We extend the results of Deligne and Illusie on liftings modulo $p^2$ decompositions de Rham complex in several ways. show that for a smooth scheme $X$ over perfect field $k$ characteristic $p>0$, truncations $\max(p-1, 2)$ consecutive degrees can be reconstructed as objects derived category terms its truncation at most one (or, equivalently, obstruction class to lifting $p^2$). Consequently, t...

GPUs are dedicated processors used for complex calculations and simulations and they can be effectively used for tropical algebra computations. Tropical algebra is based on max-plus algebra and minplus algebra. In this paper we proposed and designed a library based on Tropical Algebra which is used to provide standard vector and matrix operations namely Basic Tropical Algebra Subroutines (BTAS)...

Model predictive control for max-plus-linear discrete event systems * B. De Schutter and T. van den Boom If you want to cite this report, please use the following reference instead: B. De Schutter and T. van den Boom, " Model predictive control for max-plus-linear discrete event systems, " The conventional model predictive control framework is extended and adapted to max-plus-linear systems, i....

In this paper, we address the problem of failure detection and localization in a Timed Discrete Event System (TDES) such $(\max \limits ,+)$ -linear system graphically modeled by Graph (TEG). The considered failures are changes on holding times or tokens TEG places that can provoke shifts between an observed outcoming timed flow expected (for given incoming flow). Indicators built to first dete...