The complete set of symmetry operators of the schrödinger equation

The complete set of symmetry operators of an arbitrary order associated with the Schrödinger equation is found. It is shown that this equation is invariant with respect to a 28-dimensional Lie algebra, realized in the class of differential operators of the second order. Higher-order symmetries of the Levi-Leblond equation are investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1521–1526, November, 1991.     

Chernoff efficiency of the sign and Wilcoxon tests for testing the symmetry hypothesis

The local Chernoff efficiency of the sign and Wilcoxon statistics are derived for the testing of symmetry on the basis of the analysis of the probabilities of large deviations of these statistics under the hypothesis and the alternative.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 101–107, 1989.     

Similar quartz crystallographic textures in rocks of continental earth’s crust (by neutron diffraction data): II. Quartz textures in monophase rocks

The types of quartz textures found in a large collection of multiphase rocks from different regions of the earth are analyzed. Crystallographic textures of granulite, amphibolite, slate, and gneiss samples are measured, classified, and compared with the similar textures of monomineral rocks.     

Bahadur effectiveness of Watson-Darling goodness-of-fit tests

The rough asymptotic behavior of the probability of large deviations is found for Watson-Darling goodness-of-fit tests, which are centered versions of Kolomogorov-Smirnov statistics. Their Bahadur effectiveness is calculated and conditions for local asymptotic optimality for the alternative of translation are studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 138–145, 1987.     

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.     

Specific C-H⋯N intramolecular interactions in the vinyloxy- and vinylthiopyridine series

A weak hydrogen bond with the participation of the vinyl group -hydrogen atom arises in 2-vinyloxypyridine and 2-vinylthiopyridine, which primarily exist in the s-trans-conformation, according to the ¹H and ¹³C NMR data. This interaction does not take place in 2-vinyloxymethyl- and 2-vinyloxyethylpyridines, which primarily exist in the s-cis-conformation. The C-H...N intramolecular interaction also does not occur in o-vinyloxyaniline due to the specific features of the stereoelectronic state of the amino group nitrogen atom.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1077–1081, August, 1991.     

A study of complexation in the system constituted by water,carbamide, and sulfur dioxide at 293 K

Electronic absorption spectroscopy and potentiometry were applied to study complexation at 293 K in a system constituted by water, carbamide, and sulfur dioxide. The composition and stability of the molecular and ionic complexes formed was determined in relation to the concentration of components in solution.Translated from Zhurnal Prikladnoi Khimii, Vol. 77, No. 8, 2004, pp. 1266–1270.Original Russian Text Copyright © 2004 by Khoma, Gavrilenko, Nikitin.     

Construction of basis sets of hybrid atomic orbitals for describing the nonequivalent bonds of an atom with four neighboring atoms (sp 3 hybridization)

Methods for constructing the basis sets of sp³ hybrid atomic orbitals for atoms surrounded with four neighboring atoms are discussed in detail. The results obtained are generalized as a theorem of sp³ hybridization. A general method is proposed for constructing basis sets of orthogonal sp³ hybrid atomic orbitals for atoms with distorted tetrahedral environments. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 6, pp.969–975, November–December, 1995. Translated by I. Izvekova     

Thermal analysis of some metal benzohydroxamates

The preparation and thermal analysis of metal chelates of benzohydroxarnic acid (BHA) with Al(III), Cd(II), Co(II), Cu(II) (two compounds), Fe(III), La(III), Pb(II), Mn(II), Ni(II), U(VI) and Zn(II) is discussed. The Al(III), La(III), Pb(II) and Mn(II) chelates are new compounds. DTA and TGA curves of the chelates and of BHA are presented, and the heats of decomposition of the chelates are estimated.