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

System for detecting and tracking moving objects

This paper considers the construction of a system for detecting and tracking moving objects. It is proposed to pre-process the frame using digital image stabilization algorithms based on optical flow. To detectobjects, it is supposed to use the longest optical flow vectors formed after stabilization, and to implement tracking using several classical algorithms using a prefetch mechanism built on classification neural networks

A new basis for eigenmodes on the Sphere

The usual spherical harmonics $Y_{\ell m}$ form a basis of the vector space ${\cal V} ^{\ell}$ (of dimension $2\ell+1$) of the eigenfunctions of the Laplacian on the sphere, with eigenvalue $\lambda_{\ell} = -\ell ~(\ell +1)$. Here we show the existence of a different basis $\Phi ^{\ell}_j$ for ${\cal V} ^{\ell}$, where $\Phi ^{\ell}_j(X) \equiv (X \cdot N_j)^{\ell}$, the $\ell ^{th}$ power of the scalar product of the current point with a specific null vector $N_j$. We give explicitly the transformation properties between the two bases. The simplicity of calculations in the new basis allows easy manipulations of the harmonic functions. In particular, we express the transformation rules for the new basis, under any isometry of the sphere. The development of the usual harmonics $Y_{\ell m}$ into thee new basis (and back) allows to derive new properties for the $Y_{\ell m}$. In particular, this leads to a new relation for the $Y_{\ell m}$, which is a finite version of the well known integral representation formula. It provides also new development formulae for the Legendre polynomials and for the special Legendre functions.Comment: 6 pages, no figure; new version: shorter demonstrations; new references; as will appear in Journal of Physics A. Journal of Physics A, in pres

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

Motion of vortices in ferromagnetic spin-1 BEC

The paper investigates dynamics of nonsingular vortices in a ferromagnetic spin-1 BEC, where spin and mass superfluidity coexist in the presence of uniaxial anisotropy (linear and quadratic Zeeman effect). The analysis is based on hydrodynamics following from the Gross-Pitaevskii theory. Cores of nonsingular vortices are skyrmions with charge, which is tuned by uniaxial anisotropy and can have any fractal value between 0 and 1. There are circulations of mass and spin currents around these vortices. The results are compared with the equation of vortex motion derived earlier in the Landau-Lifshitz-Gilbert theory for magnetic vortices in easy-plane ferromagnetic insulators. In the both cases the transverse gyrotropic force (analog of the Magnus force in superfluid and classical hydrodynamics) is proportional to the charge of skyrmions in vortex cores.Comment: 19 pages, 2 figures, to be published in the special issue of Fizika Nizkikh Temperatur dedicated to A.M.Kosevich. arXiv admin note: substantial text overlap with arXiv:1801.0109

Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method

For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained for a number of diatomic molecules and the results are compared with the findings of the super-symmetry, the hypervirial perturbation, the Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of Physics A: Mathematical and Genera

AC Conductance in Dense Array of the Ge0.7_{0.7}Si0.3_{0.3} Quantum Dots in Si

Complex AC-conductance, $\sigma^{AC}$, in the systems with dense Ge$_{0.7}$Si$_{0.3}$ quantum dot (QD) arrays in Si has been determined from simultaneous measurements of attenuation, $\Delta\Gamma=\Gamma(H)-\Gamma(0)$, and velocity, $\Delta V /V=(V(H)-V(0)) / V(0)$, of surface acoustic waves (SAW) with frequencies $f$ = 30-300 MHz as functions of transverse magnetic field $H \leq$ 18 T in the temperature range $T$ = 1-20 K. It has been shown that in the sample with dopant (B) concentration 8.2$\times 10^{11}$ cm$^{-2}$ at temperatures $T \leq$4 K the AC conductivity is dominated by hopping between states localized in different QDs. The observed power-law temperature dependence, $\sigma_1(H=0)\propto T^{2.4}$, and weak frequency dependence, $\sigma_1(H=0)\propto \omega^0$, of the AC conductivity are consistent with predictions of the two-site model for AC hopping conductivity for the case of $\omega \tau_0 \gg$1, where $\omega=2\pi f$ is the SAW angular frequency and $\tau_0$ is the typical population relaxation time. At $T >$ 7 K the AC conductivity is due to thermal activation of the carriers (holes) to the mobility edge. In intermediate temperature region 4$< T<$ 7 K, where AC conductivity is due to a combination of hops between QDs and diffusion on the mobility edge, one succeeded to separate both contributions. Temperature dependence of hopping contribution to the conductivity above $T^*\sim$ 4.5 K saturates, evidencing crossover to the regime where $\omega \tau_0 <$1. From crossover condition, $\omega \tau_0(T^*)$ = 1, the typical value, $\tau_0$, of the relaxation time has been determined.Comment: revtex, 3 pages, 6 figure

Overlap integral for quantum skyrmions

We made use a simplified form for the quantum skyrmion wave function based on the spin coherent states to obtain the analytical expression for appropriate overlap integral.Comment: 5 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