A Note on the least squarefree number in an arithmetic progression

We prove an asymptotic formula for squarefree in arithmetic progressions with squarefree moduli, improving previous results by Prachar. The main tool is an estimate for counting solutions of a congruence inside a box that goes beyond what can be obtained by using the Weil bound.Comment: 6 pages, no figure

Microseismic study of the interandine valley between Latacunga and Cuayllabamba

The present state of two active volcanoes and the principal active seismic faults in a 100 km area from Quito to Toacaso, Ecuador was studied. A brief seismic history of the region is reviewed

Studying the interaction between microquasar jets and their environments

In high-mass microquasars (HMMQ), strong interactions between jets and stellar winds at binary system scales could occur. In order to explore this possibility, we have performed numerical 2-dimensional simulations of jets crossing the dense stellar material to study how the jet will be affected by these interactions. We find that the jet head generates strong shocks in the wind. These shocks reduce the jet advance speed, and compress and heat up jet and wind material. In addition, strong recollimation shocks can occur where pressure balance between the jet side and the surrounding medium is reached. All this, altogether with jet bending, could lead to the destruction of jets with power $<10^{36} \rm{erg/s}$. The conditions around the outflow shocks would be convenient for accelerating particles up to $\sim$TeV energies. These accelerated particles could emit via synchrotron and inverse Compton (IC) scattering if they were leptons, and via hadronic processes in case they were hadrons.Comment: 4 pages. Contribution to the proceedings of High Energy Phenomena in Relativistic Outflows, held in Dublin, Ireland, September 24-28, 200

Hawking Radiation in String Theory and the String Phase of Black Holes

The quantum string emission by Black Holes is computed in the framework of the `string analogue model' (or thermodynamical approach), which is well suited to combine QFT and string theory in curved backgrounds (particulary here, as black holes and strings posses intrinsic thermal features and temperatures). The QFT-Hawking temperature T_H is upper bounded by the string temperature T_S in the black hole background. The black hole emission spectrum is an incomplete gamma function of (T_H - T_S). For T_H << T_S, it yields the QFT-Hawking emission. For T_H \to T_S, it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic `minimal' black hole of mass M_{\min} or radius r_{\min} (inversely proportional to T_S) and string temperature T_S. The semiclassical QFT black hole (of mass M and temperature T_H) and the string black hole (of mass M_{min} and temperature T_S) are mapped one into another by a `Dual' transform which links classical/QFT and quantum string regimes. The string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations with mass M_+ (radius r_+) and temperature T_+) is computed. Both, the QFT and string black hole regimes are well defined and bounded: r_{min} leq r_+ \leq r_S, M_{min} \leq M_+ \leq M, T_H \leq T_+ \leq T_S. The string `minimal' black hole has a life time tau_{min} \simeq \frac{k_B c}{G \hbar} T^{-3}_S.Comment: LaTex, 31 pages, no figure

AutoParallel: A Python module for automatic parallelization and distributed execution of affine loop nests

The last improvements in programming languages, programming models, and frameworks have focused on abstracting the users from many programming issues. Among others, recent programming frameworks include simpler syntax, automatic memory management and garbage collection, which simplifies code re-usage through library packages, and easily configurable tools for deployment. For instance, Python has risen to the top of the list of the programming languages due to the simplicity of its syntax, while still achieving a good performance even being an interpreted language. Moreover, the community has helped to develop a large number of libraries and modules, tuning them to obtain great performance. However, there is still room for improvement when preventing users from dealing directly with distributed and parallel computing issues. This paper proposes and evaluates AutoParallel, a Python module to automatically find an appropriate task-based parallelization of affine loop nests to execute them in parallel in a distributed computing infrastructure. This parallelization can also include the building of data blocks to increase task granularity in order to achieve a good execution performance. Moreover, AutoParallel is based on sequential programming and only contains a small annotation in the form of a Python decorator so that anyone with little programming skills can scale up an application to hundreds of cores.Comment: Accepted to the 8th Workshop on Python for High-Performance and Scientific Computing (PyHPC 2018