Kernel-based meshless methods for approximating functions and solutions of partial differential equations have many applications in engineering fields. As only scattered data are used, meshless methods using radial basis functions can be extended to complicated geometry and high-dimensional problems. In this thesis, kernel-based least-squares methods will be used to solve several direct and inverse problems. In chapter 2, we consider discrete least-squares methods using radial basis functions. A general l^2-Tikhonov regularization with W_2^m-penalty is considered. We provide error estimates that are comparable to kernel-based interpolation in cases in which the function being approximated is within and is outside of the native space of the kernel. These results are extended to the case of noisy data. Numerical demonstrations are provided to verify the theoretical results. In chapter 3, we apply kernel-based collocation methods to elliptic problems with mixed boundary conditions. We propose some weighted least-squares formulations with different weights for the Dirichlet and Neumann boundary collocation terms. Besides fill distance of discrete sets, our weights also depend on three other factors: proportion of the measures of the Dirichlet and Neumann boundaries, dimensionless volume ratios of the boundary and domain, and kernel smoothness. We determine the dependencies of these terms in weights by different numerical tests. Our least-squares formulations can be proved to be convergent at the H^2 (Ω) norm. Numerical experiments in two and three dimensions show that we can obtain desired convergent results under different boundary conditions and different domain shapes. In chapter 4, we use a kernel-based least-squares method to solve ill-posed Cauchy problems for elliptic partial differential equations. We construct stable methods for these inverse problems. Numerical approximations to solutions of elliptic Cauchy problems are formulated as solutions of nonlinear least-squares problems with quadratic inequality constraints. A convergence analysis with respect to noise levels and fill distances of data points is provided, from which a Tikhonov regularization strategy is obtained. A nonlinear algorithm is proposed to obtain stable solutions of the resulting nonlinear problems. Numerical experiments are provided to verify our convergence results. In the final chapter, we apply meshless methods to the Gierer-Meinhardt activator-inhibitor model. Pattern transitions in irregular domains of the Gierer-Meinhardt model are shown. We propose various parameter settings for different patterns appearing in nature and test these settings on some irregular domains. To further simulate patterns in reality, we construct different kinds of domains and apply proposed parameter settings on different patches of domains found in nature.

Peixoto, A. A. T. Detecção multiusuário baseada em tensores para sistemas de comunicação sem fio cooperativos. 2017. 115 f. Dissertação (Mestrado em Engenharia Elétrica e da Computação) - Campus de Sobral, Universidade Federal do Ceará, Sobral, 2017. / Submitted by Programa de Pós-Graduação Engenharia Elétrica e de Computação (secretaria_ppgeec@sobral.ufc.br) on 2017-08-14T13:53:24Z No. of bitstreams: 1 2017_dis_aatpeixoto.pdf: 1646922 bytes, checksum: a562da60d08daac64247b2013ca22436 (MD5) / Approved for entry into archive by Djeanne Costa (djeannecosta@gmail.com) on 2017-08-17T11:50:56Z (GMT) No. of bitstreams: 1 2017_dis_aatpeixoto.pdf: 1646922 bytes, checksum: a562da60d08daac64247b2013ca22436 (MD5) / Made available in DSpace on 2017-08-17T11:50:56Z (GMT). No. of bitstreams: 1 2017_dis_aatpeixoto.pdf: 1646922 bytes, checksum: a562da60d08daac64247b2013ca22436 (MD5) Previous issue date: 2017-07 / Signal processing applications in wireless communications may sometimes take advantage of multilinear algebra concepts. This can be done by modeling the signals as high order tensors. From this context, tensor decompositions such as the Parallel Factor analysis (PARAFAC), may be found useful. On the other hand, cooperative communications and Multiple-Input Multiple-Output (MIMO) systems are ways for granting better data rates, capacity, fading mitigation and coverage. Joining the signal processing capabilities of tensor algebra, MIMO and cooperative communications can bring great benefits in wireless communications systems. In this dissertation, two receivers are proposed for two system models that are a multiuser DS-CDMA (Direct-Sequence Code-Division Multiple-Access) uplink based on multirelay cooperative communications. The two system models are almost the same, except that in one of them, multiuser interference is considered at the relays. The Amplify-and-Forward (AF) protocol is used on all the relays, thus exploiting cooperative diversity. For the received signal of the first system model, a quadrilinear PARAFAC decomposition will be adopted and by doing so, the proposed tensor-based semi-blind receiver can jointly estimate the transmitted symbols, channel gains and spatial signatures of all users by assuming previous knowledge of the users spreading codes and a few transmitted symbols. For the second system model, multiuser interference is considered at the relays, then, a receiver based on a trilinear PARAFAC decomposition is proposed. The estimation of the second receiver is done in two phases with the first phase being a supervised stage where non-orthogonal training sequences are sent by all users. During the second phase, the users' data symbols are then estimated. Both receivers use the Alternating Least Squares (ALS) algorithm to fit the tensor models, assuming no channel state information (CSI) at the base station neither at the relays. With computational simulations, we will also provide performance evaluation of the proposed receivers for various cases and system variations. / As aplicações de processamento de sinal em sistemas de comunicações sem fio às vezes podem tirar proveito de conceitos de álgebra multilinear. Isso pode ser feito modelando os sinais como tensores de ordem elevada. Neste contexto, as decomposições tensoriais, tais como a análise de fatores paralelos (Parallel Facor - PARAFAC), podem ser úteis. Por outro lado, as comunicações cooperativas e a área de sistemas de múltiplas-entradas e múltiplas-saídas (Multiple-Input Multiple-Ouput - MIMO) são uma maneira de se alcançar melhores taxas de dados, capacidade, qualidade de transmissão e cobertura. Juntando-se as capacidades de processamento de sinal da álgebra tensorial, dos sistemas MIMO e das comunicações cooperativas, podemos obter grandes benefícios nos sistemas de comunicações sem fio. Nesta dissertação, dois receptores são propostos para dois modelos de sistema, que são o enlace reverso de um sistema DS-CDMA multiusuário baseado em comunicações cooperativas auxiliadas por múltiplos retransmissores. Os dois modelos de sistema são quase iguais, exceto que em um deles, a interferência de múltiplos usuários é considerada nos retransmissores. O protocolo Amplify-and-Forward (AF) é aplicado em cada retransmissor, explorando a diversidade cooperativa. Para o sinal recebido no primeiro modelo de sistema, uma decomposição tensorial PARAFAC quadrilinear será adotada e, ao fazê-lo, o receptor semi-cego proposto pode estimar conjuntamente os símbolos transmitidos, ganhos de canais e assinaturas espaciais de todos os usuários, assumindo o conhecimento prévio dos códigos de espalhamento dos usuários e alguns símbolos transmitidos. Para o segundo modelo de sistema, interferência multiusuário é considerada nos retransmissores dos usuários, então, um receptor baseado em uma decomposição PARAFAC trilinear é proposto. O segundo receptor realiza as estimações em duas fases, sendo a primeira fase um estágio supervisionado em que todos os usuários enviam sequências de treinamento não ortogonais. Durante a segunda fase, os símbolos de dados dos usuários são então estimados. Ambos os receptores usam o algoritmo ALS (Alternating Least Squares) para ajustar os modelos tensoriais, assumindo nenhuma informação de estado do canal (CSI - Channel State Information) na estação base nem nos retransmissores. Com simulações computacionais, também forneceremos avaliação de desempenho dos receptores propostos para vários casos e variações do sistema.

O estudo do comportamento reológico de fluidos não Newtonianos tem grande importância em diversas áreas da engenharia. O aumento na demanda destes fluidos por exemplo, no uso doméstico, pessoal e em processos químicos acarreta em dificuldades que vão desde o processo de sua mistura ao seu manuseio. Dentre os fluidos não Newtonianos estão os viscoelásticos, os quais exibem deformação aparente quando os níveis de tensões são inferiores ao limite de escoamento do material e, dentro desta classe, alguns ainda podem apresentam comportamento elástico quando submetidos à baixa taxa de cisalhamento. Juntamente com os efeitos elasto-viscoplásticos, os materiais podem apresentar comportamento tixotrópico, onde devido as tensões sua reestruturação não é instantânea. Na presente Tese, fez-se um estudo numérico a fim de analisar o problema especifico de escoamentos de fluidos elasto-viscoplásticos com comportamento tixotrópico em uma expansão planar abrupta na razão de aspecto 4 : 1. O modelo mecânico aplicado consiste de uma equação viscoelástica para o campo de tensões, uma evolutiva para o parâmetro de estrutura do material, bem como as equações de conservação de massa e momento. O modelo mecânico aplicado mostrou-se capaz de prever o comportamento tixotrópico. A aproximação numérica do modelo aplicado foi feita através do método estabilizado de elementos finitos, especificamente o método Galerkin Mínimos-Quadrados (GLS), o qual foi implementado no código de elementos finitos para fluidos não Newtonianos em desenvolvimento no Laboratório de Mecânica dos Fluidos Aplicada e Computacional (LAMAC) da Universidade Federal do Rio Grande do Sul. Os fenômenos reológicos presentes no problema foram analisados a partir da influência da cinemática do escoamento, da elasticidade e da tixotropia, no nível de estruturação do material, na posição e tamanho das regiões não escoadas e na deformação elástica do material. Os resultados mostraram-se satisfatórios, pois condizem com os apresentados na literatura, apontando a boa predição do modelo mecânico aplicado bem como a robustez de sua implementação computacional. / The rheological behavior of non-Newtonian uids study is of great then importance in many areas of engineering. The increase in demand of these uids - for example, domestic use, personal and processes chemical - causes di culties ranging from the process of mixing it to handling. Among the non-Newtonian uids are viscoelastic, which exhibit apparent deformation when stress levels are lower than the yield limit of the material and, within this class, some still have elastic behavior when subjected to low shear rates. Together with the elastic-viscoplastic e ects, materials may exhibit thixotropic behavior, ie, due the restructuring strain is not instantaneous. In this thesis was made a numerical study to simulate the speci c problem of ow of elastic-viscoplastic uids with thixotropic behavior in abrupt planar expansion { common geometry in industrial systems associated with elastic-viscoplastic uids, whose ratio the aspect is 4:1. The mechanical behavior of most of these structured materials, are highly non-Newtonian, with this, there is need to make them more pseudoplastic, causing undesirable behaviors such as thixotropic which is a phenomenon somewhat characterized and modeled in the literature. The mechanical model applied is able to predict thixotropic behavior and is composed of a viscoelastic equation for the stress eld and an evolutionary to the material structure parameter in addition to the mass and momentum conservation equations. This mechanical model is approximated by a stabilized nite element model, called the Galerkin method of least squares (GLS). In order to study the rheological phenomena present in the problem is analyzed the in uence of the ow kinematics, elasticity and thixotropy in the level of structure of the material, in position and size of unyielded regions and the elastic deformation of the material. The results were satisfactory, since the the study of intensity the U the results agree with those reported in the literature pointing to good prediction of the mechanical model applied well as the hardiness of their computational implementation.The results of the elasticity showed quite spectacular behavior of unyielded regions of the material since for high values of relaxation time, the unyielded region of channel larger has the form of " ngers"because of the high exibility of the material along the line of symmetry of the channel. The results of the analysis of the elastic deformation show, that model correctly dosing the elasticity in the unyielded regions. The thixotropic e ects reported a slower structuring of the material with increasing characteristic time, in response to strain change caused by the expansion, results indicate that for high values of relaxation time, higher the distance between the unyielded regions of smaller channel and larger.

Food inflation in South Africa has been viewed as an important source of underlying inflationary pressures in the economy due to its persistence beyond that of other commodities. Although several studies found food to be one of the factors that influence purchase decisions, there still appears to be an absence of research that directly links food inflation to consumers’ decisions, especially when financing the purchase of new passenger vehicles in South Africa. In this regard, this study investigated whether the increase in the prices of food products has a significant effect on passenger vehicle purchases in South Africa. Leaning on the literature that argues that economic factors do not play much of a role in passenger vehicle purchase decisions in South Africa, it was hypothesised that there is no supported relationship between food inflation and passenger vehicle purchases in South Africa. Using secondary time series data, the Pearson correlation test revealed a negative but insignificant relationship between food inflation and vehicle purchases in South Africa. The ordinary least squares estimate of the purchase function, taking into account several economic factors that influence passenger vehicle purchase decisions in the literature, showed that disposable income of households along with vehicle purchases of the previous period are to be considered as main determinants of vehicle purchases in South Africa. In addition, it was also revealed that new vehicle prices are also a significant determinant of vehicle purchases. The Johansen cointegration test revealed that the variables in the vehicle purchase function were cointegrated in the long run. The vector error correction model showed a long-run relationship, albeit insignificant, between food inflation and vehicle purchases and no relationship between the two variables in the short run. The Granger causality test revealed that food inflation and vehicle purchases are independent from each other, meaning that no causal effect was found between the variables, regardless of the direction of the test. This study concluded that economic factors such as interest rate and fuel price have an insignificant influence on passenger vehicle purchases in South Africa. In the same line, the impact of food inflation on passenger vehicle purchases in South Africa was found to be insignificant, therefore, the conclusion was drawn that the increase in the prices of food products will not play a considerable role in consumers’ decisions regarding passenger vehicle purchase in South Africa. / Business Management / M. Com. (Business Management)

This study aims at developing a model to estimate flood damage cost caused in Gonaives, Haiti by Hurricane Jeanne in 2004. In order to reach this goal, the influence of income, inundation duration and inundation depth, slope, population density and distance to major roads on the loss costs was investigated. Surveyed data were analyzed using Excel and ArcGIS 10 software. The ordinary least square and the geographically weighted regression analyses were used to predict flood damage costs. Then, the estimates were delineated using voronoi geostatistical map tool. As a result, the factors account for the costs as high as 83%. The flood damage cost in a household varies between 24,315 through 37,693 Haitian Gourdes (approximately 607.875 through 942.325 U.S. Dollars). Severe damages were spotted in the urban area and in the rural section of Bassin whereas very low and low losses are essentially found in Labranle. The urban area was more severely affected by comparison with the rural area. Damages in the urban area are estimated at 41,206,869.57USD against 698,222,174.10 17,455,554.35USD in the rural area. In the urban part, damages were more severe in Raboteau-Jubilée and in Downtown but Bigot-Parc Vincent had the highest overall damage cost estimated at 9,729,368.95 USD. The lowest cost 7,602,040.42USD was recorded in Raboteau. Approximately, 39.38% of the rural area underwent very low to moderate damages. Bassin was the most severely struck by the 2004 floods, but Bayonnais turned out to have the highest loss cost: 4,988,487.66 USD. Bassin along with Labranle had the least damage cost, 2,956,131.11 and 2,268,321.41 USD respectively. Based on the findings, we recommended the implementation and diversification of income-generating activities, the maintenance and improvement of drains, sewers and gullies cleaning and the establishment of conservation practices upstream of the watersheds. In addition, the model should be applied and validated using actual official records as reference data. Finally, the use of a calculation-based approach is suggested to determine flood damage costs in order to reduce subjectivity during surveys.

Os serviços de emergências hospitalares (EH) desempenham um papel fundamental no sistema de saúde, servindo de porta de entrada para hospitais e fornecendo cuidados para pacientes com lesões e doenças graves. No entanto, as EH em todo o mundo sofrem com o aumento da demanda e superlotação. Múltiplos fatores convergem simultaneamente para resultar nessa superlotação, porém a otimização do gerenciamento do fluxo dos pacientes pode auxiliar na redução do problema. Nesse contexto, o tempo de permanência dos pacientes na EH (TPEH) é consolidado na literatura como indicador de qualidade do fluxo de pacientes. O tema desta dissertação é a previsão e gestão da demanda em EH com alto grau de congestionamento, que é abordado através de três artigos científicos. O objeto de estudo é o Hospital de Clínicas de Porto Alegre (HCPA). No primeiro artigo, são aplicados quatro modelos de previsão da procura por atendimento na EH, avaliando-se a influência de fatores climáticos e de calendário. O segundo artigo utiliza a técnica de regressão por mínimos quadrados parciais (PLS – partial least squares) para previsão de quatro indicadores relacionados ao TPEH para hospitais com alto grau de congestionamento. O tempo médio de permanência (TM) na EH resultou em um modelo preditivo com melhor ajuste, com erro médio absoluto percentual (MAPE - mean absolute percent error) de 5,68%. O terceiro artigo apresenta um estudo de simulação para identificação dos fatores internos do hospital que influenciam o TPEH. O número de exames de tomografias e a taxa de ocupação nas enfermarias clínicas e cirúrgicas (ECC) foram as que mais influenciaram. / Emergency departments (ED) play a key role in the health system, serving as gateway to hospitals and providing care for patients with injuries and serious illnesses. However, EDs worldwide suffer from increased demand and overcrowding. Multiple factors simultaneously converge to result in such overcrowding, and the optimization of patient flow management can help reduce the problem. In this context, the length of stay of patients in ED (LSED) is consolidated in the literature as a patient flow quality indicator. This thesis deals with forecast and demand management in EDs with a high degree of congestion. The subject is covered in three scientific papers, all analyzing data from the Hospital de Clínicas de Porto Alegre’s ED. In the first paper we apply four demand forecasting models to predict demand for service in the ED, evaluating the influence of climatic and calendar factors. The second article uses partial least squares (PLS) regression to predict four indicators related to LSED. The mean length of stay in the ED resulted in a model with the best fit, with mean percent absolute error (MAPE) of 5.68%. The third article presents a simulation study to identify the internal hospital factors influencing LSED. The number of CT exams and the occupancy rate in the clinical and surgical wards were the most influential factors.

Este trabalho avaliou o potencial da aplicação da técnica recursiva dos mínimos quadrados (MQR) para o ajuste em tempo atual dos parâmetros de modelos autorregressivos com variáveis exógenas (ARX), as quais são constituídas pelos níveis de montante para melhorar o desempenho das previsões de níveis fluviais em tempo atual. Três aspectos foram estudados em conjunto: variação do alcance escolhido para a previsão, variação da proporção da área controlada em bacias a montante e variação da área da bacia da seção de previsão. A pesquisa foi realizada em três dimensões principais: a) metodológica (sem recursividade; com recursividade; com recursividade e fator de esquecimento); b) temporal (6 alcances diferentes: 10, 24, 34, 48, 58 e 72 horas); e c) espacial (variação da área controlada da bacia e da área da bacia definida pela seção de previsão). A área de estudo escolhida para essa pesquisa foi a bacia do rio Uruguai com exutório no posto fluviométrico de Uruguaiana (190.000 km²) e as suas sub-bacias embutidas de Itaqui (131.000 km²), Passo São Borja (125.000km²), Garruchos (116.000 km²), Porto Lucena (95.200 km²), Alto Uruguai (82.300 km²) e Iraí (61.900 km²). Os dados de níveis fluviométricos, com leituras diárias às 07:00 e às 17:00 horas, foram fornecidos pela Companhia de Pesquisa de Recursos Minerais (CPRM), sendo utilizados os dados de 1/1/1991 a 30/6/2015. Para a análise de desempenho dos modelos, foi aplicado como estatística de qualidade o coeficiente de Nash-Sutcliffe (NS) e o quantil 0,95 dos erros absolutos (EA(0,95): erro que não foi ultrapassado com a frequência de 0,95). Observou-se que os erros EA(0,95) dos melhores modelos obtidos para cada bacia sempre aumentam com a redução da área controlada, ou seja, a qualidade das previsões diminui com o deslocamento da seção de controle de jusante para montante. O ganho na qualidade das previsões com a utilização dos recursos adaptativos torna-se mais evidente, especialmente quando observam-se os valores de EA(0,95), pois esta estatística é mais sensível, com diferenças maiores em relação ao coeficiente NS. Além disso, este é mais representativo para os erros maiores, que ocorrem justamente durante os eventos de inundações. De modo geral, foi observado que, à medida que diminui a área da bacia, é possível obter previsões com alcances cada vez menores. Porém a influência do tamanho da área controlada de bacias a montante melhora o desempenho de bacias menores quando se observam principalmente os erros EA(0,95). Por outro lado, se a proporção da bacia controlada de montante já é bastante grande, como é o caso das alternativas 1 e 2 utilizadas para previsão em Itaqui (entre 88,5% e 95,4 %, respectivamente), os recursos adaptativos não fazem muita diferença na obtenção de melhores resultados. Todavia, quando se observam bacias com menores áreas de montante controladas, como é o caso de Porto Lucena para a alternativa 2 (65% de área controlada), o ganho no desempenho dos modelos com a utilização dos recursos adaptativos completos (MQR+f.e: mínimos quadrados recursivos com fator de esquecimento) torna-se relevante. / This study evaluated the potential of the application of the recursive least squares technique (RLS) to adjust in real time the model parameters of the autoregressive models with exogenous variables (ARX), which consists of the upstream levels, to improve the performance of the forecasts of river levels in real time. Three aspects were studied jointly: the variation of the lead time chosen for the forecast, the variation in the proportion of controlled area in upstream basins and variation in the area of forecasting section of the basin. The research was conducted in three main dimensions: a) methodological (without recursion; with recursion; with recursion and forgetting factor); b) temporal (6 different lead times: 10, 24, 34, 48, 58 and 72 hours); and c) spatial (variation in the controlled area of the basin and the area of the basin defined by the forecast section). The study area chosen for this research was the Uruguay River basin with its outflow at the river gage station of Uruguaiana (190,000 km²) and its entrenched sub-basins in Itaqui (131,000 km²), Passo São Borja (125,000 km²), Garruchos (116,000 km²), Porto Lucena (95,200 km²), Alto Uruguai (82,300 km²), and Iraí (61,900 km²). The river levels data, with daily readings at 7am and 5pm, were provided by the Company of Mineral Resources Research (CPRM), with the data used from January 1, 1991 to June 30, 2015. We applied the Nash-Sutcliffe coefficient (NS) and the quantile 0.95 of absolute errors (EA(0,95): error has not been exceeded at the rate of 0.95) for the analysis of models performances. We observed that the errors EA(0.95) of the best models obtained for each basin always increase with the reduction of the controlled area then the quality of the forecasts decreases with displacement of the downstream control section upstream. The gain in quality of the forecasts with the use of adaptive resources becomes more evident especially when the observed values of EA(0.95) as this statistic is more sensitive with greater differences in relation to the Nash-Sutcliffe Coefficient (NS). Moreover, this is most representative for larger errors which occur precisely during flooding events. In general, we observed that, as much as the area of the basin decreases, it is possible to obtain forecasts with smaller lead times, but the influence of the size of the area controlled upstream basins improves the performance of smaller basins when observing, especially the errors EA (0.95). However, if the proportion of the upstream of controlled basin is already quite large - as in the case of the alternatives 1 and 2 used for forecast in Itaqui (between 88.5% and 95.4%, respectively) - the adaptive resources do not differ too much in getting better results. However, when observing basins with smaller areas controlled upstream - as is the case of Porto Lucena to alternative 2 (65% controlled area) - the performance gain of the models with the use of the complete adaptive resources (MQR+f.e.) becomes relevant.

Submitted by Ana Hilda Fonseca (anahilda@ufba.br) on 2016-04-25T19:12:13Z No. of bitstreams: 1 dissertação_Alessandra_Tanajura.pdf: 2001226 bytes, checksum: a576db33c19369751b0c8a9de53e91d7 (MD5) / Approved for entry into archive by Ana Hilda Fonseca (anahilda@ufba.br) on 2016-05-12T15:48:44Z (GMT) No. of bitstreams: 1 dissertação_Alessandra_Tanajura.pdf: 2001226 bytes, checksum: a576db33c19369751b0c8a9de53e91d7 (MD5) / Made available in DSpace on 2016-05-12T15:48:44Z (GMT). No. of bitstreams: 1 dissertação_Alessandra_Tanajura.pdf: 2001226 bytes, checksum: a576db33c19369751b0c8a9de53e91d7 (MD5) / CNPq / Com o aumento da demanda de biodiesel como combustível surge a necessidade de se desenvolver novos métodos analíticos para determinar propriedades químicas e físico- químicas do mesmo. Um dos problemas associados ao biodiesel diz respeito a sua baixa estabilidade oxidativa. A oxidação pode causar aumento na viscosidade e na acidez do combustível. No presente trabalho foi desenvolvido um método para predição da viscosidade, estabilidade oxidativa e massa específica de biocombustíveis utilizando espectrofluorimetria e PLS. O método consiste na obtenção de um modelo matemático obtido entre dados espectrais resultantes de análises espectrofluorimétricas e dados de análises de viscosidade cinemática, massa específica ou estabilidade oxidativa através da aplicação de Análise Multivariada por Mínimos Quadrados Parciais (PLS). Os espectros de emissão fluorescente das amostras foram realizados em um espectrofluorímetro, onde a emissão foi detectada de 230 a 800 nm em intervalos de 0,5 nm enquanto as moléculas presentes na amostra sofriam excitação em comprimentos de onda fixos na faixa de 200 a 775 nm. Foram analisadas 46 amostras em diversas concentrações de biodiesel em diesel e 06 amostras de óleos comerciais. Todos foram analisados através da Espectroscopia de Fluorescência Total associada a PLS e foi possível obter valores de R-quadrado próximos de 1 para cada um dos modelos PLS construídos. Preliminarmente foi feita uma busca de anterioridade de patentes para o uso de métodos ópticos para determinar oxidação, viscosidade e massa específica e verificou-se que nenhuma das patentes encontradas sugere o uso da espectrofluorimetria combinada com calibração multivariada para a predição das propriedades químicas e físico-químicas estudadas. Com isso foi depositada no INPI uma patente sobre o método desenvolvido. / With increasing demand for biodiesel fuel as the need arises to develop new analytical methods for determining chemical and physicochemical properties thereof. One of the problems associated with biodiesel relates to its low oxidative stability. The oxidation can cause an increase in viscosity and acidity of the fuel. In this work we developed a method for predicting the viscosity, oxidative stability and density of biofuels using spectrofluorimetry and PLS. The method consists in obtaining a mathematical model obtained between spectral data derived from spectrofluorimetry analysis and values of kinematic viscosity, density or oxidative stability by applying multivariate partial least squares (PLS). The fluorescence emission spectra of the samples were performed in a spectrofluorometer where the emission was detected 230-800 nm in steps of 0.5 nm while the molecules present in the sample suffered excitation wavelengths in the range fixed 200-775 nm. We analyzed 46 samples in different concentrations of biodiesel in diesel and 06 samples of commercial oils. All were analyzed by fluorescence spectroscopy total associated with PLS and it was possible to obtain values of R-squared near 1 for each PLS-models. Preliminarily, a search was made for prior patents using optical methods for determining oxidation and viscosity and found that none of the patents found suggests the use of spectrofluorimetry combined with multivariate calibration for the prediction of chemical and physical chemical properties studied. With that was deposited on INPI a patent related to the method developed.

The objectives of this study was to calculate the genetic gain corn grain yield in southern Brazil and calculate the genetic gain in two classes of altitude. The methods used were the Vencovsky et al. (1988) based on linear models with inference least squares (ML/MQ) and the Borges et al. (2009), based on mixed models with inference by residual likelihood (MM/REML). We used a database with 30,292 yield observation from corn grain but resulting in 135 genotypes in 2,826 trials conducted in 13 years, from 2001 to 2013, being the year regarding the planting date of the trials. For the stratification of trials, in order to form similar environments, we used as criteria the altitude, down and up to 700m. The methodology of ML/MQ annual mean genetic gain was 121 kg ha-1 year-1 with a confidence interval to 95% [11;232] kg ha-1 year-1, and by MM/REML methodology was 79 kg ha-1 year-1 with a confidence interval to 95% [70; 98] kg ha-1 year-1 for the entire southern region of Brazil. In regions with altitude of 700 m, the genetic gain was 94 kg ha-1 year-1 and in regions with altitude less than 700 mo genetic gain was 74 kg ha-1 year-1.MM/REML methodology provided intervals more accurate and reliable values of genetic gain lower when compared to ML/MQ methodology. In all cases analyzed, the genetic gain was positive and significant between the years 2001-2013. / Os objetivos deste trabalho foram calcular o ganho genético de produtividade de grãos de milho na região Sul do Brasil e calcular o ganho genético em duas classes de altitude. As metodologias utilizadas foram a de Vencovsky et al. (1988), baseada em modelos lineares com inferência por mínimos quadrados (ML/MQ) e a de Borges et al. (2009), baseada em modelos mistos com inferência por verossimilhança residual (MM/REML). Foi utilizada uma base de dados com 30.292 observações de produtividade de grãos de milho, resultantes de 135 genótipos avaliados em 2.826 ensaios conduzidos em 13 anos, de 2001 a 2013, sendo o ano referente à data de semeadura do ensaio. Para a estratificação dos ensaios, com o objetivo de formar classes de altitude, utilizou-se como critério da altitude, inferior e superior a 700m. Pela metodologia de ML/MQ o ganho genético médio anual foi de 121 kg ha-1 ano-1 com intervalo de confiança a 95% de [11;232] kg ha-1.ano-1, e pela metodologia de MM/REML foi de 79 kg ha-1 ano-1 com intervalo de confiança a 95% de [70;98] kg ha-1 ano-1, para a região sul do Brasil. Em altitude superior a 700 m, o ganho genético foi de 94 kg ha-1 ano-1 e em altitude inferior a 700 m o ganho genético foi de 74 kg ha-1 ano-1. A metodologia MM/REML proporcionou intervalos de confiança mais precisos e valores de ganho genético inferiores quando comparada à metodologia de ML/MQ. Em todas as situações analisadas o ganho genético foi positivo, e significativo entre os anos de 2001 a 2013.

In this thesis, we first review the current development of optimal regression designs under the second-order least squares estimator in the literature. The criteria include A- and D-optimality. We then introduce a new formulation of A-optimality criterion so the result can be extended to c-optimality which has not been studied before. Following Kiefer's equivalence results, we derive the optimality conditions for A-, c- and D-optimal designs under the second-order least squares estimator. In addition, we study the number of support points for various regression models including Peleg models, trigonometric models, regular and fractional polynomial models. A generalized scale invariance property for D-optimal designs is also explored. Furthermore, we discuss one computing algorithm to find optimal designs numerically. Several interesting applications are presented and related MATLAB code are provided in the thesis. / Graduate