Photon spheres in Einstein and Einstein-Gauss-Bonnet theories and circular null geodesics in axially-symmetric spacetimes

In this article we extend a recent theorem proven by Hod (Phys. Lett. B, {\bf 727}, 345--348, 2013) to $n$-dimensional Einstein and Einstein-Gauss-Bonnet theories, which gives an upper bound for the photon sphere radii of spherically symmetric black holes. As applications of these results we give a universal upper bound for the real part of quasinormal modes in the WKB limit and a universal lower bound for the position of the first relativistic image in the strong lensing regime produced by these type of black holes. For the axially-symmetric case, we also make some general comments (independent of the underlying gravitational theory) on the relation between circular null geodesics and the fastest way to circle a black hole.Comment: In this post-publisher version two typos were corrected: the signature of the metric in eq.(1) and a factor in eq.(102). We thanks Gary Gibbons and Chris Pope for bringing to our attention these typo

A Jacobian elliptic single-field inflation

In the scenario of single-field inflation, this field is done in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analysed using the Hamilton-Jacobi approach and then, the main results are contrasted with the recent measurements obtained from the Planck 2015 data.Comment: 7 pages, 5 figure

Trade based on economies of scale under monopolistic competition: a clarification of Krugman's model

Although a major contribution to trade theory, Krugman’s 1979 demonstration that ‘trade can arise and lead to mutual gains even when countries are similar’ fails to make explicit the economic mechanisms that lead up to this result. The current paper attempts to fill this gap by addressing several questions that are implicit in Krugman’s demonstration but which he does not explicitly analyze: - What is the effect of trade upon the demand curve faced by the typical firm in each nation? - How do firms react to the change in the demand curves they face, and what is the short-term outcome of their behaviour? - Why do some firms fail? - What is the role of the failure of firms in the adjustment to the final free trade equilibrium?Krugman, intra-industry trade, economies of scale, monopolistic competition.

On the maximum observed wind speed in a randomly sampled hurricane

Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 23 (2010): 1262-1265, doi:10.1175/2009JCLI2803.1.There is considerable interest in detecting a long-term trend in hurricane intensity possibly related to large-scale ocean warming. This effort is complicated by the paucity of wind speed measurements for hurricanes occurring in the early part of the observational record. Here, results are presented regarding the maximum observed wind speed in a sparsely randomly sampled hurricane based on a model of the evolution of wind speed over the lifetime of a hurricane.Support for this work was provided by NOAA Grant NA17RJ1223