Asymptotic behaviour of the Urbanik semigroup

We revisit the product convolution semigroup of probability densities e_c(t),c>0 on the positive half-line with moments (n!)^c and determine the asymptotic behaviour of e_c(t) for large and small t>0. This shows that (n!)^c is indeterminate as Stieltjes moment sequence if and only if c>2Comment: 13 page

Regular solutions to a supercritical elliptic problem in exterior domains

We consider the supercritical elliptic problem -\Delta u = \lambda e^u, \lambda > 0, in an exterior domain $\Omega = \mathbb{R}^N \setminus D$ under zero Dirichlet condition, where D is smooth and bounded in \mathbb{R}^N, N greater or equal than 3. We prove that, for \lambda small, this problem admits infinitely many regular solutions

A social stigma model of child labor

This paper constructs a model in which a social norm is internalized. The social disapproval of people who violate the norm -stigmatization-- is incorporated as a reduction in their utility. That reduction in utility is lower as the proportion of the population that violates the norm increases. In the model, society disapproves of people sending their children to work and parents care about that “embarrassment”. An equilibrium is constructed in which the expected and realized stigma costs are the same; and the wages rates of child and adult labor are such as to equate demand and supply for each kind of labor.

Observed quantum dynamics: classical dynamics and lack of Zeno effect

We examine a case study where classical evolution emerges when observing a quantum evolution. By using a single-mode quantum Kerr evolution interrupted by measurement of the double-homodyne kind (projecting the evolved field state into classical-like coherent states or quantum squeezed states), we show that irrespective of whether the measurement is classical or quantum there is no quantum Zeno effect and the evolution turns out to be classical.Comment: 7 pages, 1 figur

New Series Expansions of the Gauss Hypergeometric Function

The Gauss hypergeometric function ${}_2F_1(a,b,c;z)$ can be computed by using the power series in powers of $z, z/(z-1), 1-z, 1/z, 1/(1-z),(z-1)/z$. With these expansions ${}_2F_1(a,b,c;z)$ is not completely computable for all complex values of $z$. As pointed out in Gil, {\it et al.} [2007, \S2.3], the points $z=e^{\pm i\pi/3}$ are always excluded from the domains of convergence of these expansions. B\"uhring [1987] has given a power series expansion that allows computation at and near these points. But, when $b-a$ is an integer, the coefficients of that expansion become indeterminate and its computation requires a nontrivial limiting process. Moreover, the convergence becomes slower and slower in that case. In this paper we obtain new expansions of the Gauss hypergeometric function in terms of rational functions of $z$ for which the points $z=e^{\pm i\pi/3}$ are well inside their domains of convergence . In addition, these expansion are well defined when $b-a$ is an integer and no limits are needed in that case. Numerical computations show that these expansions converge faster than B\"uhring's expansion for $z$ in the neighborhood of the points $e^{\pm i\pi/3}$, especially when $b-a$ is close to an integer number.Comment: 18 pages, 6 figures, 4 tables. In Advances in Computational Mathematics, 2012 Second version with corrected typos in equations (18) and (19

Relaxation oscillations, pulses, and travelling waves in the diffusive Volterra delay-differential equation

The diffusive Volterra equation with discrete or continuous delay is studied in the limit of long delays using matched asymptotic expansions. In the case of continuous delay, the procedure was explicitly carried out for general normalized kernels of the form Sigma/sub n=p//sup N/ g/sub n/(t/sup n//T/sup n+1/)e/sup -t/T/, pges2, in the limit in which the strength of the delayed regulation is much greater than that of the instantaneous one, and also for g/sub n/=delta/sub n2/ and any strength ratio. Solutions include homogeneous relaxation oscillations and travelling waves such as pulses, periodic wavetrains, pacemakers and leading centers, so that the diffusive Volterra equation presents the main features of excitable media

Semblanzas Ictiológicas: Matías Pandolfi

través de esta serie intentaremos conocer diferentes facetas personales de los integrantes de nuestra “comunidad”. El cuestionario, además de su principal objetivo, con sus respuestas quizás nos ayude a encontrar entre nosotros puntos en común que vayan más allá de nuestros temas de trabajo y sea un aporte a futuros estudios históricos. Esperamos que esta iniciativa pueda ser otro nexo entre los ictiólogos de la región,ya que consideramos que el resultado general trascendería nuestras fronteras