444 research outputs found
On the Two q-Analogue Logarithmic Functions
There is a simple, multi-sheet Riemann surface associated with e_q(z)'s
inverse function ln_q(w) for 0< q < 1. A principal sheet for ln_q(w) can be
defined. However, the topology of the Riemann surface for ln_q(w) changes each
time "q" increases above the collision point of a pair of the turning points of
e_q(x). There is also a power series representation for ln_q(1+w). An
infinite-product representation for e_q(z) is used to obtain the ordinary
natural logarithm ln{e_q(z)} and the values of sum rules for the zeros "z_i" of
e_q(z). For |z|<|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power
series in terms of values of these sum rules. The values of the sum rules for
the q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the
usual Bernoulli numbers.Comment: This is the final version to appear in J.Phys.A: Math. & General.
Some explict formulas added, and to update the reference
Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomials
Using the Baker-Akhiezer function technique we construct a separation of
variables for the classical trigonometric 3-particle Ruijsenaars model
(relativistic generalization of Calogero-Moser-Sutherland model). In the
quantum case, an integral operator M is constructed from the Askey-Wilson
contour integral. The operator M transforms the eigenfunctions of the commuting
Hamiltonians (Macdonald polynomials for the root sytem A2) into the factorized
form S(y1)S(y2) where S(y) is a Laurent polynomial of one variable expressed in
terms of the 3phi2(y) basic hypergeometric series. The inversion of M produces
a new integral representation for the A2 Macdonald polynomials. We also present
some results and conjectures for general n-particle case.Comment: 31 pages, latex, no figures, Proposition 12 correcte
Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams
We present an alternative technique for evaluating multiloop Feynman
diagrams, using the integration by fractional expansion method. Here we
consider generic diagrams that contain propagators with radiative corrections
which topologically correspond to recursive constructions of bubble type
diagrams. The main idea is to reduce these subgraphs, replacing them by their
equivalent multiregion expansion. One of the main advantages of this
integration technique is that it allows to reduce massive cases with the same
degree of difficulty as in the massless case.Comment: 38 pages, 46 figures, 4 table
Mechanism of hepatic glycogen synthase inactivation induced by Ca2+-mobilizing hormones. Studies using phospholipase C and phorbol myristate acetate
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
Completeness of Coherent States Associated with Self-Similar Potentials and Ramanujan's Integral Extension of the Beta Function
A decomposition of identity is given as a complex integral over the coherent
states associated with a class of shape-invariant self-similar potentials.
There is a remarkable connection between these coherent states and Ramanujan's
integral extension of the beta function.Comment: 9 pages of Late
Topological Interactions in Warped Extra Dimensions
Topological interactions will be generated in theories with compact extra
dimensions where fermionic chiral zero modes have different localizations. This
is the case in many warped extra dimension models where the right-handed top
quark is typically localized away from the left-handed one. Using
deconstruction techniques, we study the topological interactions in these
models. These interactions appear as trilinear and quadrilinear gauge boson
couplings in low energy effective theories with three or more sites, as well as
in the continuum limit. We derive the form of these interactions for various
cases, including examples of Abelian, non-Abelian and product gauge groups of
phenomenological interest. The topological interactions provide a window into
the more fundamental aspects of these theories and could result in unique
signatures at the Large Hadron Collider, some of which we explore.Comment: 40 pages, 10 figures, 2 tables; modifications in the KK parity
discussion, final version at JHE
Laplace approximation of Lauricella functions F A and F D
The Lauricella functions, which are generalizations of the Gauss hypergeometric function 2 F 1, arise naturally in many areas of mathematics and statistics. So far as we are aware, there is little or nothing in the literature on how to calculate numerical approximations for these functions outside those cases in which a simple one-dimensional integral representation or a one-dimensional series representation is available. In this paper we present first-order and second-order Laplace approximations to the Lauricella functions F(n)A and F(n)D. Our extensive numerical results show that these approximations achieve surprisingly good accuracy in a wide variety of examples, including cases well outside the asymptotic framework within which the approximations were derived. Moreover, it turns out that the second-order Laplace approximations are usually more accurate than their first-order versions. The numerical results are complemented by theoretical investigations which suggest that the approximations have good relative error properties outside the asymptotic regimes within which they were derived, including in certain cases where the dimension n goes to infinity
Thermostatistics of deformed bosons and fermions
Based on the q-deformed oscillator algebra, we study the behavior of the mean
occupation number and its analogies with intermediate statistics and we obtain
an expression in terms of an infinite continued fraction, thus clarifying
successive approximations. In this framework, we study the thermostatistics of
q-deformed bosons and fermions and show that thermodynamics can be built on the
formalism of q-calculus. The entire structure of thermodynamics is preserved if
ordinary derivatives are replaced by the use of an appropriate Jackson
derivative and q-integral. Moreover, we derive the most important thermodynamic
functions and we study the q-boson and q-fermion ideal gas in the thermodynamic
limit.Comment: 14 pages, 2 figure
British Association of Dermatologists' guidelines for the investigation and management of generalized pruritus in adults without an underlying dermatosis, 2018
- …