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

Landau (\Gamma,\chi)-automorphic functions on \mathbb{C}^n of magnitude \nu

We investigate the spectral theory of the invariant Landau Hamiltonian \La^\nu acting on the space ${\mathcal{F}}^\nu_{\Gamma,\chi}$ of $(\Gamma,\chi)$-automotphic functions on \C^n, for given real number $\nu>0$, lattice $\Gamma$ of \C^n and a map $\chi:\Gamma\to U(1)$ such that the triplet $(\nu,\Gamma,\chi)$ satisfies a Riemann-Dirac quantization type condition. More precisely, we show that the eigenspace {\mathcal{E}}^\nu_{\Gamma,\chi}(\lambda)=\set{f\in {\mathcal{F}}^\nu_{\Gamma,\chi}; \La^\nu f = \nu(2\lambda+n) f}; \lambda\in\C, is non trivial if and only if $\lambda=l=0,1,2, ...$. In such case, ${\mathcal{E}}^\nu_{\Gamma,\chi}(l)$ is a finite dimensional vector space whose the dimension is given explicitly. We show also that the eigenspace ${\mathcal{E}}^\nu_{\Gamma,\chi}(0)$ associated to the lowest Landau level of \La^\nu is isomorphic to the space, {\mathcal{O}}^\nu_{\Gamma,\chi}(\C^n), of holomorphic functions on \C^n satisfying g(z+\gamma) = \chi(\gamma) e^{\frac \nu 2 |\gamma|^2+\nu\scal{z,\gamma}}g(z), \eqno{(*)} that we can realize also as the null space of the differential operator $\sum\limits_{j=1}\limits^n(\frac{-\partial^2}{\partial z_j\partial \bar z_j} + \nu \bar z_j \frac{\partial}{\partial \bar z_j})$ acting on $\mathcal C^\infty$ functions on \C^n satisfying $(*)$.Comment: 20 pages. Minor corrections. Scheduled to appear in issue 8 (2008) of "Journal of Mathematical Physics

h analogue of Newton's binomial formula

In this letter, the $h$--analogue of Newton's binomial formula is obtained in the $h$--deformed quantum plane which does not have any $q$--analogue. For $h=0$, this is just the usual one as it should be. Furthermore, the binomial coefficients reduce to $\frac{n!}{(n-k)!}$ for $h=1$. \\ Some properties of the $h$--binomial coefficients are also given. \\ Finally, I hope that such results will contribute to an introduction of the $h$--analogue of the well--known functions, $h$--special functions and $h$--deformed analysis.Comment: 6 pages, latex Jounal-ref: J. Phys. A: Math. Gen. 31 (1998) L75

Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential

The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.Comment: 10 page

q-Ultraspherical polynomials for q a root of unity

Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogs of $q$-beta integrals of Ramanujan.Comment: 7 pages, LATE

The Schrodinger equation with Hulthen potential plus ring-shaped potential

We present the solutions of the Schr$\ddot{o}$dinger equation with the Hulth$\acute{e}$n potential plus ring-shape potential for $\ell\neq 0$ states within the framework of an exponential approximation of the centrifugal potential.Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional Nikiforov-Uvarov method. The normalization constant for the Hulth$\acute{e}$n potential is also computed.Comment: Typed with LateX,12 Pages, Typos correcte

Thyroseq V3 Molecular Profiling for Tailoring the Surgical Management of Hürthle Cell Neoplasms.

Hürthle cell predominant thyroid nodules often confound the diagnostic utility of fine needle aspiration biopsy (FNAB) with cytology often interpreted as a Hürthle cell lesion with an indeterminate risk of malignancy, Bethesda category (BC) III or IV. Molecular diagnostics for Hürthle cell predominant nodules has also been disappointing in further defining the risk of malignancy. We present a case of a slowly enlarging nodule within a goiter initially reported as benign on FNAB, BC II but on subsequent FNAB suspicious for a Hürthle cell neoplasm, BC IV. The patient had initially requested a diagnostic lobectomy for a definitive diagnosis despite a higher risk of malignancy based on the size of the nodule \u3e 4 cm alone. To better tailor this patient\u27s treatment plan, a newer expanded gene mutation panel, ThyroSeq® v3 that includes copy number alterations (CNAs) and was recently found to have greater positive predictive value (PPV) for identifying Hürthle cell carcinoma (HCC), was performed on the FNAB material. Molecular profiling with ThyroSeq® v3 was able to predict a greater risk of carcinoma, making a more convincing argument in favor of total thyroidectomy. Surgical pathology confirmed a Hürthle cell carcinoma with 5 foci of angioinvasion and foci of capsular invasion

Scalar, electromagnetic and Weyl perturbations of BTZ black holes: quasi normal modes

We calculate the quasinormal modes and associated frequencies of the Banados, Zanelli and Teitelboim (BTZ) non-rotating black hole. This black hole lives in 2+1-dimensions in an asymptotically anti-de Sitter spacetime. We obtain exact results for the wavefunction and quasi normal frequencies of scalar, electromagnetic and Weyl (neutrino) perturbations.Comment: Latex, 14 page

Проект ЭСПЦ по производству нержавеющих марок стали в условиях Урала производительностью 650 тыс. тонн стали в год

Реферат Выпускная квалификационная работа 131 листов, 13 рисунков, 36 источников, 2 приложения. Ключевые слова: электросталеплавильный цех, электродуговая печь, АКР, электрофильтр, МНЛЗ, блюм. Объектом исследования является ЭСПЦ производительностью 650 тыс. тонн в год нержавеющих марок стали в условия Урала. Цели исследования: выбор основного оборудования, расчет цеха и оборудования, баланса металла и шихты в цехе, социальная ответственность и экономическое обоснование строительства цеха. Работа представлена введением, 5 разделами и заключением, список использованных источников. В разделе 슫Объект исследования슻 описан проектируемый ЭСПЦ, рассмотрены основные пролеты и располагающееся в них оборудование. Во разделе 슫Расчеты и аналитика슻 представлены расчет баланса металла в цехе и шAbstract Abstract The graduation work consists of 131 pages, 13 figures, 36 sources, 2 appendices. Keywords: arc furnace plant, electric arc furnace, AOD, electrostatic precipitator, continuous casting machines, bloom. The object of study is the EAF shop with the capacity of 650 thousand tons a year of stainless steels under the conditions of the Urals. The aim of the study: choice of the basic equipment, calculation of plant and equipment, the balance of metal and charge in the plant, social responsibility and economic feasibility of the plant construction. The work includes the introduction, 5 sections and conclusion, list of references. In the section «Object of study» describe the designed EAF shop, considere the main spans and equipment located in them. In the section «Calculation a