Study of extremely reddened AGB stars in the Galactic bulge

Context. Extremely reddened AGB stars lose mass at high rates of >10^-5 Msun/yr. This is the very last stage of AGB evolution, in which stars in the mass range 2.0--4.0 Msun (for solar metallicity) should have been converted to C stars already. The extremely reddened AGB stars in the Galactic bulge are however predominantly O-rich, implying that they might be either low-mass stars or stars at the upper end of the AGB mass range. Aims. To determine the mass range of the most reddened AGB stars in the Galactic bulge. Methods. Using Virtual Observatory tools, we constructed spectral energy distributions of a sample of 37 evolved stars in the Galactic bulge with extremely red IRAS colours. We fitted DUSTY models to the observational data to infer the bolometric fluxes. Applying individual corrections for interstellar extinction and adopting a common distance, we determined luminosities and mass-loss rates, and inferred the progenitor mass range from comparisons with AGB evolutionary models. Results. The observed spectral energy distributions are consistent with a classification as reddened AGB stars, except for two stars, which are proto-planetary nebula candidates. For the AGB stars, we found luminosities in the range 3000--30,000 Lsun and mass-loss rates 10^-5--3x10^-4 Msun/yr. The corresponding mass range is 1.1--6.0 Msun assuming solar metallicity. Conclusions. Contrary to the predictions of the evolutionary models, the luminosity distribution is continuous, with many O-rich AGB stars in the mass range in which they should have been converted into C stars already. We suspect that bulge AGB stars have higher than solar metallicity and therefore may avoid the conversion to C-rich. The presence of low-mass stars in the sample shows that their termination of the AGB evolution also occurs during a final phase of very high mass-loss rate, leading to optically thick circumstellar shells

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.Comment: LaTex, 22 page

Self-adjointness of Dirac operators via Hardy-Dirac inequalities

Distinguished selfadjoint extensions of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, $-|x|^{-1}$. The method uses Hardy-Dirac inequalities and quadratic form techniques.Comment: PACS 03.65.P, 03.3

Computing continuous-time growth models with boundary conditions via wavelets

This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are give

Valuation of boundary-linked assets

This article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a wavelet-collocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked asset

Worst-case estimation and asymptotic theory for models with unobservables

This paper proposes a worst-case approach for estimating econometric models containing unobservable variables. Worst-case estimators are robust against the adverse effects of unobservables. In contrast to the classical literature, there are no assumptions about the statistical nature of the unobservables in a worst-case estimation. This method is robust with respect to the unknown probability distribution of the unobservables and should be seen as a complement to standard methods, as cautious modelers should compare different estimations to determine robust models. The limit theory is obtained. A Monte Carlo study of finite sample properties has been conducted. An economic application is included

Strategic Targeted Advertising and Market Fragmentation

This paper proves that oligopolistic price competition with both targeted advertising and targeted prices can lead to a permanent fragmentation of the market into a local monopoly. However, compared to mass advertising, targeting increases social welfare and turns out to be more beneficial for consumers than for firms.discount coupons.

Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal potentials related to the weights in the above mentioned inequalities.Comment: 16 page

Do business density and variety determine retail performance?

Outlet location plays a crucial role in retail strategy. In this paper we study the relationship between spatial density (concentration) of retailers in the trade area and their economic performance. This analysis will help managers figure out the economic potential of starting a retail business in a given area, reducing business start-up risks. We find that retail businesses located in high and low retail density zones enjoy higher performance levels, consistent with competitive advantage arising from agglomeration economies and local market power respectively. We also find that retail businesses located in intermediate density areas use a differentiation strategy based on business variety (diversification across stores). Outlets located in areas with the highest variety enjoy performance levels similar to those achieved in the agglomeration and low density areas. The results suggest that retail companies should jointly consider variety and density to determine location