Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups

We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a ``q-deformation'' of the Gel'fand-Kirillov conjecture which we partially prove. We propose a construction of automorphisms of certain non-commutaive rings of quotients coming from complex powers of quantum group generators; this is applied to explicit calculation of singular vectors in Verma modules over U_{q}(\gtsl_{n+1}). We finally give a definition of a $q-$connection with coefficients in a ring of skew polynomials and study the structure of quantum group modules twisted by a $q-$connection.Comment: 25 page

The Comparison of Two Calculation Methods of Billets Heating in Furnaces with the Help of Zone and FVM Methods

The comparison of two modelling methods for radiation heat exchange – finite volume and zonal methods – has been provided. The mathematical model of heating concast bars ring furnace has been created. Modelling of different heat modes of this furnace has been completed. In the result of modelling, it is shown that these methods demonstrate similar accuracy of obtained temperature values (not exceeding 50∘C). The calculation time of FVM method is greater than zonal method to 13%, because recalculations of absorption coefficients by EWBM method is needed. Keywords: radiation transfer, mathematical modeling, zonal method, discrete transfer zonal metho

View factors for surface zones

Methods of calculating view factors with different surface configurations are compared. A simple approach is proposed for estimating the error in calculating the view factors. An algorithm is formulated for selection of the method and the number of points of integration prior to the calculation. The algorithm significantly reduces the computation time by minimizing the number of integration points required, without loss of precision. © 2013 Allerton Press, Inc

An internally consistent approach to the estimation of market power and cost efficiency with an application to U.S. banking

We develop a novel unified econometric methodology for the formal examination of the market power – cost efficiency nexus. Our approach can meaningfully accommodate a mutually dependent relationship between the firm’s cost efficiency and marker power (as measured by the Lerner index) by explicitly modeling the simultaneous determination of the two in a system of nonlinear equations consisting of the firm’s cost frontier and the revenue-to-cost ratio equation derived from its stochastic revenue function. Our framework places no a priori restrictions on the sign of the dependence between the firm’s market power and efficiency as well as allows for different hierarchical orderings between the two, enabling us to discriminate between competing quiet life and efficient structure hypotheses. Among other benefits, our approach completely obviates the need for second-stage regressions of the cost efficiency estimates on the constructed market power measures which, while widely prevalent in the literature, suffer from multiple econometric problems as well as lack internal consistency/validity. We showcase our methodology by applying it to a panel of U.S. commercial banks in 1984–2007 using Bayesian MCMC methods

Simulation of the solidification of the melt in the Vanyukov furnace in the case of emergency stoppage

A mathematical model of the Vanyukov furnace, which makes it possible to predict the behavior of an object in the emergency operational mode (upon the disconnection of the oxygen supply) and develop an effective system of additional heating which damps the consequences of the emergency mode and lowers the costs for the renovation of the furnace operation, is created. It is shown how solidification upon cooling the furnace with time is simulated using the enthalpy and porosity method. The mathematical model is adopted for existing production conditions, which are weakly defined. The energy characteristics of the mode for the solidifying furnace bath, which ensures its holding for a long time in the ready state to rapid firing, are found. Thus, the problem of excessively expensive furnace firing after prolonged production stoppage is solved in the conjugated statement with a calculation of the heating system of the overbath space. © 2013 Allerton Press, Inc

Modification of Structure and Strength Properties of Permanent Joints Under Laser Beam Welding with Application of Nanopowder Modifiers

In the paper we present the results of experimental study of specially prepared nanosize metal-ceramic compositions impact upon structure, microhardness and mechanical properties of permanent joints produced by laser-beam welding of steel and titanium alloy plates

Magnetic force microscopy of epitaxial Fe2CoAl and Co2FeAl Heusler alloy films and microstructures

Research supported by RFBR grant 17-57-45024 IND-a