Sub-Riemannian distance on the Lie group SL(2)

We find the distances between arbitrary elements of the Lie group SL(2) for the left invariant sub-Riemannian metric also invariant with respect to the right shifts by elements of the Lie subgroup SO(2) ? SL(2), in other words, the invariant sub-Riemannian metric on the weakly symmetric space (SL(2) × SO(2))/ SO(2) of Selberg.     

Catalysis of the alkaline hydrolysis of 4-nitrophenyl diethyl phosphonate by cationic dimeric surfactant micelles

Dimeric (gemini) surfactants containing hydroxyl functional groups have been synthesized and studied. These new surfactants have low critical micelle formation concentrations (<5·10⁻⁵ mol/L) and Krafft temperatures (≤0 °C). Depending on the pH of the medium, the alkaline hydrolysis of 4-nitrophenyl diethyl phosphonate, which is a model of organophosphorus ecotoxicants, proceeds 20–80 times more rapidly in the presence of gemini surfactant micelles than in water.     

Equilibrium configurations of the conducting liquid surface in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid deformed by a nonuniform external electric field are investigated. The liquid rests on an electrode that has the shape of a dihedral angle formed by two intersecting equipotential half-planes (conducting wedge). It is assumed that the problem has plane symmetry: the surface is invariant under shift along the edge of the dihedral angle. A one-parametric family of exact solutions for the shape of the surface is found in which the opening angle of the region above the wedge serves as a parameter. The solutions are valid when the pressure difference between the inside and outside of the liquid is zero. For an arbitrary pressure difference, approximate solutions to the problem are constructed and it is demonstrated the approximation error is small. It is found that, when the potential difference exceeds a certain threshold value, equilibrium solutions are absent. In this case, the region occupied by the liquid disintegrates, the disintegration scenario depending on the opening angle.     

Exact Solutions to the Problem of Dynamics of a Liquid with a Free Surface between Two Approaching Vertical Walls

Doklady Physics - Exact solutions of the classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite...     

Compression of a Runaway Electron Flow in an Air Gap with a Nonuniform Magnetic Field

JETP Letters - The first results of study of the compression of a picosecond runaway electron flow in an air electrode gap by a pulsed guiding magnetic field increasing along the electron...     

Abnormal Extremals of Left-Invariant Sub-Finsler Quasimetrics on Four-Dimensional Lie Groups

Siberian Mathematical Journal - We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined by a&nbsp;seminorm on a...     

Stereoselective hydrogenation of a menthone-isomenthone mixture on heterogeneous nickel,nickel-cobalt,and cobalt catalysts

A study was carried out on the effect of the nature of the catalysts, additives, and solvents on the stereoselectivity of the liquid-phase hydrogenation of an equilibrium menthone-isomenthone mixture to give menthols. Neoisomenthol, which is the least stable of all the menthol isomers, was predominantly formed on a cobalt catalyst modified by (+)-tartaric acid in ethyl acetate at 130°C and 10 MPa.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1920–1923, August, 1989.     

Molecular structure and biological activity of 2,3-[(4-benzoyl)benzo]-15-crown-5

Institute of Chemical Physics and Institute of Physiologically Active Compounds. Translated from Zhurnal Strukturnoi Khimii, Vol. 31, No. 5, pp. 96–102, September–October, 1990.     

Synthesis and Antiradical Activity of 5-Acetyl-2-alkylthio-4-aryl-6-methyl-1,4-dihydropyridine-3-carboxylic Acid Nitriles

The alkylation of 3-cyano-1,4-dihydropyridine-2(3H)-thiones or the condensation of an aromatic aldehyde, cyanothioacetamide, acetylacetone, and methyl iodide in the presence of piperidine has given a series of novel 5-acetyl-2-alkylthio-4-aryl-6-methyl-1,4-dihydropyridine-3-carboxylic acid nitriles. A compound was obtained from 3,5-di(tert-butyl)-4-hydroxybenzaldehyde in the molecule of which were combined the active part of the antioxidant ionol and a 1,4-dihydropyridine ring. It was found that, among the compounds synthesized, the highest antiradical activity occurred in a compound having two hydroxyl groups in the 4-phenyl substituent.     

Reactivity of N-alkyl derivatives of hydroxylamine in decomposition of 4-nitrophenyl diethylphosphonate in water and in cetyltrimethylammonium bromide micelles

Neutral forms of hydroxylamine, N-methylhydroxylamine, and N,N-dimethylhydroxylamine are typical α-nucleophiles in water. In comparison with aryl anions of similar basicity their rate of reaction in the decomposition of 4-nitrophenyl diethylphosphonate is increased by about 10² times. Decomposition of the substrate is accelerated in cetyltrimethylammonium bromide micelles (about 4 to 30 fold). Hydroxylamine and its N-alkyl derivatives are the most effective low basicity nucleophiles. The sole factor responsible for the micellar effects is the concentration of the reagent in the surfactant micelles. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 4, pp. 231–236, July–August, 2007.