Numerical values of the real-number factorial in the equation of elution adsorption dynamics

It is proposed to use the equation of elution adsorption dynamics in the discrete model of an equilibrium adsorption layer with a continuous length coordinate. An algorithm for calculating the real-number factorial has been substantiated, and it is shown that the integral obtained is identical to the gamma-function known in mathematics. The properties of the equation proposed were analyzed.     

Structure and lattice distortions of orthorhombic crystals with 3d ions

Formation of the orthorhombic phase of perovskite crystals with 3d elements has been considered and models of the crystal structures of LaMnO₃, LaTiO₃, YTiO₃, LaVO₃, and YVO₃ have been constructed. A generalization of the results of previous studies has been performed with allowance for the effect of T _2g distortions. An analysis of local symmetrized distortions has shown that the structure of compounds with Ti³⁺ and V³⁺ ions is determined by the “rotational” distortions of the T _1g type (Q _x , Q _y , Q _z ); the T _2g distortions are only secondary. At the same time, in LaMnO₃ of special importance are Jahn-Teller E _g distortions. All the crystals examined exhibit a strong coupling between the lattice and electronic degrees of freedom, which manifests itself in strong vibronic effects. In particular, the terms of the vibronic Hamiltonian that are quadratic in Q _x , Q _y , and Q _z determine the orbital structure of t _2g compounds.     

Determination of phosphate concentration in boiler water using conductivity measurements

The impossibility of unambiguously estimating phosphate concentration by measuring boiler-water conductivity in a high-pressure drum boiler (p _b = 13.8 MPa) is shown. Mathematical models of ion equilibria in boiler water, which allow one to determine the concentration of phosphates and other ion admixtures from the measurement data obtained with the use of standard (conductormeters and pH-meters) in cooled samples of feedwater and boiler water, are described.     

Unit for determining the cross-sectional area of threads,fiber tows,and samples of unidirectional plastic material

An experimental unit for determining the cross-sectional area and stresses of unidirectional plastic materials is created. With the use of the unit, it is possible to precisely specify the physico-mechanical characteristics of composite materials before destruction.     

Electric field distribution at the electrode edge during surface discharge

The distribution of the electric field at the electrode edge near a dielectric surface in a gas has been calculated. The computational program was based on the finite-element method and took into account the field of electric charges, which are accumulated at the barrier surface during the development of the surface discharge from the electrode edge under the action of an applied high voltage. The aim of this study was to justify the experimental results obtained previously [1], which showed that the surface microdischarge channel occurs at a distance of 0.6–1.5 mm above the barrier surface. Calculations showed that the position of the microdischarge channel relative to the barrier surface depends on the density of the charge accumulated on this surface during the discharge and on the character of the charge distribution.     

The FLINT setup for studying cumulative processes with photon production

A setup is developed at the Institute for Theoretical and Experimental Physics for studying cumulative processes in hA and AA interactions with photon and π ⁰-meson production in the central region of rapidities at high transverse momenta. Lead glass calorimeters and a charged particle rejection system are the main components of the setup. A fast trigger for a high-energy cumulative particle, based on detection of Cherenkov radiation in the lead glasses, is realized in the setup.     

About the Newton iteration for spectral factorization

It is shown, that Theorem 1.2 of Willems (Operators, Systems and Linear Algebra (Kaiserslautern, 1997), European Consort. Math. Indust., Jeubner, Stuggart, 1997, pp. 214–223), is analog of the outcomes of the statement 5 (Aliev and Lorin, Systems Contr. Lett. 21 (1993) 485–491).