Results 41 to 50 of about 79,949 (254)

A NEW CHARACTERIZATION OF 𝑞-CHEBYSHEV POLYNOMIALS OF THE SECOND KIND

Проблемы анализа
In this work, we introduce the notion of $\cal{U}_{(q, \mu)}$-classical orthogonal polynomials, where $\cal{U}_{(q, \mu)}$ is the degree raising shift operator defined by $\cal{U}_{(q, \mu)}$ $:= x(xH_q + q^{-1}I_{\cal{P}}) + \mu H_q$, where $\mu$ is a
S. Jbeli
doaj   +1 more source

Parameter Derivatives of the Jacobi Polynomials with Three Variables on the Simplex

MATEC Web of Conferences, 2016
In this paper, an attempt has been made to derive parameter derivatives of Jacobi polynomials with three variables on the simplex. They are obtained via parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x) with respect to their parameters.
Aktaş Rabia
doaj   +1 more source

Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

Mathematics, 2018
This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim, Dae San Kim, Jongkyum Kwon, Dmitry V. Dolgy   +3 more
doaj   +1 more source

Some New Connection Relations Related to Classical Orthogonal Polynomials

Journal of Mathematics, 2020
In this paper, we deal with a problem of positivity of linear functionals in the linear space ℙ of polynomials in one variable with complex coefficients.
Wathek Chammam, Wasim Ul-Haq
doaj   +1 more source

On Spectral Vectorial Differential Equation of Generalized Hermite Polynomials

Axioms, 2022
In this paper, we first give some results on monic generalized Hermite polynomials (GHP) {Hn(μ)(x)}n≥0, orthogonal with respect to the positive weight |x|2μe−x2,μ>−12,x∈R, which will lead to the formulation of the second-order spectralvectorial ...
Mohamed Jalel Atia, Majed Benabdallah
doaj   +1 more source

Topological Point Defects in SmC* Liquid Crystals Under Mechanical Disturbance

Advanced Materials Interfaces, EarlyView.
Tangetial air jet shear inducess island formation and nucleates topological point defects in uniform SmC films. Island bounded by edge dislocation loops shrink and transform into isolated point defects under continued shear. Mechanical perturbatio provides a controllable route for defect engineering in smectric liquid crystal thin films.
Gunganist Kongklad, Vandana Molahalli, Apichart Pattanaporkratana, Nattaporn Chattham   +3 more
wiley   +1 more source

New fractional-order shifted Gegenbauer moments for image analysis and recognition

Journal of Advanced Research, 2020
Orthogonal moments are used to represent digital images with minimum redundancy. Orthogonal moments with fractional-orders show better capabilities in digital image analysis than integer-order moments.
Khalid M. Hosny, Mohamed M. Darwish, Mohamed Meselhy Eltoukhy   +2 more
doaj   +1 more source

Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials

, 2004
The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation parameter) instead of an ...
Andrews G E, Awata H, Bordner A J, Calogero F, Calogero F, Calogero F, Calogero F, Chihara T S, Corrigan E, Jing S Yang W, Khastgir S P, Koekoek R Swarttouw R F, M Ruijsenaars S N, Macdonald I G, Mimachi K, Moser J, Moser J, Odake S, R Sasaki, Ragnisco O, S Odake, Sasaki R, Shiraishi J, Stanley R P, Sutherland B, Szegö G, van Diejen J F, van Diejen J F, van Diejen J F, van Diejen J F   +29 more
core   +3 more sources

Hard‐Magnetic Soft Millirobots in Underactuated Systems

Advanced Robotics Research, EarlyView.
This review provides a comprehensive overview of hard‐magnetic soft millirobots in underactuated systems. It examines key advances in structural design, physics‐informed modeling, and control strategies, while highlighting the interplay among these domains.
Qiong Wang, Zixuan Zhang, Bingyan Li, Junkai Wang, Hongcheng Gu   +4 more
wiley   +1 more source

Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices

, 2005
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.
A. F. Nikiforov, A. F. Nikiforov, A. Mingarelli, A. N. Sergeev, B. L. Feigin, D. A. Leites, I. G. Macdonald, J. Dixmier, J. Dixmier, L. Littlejohn, M. Vasiliev, N. Ja. Vilenkin, S. Leng, S. Montgomery, V. Derkach, V. Kac   +15 more
core   +1 more source