The Bessel expression is an ordinary diff erential equation of second order (EDOPO), whose solutions are spherical and can be solved by Frobenius' methods, indeterminate series, and coeffi cients; whose values can be used very well and easily in food engineering and technology. Their solutions are specifi ed in four parts, of which those of the type are those that have an application in the present study. The Bessel EDOPO was solved in its four possibilities, in which the values and behaviors are given in tables and graphs in detail. Th e corresponding values were used in the temperature distribution for cylindrical containers of known dimensions using the equations of heat transfer by conduction, preferably, coming from the Fourier theory, facilitating the improvement, modifi cation, and design of new processes. The results of the temperature distribution were calculated by the respecti...

The rheological properties of different liquid foods and especially of fruit-based syrups depend on different aspects, among which are composition and temperature. One of the most influential aspects is the water content of the syrup and, in general, when the moisture content increases, the viscosity of the fruit syrup decreases. The objective of this work was to determine the physicochemical rheology of the fruit syrup (honey) for the Peruvian nougat "Doña pepa", to obtain the best percentage of synergism of the xanthan and tara gums, and the most suitable formulation for the fruit syrup. Six concentrations of 0.60 %, 0.80 %, 1.00 %, 1.20 %, 1.20 %, 1.40 % and 1.60 % were determined for the two gums. At each of these percentages the apparent viscosity was determined, thus characterizing the flow behavior of the product. The results of pH, soluble solids, and dynamic viscosity of the co...

The study describes the biotechnological process, a product of the hydrolyzed starch's fermentation using Saccharomyces cerevisiae Meyen ex E.C. Hansen as an enzyme agent. The behavior and speeds of the three intervening components (consumed substrate [Sc], product [P], and enzymatic agent [E]) were evaluated and was formulated the corresponding logistic models, independently, for each of the components and their subsequent application and analysis. Also, the saturation constant of the substrate [Km] was determined. The maximumconcentration for the enzyme reached a value of 9.80 g·L-1, and the reaction rate constants were 0.27 h-1, 0.20 h-1, and 0.22 h-1, for the concentrations of E, Sc, and P, respectively. The maximum speeds (and the optimal times) for the enzyme, substrate consumed, and product were 0.66 gL-1h-1 (6.80 h), 6.68 gL-1h-1 (11.50h), and 3,15 gL-1h-1 (11.40h), respectively...

The effects of concentration and temperature on the thermo-physical properties of apple juice were studied, in which density and viscosity were measured at different temperature and concentration conditions, varying from 20°C to 80°C and from 12 to 70° Brix, respectively. Density was determined by the pycnometer method and viscosity by Hooke's falling sphere method, based on Stokes' law. The density results were correlated several times, arriving, by the least squares method, at a multiple linear regression model, of three terms; while the viscosity results proved to be more difficult to correlate, which, by the least squares method, arrived at a multiple linear regression model, of six terms.  The experimental mathematical models can be used to obtain the density and viscosity data within the temperature and concentration conditions indicated in the study. Key words: density –...

While it is true that vaccines generate immunity with a high degree of effectiveness and that in Peru, a certain time was spent initiating the COVID-19 disease, a vaccination process that was developed logistically. The objective was to obtain the mathematical model of the COVID-19 vaccination process in Peru, to estimate the number of people vaccinated, the critical time for which the estimated rate of vaccinated people has been the highest value, and to specify the date on which the highest number of people vaccinated has occurred. The methodology was based on determining the form of dispersion of the vaccination process, this being a logistic distribution and considering that a mathematical model is a mathematical description, by means of a function of a real-world phenomenon, such as the number of people vaccinated against the COVID-19 disease. The model presented a correlation coeff...

The calculation of Bernoulli numbers is because there are numerous mathematical expressions and environmental engineering phenomena in which they can be applied. Although it is true that, with the aid of the computer and the use of programs, there are a great number of them; in the current references they are published in a reduced number and, therefore, when using them, unsatisfactory approximations are made. The purpose was to calculate the first 20 Bernoulli numbers, apply them to mathematics (∫ ln(cosx)dx) and environmental engineering, quantifying the alkalinity of natural water in the form of calcium carbonate (CaCO3)(mg/l ), measuring carbon dioxide (CO2). There is a great variety of relations containing Bernoulli numbers presented in several practical applications of mathematics. The best relationships used here are binomial developments. Employing the appropriate equations, th...

The objective of the work was to develop a mathematical model to analyze the behavior of mortality in the People’s Republic of China caused by COVID-2019. The logistic model was applied to the data reported in Table 1, between January 11 and April 12, 2020. The model formulated was linearized and presented in two forms, which, with the same value of B, introducing a correction factor for the independent variable, t, which serves as “period” and applying the method of minimum squares, the parameters A, k and r were determined, obtaining the respective model (Equation 10), which was analyzed with Pearson’s correlation coefficient, obtaining the correlation coefficient r=-0.9668 and the determination coefficient r^2×100=93.48 %; deducing the best estimate of the model to the process in modeling (Equation 10) to analyze the mortality phenomenon. Likewise, the mortality rate was eval...

El objetivo del trabajo fue desarrollar un modelo matemático que haga la predicción del comportamiento epidemiológico causado por SARS-CoV2 (COVID-19) en la República Popular de China. El modelo de basó en determinar la relación entre la variación del número de casos reportados (dN) y la variación del tiempo transcurrido (dt), denominado velocidad con que el fenómeno de casos reportados en China. La velocidad del fenómeno se determinó por diferenciación gráfica, con el propósito de encontrar una Ecuación Diferencial Ordinaria de Primer Orden (EDOPO), tipo lineal. Esta ecuación fue resuelta entre las condiciones iniciales de los datos reportados (t=1 día, N=278 casos reportados), llegando a obtener el modelo predictivo correspondiente. El modelo predictivo (Ecuación 15) fue validado estadísticamente, evaluando su coeficiente de correlación r de Pearson, cuyo valor es ...

The use of citrus by-products was evaluated through the fermentation of the orange peel by means of Aspergillus niger van Tieghem strain, 1867, which was obtained by inoculation in a petri dish, at a temperature of 35°C and a pH of 4,3. The crushed orange peel was used as a substrate, partially dehydrated, spread on trays, dried in cardboard trays and without heat pretreatment, adding only components and mineral nutrients, and A. niger was cultivated at different fermentation temperatures between 8°C and 40 °C. Upon completion of the fermentation process of the pretreated orange peel, maximum percentages of transformation of mineral nitrogen to organic nitrogen of 34.5% were obtained, for a value of the thermal integral between 0°C and 320°C per day, obtaining for a kg of dry matter, 6.6% protein for 600 g of product (feed) with 18% protein. Finally, the variation of the pH of the s...

The study describes the biotechnological process, a product of the hydrolyzed starch's fermentation using Saccharomyces cerevisiae Meyen ex E.C. Hansen as an enzyme agent. The behavior and speeds of the three intervening components (consumed substrate [Sc], product [P], and enzymatic agent [E]) were evaluated and was formulated the corresponding logistic models, independently, for each of the components and their subsequent application and analysis. Also, the saturation constant of the substrate [Km] was determined. The maximumconcentration for the enzyme reached a value of 9.80 g·L-1, and the reaction rate constants were 0.27 h-1, 0.20 h-1, and 0.22 h-1, for the concentrations of E, Sc, and P, respectively. The maximum speeds (and the optimal times) for the enzyme, substrate consumed, and product were 0.66 gL-1h-1 (6.80 h), 6.68 gL-1h-1 (11.50h), and 3,15 gL-1h-1 (11.40h), respectively...

The effects of concentration and temperature on the thermo-physical properties of apple juice were studied, in which density and viscosity were measured at different temperature and concentration conditions, varying from 20°C to 80°C and from 12 to 70° Brix, respectively. Density was determined by the pycnometer method and viscosity by Hooke's falling sphere method, based on Stokes' law. The density results were correlated several times, arriving, by the least squares method, at a multiple linear regression model, of three terms; while the viscosity results proved to be more difficult to correlate, which, by the least squares method, arrived at a multiple linear regression model, of six terms.  The experimental mathematical models can be used to obtain the density and viscosity data within the temperature and concentration conditions indicated in the study. Key words: density –...

The Bessel expression is an ordinary diff erential equation of second order (EDOPO), whose solutions are spherical and can be solved by Frobenius' methods, indeterminate series, and coeffi cients; whose values can be used very well and easily in food engineering and technology. Their solutions are specifi ed in four parts, of which those of the type are those that have an application in the present study. The Bessel EDOPO was solved in its four possibilities, in which the values and behaviors are given in tables and graphs in detail. Th e corresponding values were used in the temperature distribution for cylindrical containers of known dimensions using the equations of heat transfer by conduction, preferably, coming from the Fourier theory, facilitating the improvement, modifi cation, and design of new processes. The results of the temperature distribution were calculated by the respecti...

The rheological properties of different liquid foods and especially of fruit-based syrups depend on different aspects, among which are composition and temperature. One of the most influential aspects is the water content of the syrup and, in general, when the moisture content increases, the viscosity of the fruit syrup decreases. The objective of this work was to determine the physicochemical rheology of the fruit syrup (honey) for the Peruvian nougat "Doña pepa", to obtain the best percentage of synergism of the xanthan and tara gums, and the most suitable formulation for the fruit syrup. Six concentrations of 0.60 %, 0.80 %, 1.00 %, 1.20 %, 1.20 %, 1.40 % and 1.60 % were determined for the two gums. At each of these percentages the apparent viscosity was determined, thus characterizing the flow behavior of the product. The results of pH, soluble solids, and dynamic viscosity of the co...

Monkeypox (mpox) is a virus of the same family as human smallpox, detected in tropical forest regions in May 2022 in the United Kingdom and subsequently in Latin America. The objective of the present investigation was to study, by means of mathematical models, the infectivity of Monkeypox in North America in epidemiological comparison with South America. Data on monkeypox infectivity in both North and South America between the beginning of June 2022 and the end of February 2023 have been taken into account. By performing the pandemic dispersion, it was determined that the mathematical model of estimation is: ; with which the number of people infected with monkeypox in both North and South America was estimated. The mathematical model for estimating the rate of infection with monkeypox in both North and South America was determined: . At the 5% significance level, the variances of the con...

Se ha desarrollado un modelo matemático que permita analizar el comportamiento de la mortalidad en la República Popular de China ocasionado por COVID-2019. Se aplicó el modelo logístico para los datos reportados entre 11 de enero y el 12 de abril del 2020. El modelo formulado fue linealizado y planteado en dos formas. La primera, evaluando el factor de corrección B, que hace las veces de cantidad máxima de fallecidos. Se determinaron los parámetros A, k y r, obteniendo el modelo (Ecuación 7), con un coeficiente de correlación r=-0,9660 y el coeficiente de determinación r^2×100=93,31 %. La segunda forma, con el mismo valor de B, introduciendo un factor de corrección para la variable independiente, t, que hace las veces de “periodo”. Se determinaron los parámetros A, k y r, obteniendo el modelo (Ecuación 10), con un coeficiente de correlación r=-0,9668 y el coeficiente d...

Objective. Determine was mathematically modeled using the expression=(1+×−×)⁄, which is a predictive equation. Using this model, the number of deaths due to COVID-19 worldwide was estimated.Design. Correlational, prospective, predictive and transversal study. Participans.The data on deceased individuals due to the COVID-19 disease up to November 5, 2022, was considered. Main measurement.This data was used to analyze the pandemic dispersion, which was determined to exhibit logistic sigmoidal behavior. By deriving Equation 3, the rate of deaths due to COVID-19 worldwide was calculated, obtaining the predictive model represented in Figure 3.Results. Using Equation (5), the critical time=447and the maximum speed (̂)á=1525028,553/and the date when the global death rate due to COVID-19 reached its maximum was July 6, 2021. The Pearson correlation coefficient between the elapsed time ()...

Se ha obtenido pan enriquecido con minerales (Ca, P y Fe) y proteínas a base de la incorporación de harinas de sangre de pollo (Gallus domésticus) y de muña (Minthostachis mollis), las mismas que han sido caracterizadas química y nutricionalmente. El método experimental utilizado fue para predecir lo que al final se esperaba, previo planteamiento de trabajo en condiciones optimas de laboratorio, con variables controladas y un diseño experimental de 24 repeticiones. Los materiales, equipos y métodos de análisis fueron los idóneos para cumplir con los objetivos planteados en la investigación. Las materias primas se obtuvieron adecuadamente, de lugares adecuados, bajo condiciones idóneas en todo sentido. La técnica fue la recolección de datos de observación de campo, donde se determinó el dominio y rango de las variables, tanto dependientes como independientes. Los datos se ...

The objective was to evaluate the effect of the COVID-19 pandemic on the eating habits and physical activity of students from the Federico Villarreal National University. For this purpose, a structured multiple-choice questionnaire was distributed via WhatsApp and email, which was subdivided into the sections of Generalities, Physical Activity and Eating Habits (HA), and the data was processed with Excel Microsoft 365. 215 people were surveyed, it was determined that physical activity during social isolation (SA) changed from vigorous to sedentary, with men reducing their practice of exercises that required greater physical effort. It was determined that the average frequencies before the pandemic / during social isolation / current for men were: 2,0 / 1,9 / 2,0 days respectively and for women 1,8 / 1,9 / 1,8 days, the intake of food prepared at home increased, varying the composition an...

The objective was to relate eating habits with the body mass index and physical activity of university students. 237 students from the National University Federico Villarreal and 163 students from the National University of Engineering were surveyed in 2022, using an online form whose items were distributed in demographic data to characterize the students and their eating behavior (EB). Th e Likert scale was used. Th e data was analyzed with Microsoft Offi ce Excel updated to 2023. It was found that the average Body Mass Index (BMI) of the students is 24.5, falling within the normal classifi cation, they tend to eat more foods prepared at home, the Nutritional quality is subject to accessibility due to time and money; they usually consume lunch, omitting other meals. A low percentage considers they have Good eating habits. For the study group, physical activity was reduced during the dev...

La Organización Mundial de la Salud recibió un informe de la República Popular China sobre neumonía atípica en la ciudad de Wuhan, el 31 de diciembre de 2019. Desde el primer reporte han pasado 105 días (30 de abril), y es poco lo que se conoce sobre el nuevo coronavirus (SARS-CoV2) y la enfermedad COVID-19. Los estudios epidemiológicos de los últimos años ya alertaban sobre nuevos brotes de coronavirus, pero no fueron tomados en consideración, y esto dio lugar a que SARS-CoV2 sea el primer beta-coronavirus que alcanza el estado de pandemia. El diagnóstico está basado en pruebas moleculares para detección del virus y, en pruebas serológicas para la enfermedad. Adicionalmente, se conoce poco sobre los mecanismos de contagio y de transmisión. Aún se está investigando los mecanismos celulares y moleculares que emplea el virus para la infección, adicionando los procesos sim...