Fitzpatrick en [1] demostró que todo operador monótono maximal es un operador re- presentable en espacios vectoriales topológicos. Por lema de Zorn, todo operador monótono tiene extensión monótona maximal; por lo tanto, todo operador monótono posee extensión representable y la menor de todas las extensiones representables es llamada la clausura representable. Por otro lado, la clausura polar monótona de un operador monótono, que la podemos ver como la intersección de todas las extensiones monótonas maximales, tiene la propiedad de ser representable y además contiene a la clausura representable. El objetivo de la tesis es saber cuándo estas dos clausuras son iguales en espacios vectoriales topológicos. Además, demostrar que estas dos clausuras son iguales, sin ninguna hipótesis, en espacios de dimensión finita.

The thesis has two purposes: The first one is to build a mathematical model that better approximates (with respect to the mathematical model in [2]) to the behaviour of the wine fermentation process with the addition of certain amount of nitrogen at some instant of time, based in [2]. This mathematical model is described by mean ordinary differential equations including some parameters which will be identified solving some optimization problems. The second purpose of the thesis is to study the improved model but introducing some control variables in order to stabilize in an appropriated sense the corresponding dynamical system of the new model. This is a kind of MIMO nonlinear system control problems and will be solved using the tools in [6].

The thesis has two purposes: The first one is to build a mathematical model that better approximates (with respect to the mathematical model in [2]) to the behaviour of the wine fermentation process with the addition of certain amount of nitrogen at some instant of time, based in [2]. This mathematical model is described by mean ordinary differential equations including some parameters which will be identified solving some optimization problems. The second purpose of the thesis is to study the improved model but introducing some control variables in order to stabilize in an appropriated sense the corresponding dynamical system of the new model. This is a kind of MIMO nonlinear system control problems and will be solved using the tools in [6].La tesis tiene dos objetivos: El primero es construir un modelo matemático que aproxime mejor (con respecto al modelo matemático en “Modeling th...