monoboro- and monochlorocyclopropanes was obtained with preparative yield of 60–70% in preparative electroreduction in methanol against a background of 0.1 M LiClO₄. In the case of bromine derivatives of cyclopropanes (except when R = CN) an effect was found on the part of the current density on the ratio of cis and trans isomers, which was interpreted as a change, in dependence on current density, of the contributions of the reactions of reduction of the starting compounds (S_N2 mechanism) and ionic pairs (S_N1 mechanism). The effect of the solvent (CHCl₃, DMF, DMSO, MeOH) and background salt (LiClO₄, Et₄NBr) on the ratio of stereoisomers is in agreement with this interpretation.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Science Center, Russian Academy of Sciences, Kazan. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 9, pp. 2023–2032, September, 1992.     

On the function of action on a manifold of ground state solutions

The functions of action and energy are introduced on a manifold of ground states of the Euclidian scalar field functional of action. The differential identity connecting these two functions is proved.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 438–449, December, 1995.