The Dirichlet Problem for Curvature Equations in Riemannian Manifolds

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to extend some of the existence theorems of Caffarelli, Nirenberg and Spruck [4] and Ivochkina, Trundinger and Lin [19] to more general curvature functions and less convex domains.Comment: 32 pages, no figures. Final version. Paper accepted to publication in Indiana University Mathematics Journa

STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations

The inference of the underlying state of the plasma in the solar chromosphere remains extremely challenging because of the nonlocal character of the observed radiation and plasma conditions in this layer. Inversion methods allow us to derive a model atmosphere that can reproduce the observed spectra by undertaking several physical assumptions. The most advanced approaches involve a depth-stratified model atmosphere described by temperature, line-of-sight velocity, turbulent velocity, the three components of the magnetic field vector, and gas and electron pressure. The parameters of the radiative transfer equation are computed from a solid ground of physical principles. To apply these techniques to spectral lines that sample the chromosphere, NLTE effects must be included in the calculations. We developed a new inversion code STiC to study spectral lines that sample the upper chromosphere. The code is based the RH synthetis code, which we modified to make the inversions faster and more stable. For the first time, STiC facilitates the processing of lines from multiple atoms in non-LTE, also including partial redistribution effects. Furthermore, we include a regularization strategy that allows for model atmospheres with a complex stratification, without introducing artifacts in the reconstructed physical parameters, which are usually manifested in the form of oscillatory behavior. This approach takes steps toward a node-less inversion, in which the value of the physical parameters at each grid point can be considered a free parameter. In this paper we discuss the implementation of the aforementioned techniques, the description of the model atmosphere, and the optimizations that we applied to the code. We carry out some numerical experiments to show the performance of the code and the regularization techniques that we implemented. We made STiC publicly available to the community.Comment: Accepted for publication in Astronomy & Astrophysic

Programming languages in economics: a comparison among Fortran77, C++, and Java

The main objective of this paper was to compare the computer programming languages Fortran77, C++, and Java under four aspects: runtime efficiency, readability, ease of learning, and reliability. For this comparison, we revised the specialized literature on programming languages and used pieces of codes of these three programming languages. The purpose of this comparison was to provide some objective information for economists interested in learning one or more of these languages.Programming language, Runtime efficiency, Readability, Reliability, Teaching/Communication/Extension/Profession,