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 $a_4$, 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