Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem (WPT)

An analogue of the Wedderbur principal theorem (WPT) is considered for finite dimensional Jordan superalgebras A with solvable radical N, such that N^2=0 and A/N is isomorphic to Josp_n|2m(F), where F is an algebraicallly closed field of characteristic zero. Let's we prove that the WPT is valid under some restrictions over the irreducible Josp_n|2m(F)-bimodules contained in N, and it is shown with counter-examples that these restrictions can not be weakened.Comment: 13 page

Analysis of a chemo-repulsion model with nonlinear production: The continuous problem and unconditionally energy stable fully discrete schemes

We consider the following repulsive-productive chemotaxis model: Let $p\in (1,2)$, find $u \geq 0$, the cell density, and $v \geq 0$, the chemical concentration, satisfying \begin{equation}\label{C5:Am} \left\{ \begin{array} [c]{lll} \partial_t u - \Delta u - \nabla\cdot (u\nabla v)=0 \ \ \mbox{in}\ \Omega,\ t>0,\\ \partial_t v - \Delta v + v = u^p \ \ \mbox{in}\ \Omega,\ t>0, \end{array} \right. \end{equation} in a bounded domain $\Omega\subseteq \mathbb{R}^d$, $d=2,3$. By using a regularization technique, we prove the existence of solutions of this problem. Moreover, we propose three fully discrete Finite Element (FE) nonlinear approximations, where the first one is defined in the variables $(u,v)$, and the second and third ones by introducing ${\boldsymbol\sigma}=\nabla v$ as an auxiliary variable. We prove some unconditional properties such as mass-conservation, energy-stability and solvability of the schemes. Finally, we compare the behavior of the schemes throughout several numerical simulations and give some conclusions.Comment: arXiv admin note: substantial text overlap with arXiv:1807.0111

Forecasting Food Price Inflation in Developing Countries with Inflation Targeting Regimes: the Colombian Case

Many developing countries are adopting inflation targeting regimes to guide monetary policy decisions. In such countries the share of food in the consumption basket is high and policy makers often employ total inflation (as opposed to core inflation) to set inflationary targets. Therefore, central banks need to develop reliable models to forecast food inflation. Our literature review suggests that little has been done in the construction of models to forecast short-run food inflation in developing countries. We develop a model to improve short-run food inflation forecasts in Colombia. The model disaggregates food items according to economic theory and employs Flexible Least Squares given the presence of structural changes in the inflation series. We compare the performance of this new model to current models employed by the central bank. Next, we apply econometric methods to combine forecasts from alternative models and test whether such combination outperforms individual models. Our results indicate that forecasts can be improved by classifying food basket items according to unprocessed, processed and food away from home and by employing forecast combination techniques.Food Inflation, Time Series,