32,899 research outputs found
Convergent Asymptotic Expansions of Charlier, Laguerre and Jacobi Polynomials
Convergent expansions are derived for three types of orthogonal polynomials:
Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for
large values of the degree. The expansions are given in terms of functions that
are special cases of the given polynomials. The method is based on expanding
integrals in one or two points of the complex plane, these points being saddle
points of the phase functions of the integrands.Comment: 20 pages, 5 figures. Keywords: Charlier polynomials, Laguerre
polynomials, Jacobi polynomials, asymptotic expansions, saddle point methods,
two-points Taylor expansion
Multi-point Taylor Expansions of Analytic Functions
Taylor expansions of analytic functions are considered with respect to
several points, allowing confluence of any of them. Cauchy-type formulas are
given for coefficients and remainders in the expansions, and the regions of
convergence are indicated. It is explained how these expansions can be used in
deriving uniform asymptotic expansions of integrals. The method is also used
for obtaining Laurent expansions in several points as well as Taylor-Laurent
expansions.Comment: 20 pages, 7 figures. Keywords: multi-point Taylor expansions,
Cauchy's theorem, analytic functions, multi-point Laurent expansions, uniform
asymptotic expansions of integral
The bulge luminosity functions in the MSX infrared bands
We use an inversion technique to derive the luminosity functions of the
Galactic bulge from point source counts extracted from the Midcourse Space
Experiment's Point Source Catalog (version 1.2).Comment: 5 pages, 2 figures, to be published in A&
A variant transfer matrix method suitable for transport through multi-probe systems
We have developed a variant transfer matrix method that is suitable for
transport through multi-probe systems. Using this method, we have numerically
studied the quantum spin Hall effect (QSHE) on 2D graphene with both intrinsic
(Vso) and Rashba (Vr) spin-orbit (SO) couplings. The integer QSHE arises in the
presence of intrinsic SO interaction and is gradually destroyed by the Rashba
SO interaction and disorder fluctuation. We have numerically determined the
phase boundaries separating integer QSHE and spin Hall liquid. We have found
that when Vso> 0.2t with t the hopping constant the energy gap needed for the
integer QSHE is the largest satisfying |E|<t. For smaller Vso the energy gap
decreases linearly. In the presence of Rashba SO interaction or disorders, the
energy gap diminishes. With Rashba SO interaction the integer QSHE is robust at
the largest energy within the energy gap while at the smallest energy within
the energy gap the integer QSHE is insensitive to the disorder
Toward Supergravity Spectral Action
A spectral action of Euclidean supergravity is proposed. We calculate up to
, the Seeley-Dewitt coefficients in the expansion of the spectral action
associated to the supergravity Dirac operator. This is possible because in
simple supergravity, as in pure gravity, a well defined and mathematically
consistent Dirac operator can be constructed.Comment: 10pages, no figures, matches published versio
Eviction of a 125 GeV "heavy"-Higgs from the MSSM
We prove that the present experimental constraints are already enough to rule
out the possibility of the ~125 GeV Higgs found at LHC being the second
lightest Higgs in a general MSSM context, even with explicit CP violation in
the Higgs potential. Contrary to previous studies, we are able to eliminate
this possibility analytically, using simple expressions for a relatively small
number of observables. We show that the present LHC constraints on the diphoton
signal strength, tau-tau production through Higgs and BR(B -> X_s gamma) are
enough to preclude the possibility of H_2 being the observed Higgs with m_H~125
GeV within an MSSM context, without leaving room for finely tuned
cancellations. As a by-product, we also comment on the difficulties of an MSSM
interpretation of the excess in the gamma-gamma production cross section
recently found at CMS that could correspond to a second Higgs resonance at
m_H~136 GeV.Comment: 38 pages, 9 figures. Final version accepted at JHEP. Sections 2, 3
and appendices simplified. Experimental results updated, several references
added. Small typos corrected and a new comparison of approximate formulas
with full expressions include
Testing strong line metallicity diagnostics at z~2
High-z galaxy gas-phase metallicities are usually determined through
observations of strong optical emission lines with calibrations tied to the
local universe. Recent debate has questioned if these calibrations are valid in
the high-z universe. We investigate this by analysing a sample of 16 galaxies
at z~2 available in the literature, and for which the metallicity can be
robustly determined using oxygen auroral lines. The sample spans a redshift
range of 1.4 < z < 3.6, has metallicities of 7.4-8.4 in 12+log(O/H) and stellar
masses 10^7.5-10^11 Msun. We test commonly used strong line diagnostics (R23,
O3, O2, O32, N2, O3N2 and Ne3O2 ) as prescribed by four different sets of
empirical calibrations, as well as one fully theoretical calibration. We find
that none of the strong line diagnostics (or calibration set) tested perform
consistently better than the others. Amongst the line ratios tested, R23 and O3
deliver the best results, with accuracies as good as 0.01-0.04 dex and
dispersions of ~0.2 dex in two of the calibrations tested. Generally, line
ratios involving nitrogen predict higher values of metallicity, while results
with O32 and Ne3O2 show large dispersions. The theoretical calibration yields
an accuracy of 0.06 dex, comparable to the best strong line methods. We
conclude that, within the metallicity range tested in this work, the locally
calibrated diagnostics can still be reliably applied at z~2.Comment: 12 pages, 8 Figures, accepted for publication in MNRA
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