Results 51 to 60 of about 2,941 (107)

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials. [PDF]

Proc Natl Acad Sci U S A, 2010
Corteel S, Williams LK.
europepmc   +1 more source

Askey-Wilson relations and Leonard pairs

Askey-Wilson relations and Leonard pairs
It is known that if $ (A, A^*) $ is a Leonard pair, then the linear transformations $ A $, $ A^* $ satisfy the Askey-Wilson relations $ A^2A^* − \betaAA^*A + A^*A^2 − gamma(AA^* + A^*A) − sigmaA^* = gamma^*A^2 + omegaA + etaI, A^*2A − \betaA^*AA^* + AA^*2 − gamma^*(A^*A + AA^*) − sigma^*A = gammaA^*2 + omegaA^* + eta^*I $, for some scalars $ \beta $, $
openaire  

Normalized Leonard pairs and Askey-Wilson relations

Normalized Leonard pairs and Askey-Wilson relations
Let $ V $ denote a vector space with finite positive dimension, and let $ (A, A^*) $ denote a Leonard pair on $ V $. As is known, the linear transformations $ A $, $ A^* $ satisfy the Askey-Wilson relations $ A^2A^* − \betaAA^*A + A^*A^2 − gamma(AA^* + A^*A) − sigmaA^* = gamma^*A^2 + omegaA + etaI, A^2A − \betaA^*AA^* + AA^*2 − gamma^*(A^*A + AA ...
openaire  

Measuring sexual behaviour: methodological challenges in survey research. [PDF]

Sex Transm Infect, 2001
Fenton KA, Johnson AM, McManus S, Erens B, Erens B.   +4 more
europepmc   +1 more source

Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials

Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians. which are deformations of those for the Wilson and Askey-Wilson polynomials in terms of a degree l (l = 1, 2
openaire