En este trabajo se muestra la construcción de una función polinomial de grado n, dando previamente un conjunto de n puntos , los cuales serán puntos fijos de dicha función. Este estudio aborda el problema inverso en el caso polinomial; pues en el sentido clásico se tiene a priori una función; y de allí se hace el estudio sobre la existencia de puntos fijos. Además, se estudia el comportamiento de los puntos fijos a través del análisis de la estabilidad, a partir del uso de un parámetro.

In this paper we construct a vector function with a fixed point given previously, from the fixed points of a quadratic function. Our goal is to provide a criterion for the assignment of values to the elements of the matrix associated to the vector function, which will allow to establish the stability of the system, ensuring that said fixed point is an attractor.

En este trabajo se muestra la construcción de una función polinomial de grado n, dando previamente un conjunto de n puntos , los cuales serán puntos fijos de dicha función. Este estudio aborda el problema inverso en el caso polinomial; pues en el sentido clásico se tiene a priori una función; y de allí se hace el estudio sobre la existencia de puntos fijos. Además, se estudia el comportamiento de los puntos fijos a través del análisis de la estabilidad, a partir del uso de un parámetro.

In this paper we construct a vector function with a fixed point given previously, from the fixed points of a quadratic function. Our goal is to provide a criterion for the assignment of values to the elements of the matrix associated to the vector function, which will allow to establish the stability of the system, ensuring that said fixed point is an attractor.

The aim this work was to compare the extraction process optimization of total glucosinolates of maca flour (Lepidium meyenii) (ETGMF) using RS for Box-Behnken (RSBB) Design with that of GA, according to x1: temperature (°C), x2: ethanol (%), x3: ratio solvent/raw material and x4: extraction time (min). TG were identified and quantified using HPLC. The variables (x1, x2, x3, x4) that influence their extraction were evaluated using a RSBB with the software Statistica and Wolfram Mathematica for the AG. From the development of the RSBB, a second order equation with R2 = 0.74794, p = 1.88248E-10 << 0.05 with 11% average absolute error was obtained; it showed the consistency of the model. It was not possible to obtain an optimal value of the ETGMF using RSBB because of the existence of two optimal zones due to the configuration of a chair surface. After 2000 iterations using GA, the ma...

A bi-factorial experimental design was considered to assess moisture variation of sweet potato-quinoa-kiwicha flakes (SP-Q-K) caused by the changes in the rotational speed and steam pressure of a rotary drum dryer (RDD). As it is a design with discrete variables, there is a limitation in the modeling and optimization thus techniques of Artificial Intelligence (AI): Artificial Neural Networks (ANN), Fuzzy Logic (FL) and Genetic Algorithms (GA), were applied, and their prediction ability evaluated. Due to the limitation of data for proper training, the ANN did not allow a correct prediction of the experimental data. Response Surface Methodology (RSM) was employed to obtain the relational equation among the experimental variables, which was used as the objective function with GA, and this allowed moisture optimization. Because of this, it is recommended to integrate RSM and GA into optimiza...

The aim this work was to compare the extraction process optimization of total glucosinolates of maca flour (Lepidium meyenii) (ETGMF) using RS for Box-Behnken (RSBB) Design with that of GA, according to x1: temperature (°C), x2: ethanol (%), x3: ratio solvent/raw material and x4: extraction time (min). TG were identified and quantified using HPLC. The variables (x1, x2, x3, x4) that influence their extraction were evaluated using a RSBB with the software Statistica and Wolfram Mathematica for the AG. From the development of the RSBB, a second order equation with R2 = 0.74794, p = 1.88248E-10 << 0.05 with 11% average absolute error was obtained; it showed the consistency of the model. It was not possible to obtain an optimal value of the ETGMF using RSBB because of the existence of two optimal zones due to the configuration of a chair surface. After 2000 iterations using GA, the ma...

A bi-factorial experimental design was considered to assess moisture variation of sweet potato-quinoa-kiwicha flakes (SP-Q-K) caused by the changes in the rotational speed and steam pressure of a rotary drum dryer (RDD). As it is a design with discrete variables, there is a limitation in the modeling and optimization thus techniques of Artificial Intelligence (AI): Artificial Neural Networks (ANN), Fuzzy Logic (FL) and Genetic Algorithms (GA), were applied, and their prediction ability evaluated. Due to the limitation of data for proper training, the ANN did not allow a correct prediction of the experimental data. Response Surface Methodology (RSM) was employed to obtain the relational equation among the experimental variables, which was used as the objective function with GA, and this allowed moisture optimization. Because of this, it is recommended to integrate RSM and GA into optimiza...