A virtual learning environment for pregraduate mathematical students

Peer-reviewed

Minimization of the experimental workload for the prediction of pollutants propagation in rivers. Mathematical modelling and knowledge re-use

The present thesis in focused on the minimization of experimental efforts for the prediction of pollutant propagation in rivers by mathematical modelling and knowledge re-use. Mathematical modelling is based on the well known advection-dispersion equation, while the knowledge re-use approach employs the methods of case based reasoning, graphical analysis and text mining. The thesis contribution to the pollutant transport research field consists of: (1) analytical and numerical models for pollutant transport prediction; (2) two novel techniques which enable the use of variable parameters along rivers in analytical models; (3) models for the estimation of pollutant transport characteristic parameters (velocity, dispersion coefficient and nutrient transformation rates) as functions of water flow, channel characteristics and/or seasonality; (4) the graphical analysis method to be used for the identification of pollution sources along rivers; (5) a case based reasoning tool for the identification of crucial information related to the pollutant transport modelling; (6) and the application of a software tool for the reuse of information during pollutants transport modelling research. These support tools are applicable in the water quality research field and in practice as well, as they can be involved in multiple activities. The models are capable of predicting pollutant propagation along rivers in case of both ordinary pollution and accidents. They can also be applied for other similar rivers in modelling of pollutant transport in rivers with low availability of experimental data concerning concentration. This is because models for parameter estimation developed in the present thesis enable the calculation of transport characteristic parameters as functions of river hydraulic parameters and/or seasonality. The similarity between rivers is assessed using case based reasoning tools, and additional necessary information can be identified by using the software for the information reuse. Such systems represent support for users and open up possibilities for new modelling methods, monitoring facilities and for better river water quality management tools. They are useful also for the estimation of environmental impact of possible technological changes and can be applied in the pre-design stage or/and in the practical use of processes as well.

Automatic evaluation and data generation for analytical chemistry instrumental analysis exercises

In general, laboratory activities are costly in terms of time, space, and money. As such, the ability to provide realistically simulated laboratory data that enables students to practice data analysis techniques as a complementary activity would be expected to reduce these costs while opening up very interesting possibilities. In the present work, a novel methodology is presented for design of analytical chemistry instrumental analysis exercises that can be automatically personalized for each student and the results evaluated immediately. The proposed system provides each student with a different set of experimental data generated randomly while satisfying a set of constraints, rather than using data obtained from actual laboratory work. This allows the instructor to provide students with a set of practical problems to complement their regular laboratory work along with the corresponding feedback provided by the system's automatic evaluation process. To this end, the Goodle Grading Management System (GMS), an innovative web-based educational tool for automating the collection and assessment of practical exercises for engineering and scientific courses, was developed. The proposed methodology takes full advantage of the Goodle GMS fusion code architecture. The design of a particular exercise is provided ad hoc by the instructor and requires basic Matlab knowledge. The system has been employed with satisfactory results in several university courses. To demonstrate the automatic evaluation process, three exercises are presented in detail. The first exercise involves a linear regression analysis of data and the calculation of the quality parameters of an instrumental analysis method. The second and third exercises address two different comparison tests, a comparison test of the mean and a t-paired test.

Mathematical equation correction to spectral and transport interferences in high-resolution continuum source flame atomic absorption spectrometry: determination of lead in phosphoric acid

In this work, a new mathematical equation correction approach for overcoming spectral and transport interferences was proposed. The proposal was applied to eliminate spectral interference caused by PO molecules at the 217.0005 nm Pb line, and the transport interference caused by variations in phosphoric acid concentrations. Correction may be necessary at 217.0005 nm to account for the contribution of PO, since Atotal217.0005 nm = A Pb217.0005 nm + A PO217.0005 nm. This may be easily done by measuring other PO wavelengths (e.g. 217.0458 nm) and calculating the relative contribution of PO absorbance (A PO) to the total absorbance (Atotal) at 217.0005 nm: A Pb217.0005 nm = Atotal217.0005 nm - A PO217.0005 nm = Atotal217.0005 nm - k (A PO217.0458 nm). The correction factor k is calculated from slopes of calibration curves built up for phosphorous (P) standard solutions measured at 217.0005 and 217.0458 nm, i.e. k = (slope217.0005 nm/slope217.0458 nm). For wavelength integrated absorbance of 3 pixels, sample aspiration rate of 5.0 ml min-1, analytical curves in the 0.1 - 1.0 mg L-1 Pb range with linearity better than 0.9990 were consistently obtained. Calibration curves for P at 217.0005 and 217.0458 nm with linearity better than 0.998 were obtained. Relative standard deviations (RSD) of measurements (n = 12) in the range of 1.4 - 4.3% and 2.0 - 6.0% without and with mathematical equation correction approach were obtained respectively. The limit of detection calculated to analytical line at 217.0005 nm was 10 µg L-1 Pb. Recoveries for Pb spikes were in the 97.5 - 100% and 105 - 230% intervals with and without mathematical equation correction approach, respectively.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

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.

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.

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I-100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

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.

Mathematical simulation parameters for drying of cassava starch pellets

Based on experimental tests, it was obtained the equations for drying, equilibrium moisture content, latent heat of vaporization of water contained in the product and the equation of specific heat of cassava starch pellets, essential parameters for realizing modeling and mathematical simulation of mechanical drying of cassava starch for a new technique proposed, consisting of preformed by pelleting and subsequent artificial drying of starch pellets. Drying tests were conducted in an experimental chamber by varying the air temperature, relative humidity, air velocity and product load. The specific heat of starch was determined by differential scanning calorimetry. The generated equations were validated through regression analysis, finding an appropriate correlation of the data, which indicates that by using these equations, can accurately model and simulate the drying process of cassava starch pellets.

Flexible multibody approach in bone strain estimation during physical activity:

Bone strain plays a major role as the activation signal for the bone (re)modeling process, which is vital for keeping bones healthy. Maintaining high bone mineral density reduces the chances of fracture in the event of an accident. Numerous studies have shown that bones can be strengthened with physical exercise. Several hypotheses have asserted that a stronger osteogenic (bone producing) effect results from dynamic exercise than from static exercise. These previous studies are based on short-term empirical research, which provide the motivation for justifying the experimental results with a solid mathematical background. The computer simulation techniques utilized in this work allow for non-invasive bone strain estimation during physical activity at any bone site within the human skeleton. All models presented in the study are threedimensional and actuated by muscle models to replicate the real conditions accurately. The objective of this work is to determine and present loading-induced bone strain values resulting from physical activity. It includes a comparison of strain resulting from four different gym exercises (knee flexion, knee extension, leg press, and squat) and walking, with the results reported for walking and jogging obtained from in-vivo measurements described in the literature. The objective is realized primarily by carrying out flexible multibody dynamics computer simulations. The dissertation combines the knowledge of finite element analysis and multibody simulations with experimental data and information available from medical field literature. Measured subject-specific motion data was coupled with forward dynamics simulation to provide natural skeletal movement. Bone geometries were defined using a reverse engineering approach based on medical imaging techniques. Both computed tomography and magnetic resonance imaging were utilized to explore modeling differences. The predicted tibia bone strains during walking show good agreement with invivo studies found in the literature. Strain measurements were not available for gym exercises; therefore, the strain results could not be validated. However, the values seem reasonable when compared to available walking and running invivo strain measurements. The results can be used for exercise equipment design aimed at strengthening the bones as well as the muscles during workout. Clinical applications in post fracture recovery exercising programs could also be the target. In addition, the methodology introduced in this study, can be applied to investigate the effect of weightlessness on astronauts, who often suffer bone loss after long time spent in the outer space.

Training executive functions in the laboratory and in real life : cognitive consequences of computer-based exercises and bilingualism

The question of the trainability of executive functions and the impact of such training on related cognitive skills has stirred considerable research interest. Despite a number of studies investigating this, the question has not yet been solved. The general aim of this thesis was to investigate two very different types of training of executive functions: laboratory-based computerized training (Studies I-III) and realworld training through bilingualism (Studies IV-V). Bilingualism as a kind of training of executive functions is based on the idea that managing two languages requires executive resources, and previous studies have suggested a bilingual advantage in executive functions. Three executive functions were studied in the present thesis: updating of working memory (WM) contents, inhibition of irrelevant information, and shifting between tasks and mental sets. Studies I-III investigated the effects of computer-based training of WM updating (Study I), inhibition (Study II), and set shifting (Study III) in healthy young adults. All studies showed increased performance on the trained task. More importantly, improvement on an untrained task tapping the trained executive function (near transfer) was seen in Study I and II. None of the three studies showed improvement on untrained tasks tapping some other cognitive function (far transfer) as a result of training. Study I also used PET to investigate the effects of WM updating training on a neurotransmitter closely linked to WM, namely dopamine. The PET results revealed increased striatal dopamine release during WM updating performance as a result of training. Study IV investigated the ability to inhibit task-irrelevant stimuli in bilinguals and monolinguals by using a dichotic listening task. The results showed that the bilinguals exceeded the monolinguals in inhibiting task-irrelevant information. Study V introduced a new, complementary research approach to study the bilingual executive advantage and its underlying mechanisms. To circumvent the methodological problems related to natural groups design, this approach focuses only on bilinguals and examines whether individual differences in bilingual behavior correlate with executive task performances. Using measures that tap the three above-entioned executive functions, the results suggested that more frequent language switching was associated with better set shifting skills, and earlier acquisition of the second language was related to better inhibition skills. In conclusion, the present behavioral results showed that computer-based training of executive functions can improve performance on the trained task and on closely related tasks, but does not yield a more general improvement of cognitive skills. Moreover, the functional neuroimaging results reveal that WM training modulates striatal dopaminergic function, speaking for training-induced neural plasticity in this important neurotransmitter system. With regard to bilingualism, the results provide further support to the idea that bilingualism can enhance executive functions. In addition, the new complementary research approach proposed here provides some clues as to which aspects of everyday bilingual behavior may be related to the advantage in executive functions in bilingual individuals.