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.

Disruptive innovations at the bottom of the pyramid : can they impact the sustainability of today´s top companies?

Due to the different dynamics required for organizations to serve the emerging market which contains billions of people at the bottom of the pyramid (BOP) coupled with the increasing desire for organizations to grow and be more multinational, organizations need to continually innovate. However, the tendency for large and established companies to ignore the BOP market and rather focus on existing markets, gives an indication of the existence of a vulnerability that potentially disruptive innovations from the BOP will not be recognized in good time for a counter measure. This can be deduced from the fact that good management practice advocates that managers should learn and listen to their customers. Therefore majority of the large existing companies continually focus on their main customer/market with sustaining innovations which leaves aspiring new entrants with an underserved BOP market to experiment with. With the aid of research interviews and an agent-based model (ABM) simulation, this thesis examines the attributes of BOP innovations that can qualify them as disruptive and the possibilities of tangible disruptive innovations arising from the bottom of the pyramid and their underlying drivers. The thesis Furthermore, examines the associated impact of such innovations on the future sustainability of established large companies that are operating in the developed world, particularly those with a primary focus which is targeted towards the market at the top of the pyramid (TOP). Additionally, with the use of a scenario planning model, the research provides an evaluation of the possible evolution and potential sustainability impacts that could emerge, from the interplay of innovations at the two pyramidal market levels and the chosen market focus of organizations – TOP or BOP. Using four scenario quadrants, the thesis demonstrates the resulting possibilities from the interaction between the rate of innovations and the segment focused on by organizations with disruptive era characterizing the paradigm shift quadrant. Furthermore, a mathematical model and two theoretical propositions are developed for further research. As recommendations, the thesis also extends the ambidextrous organizational theory, business model innovation and portfolio diversification as plausible recommendations to limit a catastrophic impact, resulting from disruptive innovations.

Mathematical modeling of laboratory scale three-phase fixed bed reactors

Detta arbete fokuserar på modellering av katalytiska gas-vätskereaktioner som genomförs i kontinuerliga packade bäddar. Katalyserade gas-vätskereaktioner hör till de mest typiska reaktionerna i kemisk industri; därför behandlas här packade bäddreaktorer som ett av de populäraste alternativen, då kontinuerlig drift eftersträvas. Tack vare en stor katalysatormängd per volym har de en kompakt struktur, separering av katalysatorn behövs inte och genom en professionell design kan den mest fördelaktiga strömningsbilden upprätthållas i reaktorn. Packade bäddreaktorer är attraktiva p.g.a. lägre investerings- och driftskostnader. Även om packade bäddar används intensivt i industri, är det mycket utmanande att modellera. Detta beror på att tre faser samexisterar och systemets geometri är komplicerad. Existensen av flera reaktioner gör den matematiska modelleringen även mera krävande. Många förenklingar blir därmed nödvändiga. Modellerna involverar typiskt flera parametrar som skall justeras på basis av experimentella data. I detta arbete studerades fem olika reaktionssystem. Systemen hade studerats experimentellt i vårt laboratorium med målet att nå en hög produktivitet och selektivitet genom ett optimalt val av katalysatorer och driftsbetingelser. Hydrering av citral, dekarboxylering av fettsyror, direkt syntes av väteperoxid samt hydrering av sockermonomererna glukos och arabinos användes som exempelsystem. Även om dessa system hade mycket gemensamt, hade de också unika egenskaper och krävde därför en skräddarsydd matematisk behandling. Citralhydrering var ett system med en dominerande huvudreaktion som producerar citronellal och citronellol som huvudprodukter. Produkterna används som en citrondoftande komponent i parfymer, tvålar och tvättmedel samt som plattform-kemikalier. Dekarboxylering av stearinsyra var ett specialfall, för vilket en reaktionsväg för produktion av långkedjade kolväten utgående från fettsyror söktes. En synnerligen hög produktselektivitet var karakteristisk för detta system. Även processuppskalning modellerades för dekarboxylerings-reaktionen. Direkt syntes av väteperoxid hade som målsättning att framta en förenklad process att producera väteperoxid genom att låta upplöst väte och syre reagera direkt i ett lämpligt lösningsmedel på en aktiv fast katalysator. I detta system förekommer tre bireaktioner, vilka ger vatten som oönskad produkt. Alla dessa tre reaktioner modellerades matematiskt med hjälp av dynamiska massbalanser. Målet med hydrering av glukos och arabinos är att framställa produkter med en hög förädlingsgrad, nämligen sockeralkoholer, genom katalytisk hydrering. För dessa två system löstes ämnesmängd- och energibalanserna simultant för att evaluera effekter inne i porösa katalysatorpartiklar. Impulsbalanser som bestämmer strömningsbetingelser inne i en kemisk reaktor, ersattes i alla modelleringsstudier med semi-empiriska korrelationsuttryck för vätskans volymandel och tryckförlust och med axiell dispersionsmodell för beskrivning av omblandningseffekter. Genom att justera modellens parametrar kunde reaktorns beteende beskrivas väl. Alla experiment var genomförda i laboratorieskala. En stor mängd av kopplade effekter samexisterade: reaktionskinetik inklusive adsorption, katalysatordeaktivering, mass- och värmeöverföring samt strömningsrelaterade effekter. En del av dessa effekter kunde studeras separat (t.ex. dispersionseffekter och bireaktioner). Inverkan av vissa fenomen kunde ibland minimeras genom en noggrann planering av experimenten. På detta sätt kunde förenklingar i modellerna bättre motiveras. Alla system som studerades var industriellt relevanta. Utveckling av nya, förenklade produktionsteknologier för existerande kemiska komponenter eller nya komponenter är ett gigantiskt uppdrag. Studierna som presenterades här fokuserade på en av den teknisk-vetenskapliga utfärdens första etapper.

Mathematical modeling of level of anaesthesia from EEG measurements

Problem of modeling of anaesthesia depth level is studied in this Master Thesis. It applies analysis of EEG signals with nonlinear dynamics theory and further classification of obtained values. The main stages of this study are the following: data preprocessing; calculation of optimal embedding parameters for phase space reconstruction; obtaining reconstructed phase portraits of each EEG signal; formation of the feature set to characterise obtained phase portraits; classification of four different anaesthesia levels basing on previously estimated features. Classification was performed with: Linear and quadratic Discriminant Analysis, k Nearest Neighbours method and online clustering. In addition, this work provides overview of existing approaches to anaesthesia depth monitoring, description of basic concepts of nonlinear dynamics theory used in this Master Thesis and comparative analysis of several different classification methods.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Spontaneous Focusing on Numerosity in the Development of Early Mathematical Skills

The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

A mathematical framework for group analysis of von Willebrand factor multimeric composition following luminography

The objective of the present study was to establish a method for quantitative analysis of von Willebrand factor (vWF) multimeric composition using a mathematical framework based on curve fitting. Plasma vWF multimers from 15 healthy subjects and 13 patients with advanced pulmonary vascular disease were analyzed by Western immunoblotting followed by luminography. Quantitative analysis of luminographs was carried out by calculating the relative densities of low, intermediate and high molecular weight fractions using laser densitometry. For each densitometric peak (representing a given fraction of vWF multimers) a mean area value was obtained using data from all group subjects (patients and normal individuals) and plotted against the distance between the peak and IgM (950 kDa). Curves were constructed for each group using nonlinear fitting. Results indicated that highly accurate curves could be obtained for healthy controls and patients, with respective coefficients of determination (r²) of 0.9898 and 0.9778. Differences were observed between patients and normal subjects regarding curve shape, coefficients and the region of highest protein concentration. We conclude that the method provides accurate quantitative information on the composition of vWF multimers and may be useful for comparisons between groups and possibly treatments.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Mathematical modeling of electro-rotation spectra of small particles in liquid solutions: Application to human erythrocyte aggregates

Electro-rotation can be used to determine the dielectric properties of cells, as well as to observe dynamic changes in both dielectric and morphological properties. Suspended biological cells and particles respond to alternating-field polarization by moving, deforming or rotating. While in linearly polarized alternating fields the particles are oriented along their axis of highest polarizability, in circularly polarized fields the axis of lowest polarizability aligns perpendicular to the plane of field rotation. Ellipsoidal models for cells are frequently applied, which include, beside sphere-shaped cells, also the limiting cases of rods and disks. Human erythrocyte cells, due to their particular shape, hardly resemble an ellipsoid. The additional effect of rouleaux formation with different numbers of aggregations suggests a model of circular cylinders of variable length. In the present study, the induced dipole moment of short cylinders was calculated and applied to rouleaux of human erythrocytes, which move freely in a suspending conductive medium under the effect of a rotating external field. Electro-rotation torque spectra are calculated for such aggregations of different length. Both the maximum rotation speeds and the peak frequencies of the torque are found to depend clearly on the size of the rouleaux. While the rotation speed grows with rouleaux length, the field frequency nup is lowest for the largest cell aggregations where the torque shows a maximum.