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In this paper, we investigate some properties of Chebyshev polynomials arising from non-linear differential equations. From our investigation, we derive some new and interesting identities on Chebyshev polynomials.
In this paper we present a method for computing the total probability corresponding to the processes of fermion pair production in dipole magnetic field and external Coulomb field in a de Sitter geometry. For that we rewrite the functions…
Pascal's triangle is widely used as a pedagogical tool to explain the "first-order" multiplet patterns that arise in the spectra of $I_N S$ coupled spin-1/2 systems in magnetic resonance. Various other combinatorial structures, which may be…
Carlson, Carone and Lebed have derived the Feynman rules for a consistent formulation of noncommutative QCD. The results they obtained were used to constrain the noncommutativity parameter in Lorentz violating noncommutative field theories.…
Quantum--mechanical multiple--well oscillators exhibit curious complex eigenvalues that resemble resonances in models with continuum spectra. We discuss a method for the accurate calculation of their real and imaginary parts.
We analyze a class of parametrized Random Matrix models, introduced by Rosenzweig and Porter, which is expected to describe the energy level statistics of quantum systems whose classical dynamics varies from regular to chaotic as a function…
Emission process of a charged particle propagating in a medium with a curved magnetic field is considered. This mechanism combines features of conventional Cherenkov and curvature emission. Thus, presence of a medium with the index of…
Let $s_{ij}$ represent a tranposition in $S_n$. A polynomial $P$ in $\mathbb{Q}[X_n]$ is said to be $m$-quasiinvariant with respect to $S_n$ if $(x_i-x_j)^{2m+1}$ divides $(1-s_{ij})P$ for all $1 \leq i, j \leq n$. We call the ring…
We find a new approach to computing the remainder of a polynomial modulo $x^n-1$; such a computation is called modular enumeration. Given a polynomial with coefficients from a commutative $\mathbb{Q}$-algebra, our first main result…
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The asymptotic…
This paper proposes a quantum circuit for computing the mean value from a given set of quantum states. The circuit consults a Quantum Random Access Memory to get the values of the set, and by using superposition, interference and…
We propose a generalization of Carmichael numbers, where the multiplicative group $\mathbb G_\mathrm{m} = \mathrm{GL}(1)$ is replaced by $\mathrm{GL}(m)$ for $m\geq 2$. We prove basic properties of these families of numbers and give some…
The connection of orthogonal polynomials on the unit circle (OPUC) to the defocusing Ablowitz-Ladik integrable system involves the definition of a Poisson structure on the space of Verblunsky coefficients. In this paper, we compute the…
Closed-form expressions for the singular-potential integrals <m| x^-alpha |n> are obtained with respect to the Gol'dman and Krivchenkov eigenfunctions for the singular potential V(x) = B x^2 + A/x^2, B > 0, A >= 0. These formulas are…
We investigate Chebyshev polynomials corresponding to Jacobi weights and determine monotonicity properties of their related Widom factors. This complements work by Bernstein from 1930-31 where the asymptotical behavior of the related…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
In an effort to achieve our aims (getting larger quantum system) in the recent reformulation of quantum mechanics without potential function [1-5], we obtained a new quantum system associated with Meixner Pollaczek Orthogonal polynomial…
In this paper, we consider Poisson-Charlier and poly-Cauchy mixed type polynomials and give various identities of those polynomials which are derived from umbral calculus.
We derive a formula for the weight system of the multivariable Alexander polynomial using determinants, show that it obeys known relations, and satisfies some of the same relations as the single variable polynomial.
A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation…