1,118 research outputs found
Investigating Exponential and Geometric Polynomials with Euler-Seidel Algorithm
In this paper we use Euler-Seidel matrices method to find out some properties
of exponential and geometric polynomials and numbers. Some known results are
reproved and some new results are obtained.Comment: 12 page
Kahler submanifolds and the Umehara algebra
We show that an indefinite Euclidean complex space is not a relative of an
indefinite non-flat complex space form. We further study whether two compact
Fubini-Study spaces are relatives or not
The Quantum Dynamics of the Compactified Trigonometric Ruijsenaars-Schneider Model
We quantize a compactified version of the trigonometric
Ruijse\-naars-Schneider particle model with a phase space that is
symplectomorphic to the complex projective space CP^N. The quantum Hamiltonian
is realized as a discrete difference operator acting in a finite-dimensional
Hilbert space of complex functions with support in a finite uniform lattice
over a convex polytope (viz., a restricted Weyl alcove with walls having a
thickness proportional to the coupling parameter). We solve the corresponding
finite-dimensional (bispectral) eigenvalue problem in terms of discretized
Macdonald polynomials with q (and t) on the unit circle. The normalization of
the wave functions is determined using a terminating version of a recent
summation formula due to Aomoto, Ito and Macdonald. The resulting eigenfunction
transform determines a discrete Fourier-type involution in the Hilbert space of
lattice functions. This is in correspondence with Ruijsenaars' observation
that---at the classical level---the action-angle transformation defines an
(anti)symplectic involution of CP^N. From the perspective of algebraic
combinatorics, our results give rise to a novel system of bilinear summation
identities for the Macdonald symmetric functions
Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections
We present three new identities in law for quadratic functionals of
conditioned bivariate Gaussian processes. In particular, our results provide a
two-parameter generalization of a celebrated identity in law, involving the
path variance of a Brownian bridge, due to Watson (1961). The proof is based on
ideas from a recent note by J. R. Pycke (2005) and on the stochastic Fubini
theorem for general Gaussian measures proved in Deheuvels et al. (2004)
- …