Facile synthesis of C-phosphanylformamidines via a carbene pathway

A direct synthetic approach to C-phosphanyl-N,N-dialkyl-N′-aryl(alkyl)-formamidines was developed. It was shown that phosphorylation of the formamidines proceeds at the nitrogen atom affording N-phosphanylformamidinium salts. Upon deprotonation, these salts gave C-phosphanylformamidines via formation of carbenes followed by a 1,2-phosphorus shift.     

On the Algebra of Symmetry of the Dirac Equation in Flat Space and De Sitter Space

The structure of the quadratic algebras of spinor symmetry operators for the Dirac equation is studied in a four-dimensional flat space and in the de Sitter space of arbitrary signature. The algebras are shown to be standard equivalent. Linear noncommutative subalgebras meeting the conditions of the noncommutative integrability theorem are found in these algebras.     

Integration of Dirac equation in Riemannian spaces with five-dimensional group of motions

In the present article a classification of Riemannian spaces with five-dimensional group of motion is described from the point of view of a solution of the Dirac equation. A class of spaces is identified in which the Dirac equation does not admit a complete separation of variables, and exact solutions of the Dirac equation are obtained in these spaces by means of the method of noncommutative integration. Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 24–28, August, 1997.     

Peculiarities of resonant interaction in paired impurity centers of 2-fluoronaphthalene in naphthalene

Abstract

Fluorescence and absorption spectra of the 2-fluoronaphthalene admixtures in naphthalene were studied at low temperature (T?=?4.2 К). Two types of pairwise impurity centers were formed at admixture concentrations of more than 1?wt%. Polarization of absorption bands was detected; these spectra were determined by resonance interactions between molecules of the impurity center. Resonant splitting of electronic levels for the translationally nonequivalent molecules in the unit cell of the naphthalene crystal was analyzed for the case, when one molecule was in the similar phase with the incident light wave and the other one was in antiphase.     

A representative of p,p,p-trihalogenylides: synthesis and structure

The representative of P,P,P-trichloroylides-5-methyl-2-phenyl-4-(trichlorophosphoranylidene)-2,4-dihydro-3H-pyrazol-3-one-was synthesized. Its constitution was confirmed by 1H, 13C, and 31P NMR spectroscopy and by X-ray analysis. Some chemical properties were studied and compared with ones of P,P,P-trimethylylide-5-methyl-2-phenyl-4-(trimethylphosphoranylidene)-2,4-dihydro-3H-pyrazol-3-one. DFT calculations of the model molecules were carried out.     

Additional constraints on quasi-exactly solvable systems

We consider constraints on two-dimensional quantum mechanical systems in domains with boundaries. The constraints result from the Hermiticity requirement for the corresponding Hamiltonians. We construct new two-dimensional families of formally exactly solvable systems. Taking the mentioned constraints into account, we show that the systems are in fact quasi-exactly solvable at best. Nevertheless, in the context of pseudo-Hermitian Hamiltonians, some of the constructed families are exactly solvable. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 237–248, February, 2007.     

Some Problems of the Existence of Symmetry Spinor Operators for the Dirac Equation

Conditions necessary for the existence of a class of fields that can be used to construct the spinor symmetry operators for the Dirac equation in Riemannian space are specified in the present paper. The metrics of spaces with four-dimensional groups of motions in which these fields exist are indicated. A class of spaces is identified in which the Dirac equation admits no separation of variables within the framework of the definition adopted, but the algebra of symmetry of the Dirac equation satisfies the conditions of theorems of the noncommutative intergrability.     

Photoluminescence of montmorillonite clay minerals modified by cetyltrimethylammonium bromide

The structure and photoluminescent properties of natural montmorillonite (MMT) aluminosilicates from three mineral deposits that were modified by cations of sodium or the surfactant cetyltrimethylammonium bromide (CTAB) have been investigated. X-ray fluorescence analysis showed significant differences in the concentrations of the inorganic dopants in these materials. An x-ray diffraction analysis established that incorporation of the CTA⁺ long-chain cations into the MMTs expands remarkably the mineral interplanar distances, the values of which are close to each other for all organoclay samples under study and equal to 1.8–2.0 nm. The photoluminescent properties of the Na-form of the MMTs are shown to depend on the amount of introduced dopant capable of either enhancing or quenching the emission. Deposition of CTAB on the mineral surface influences the luminescence pattern, the spectral contour and wavelength range being practically the same for all modified samples. The emission may intensify or weaken because of such surface modification.