Results 61 to 70 of about 45,476 (265)

The Universal Askey-Wilson Algebra and DAHA of Type (C_1^∨,C_1)

Symmetry, Integrability and Geometry: Methods and Applications, 2013
Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $Delta_q$ of AW(3) called the universal Askey-Wilson algebra.
Paul Terwilliger
doaj   +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

The Universal Askey-Wilson Algebra

Symmetry, Integrability and Geometry: Methods and Applications, 2011
In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in ...
Paul Terwilliger
doaj   +1 more source

Factorization of colored knot polynomials at roots of unity

Physics Letters B, 2015
HOMFLY polynomials are the Wilson-loop averages in Chern–Simons theory and depend on four variables: the closed line (knot) in 3d space–time, representation R of the gauge group SU(N) and exponentiated coupling constant q.
Ya. Kononov, A. Morozov
doaj   +1 more source

Effects of nitrogen deposition on territory numbers of breeding birds. [PDF]

Conserv Biol
Abstract Deposition of atmospheric N (nitrogen) is assumed to be a major cause of biodiversity decline in Europe. To date, few studies on the direct or indirect effects of N on bird species have been conducted. Using Swiss bird count data and habitat data, we analyzed the correlation of N deposition with numbers of territories of 112 breeding bird ...
Meichtry-Stier K, Korner P, Birrer S, Knaus P.   +3 more
europepmc   +2 more sources

Design and Analysis for Digital Twin Optimization

Quality and Reliability Engineering International, EarlyView.
ABSTRACT Digital twins (DTs) provide dynamic, virtual representations of physical systems, facilitating real‐time monitoring, prediction, and optimization through the integration of sensor data, computational models, and feedback mechanisms. Despite their potential, deploying DTs in complex systems often entails substantial computational costs.
Xueru Zhang, Dennis K. J. Lin, Peiyao Liu   +2 more
wiley   +1 more source

Bivariate Bannai-Ito polynomials

, 2018
A two-variable extension of the Bannai-Ito polynomials is presented. They are obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is obtained. These
Lemay, Jean-Michel, Vinet, Luc
core   +1 more source

Double Affine Hecke Algebras of Rank 1 and the Z_3-Symmetric Askey-Wilson Relations

Symmetry, Integrability and Geometry: Methods and Applications, 2010
We consider the double affine Hecke algebra H=H(k_0,k_1,k_0^v,k_1^v;q) associated with the root system (C_1^v,C_1). We display three elements x, y, z in H that satisfy essentially the Z_3-symmetric Askey-Wilson relations.
Paul Terwilliger, Tatsuro Ito
doaj   +1 more source

Microstructure Development in a New Generation S1300‐Type Ultrahigh‐Strength Structural Steel on Tempering

steel research international, EarlyView.
Here, the microstructure evolution of a new generation ultrahigh‐strength S1300‐type structural steel has been investigated for direct‐quench and tempering route. Various stages of tempering are elucidated by thorough characterization, and a new strain‐size parameter of martensite is proposed to have a correlation with hardness, which will be useful in
Buddhadev Jana, Radhakanta Rana
wiley   +1 more source

Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz

Nuclear Physics B, 2019
An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in the form of ...
Pascal Baseilhac, Rodrigo A. Pimenta
doaj   +1 more source