Electronic structure of copper halides CuI and CuCl: A comparative X-Ray photoelectron and absorption spectroscopy study

The energy distributions of the occupied and unoccupied electronic states for copper halides CuCl and CuI have been investigated using X-ray photoemission and absorption spectroscopy with a highenergy resolution on the equipment of the Russian-German beamline for outlet and monochromatization of synchrotron radiation from the electron storage ring BESSY II. A quasi-molecular analysis of the obtained experimental spectra has revealed that there is a fundamental similarity of the energy structures of the valence band and the conduction band of copper halides CuX (X = Cl, I) due to the identical atomic structure of the studied compounds. The differences in the positions of individual energy subbands in the valence band and the conduction band of CuX and in their intensities in the spectra are associated with different degrees of hybridization of the Cu 3d, 4s and X(n + 1)s, np valence states, as well as with different sizes of structural units (CuCl₄ and CuI₄ quasi-molecules) of the studied crystals.     

Experimental study of the amplification (intensification) of light in CO2+N2+He (H2O) mixtures during expansion in a supersonic nozzle

The results of an experimental investigation on the amplification of light by carbon dioxide molecules in various mixtures during the expansion of the gas through a supersonic nozzle at the end of a shock tube are presented. The experimental results are compared with theory, and satisfactory agreement is obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 18–24, July–August, 1973.     

Calculation of the characteristics of a gas-dynamic laser

The dependence of the radiated power on the characteristics of optical cavities in the case of flow systems has been investigated in a number of papers [1–3], in which it is assumed that population inversion of the laser levels is obtained until entry into the cavity. The operation of a cavity is analyzed in [1] in the geometric-optical approximation with allowance for vibrational relaxation in the gas flow. A simplified system of relaxation equations is solved under steady-state lasing conditions and an expression derived for the laser output power on the assumption of constant temperature, density, and flow speed. The vibrational relaxation processes in the cavity itself are ignored in [2, 3]. It is shown in those studies that the solution has a singularity at the cavity input within the context of the model used. In the present article the performance characteristics of a CO₂-N₂-He gas-dynamic laser with a plane cavity are calculated. A set of equations describing the processes in the cavity is analyzed and solved numerically. Population inversion of the CO₂ laser levels is created by pre-expansion of the given mixture through a flat hyperbolic nozzle. The dependence of the output power on the reflectivities of the mirrors, the cavity length, the pressure, and the composition of the active gas medium is determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi FiziM, No. 5, pp. 33–40, September–October, 1972.     

Hochschild cohomology for self-injective algebras of tree class D n . I

The minimal projective bimodule resolution is constructed for algebras in a family of self-injective algebras of finite representation type with tree class D_n. Using this resolution, we calculate the dimensions of the Hochschild cohomology groups for the algebras under consideration. The described resolution is periodic, and thus the Hochschild cohomology of these algebras is periodic as well. Bibliography: 11 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 121–182.     

A combinatorial proof of Euler-Fermat’s theorem on the representation of the primes p=8k+3 by the quadratic form x2+2y2

An elementary and extremely short proof of the theorem on the representation of the primes p = 8k + 3 by the quadratic form x₂ + 2y₂ with integers x and y. Bibliography: 1 title. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 155–157.     

Critical RF losses in fine particles of La1−xAgyMnO3+δ: Prospects for temperature-controlled hyperthermia

Temperature and frequency dependencies of the real (χ′) and imaginary (χ″) parts of the dynamic magnetic susceptibility were studied experimentally in fine particles of La-Ag manganites prepared by various methods. The samples under study have the Curie points in the range T_C=42-48 °C, which is a medical hyperthermia range of interest. When approaching T_C from below, a critical peak of χ″ was revealed, followed by a steep drop while passing to the paramagnetic phase. The experiments on the magnetic radio-frequency (RF) heating of the manganite aqueous suspensions demonstrated good autostabilization of the temperature near T_C. Peculiar instability is found in the heating kinetics, caused by the observed critical behavior of the RF losses. The prospects of the La-Ag manganites as candidates for application in the temperature-controlled hyperthermia are discussed.     

Cohomology of Algebras of Dihedral Type. III: the Family D\left( {2{\mathcal{A}}} \right)

For algebras of dihedral Type that form the family (from K. Erdmann's list), the Yoneda algebras are described in terms of quivers with relations. Bibliography: 8 titles.