Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type.Comment: LaTeX, 19 pages, (late submission to arXiv.org

Mathematical Structure of Relativistic Coulomb Integrals

We show that the diagonal matrix elements $,$ where $O$ $={1,\beta,i\mathbf{\alpha n}\beta}$ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as difference analogs of the radial wave functions. Such structure provides an independent way of obtaining closed forms of these matrix elements by elementary methods of the theory of difference equations without explicit evaluation of the integrals. Three-term recurrence relations for each of these expectation values are derived as a by-product. Transformation formulas for the corresponding generalized hypergeometric series are discussed.Comment: 13 pages, no figure

Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices

We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials corresponding to Lie superlagebras. We also describe the real forms of gl(N), quasi-finite modules over gl(N), and conditions for unitarity of the quasi-finite modules. Analogs of tensors over gl(N) are also introduced.Comment: 25 pages, LaTe

Features of Dynamics of Antivibration Mounts with Inertial Hydraulic Converter Subjected to Vibro-Impact Loading

Antivibration mounts with inertial hydraulic converter are widely used to protect a variety of technical systems from shock and vibration. As it follows from existing literature, models of such a mounts on the basis of mechanical and mechanical-electrical analogies instead of real hydro-mechanical system are usually used to study their dynamic properties and design. These models are not able to describe fluid dynamics in hydraulic mount, and are not suitable to study rapidly changing processes, which is especially required for effective application of the mounts at vibro-shock loading. In this work, a model of inertial hydraulic converter, which is a system of two hydraulic cylinders of unilateral operating principle, connected by a rigid hydraulic tube, is described. Dynamics of fluid in hydraulic converter is described by the Navier-Stokes equations for a compressible fluid and the equation of state of the fluid in assumption of its isentropic motion. The results of numerical simulation of antivibration mount dynamics at shock loading by using finite element package ANSYS/LS-DYNA are presented. It is found out that increasing the length of the tube and reducing the tube diameter lead to an increase in the transmitted dynamic force