Results 41 to 50 of about 2,040 (118)

Double Affine Hecke Algebras of Rank 1 and the $Z_3$-Symmetric Askey-Wilson Relations [PDF]

, 2010
We consider the double affine Hecke algebra $H=H(k_0,k_1,k^\vee_0,k^\vee_1;q)$ associated with the root system $(C^\vee_1,C_1)$. We display three elements $x$, $y$, $z$ in $H$ that satisfy essentially the $Z_3$-symmetric Askey-Wilson relations. We obtain
Ito, Tatsuro, Terwilliger, Paul
core   +2 more sources

Some details of proofs of theorems related to the quantum dynamical Yang‐Baxter equation

International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 12, Page 793-806, 2000., 2000
This paper of tutorial nature gives some further details of proofs of some theorems related to the quantum dynamical Yang‐Baxter equation. This mainly expands proofs given in “Lectures on the dynamical Yang‐Baxter equation” by Etingof and Schiffmann, math.QA/9908064.
Tom H. Koornwinder
wiley   +1 more source

Differential representations of dynamical oscillator symmetries in discrete Hilbert space

Discrete Dynamics in Nature and Society, Volume 5, Issue 2, Page 97-106, 2000., 2000
As a very important example for dynamical symmetries in the context of q‐generalized quantum mechanics the algebra aa† − q−2a†a = 1 is investigated. It represents the oscillator symmetry SUq(1, 1) and is regarded as a commutation phenomenon of the q‐Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert ...
Andreas Ruffing
wiley   +1 more source

Wavelet transforms in generalized Fock spaces

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 657-672, 1997., 1996
A generalized Fock space is introduced as it was developed by Schmeelk [1‐5], also Schmeelk and Takači [6‐8]. The wavelet transform is then extended to this generalized Fock space. Since each component of a generalized Fock functional is a generalized function, the wavelet transform acts upon the individual entry much the same as was developed by ...
John Schmeelk, Arpad Takači
wiley   +1 more source

Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications

Symmetry, Integrability and Geometry: Methods and Applications, 2009
A unified approach is given to kernel functions which intertwine Ruijsenaars difference operators of type A and of type BC. As an application of the trigonometric cases, new explicit formulas for Koornwinder polynomials attached to single columns and ...
Yasushi Komori, Masatoshi Noumi, Jun'ichi Shiraishi   +2 more
doaj   +1 more source

On differential equations for Sobolev-type Laguerre polynomials

, 1998
We obtain all spectral type differential equations satisfied by the Sobolev-type Laguerre polynomials. This generalizes the results found in 1990 by the first and second author in the case of the generalized Laguerre polynomials defined by T.H ...
Bavinck, H., Koekoek, J., Koekoek, R.
core   +2 more sources

BGG reciprocity for current algebras [PDF]

, 2014
It was conjectured by Bennett, Chari, and Manning that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra.
Chari, Vyjayanthi, Ion, Bogdan
core   +1 more source

The Orthogonal Riesz Fractional Derivative

Axioms
The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials Cn(ν)(x)
Fethi Bouzeffour
doaj   +1 more source

Generalized Shifted Chebyshev Koornwinder’s Type Polynomials: Basis Transformations [PDF]

Symmetry, 2018
Approximating continuous functions by polynomials is vital to scientific computing and numerous numerical techniques. On the other hand, polynomials can be characterized in several ways using different bases, where every form of basis has its advantages and power.
Mohammad A. AlQudah, Maalee N. AlMheidat
openaire   +2 more sources

Capturing Aerosol‐Cloud‐Precipitation Interactions: A Physics‐Informed Sparse Regression Approach for a Coupled Multiscale System With Time Delay

Journal of Geophysical Research: Atmospheres, Volume 130, Issue 12, 28 June 2025.
Abstract Aerosols exert a net cooling effect on the climate system by reflecting solar radiation, both directly and indirectly through their role in cloud formation, known as aerosol‐cloud interactions. The multiscale nature of aerosol‐cloud interactions, and especially their mesoscale adjustments and associated challenges for their representation in ...
Meiling Cheng, Franziska Glassmeier
wiley   +1 more source