Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements

We present new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical examples show stable reconstruction of the dielectric permittivity function $\varepsilon$ for random noise level using these measurements

Determinants of elliptic hypergeometric integrals

We start from an interpretation of the BC_(2)-symmetric “Type I” (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation and then generalize this construction to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding formulas for the elliptic beta integral and symmetry transformation in a new way, by proving that both sides satisfy the same difference equations and that these difference equations satisfy a needed Galois-theoretic condition ensuring the uniqueness of the simultaneous solution

Molecular taxonomic study of Trichinella spp. from mammals of Russian Arctic and subarctic areas

Analysis of taxonomic affiliation of Trichinella species circulating in the Chukotka Autonomous Region and some subarctic areas of the Russian Federation showed that the representatives of T. spiralis and the Arctic trichinellas - T. nativa (genotype T2) and Trichinella sp. (genotype T6) can be found there. The partial sequences of Coxb (704 bp) of these Arctic Trichinella spp. from Russia differ from Coxb sequences of those genotypes (T2 and T6) deposited in NCBI GenBank (1-3 bp). The cultivated larvae of Trichinella sp., which were established from muscular tissue sample of stray cat (shot on the fur farm in Chukotka peninslula) differ at molecular level (Coxb) even more significantly; 21-24 bp difference between Trichinella sp. and T. nativa and 46-47 bp difference between the same isolate and T. spiralis were recorded

A "missing" family of classical orthogonal polynomials

We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$. We also show that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for $q=-1$.Comment: 20 page

Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity

Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schr\"odinger equation provide bases of representations of the $q$-deformed Heisenberg-Weyl algebra. When the parameter $q$ is a root of unity the functional form of the potentials can be found explicitly. The general $q^3=1$ and the particular $q^4=1$ potentials are given by the equianharmonic and (pseudo)lemniscatic Weierstrass functions respectively.Comment: 15 pp, Latex, to appear in Lett.Math.Phy

Properties of generalized univariate hypergeometric functions

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E_7 (elliptic, hyperbolic) and of type E_6 (trigonometric) using the appropriate versions of the Nassrallah-Rahman beta integral, and we derive contiguous relations using fundamental addition formulas for theta and sine functions. The top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with Ruijsenaars' relativistic hypergeometric function and the Askey-Wilson function, respectively. We show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions. We also describe an intimate connection between the hyperbolic and trigonometric theory, which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions.Comment: 46 page

Comparative analysis of the old and new versions of GOST 7.32

On July 1, 2018, a new edition of GOST 7.32–2017 «The Report on Scientific Research. Structure and rules of registration». Modern possibilities of document circulation in electronic and paper form and updated requirements for design are presented in this version. In this article, the distinctive features of the old and new versions of the standard are presentedС 1 июля 2018 года в силу вступает новая редакция ГОСТ 7.32–2017 «Отчет о научно-исследовательской работе. Структура и правила оформления». В указанной версии учтены современные возможности документооборота в электронном и бумажном виде, актуализированы и дополнены существующие требования к оформлению. В настоящей работе приведены отличительные черты старой и новой редакций стандарт

Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework

In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined by using techniques of supersymmetric quantum mechanics combined with shape invariance under parameter scaling. The resulting supersymmetric partner Hamiltonians correspond to different masses and frequencies. The exponential spectrum is proved to reduce to a previously found quadratic spectrum whenever one of the parameters $\alpha$, $\beta$ vanishes, in which case shape invariance under parameter translation occurs. In the special case where $\alpha = \beta \ne 0$, the oscillator Hamiltonian is shown to coincide with that of the q-deformed oscillator with $q > 1$ and its eigenvectors are therefore $n$-$q$-boson states. In the general case where $0 \ne \alpha \ne \beta \ne 0$, the eigenvectors are constructed as linear combinations of $n$-$q$-boson states by resorting to a Bargmann representation of the latter and to $q$-differential calculus. They are finally expressed in terms of a $q$-exponential and little $q$-Jacobi polynomials.Comment: LaTeX, 24 pages, no figure, minor changes, additional references, final version to be published in JP

Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index

We provide the geometrical meaning of the ${\cal N}=4$ superconformal index. With this interpretation, the ${\cal N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the localization method in TQFT to compute the deformed partition function since the deformed action can be written as a $\delta_\epsilon$-exact form. The critical points of the deformed action turn out to be the space of flat connections which are, in fact, zero modes of the gauge field. The one-loop evaluation over the space of flat connections reduces to the matrix integral by which the ${\cal N}=4$ superconformal index is expressed.Comment: 42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major revision, conclusions essentially unchanged, v5 published versio

Methods for removal of unwanted signals from gravity time-series : comparison using linear techniques complemented with analysis of system dynamics

We thanks the participants of the 35th General Assembly of the European Seismological Commission for comments on preliminary results. The authors are grateful to all IGETS contributors, particularly to the station operators and to ISDC/GFZ-Potsdam for providing the original gravity data used in this study. We also thank the developers of ATLANTIDA3.1 and UTide. Part of this work was performed using the ICSMB High Performance Computing Cluster, University of Aberdeen. We also thanks M. Thiel and A. Moura for reviewing a preliminary version and making comments on the methods section and M.A. Ara´ujo for comments on Lyapunov exponents. Funding: A. Valencio is supported by CNPq, Brazil [206246/2014-5]; and received a travel grant from the School of Natural and Computing Sciences, University of Aberdeen [PO2073498], for a presentation including preliminary results.Peer reviewedPostprintPublisher PD