Fields of representatives of commutative local rings and maximal scalar fields of finite-dimensional algebras

The structure of scalar fields for a directly indecomposable finite-dimensional algebra treated as a ring is studied. Scalar fields are assumed similar if their action on a ring is identical modulo an annihilator. The criterion for a class of maximal scalar fields to be unique under a similitude relation is established. Supported by RFFR grant No. 96-01-01675, and by RF State Committee of Higher Education. Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 667–686, November–December, 1998.     

Concentration variations in the optical pseudogap and refractive index of crystals of Cu6PS5I1–xClx solid solutions

The effect of anionic substitution of halogen atoms on the spectral position and shape of the optical absorption edge and the dispersion of the refractive index of crystals of Cu₆PS₅I_1–xCl_x solid solutions are studied. The concentration dependences of the width of the optical pseudogap, refractive index, and lattice parameters are shown to be interrelated in these solid solution crystals.     

Exoelectron emission from solid nitrogen

Solid nitrogen was investigated by activation spectroscopy methods – thermally stimulated luminescence and thermally stimulated exoelectron emission (TSL and TSEE) in combination with luminescence analysis. TSEE from solid nitrogen pre-irradiated by an electron beam was measured and investigated for the first time. A set of peaks both in TSL and TSEE were observed. It was found that one of the peaks in the TSEE curve is caused by release of electrons in the course of the α-β phase transition of solid nitrogen. The corresponding activation energy was estimated.     

Influence of anionic substitution on phase transitions in Cu6PS5I1− x Cl x mixed crystals

Cu₆PS₅I_{1? ?} ? _x Cl _x mixed crystals were grown using chemical vapour transport. Isoabsorption studies of optical absorption edge and optical polarization measurements were performed in the temperature range 77–320?K. The influence of anionic I?→?Cl substitution on the phase transitions in Cu₆PS₅I_{1? ?} ? _x Cl _x mixed crystals is studied. Compositional dependence of the phase-transition temperatures is obtained and the x,T-diagram for Cu₆PS₅I_{1? ?} ? _x Cl _x mixed crystals is constructed.     

On Some Solutions of Relativistic Wave Equations

In this paper we present exact solutions of the Klein-Gordon and the Dirac equations in different configurations of an electromagnetic field, which are characteristic for free-electron laser-type gauges. In the case of motion of a charge scalar particle in standing wave an energy spectrum is studied. For the motion of an electron in a so-called wiggler magnetic field a spinor wave function is proved to be obtainable. An undulator field configuration with propagating wave is treated also.     

The first carborane triflates: synthesis and reactivity of 1-trifluoromethanesulfonylmethyl- and 1,2-bis(trifluoromethanesulfonylmethyl)-o-carborane

The first carborane triflates, namely, 1-trifluoromethanesulfonylmethyl-o-carborane (2) and 1,2-bis(trifluoromethanesulfonylmethyl)-o-carborane (7), were obtained in high yields in the reactions of 1-hydroxymethyl-o-carborane (1) or 1,2-bis(hydroxymethyl)-o-carborane (6) with triflic anhydride (Tf2O) in CH2Cl2 in the presence of pyridine. When an excess of pyridine is employed, 1-o-carboranylmethylpyridinium triflate (3), which retains a closo-icosahedral structure, or a pyridinium salt (4) with a zwitterionic nido-dicarbaundecaborate anion are obtained from 1, while the nido compound 8 is formed from 6. The reaction of compound 2 or 7 with excess pyridine also gave 3 or 8, respectively. Compound 2 proved to be a convenient carboranylmethylating agent which reacts with nucleophiles (e.g., potassium phthalimide, PPh3 or KCN) to give the corresponding substitution products N-[(o-carboranyl-1-yl)methyl]phthalimide (9), o-carboranylmethylphosphonium salt 10, and 1-cyanomethyl-o-carborane (11). All compounds were characterized by 1H and 11B NMR spectroscopy. The structures of compounds 4, 7 and 8 were established by X-ray analysis.