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

Are all U.S. credit unions alike?

This paper raises concerns about the econometric approach used in the literature to estimate credit unions’ production technologies. We show that the existing studies did not recognize heterogeneity amongst credit unions’ technologies as captured by (endogenously selected) differing output mixes. Failure to account for the above leads to biased, inconsistent estimates and potentially misleading results. The estimates are also likely to be biased due to unobserved credit union specific effects that the literature broadly ignores. To address these concerns, we develop a generalized model of endogenous switching with polychotomous choice that is able to account for fixed effects in both the technology selection and the outcome equations. We use this model to estimate returns to scale for the U.S. retail credit unions from 1994 to 2011. Unlike recent studies, we find that not all credit unions enjoy increasing returns to scale. A nonnegligible number of large institutions operate at decreasing returns to scale, indicating that they should either cut back in size or switch to a more efficient technology by re-optimizing the output mix

Mirror symmetry in two steps: A-I-B

We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A-model). The second theory is an intermediate model, which we call the I-model. The equivalence between the A-model and the I-model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T-duality. On the other hand, the I-model is closely related to the twisted Landau-Ginzburg model (the B-model) that is mirror dual to the A-model. Thus, the mirror symmetry is realized in two steps, via the I-model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I-model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Comment: 50 pages; revised versio

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

Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure