Mathematical modelling of the osmotic dehydration of cherry tomato (Lycopersicon esculentum var. cerasiforme)

Osmotic dehydration of cherry tomato as influenced by osmotic agent (sodium chloride and a mixed sodium chloride and sucrose solutions) and solution concentration (10 and 25% w/w) at room temperature (25°C) was studied. Kinetics of water loss and solids uptake were determined by a two parameter model, based on Fick's second law and applied to spherical geometry. The water apparent diffusivity coefficients obtained ranged from 2.17x10-10 to 11.69x10-10 m²/s.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Application of mathematical models for the prediction of adsorption isotherms in solid mixture for mango powder refreshment

Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.

Mathematical modeling of dehydration of 'Fuji' and 'Gala' apples slices using infrared

The objective of this work was to determine and model the infrared dehydration curves of apple slices - Fuji and Gala varieties. The slices were dehydrated until constant mass, in a prototype dryer with infrared heating source. The applied temperatures ranged from 50 to 100 °C. Due to the physical characteristics of the product, the dehydration curve was divided in two periods, constant and falling, separated by the critical moisture content. A linear model was used to describe the constant dehydration period. Empirical models traditionally used to model the drying behavior of agricultural products were fitted to the experimental data of the falling dehydration period. Critical moisture contents of 2.811 and 3.103 kgw kgs-1 were observed for the Fuji and Gala varieties, respectively. Based on the results, it was concluded that the constant dehydration rates presented a direct relationship with the temperature; thus, it was possible to fit a model that describes the moisture content variation in function of time and temperature. Among the tested models, which describe the falling dehydration period, the model proposed by Midilli presented the best fit for all studied conditions.

Mathematical modeling of microbial growth in milk

A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

Evaluation of a new mathematical model to describe Clostridium perfringens growth during the cooling of cooked ground beef

A mathematical model previously developed to study microbial growth in food products under an isothermal environment was adapted to a time-varying temperature regime. The resulting model was applied to study the growth of Clostridium perfringens in meat products. This micro-organism is of particular relevance to public health and economy due to the loss of productivity caused by it. Results showed a similar performance of the model used compared to the Baranyi model under an isothermal situation and a slightly better performance under a non-isothermal temperature profile.

Mathematical modeling of microwave dried celery leaves and determination of the effective moisture diffusivities and activation energy

Celery (Apium graveolens L. var. secalinum Alef) leaves with 50±0.07 g weight and 91.75±0.15% humidity (~11.21 db) were dried using 8 different microwave power densities ranging between 1.8-20 W g-1, until the humidity fell down to 8.95±0.23% (~0.1 db). Microwave drying processes were completed between 5.5 and 77 min depending on the microwave power densities. In this study, measured values were compared with predicted values obtained from twenty thin layer drying theoretical, semi-empirical and empirical equations with a new thin layer drying equation. Within applied microwave power density; models whose coefficient and correlation (R²) values are highest were chosen as the best models. Weibull distribution model gave the most suitable predictions at all power density. At increasing microwave power densities, the effective moisture diffusivity values ranged from 1.595 10-10 to 6.377 10-12 m2 s-1. The activation energy was calculated using an exponential expression based on Arrhenius equation. The linear relationship between the drying rate constant and effective moisture diffusivity gave the best fit.

O avanço do processo de matematização na academia brasileira de economia desde a década de 1980

Looking at the economic discourse, we try to study in this article how has mathematization in economics advanced in Brazil in the last three decades. To see this, we have classified into several categories all articles published in three major economic journals of the country (Revista Brasileira de Economia, Estudos Econômicos and Revista de Economia Política) and the publications made in the meetings ANPEC from 1981 to 2010, according to the type of argument used. The total of articles analyzed adds up to 5.733. We try to see how the path of economic discourse, making it more mathematical, did develop. We found that there was an increased use of a formalized language from the mid-1990s onwards. Finally, to confirm our findings, we focus on the process of mathematization through the observation of quantitative variable: equations per article.

As definições teóricas de direitos humanos de Jürgen Habermas: o princípio legal e as correções morais[ign] [title language="en"]The theoretical definitions of human rights of Jürgen Habermas[ign]: [subtitle]legal principle and moral corrections

No entendimento de Habermas, "direito", na expressão "direitos humanos", é um conceito jurídico, donde direitos humanos, para ele, serem direitos jurídicos, normas legais declaradas em atos de fundações do Estado ou anunciadas em convenções do direito internacional e/ou constituições estatais. Ao conceber assim os direitos e tematizar os direitos humanos numa abordagem tríplice (focando-os entre moral, direito e política), ele fornece diferentes definições teóricas dos direitos humanos. O texto apresenta uma exposição sistemática dessas definições e focaliza os diferentes problemas que motivaram Habermas a alterar e ampliar suas concepções de direitos humanos.

Razão e democracia: uso público da razão e política deliberativa em Habermas[ign] [title language="en"]Reason and democracy[ign]: [subtitle]Public use of reason and deliberative politics in Habermas

O objetivo do artigo é examinar como Habermas, orientado pela intuição normativa do uso público da razão, reconstrói uma concepção procedimental de democracia deliberativa, que, sem desconsiderar da dimensão estratégica e instrumental da esfera pública e da política, reformula a dimensão epistêmica da democracia: a aceitabilidade racional dos acordos políticos. Inicialmente, apresento brevemente a análise sociológica e histórica do conceito de esfera pública crítica, realizada em Mudança Estrutural da Esfera Pública (1962), para, em seguida, expor duas linhas de argumentação sobre o conceito de esfera pública e de política deliberativa, em Direito e Democracia (1992): a que se refere ao princípio de legitimação baseado na razão pública como uma reconstrução intersubjetiva e política do conceito kantiano de autonomia; e a que concerne aos aspectos essenciais da teoria crítica da sociedade fundada na distinção entre mundo da vida e sistema e a "tradução" sociológica e institucional do uso público da razão, nos conceitos de sociedade civil e esfera pública.