Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles

Translated from Matematicheskie Zametki, Vol. 49, No. 5, pp. 37–44, May, 1991.     

An implicit characteristic-flux-averaging method for the euler equations for real gases

A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.     

Calculation of the Radiating Characteristics of a Thermodynamically Nonuniform Gas Medium

Passive methods of remote analysis of waste gases of industrial enterprises and aircrafts engines and gases ejected in eruptions of volcanos, in fires, and in other processes disturbing the atmosphere are now of limited utility because of the lack of well-developed mathematical techniques for solving the inverse problems of gas analysis. However, the advantage of these methods is obvious, since the equipment is limited to a receiving device and the gas medium serves as a radiator. At the same time, in modern techniques, the interpretation of measurements of emissivities of gases is performed using a phenomenological approach such that experimental data on radiation characteristics of various objects are approximated by simple polynomial relations whose coefficients are determined by minimization methods. This approach does not allow one to investigate the mechanism of the processes occurring in a radiating medium and gives no way of solving the inverse problem of monitoring the composition and thermodynamic parameters of a medium which disturbs the atmosphere by thermal effects. In elaborating theoretical methods of gas analysis, the elaboration of the direct problem of calculation of radiating characteristics of gases is of importance, since it is not clear how the emissivity of a gas medium depends on its thermodynamic parameters. This paper is devoted to the above problem. Here, the error is estimated that arises in modeling a nonuniform gas medium with an actual temperature distribution, which linearly depends on coordinate, by a uniform gas layer. It is shown that the difference between the radiation intensities calculated for uniform and nonuniform media can be significant in the practically important case where the recording device is in a zone of normal temperatures. This implies that the error of reconstruction of the spectroscopic and molecular parameters of gaseous compounds from high-temperature measurements of the radiating and absorbing characteristics should take into account the thermodynamic nonuniformity of the medium.     

New Heat-Resistant Polyimidates Derived from Bisphenols and Mono- and Dicarboxylic Acid Imidoyl Chlorides

New polyimidates were prepared from bisphenols and mono- and dicarboxylic acid imidoyl chlorides. The structures of the polymers were determined, and their physicochemical, chemical, and thermal properties were studied. The possibility of preparing film and compression materials with good mechanical characteristics from these polymers was examined.     

Monomial ideals

In this paper, we study the numeric characteristics (the Hilbert function and graded Betti numbers) of monomial ideals in the polynomial ring and in the exterior algebra. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 30, Algebra, 2005.     

Diffusion,solubility, and electrical properties of scandium and praseodymium in silicon

An integrated study of diffusion, solubility, and electrical properties of scandium and praseodymium in silicon annealed in various media and temperature ranges (1100–1280 °C) was performed for the first time. The tracer technique, autoradiography, measurements of isothermic capacity and current relaxation, conductivity, and the Hall effect were used for the investigations. The diffusion parameters, solubility, and an acceptor character of scandium and praseodymium impurities in silicon were determined. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 75–77, January, 2007.