Results 21 to 30 of about 73,008 (249)

On an Inequality for Legendre Polynomials

Mathematics, 2020
This paper is concerned with the orthogonal polynomials. Upper and lower bounds of Legendre polynomials are obtained. Furthermore, entropies associated with discrete probability distributions is a topic considered in this paper.
Florin Sofonea, Ioan Ţincu
doaj   +1 more source

Multi-indexed (q-)Racah Polynomials [PDF]

, 2012
As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials.
Andrews G E, Bannai E, Chakrabarti R, Darboux G, Fernández D J, Gendenshtein L E, Gladwell G M L, Grandati Y, Gómez-Ullate D, Ho C-L, Ho C-L, Ismail M E H, Koekoek R Swarttouw R F, Krein M G, Odake S, Odake S, Odake S, Parthasarathy P R, Quesne C, Quesne C, Quesne C, Ryu Sasaki, Sasaki R, Satoru Odake, Vinet L Zhedanov A   +24 more
core   +4 more sources

Joint power control and user grouping mechanism for efficient uplink non‐orthogonal multiple access‐based 5G communication: Utilising the Lèvy‐flight firefly algorithm

IET Networks, EarlyView., 2023
We utilise a metaheuristic optimisation method, inspired by nature, called the Lévy‐flight firefly algorithm (LFA), to tackle the power regulation and user grouping in the NOMA systems. Abstract The non‐orthogonal multiple access strategies have shown promise to boost fifth generation and sixth generation wireless networks' spectral efficiency and ...
Zaid Albataineh, Khaled F. Hayajneh, Haythem Bany Salameh, Raed Al Athamneh, Yaser Jararweh   +4 more
wiley   +1 more source

Trigonometric Embeddings in Polynomial Extended Mode Decomposition—Experimental Application to an Inverted Pendulum

Mathematics, 2021
The extended dynamic mode decomposition algorithm is a tool for accurately approximating the point spectrum of the Koopman operator. This algorithm provides an approximate linear expansion of non-linear discrete-time systems, which can be useful for ...
Camilo Garcia-Tenorio, Gilles Delansnay, Eduardo Mojica-Nava, Alain Vande Wouwer   +3 more
doaj   +1 more source

Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm [PDF]

, 2015
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems.
Gendenshtein L. E., Kurokawa N., Ryu Sasaki, Satoru Odake, Shintani T.   +4 more
core   +3 more sources

A Survey on q-Polynomials and their Orthogonality Properties [PDF]

, 2010
In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson polynomials (AW ...
Alfaro, Alfaro, Atakishiyev, Atkinson, Boas, Chihara, Costas-Santos, Costas-Santos, Gasper, J.F. Sánchez-Lara, Koekoek, Kuijlaars, Kwon, Marcellán, Moreno, Moreno, Moreno, Pérez, R.S. Costas-Santos, Spiridonov, Vilenkin, Álvarez de Morales   +21 more
core   +1 more source

On the analytic form of the discrete Kramer sampling theorem

International Journal of Mathematics and Mathematical Sciences, 2001
The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems.
Antonio G. García, Miguel A. Hernández-Medina, María J. Muñoz-Bouzo   +2 more
doaj   +1 more source

Variations of Stieltjes-Wigert and q-Laguerre polynomials and their recurrence coefficients

, 2014
We look at some extensions of the Stieltjes-Wigert weight functions. First we replace the variable x by x^2 in a family of weight functions given by Askey in 1989 and we show that the recurrence coefficients of the corresponding orthogonal polynomials ...
Boelen, Lies, Van Assche, Walter
core   +1 more source

Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts [PDF]

, 2017
In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented.
Odake, Satoru
core   +3 more sources

Generalized squeezed-coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality

, 2012
A set of generalized squeezed-coherent states for the finite u(2) oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the su(2) generators.
Alexei Zhedanov, Atakishiyev N M, Luc Vinet, Niederer U, Niederer U, Vincent X Genest, Vinet L, Wang X, Wigner E P   +8 more
core   +1 more source