Mathematical models to describe the volumetric shrinkage rate of red beans during drying

The present study aimed to determine the volumetric shrinkage rate of bean (Phaseolus vulgaris L.) seeds during air-drying under different conditions of air, temperature and relative humidity, and to adjust several mathematical models to the empiric values observed, and select the one that best represents the phenomenon. Six mathematical models were adjusted to the experimental values to represent the phenomenon. It was determined the degree of adjustment of each model from the value of the coefficient of determination, the behavior of the distribution of the residuals, and the magnitude of the average relative and estimated errors. The rate of volumetric shrinkage that occurred in bean seeds during drying is between 25 and 37%. It basically depends on the final moisture content, regardless of the air conditions during drying. The Modified Bala & Woods' model best represented the process.

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.

Can future systemic financial risks be quantified?: ergodic vs nonergodic stochastic processes

Different axioms underlie efficient market theory and Keynes's liquidity preference theory. Efficient market theory assumes the ergodic axiom. Consequently, today's decision makers can calculate with actuarial precision the future value of all possible outcomes resulting from today's decisions. Since in an efficient market world decision makers "know" their intertemporal budget constraints, decision makers never default on a loan, i.e., systemic defaults, insolvencies, and bankruptcies are impossible. Keynes liquidity preference theory rejects the ergodic axiom. The future is ontologically uncertain. Accordingly systemic defaults and insolvencies can occur but can never be predicted in advance.

Incerteza e não ergodicidade: crítica aos neoclássicos

The starting point of this essay is to show that, in our view, the problem of the traditional economics is not in the deductive method nor the mathematical methods used, but to attribute to economic agents "power" on the future and prescribe the existence of ergodic stochastic processes in their economic analyzes. Thus, building a theory on the ground whose bases are not able to sustain a proper understanding of the world, mainstream economics has difficulties in using the modeling for establishing deductions and conclusions that help understanding the system. Thus, the logical-mathematical rigor in economic models and deduction can be used with appropriate axioms, which is not the case of mainstream economics. Our hypothesis is that the inability of the mainstream in predicting economic crisis is due to the non-recognition of some principles that best describe the dynamics of financialized contemporary capitalism, as the principles of non-ergodicity and Keynesian uncertainty.

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Use of the swat model for hydro-sedimentologic simulation in a small rural watershed

Mathematical models have great potential to support land use planning, with the goal of improving water and land quality. Before using a model, however, the model must demonstrate that it can correctly simulate the hydrological and erosive processes of a given site. The SWAT model (Soil and Water Assessment Tool) was developed in the United States to evaluate the effects of conservation agriculture on hydrological processes and water quality at the watershed scale. This model was initially proposed for use without calibration, which would eliminate the need for measured hydro-sedimentologic data. In this study, the SWAT model was evaluated in a small rural watershed (1.19 km²) located on the basalt slopes of the state of Rio Grande do Sul in southern Brazil, where farmers have been using cover crops associated with minimum tillage to control soil erosion. Values simulated by the model were compared with measured hydro-sedimentological data. Results for surface and total runoff on a daily basis were considered unsatisfactory (Nash-Sutcliffe efficiency coefficient - NSE < 0.5). However simulation results on monthly and annual scales were significantly better. With regard to the erosion process, the simulated sediment yields for all years of the study were unsatisfactory in comparison with the observed values on a daily and monthly basis (NSE values < -6), and overestimated the annual sediment yield by more than 100 %.

Models and applications for risk assessment and prediction of Asian soybean rust epidemics

Asian rust of soybean [Glycine max (L.) Merril] is one of the most important fungal diseases of this crop worldwide. The recent introduction of Phakopsora pachyrhizi Syd. & P. Syd in the Americas represents a major threat to soybean production in the main growing regions, and significant losses have already been reported. P. pachyrhizi is extremely aggressive under favorable weather conditions, causing rapid plant defoliation. Epidemiological studies, under both controlled and natural environmental conditions, have been done for several decades with the aim of elucidating factors that affect the disease cycle as a basis for disease modeling. The recent spread of Asian soybean rust to major production regions in the world has promoted new development, testing and application of mathematical models to assess the risk and predict the disease. These efforts have included the integration of new data, epidemiological knowledge, statistical methods, and advances in computer simulation to develop models and systems with different spatial and temporal scales, objectives and audience. In this review, we present a comprehensive discussion on the models and systems that have been tested to predict and assess the risk of Asian soybean rust. Limitations, uncertainties and challenges for modelers are also discussed.

Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

Adjust of regression models to estimate the rectal temperature of broilers for the first 14 days of life

The broiler rectal temperature (t rectal) is one of the most important physiological responses to classify the animal thermal comfort. Therefore, the aim of this study was to adjust regression models in order to predict the rectal temperature (t rectal) of broiler chickens under different thermal conditions based on age (A) and a meteorological variable (air temperature - t air) or a thermal comfort index (temperature and humidity index -THI or black globe humidity index - BGHI) or a physical quantity enthalpy (H). In addition, through the inversion of these models and the expected t rectal intervals for each age, the comfort limits of t air, THI, BGHI and H for the chicks in the heating phase were determined, aiding in the validation of the equations and the preliminary limits for H. The experimental data used to adjust the mathematical models were collected in two commercial poultry farms, with Cobb chicks, from 1 to 14 days of age. It was possible to predict the t rectal of conditions from the expected t rectal and determine the lower and superior comfort thresholds of broilers satisfactorily by applying the four models adjusted; as well as to invert the models for prediction of the environmental H for the chicks first 14 days of life.

Draft prediction models for soil engaging tines in two soils of Rio Grande do Sul, Brazil

The draft forces of soil engaging tines and theoretical analysis compared to existing mathematical models, have yet not been studied in Rio Grande do Sul soils. From the existing models, those which can get the closest fitting draft forces to real measure on field have been established for two of Rio Grande do Sul soils. An Albaqualf and a Paleudult were evaluated. From the studied models, those suggested by Reece, so called "Universal Earthmoving Equation", Hettiaratchi and Reece, and Godwin and Spoor were the best fitting ones, comparing the calculated results with those measured "in situ". Allowing for the less complexity of Reece's model, it is suggested that this model should be used for modeling draft forces prediction for narrow tines in Albaqualf and Paleudut.

Mathematical modeling applied to the growth of tilapia in net cages in the sub middle of the São Francisco river

This study aimed to apply mathematical models to the growth of Nile tilapia (Oreochromis niloticus) reared in net cages in the lower São Francisco basin and choose the model(s) that best represents the conditions of rearing for the region. Nonlinear models of Brody, Bertalanffy, Logistic, Gompertz, and Richards were tested. The models were adjusted to the series of weight for age according to the methods of Gauss, Newton, Gradiente and Marquardt. It was used the procedure "NLIN" of the System SAS® (2003) to obtain estimates of the parameters from the available data. The best adjustment of the data were performed by the Bertalanffy, Gompertz and Logistic models which are equivalent to explain the growth of the animals up to 270 days of rearing. From the commercial point of view, it is recommended that commercialization of tilapia from at least 600 g, which is estimated in the Bertalanffy, Gompertz and Logistic models for creating over 183, 181 and 184 days, and up to 1 Kg of mass , it is suggested the suspension of the rearing up to 244, 244 and 243 days, respectively.

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.

Drying kinetics of jatropha seeds

Given the necessity of developing jatropha cultivation equipment, this work adjusted different mathematical models to experimental data obtained from the drying of jatropha seeds submitted to different drying conditions and selected the best model to describe the drying process. The experiment was carried out at the Federal Institute of Goiás - Rio Verde Campus. Seeds with initial moisture content of approximately 0.50 (kg water/kg dry matter) were dried in a forced air-ventilated oven, at temperatures of 45, 60, 75, 90 and 105°C to moisture content of 0.10 ± 0.005 (kg water/kg dry matter). The experimental data were adjusted to 11 mathematical models to represent the drying process of agricultural products. The models were compared using the coefficient of determination, chi-square test, relative mean error, estimated mean error and residual distribution. It was found that the increase in the air temperature caused a reduction in the drying time of seeds. The models Midilli and Two Terms were suitable to represent the drying process of Jatropha seeds and between them the use of the Midili model is recommended due to its greater simplicity.

Cytomegalovirus seroepidemiology in an urban community of São Paulo, Brazil

INTRODUCTION: After the era of rubella vaccine, cytomegalovirus (CMV) infection is one of the most frequently causes of mental retardation and congenital deafness. Seroepidemiological studies are necessary to understand the transmission dynamics of the disease. The purpose of the study was to quantify the transmission rate of CMV disease in a community in the state of São Paulo, Brazil. METHODS: Using ELISA test (IgG), a retrospective serological survey looking for CMV antibodies was performed in an non-immunized community. Frozen sera from 443 individuals, randomly selected by cluster sampling technique in the town of Caieiras, São Paulo, were collected from November 1990 to January 1991. Seroprevalence was stratified by age (0-40 years). Mathematical techniques were applied to determine the age-dependent decay function of maternal antibodies during the first year of life, the age-dependent seroprevalence function and the force of infection for CMV in this community. RESULTS: It was observed a descending phase of seropositivity in the first 9 months, but changes in antibody titration were observed between 8 months old and one year of age. The average age of the first infection was 5.02 months of age and 19.84 years, when the age-dependent seroprevalence and the force of infection were analyzed between 10 months of age and 10 years of age and from 10 to 40 years old, respectively. CONCLUSION: CMV infection is highly prevalent among the population studied and infection occurs in the first year of life. This study shows that most women at reproductive age are vulnerable to the first infection, increasing the risk for congenital infection.

Dengue and the risk of urban yellow fever reintroduction in São Paulo State, Brazil

OBJECTIVE: To propose a mathematical method for the estimation of the Basic Reproduction Number, R0, of urban yellow fever in a dengue-infested area. METHODS: The method is based on the assumption that, as the same vector (Aedes aegypti) causes both infections, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic, could be applied to yellow fever dynamics. It is demonstrated that R0 for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period. RESULTS: In this study the analysis was expanded to the epidemiological situation of dengue in São Paulo in the year 2001. The total number of dengue cases increased from 3,582 in 2000 to 51,348 in 2001. It was then calculated R0 for yellow fever for every city which have shown R0 of dengue greater than 1. It was also estimated the total number of unprotected people living in highly risky areas for urban yellow fever. CONCLUSIONS: Currently there is a great number of non-vaccinated people living in Aedes aegypti infested area in the state of São Paulo.