Esterification of Free Fatty Acids with Glycerol within the Biodiesel Production Framework

Companies in the field of the collection and treatment of waste cooking oils (WCO) for subsequent biodiesel production usually have to cope with high acidity oils, which cannot be directly transformed into fatty acid methyl esters due to soap production. Since glycerine is the main byproduct of biodiesel production, these high acidity oils could be esterified with the glycerine surplus to transform the free fatty acids (FFA) into triglycerides before performing the transesterification. In this work, commercial glycerol was esterified with commercial fatty acids and commercial fatty acid/lampante olive oil mixtures over tin (II) chloride. In the first set of experiments, the esterification of linoleic acid with glycerol excess from 20 to 80% molar over the stoichiometric was performed. From 20% glycerol excess, there was no improvement in FFA reduction. Using 20% glycerol excess, the performance of a biochar obtained from heavy metal-contaminated plant roots was compared to that of SnCl2. Then, the effect of the initial FFA content was assessed using different oleic acid/lampante olive oil mixtures. The results illustrated that glycerolysis was impeded at initial FFA contents lower than 10%. Finally, the glycerolysis of a WCO with 9.94% FFA was assayed, without success

Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out.This work was supported in part by the Ministerio de Economía, Industria y Competitividad, Spain, under Grant MTM2017-85568-P and by the Consejería de Economía y Conocimiento de la Junta de Andalucía, Spain under Grant A-FQM-456-UGR18

T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms

The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided.Ministerio de Economía, Industria y Competitividad, Spain, under Grant MTM2017-85568-PFEDER/Junta de Andalucía-Consejería de Economía y Conocimiento, Spain, Grant A-FQM-456-UGR1

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure. Some examples based on simulated sample paths and real data illustrate this development

Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary.Universita degli Studi di Salerno within the CRUI-CARE Agreemen

Recommendations for Future Articles on Knowledge, Attitudes and Practices in IJMS

N/

El papel de la cultura en la evaluación de la felicidad entre países. Una aproximación fsQCA

The happiness of countries has important effects on their image, prestige, attraction of funds ortourism. Furthermore, there are rankings and models developed to try to explain what it dependson. This paper explores the possibility of improving the World Happiness Report model intwo ways: the inclusion of cultural variables and the analysis of possible interactions betweenvariables. To this end, the original database has been supplemented with Hofstede's culturaldimensions, replicating the original regression analyses and using an fsQCA. The results showthe need to include culture in this type of studies and the existence of three different models ofcountries with high happiness scoresLa felicidad de los países tiene importantes efectos en la imagen, prestigio, captación defondos o turismo de los mismos y se elaboran rakings y modelos que intentan explicar dequé depende la misma. En este trabajo se explora la posibilidad de mejorar el modelo delWorld Happiness Report mediante dos vías: la inclusión de variables culturales y el análisis deposibles interacciones entre las variables. Para ello, se ha completado la base de datos originalcon las dimensiones culturales del conocido modelo de Hofstede, replicando los análisis deregresión originales y utilizando un analisis fsQCA. Los resultados muestran la necesidad deincluir la cultura en este tipo de estudios y la existencia de tres modelos diferentes de países conaltas puntuaciones en felicidad

Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors

Different versions of the lognormal diffusion process with exogenous factors have been used in recent years to model and study the behavior of phenomena following a given growth curve. In each case considered, the estimation of the model has been addressed, generally by maximum likelihood (ML), as has been the study of several characteristics associated with the type of curve considered. For this process, a unified version of the ML estimation problem is presented, including how to obtain estimation errors and asymptotic confidence intervals for parametric functions when no explicit expression is available for the estimators of the parameters of the model. The Gompertz-type diffusion process is used here to illustrate the application of the methodology.This work was supported in part by the Ministerio de Economía, Industria y Competitividad, Spain, under Grants MTM2014-58061-P and MTM2017-85568-P

Study of a general growth model

We discuss a general growth curve including several parameters, whose choice leads to a variety of models including the classical cases of Malthusian, Richards, Gompertz, Logistic and some their generalizations. The advantage is to obtain a single mathematically tractable equation from which the main characteristics of the considered curves can be deduced. We focus on the effects of the involved parameters through both analytical results and computational evaluations