203 research outputs found
Multivariate Bernoulli and Euler polynomials via L\'evy processes
By a symbolic method, we introduce multivariate Bernoulli and Euler
polynomials as powers of polynomials whose coefficients involve multivariate
L\'evy processes. Many properties of these polynomials are stated
straightforwardly thanks to this representation, which could be easily
implemented in any symbolic manipulation system. A very simple relation between
these two families of multivariate polynomials is provided
On Differences of Zeta Values
Finite differences of values of the Riemann zeta function at the integers are
explored. Such quantities, which occur as coefficients in Newton series
representations, have surfaced in works of Maslanka, Coffey, Baez-Duarte, Voros
and others. We apply the theory of Norlund-Rice integrals in conjunction with
the saddle point method and derive precise asymptotic estimates. The method
extends to Dirichlet L-functions and our estimates appear to be partly related
to earlier investigations surrounding Li's criterion for the Riemann
hypothesis.Comment: 18 page
Heat-kernels and functional determinants on the generalized cone
We consider zeta functions and heat-kernel expansions on the bounded,
generalized cone in arbitrary dimensions using an improved calculational
technique. The specific case of a global monopole is analysed in detail and
some restrictions thereby placed on the coefficient. The computation
of functional determinants is also addressed. General formulas are given and
known results are incidentally, and rapidly, reproduced.Comment: 26p,LaTeX.(Cosmetic changes and eqns (9.8),(11.2) corrected.
Bose-Einstein condensation of atomic gases in a harmonic oscillator confining potential trap
We present a model which predicts the temperature of Bose-Einstein
condensation in atomic alkali gases and find excellent agreement with recent
experimental observations. A system of bosons confined by a harmonic oscillator
potential is not characterized by a critical temperature in the same way as an
identical system which is not confined. We discuss the problem of Bose-Einstein
condensation in an isotropic harmonic oscillator potential analytically and
numerically for a range of parameters of relevance to the study of low
temperature gases of alkali metals.Comment: 11 pages latex with two postscript figure
The Hahn Quantum Variational Calculus
We introduce the Hahn quantum variational calculus. Necessary and sufficient
optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange
problems, are studied. We also show the validity of Leitmann's direct method
for the Hahn quantum variational calculus, and give explicit solutions to some
concrete problems. To illustrate the results, we provide several examples and
discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted:
18/June/2010; for publication in Journal of Optimization Theory and
Application
Casimir Energies for Spherically Symmetric Cavities
A general calculation of Casimir energies --in an arbitrary number of
dimensions-- for massless quantized fields in spherically symmetric cavities is
carried out. All the most common situations, including scalar and spinor
fields, the electromagnetic field, and various boundary conditions are treated
with care. The final results are given as analytical (closed) expressions in
terms of Barnes zeta functions. A direct, straightforward numerical evaluation
of the formulas is then performed, which yields highly accurate numbers of, in
principle, arbitrarily good precision.Comment: 18 pages, LaTeX, sub. Ann. Phy
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