Mathematical topics

The following article appeared in J. Math. Physics 50 (2009) 123521 and may be found at :
Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant (with K. Życzkowski)
Copyright (2009) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

Don Ramirez and I collaborated on an algorithm for finding the surface measure of ellipsoids in N-dimensional space (in fact this evaluates a Lauricella F-D type function). The algorithm and its derivation appeared in ACM TOMS 20 (1994), pp. 413-426, 427-435. Click here for the Fortran code
Also the Lauricella F-D is used to compute generalized F-distributions, (Australian & New Zealand J. Stat. 43(2001), 21-31) see  math.CA/9906095 .

The abstract of my paper  Intertwining operators and polynomials associated with the symmetric group . , Monatsh. Math. 126(1998), 181-209 ( there is a gzipped ps preprint (110K)   ). The sequel Intertwining Operators of Type B_N , CRM Proceedings and Lecture Notes, vol. 22, 1999, pp.119-134 is here (compressed ps.gz file, 77K).
An article in  J. Symb. Comp 28(1999), 819-826 , the proceedings of the ISAAC 1997 session on "Orthogonal Polynomials and Computer Algebra": Computing with Differential-Difference Operators" , (ps, 170k, revised 4/30/98); there is an accompanying Maple V, Release 4, worksheet with procedures and examples .

Algorithms for computing non-symmetric Jack and associated Hermite polynomials, in the p-basis constructed in Mh. Math. 126(1998) and Comm. Math. Phys. 197(1998), 451-487, are implemented in the Maple V, Release 4 (easily upgradeable to 5)  worksheet .

Preprint of "Planar harmonic polynomials of type B"( J. Phys.A: Math. Gen. 32 (1999), 8095-8110.A)  ( math.CA/9906041 ), gzip ps (112kb) .

Preprint of "Generating Functions Associated with Dihedral Groups", (Nov. 1999)  gzip ps (92 kb)

Note on a strange Laguerre polynomial orthogonality, see arxiv  math-ph/0011021 

Preprint (31 July  2006) of "An Intertwining Operator for the Group B2", Glasgow Math. J. 49 (2007), 291-319,  in pdf format and in gzipped ps 

To receive an e-reprint of "Hook-lengths and pairs of compositions", J. Comp. Appl. Math. 199 (2007), 39-47, send me an e-mail message.
The paper "Polynomials Associated with Dihedral Groups"  is published online (23 March 2007), SIGMA 3 (2007) , 052, 19pp. math.CA/0702107

Preprint of "A Laguerre polynomial orthogonality and the hydrogen atom",  (Analysis and Applications, 1 (2003), 177-188) in compressed ps

I participated in the Programme on Macdonald Symmetric Functions, at the  Newton Institute for Mathematical Sciences at Cambridge University, Spring 2001; and was a plenary lecturer at  the 6th International Symposium on Orthogonal Polynomials, Special Functions and Applications, in Rome, June 2001.


last updated 24 February 2012