We studied the synthesis variables of the faujasite using natural clinker of the Cotopaxi volcano, and allophane (allofanite) from the province of Santo Domingo de los Tsachilas as raw materials, as well as their physicochemical properties and their influence on the catalytic efficiency for Ecuadorian oil and asphalt. The synthesized materials were subjected to laboratory tests, like thermogravimetric characterization, BET area, FTIR, chemisorption and AFM. Tests of catalytic activity in crude oil and asphalt with different °API and percentage of Sulfur showed ranges of optimal efficiency. These ranges contributed to obtain a logistic regression model with min. 90% accuracy, which was entered into a confusion matrix. This function can be optimized in the intervals of each of the variables of any refinery. It is concluded that the logistic regression model for catalytic efficiency is sensitive to changes in the amount of faujasite and allophane (allofanite) in the catalytic cracking process. In the same way, a fundamental dependence of the surface area (BET) was found, which for the case of allophane is formed in contribution of each of the nanopores whose size is in the order of 3 to 5 nm, while the faujasite has nanopore sizes from 17 to 35 nm.

We determine the proton and electron radii by analyzing constructive resonances at minimum entropy for elements with atomic number Z ≥ 11.We note that those radii can be derived from entropy principles and published photoelectric cross sections data from the National Institute of Standards and Technology (NIST). A resonance region with optimal constructive interference is given by a principal wavelength λ of the order of Bohr atom radius. Our study shows that the proton radius deviations can be measured. Moreover, in the case of the electron, its radius converges to electron classical radius with a value of 2.817 fm. Resonance waves afforded us the possibility to measure the proton and electron radii through an interference term. This term, was a necessary condition in order to have an effective cross section maximum at the threshold. The minimum entropy means minimum proton shape deformation and it was found to be (0.830 ± 0.015) fm and the average proton radius was found to be (0.825 − 0.0341; 0.888 + 0.0405) fm.

This paper introduces Hermite's polynomials, in the description of quantum games. Hermite's polynomials are associated with gaussian probability density. The gaussian probability density represents minimum dispersion. I introduce the concept of minimum entropy as a paradigm of both Nash's equilibrium (maximum utility MU) and Hayek equilibrium (minimum entropy ME). The ME concept is related to Quantum Games. Some questions arise after carrying out this exercise: i) What does Heisenberg's uncertainty principle represent in Game Theory and Time Series?, and ii) What do the postulates of Quantum Mechanics indicate in Game Theory and Economics?.

The optimal conditions of the catalytic activation of allophane were evaluated for possible use as a catalyst within a fluidized bed catalytic cracking unit (FCC). The physicochemical properties of natural allophane and activated allophane were studied by using an alkaline activating agent, followed by a hydrothermal treatment. For the characterization, analytical techniques were used: Fourier transform infrared spectroscopy, particle size, (BET) surface area, thermogravimetry (TGA), X-ray diffraction (XRD), chemisorption, X-ray fluorescence (XRF), atomic force microscopy (AFM), and chromatography. The catalytic evaluation was determined by the (MAT) micro activity test equipment constructed according to ASTM D-3907/D3907M-2019. In addition, the Navier–Stokes 3D equations (nonlinear partial derivatives) were studied, which allow studying molecular dynamics contributing substantively to chemical kinetics describing the process of decomposition of crude oil in thermal cracking, determining the maximum temperature at which it retains its properties through the action of heat.