459,739 research outputs found
Regularity theory for fully nonlinear integro-differential equations
We consider nonlinear integro-differential equations, like the ones that
arise from stochastic control problems with purely jump L\`evy processes. We
obtain a nonlocal version of the ABP estimate, Harnack inequality, and interior
regularity for general fully nonlinear integro-differential
equations. Our estimates remain uniform as the degree of the equation
approaches two, so they can be seen as a natural extension of the regularity
theory for elliptic partial differential equations.Comment: Minor typos corrected, and some extra comments adde
Mathematics in the Baroque Period in Spain
The 17th century Spain is very advanced culturally and, in certain respects, very refined. Although Spanish culture in the reached an unprecedented peak, mathematics activity in Spain entered a period of decline and did not share in the burst of mathemathical knowledge occurring in other European countries during this century
Cosmological parameter inference with Bayesian statistics
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found
their place in the field of Cosmology. They have become important mathematical
and numerical tools, especially in parameter estimation and model comparison.
In this paper, we review some fundamental concepts to understand Bayesian
statistics and then introduce MCMC algorithms and samplers that allow us to
perform the parameter inference procedure. We also introduce a general
description of the standard cosmological model, known as the CDM
model, along with several alternatives, and current datasets coming from
astrophysical and cosmological observations. Finally, with the tools acquired,
we use an MCMC algorithm implemented in python to test several cosmological
models and find out the combination of parameters that best describes the
Universe.Comment: 30 pages, 17 figures, 5 tables; accepted for publication in Universe;
references adde
Supersymmetry and Polytopes
We make an imaginative comparison between the Minimal Supersymmetric Standard
Model and the 24-cell polytope in four dimensions, the Octacube.Comment: Presented to the Workshop on Geometry and Physics: Supersymmetry.
Bilbao, Spain. May 200
Measuring dispersion in the context of ordered qualitative scales
Producción CientíficaThe main purpose of this contribution is to measure the dispersion associated with the different results of a variable when they form a set of linguistic terms obtained after examining different qualities of people, services, etc, ordered, but with a non-homogeneous and non-quantifiable distance between the linguistic terms.Ministerio de Economía, Industria y Competitividad (project ECO2016-77900-P
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