Weighted polynomial regression of degree d with weight function Exp(£\ x) on an interval is considered. The D-optimal designs £i_d^* are completely characterized via three differential equations. Some invariant properties of £i_d^* under affine transformation are derived. The design £i_d^* as d goes to 1, is shown to converge weakly to the arcsin distribution. Comparisons of £i_d^* with the arcsin distribution are also made.

The effect of an imposed magnetic field on the thermal convection between rigid plates heated from below under the influence of gravity is numerically simulated in a computational domain with periodic horizontal extent. The numerical technique is based on solenoidal basis functions satisfying the boundary conditions for both velocity and induced magnetic field. The expansion bases for the thermal field are also constructed to satisfy the boundary conditions. The governing partial differential equations are reduced to a system of ordinary differential equations governing the time evolution of the expansion coefficients under Galerkin projection onto the subspace spanned by the dual bases. In the process, the pressure term in the momentum equation is eliminated. The system validated in the linear regime is then used for some numerical experiments in the nonlinear regime.

Müntz polynomials arise from consideration of Müntz's Theorem, which is a beautiful generalization of Weierstrass's Theorem. We prove a new surprisingly simple representation for the Müntz orthogonal polynomials on the interval of orthogonality, and in particular obtain new formulas for some of the classical orthogonal polynomials (e.g. Legendre, Jacobi, Laguerre). This allows us to determine the strong asymptotics and endpoint limit asymptotics on the interval. The zero spacing behavior follows, as well as estimates for the smallest and largest zeros. This is the first time that such asymptotics have been obtained for general Müntz exponents. We also look at the asymptotic behavior outside the interval and the asymptotic properties of the associated Christoffel functions.

Let p be an odd prime, and define f(x) as follows: f(x) as the sum from 1 to k of a_i times x raised to the power of (p to the power of (alpha_i+1)) in F_(p to the power of n)[x] where 0 is less than or equal to alpha_1 < alpha_2 < ... < alpha_k where alpha_k is equal to alpha. We consider the exponential sum S(f, n) equal to the sum_(x as x runs over the finite field with (p to the n elements) of zeta_(p to the power of Tr_n (f(x))), where zeta_p equals e to the power of (2i times pi divided by p) and Tr_n is the trace from the finite field with p to the n elements to the finite field with p elements.We provide necessary background from number theory and review the basic facts about quadratic forms over a finite field with p elements through both the multivariable and single variable approach. Our main objective is to compute S(f, n) explicitly. The sum S(f, n) is determined by two quantities: the nullity and the type of the quadratic form Tr_n (f(x)). We give an effective algorithm for the computation of the nullity. Tables of numerical values of the nullity are included. However, the type is more subtle and more difficult to determine. Most of our investigation concerns the type. We obtain "relative formulas" for S(f, mn) in terms of S(f, n) when the p-adic order of m is less than or equal to the minimum p-adic order of the alphas. The formulas are obtained in three separate cases, using different methods: (i) m is q to the s power, where q is a prime different from 2 and p; (ii) m is 2 to the s power; and (iii) m is p. In case (i), we use a congruence relation resulting from a suitable Galios action. For case (ii), in addition to the congruence in case (i), a special partition of the finite field with p to the 2n elements is needed. In case (iii), the congruence method does not work. However, the Artin-Schreier Theorem allows us to compute the trace of the extension from the finite field with p to the pn elements to the fi nite field with p to the n elements rather explicitly.When the 2-adic order of each of the alphas is equal and it is less than the 2-adic order of n, we are able to determine S(f, n) explicitly. As a special case, we have explicit formulas for the sum of the monomial, S(ax to the power of (1+ (p to the power of alpha)).Most of the results of the thesis are new and generalize previous results by Carlitz, Baumert, McEliece, and Hou.

Following [10] we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In [10] we proved that a minimal condition on the utility function alone, i.e. a minimal market independent condition, is that the asymptotic elasticity of the utility function is strictly less than 1. In this paper we show that a necessary and sufficient condition on both, the utility function and the model, is that the value function of the dual problem is finite. (authors' abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Freiburg i. Br., Univ., Dipl.-Arbeit, 2008. / Angefertig am Mathematischen Institut der Albert-Ludwigs-Universität, Stand 4. Oktober 2005. Fehler ausgebessert: 28. Juli 2008.

Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-11-06Bitstream added on 2014-06-13T18:30:57Z : No. of bitstreams: 1 casteletti_jr_me_rcla.pdf: 1198028 bytes, checksum: 64d53c9ad4dac00f0f39d72fc52d6fae (MD5) / Secretaria de Educação do Estado de São Paulo / Realizamos neste trabalho o estudo de tópicos fundamentais de Mecânica Celeste visando a aplicação em problemas de interesse atual, tal como o estudo de ressonâncias de movimentos médios em sistemas planetários extrassolares. Ênfase foi dada nos seguintes tópicos: i) formulação do problema ressonante de dois planetas em interação mútua; ii) desenvolvimento e expansão da função perturbadora; iii) solução numérica de problemas de valor inicial; iv) aplicações ao par de planetas HD10180d,e, os quais estão próximos da ressonância 3:1. A abordagem dos problemas foi realizada analítica e numericamente. Na primeira parte deste trabalho formulamos o problema geral de três corpos e reproduzimos os principais passos do desenvolvimento da função perturbadora. Na segunda parte realizamos simulações dos sistemas em questão utilizando as equações exatas de movimento (Newton) e comparamos os resultados com soluções numéricas das equações de Lagrange, i.e., equações de variação dos elementos orbitais escritas em termos da função perturbadora envolvida. Os resultados das simulações numéricas realizadas neste trabalho poderão ser aplicados para três propostas: i) comparação dos resultados entre as soluções exatas e aproximadas (Lagrange) das equações de movimento para, com isso, obter evidências numéricas do domínio de validade da aplicação da função perturbadora expandida nos problemas ressonantes; ii) estudo de dinâmica ressonante, i.e., caracterização e evolução temporal de ângulos críticos associados às ressonâncias; iii) estabilidade dinâmica de longo período dos sistemas em questão / In this work we study a fundamental Celestial Mechanics in order to apply to problems of current interest, such as dynamics of extrasolar planetary systems. Emphasis is given on the following topics: i) formulation of the problem of two resonant planets in mutual interaction, ii) dedution and expansion of the disturbing function; iii) numerical solution of initial value problems, iv) applications to the pair of planets HD10180d,e which orbits are near to the 3:1 resonance. We adopt both, analytical and numerical approaches. In the first part, we formulate the general three-body problem, and reproduce the main steps of the expansion of the disturbing function. In the second part we show the results of a great deal of numerical simulations of the systems using both the exact equations of motion (Newton) Lagrange equations. The simulations have been done with three main goals: i) comparison of the results of the exact and approximate solutions (Lagrange) equations of motion, in order to obtain numerical evidences of the validity domain of the application of the expanded disturbing function to resonant problems, ii) study of the resonant dynamics, i.e., characterization and evolution of critical angles associated with resonances, iii) investigate long-term dynamic stability of the systems in question

Submitted by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2015-11-17T16:39:06Z No. of bitstreams: 2 flaviana_miranda_goncalves.pdf: 300142 bytes, checksum: 2ec2cd0e2beed3299f69e5cdd73e9002 (MD5) license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2015-11-17T16:39:31Z (GMT) No. of bitstreams: 2 flaviana_miranda_goncalves.pdf: 300142 bytes, checksum: 2ec2cd0e2beed3299f69e5cdd73e9002 (MD5) license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) / Made available in DSpace on 2015-11-17T16:39:31Z (GMT). No. of bitstreams: 2 flaviana_miranda_goncalves.pdf: 300142 bytes, checksum: 2ec2cd0e2beed3299f69e5cdd73e9002 (MD5) license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Previous issue date: 2011-07-29 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq) / Funda??o de Amparo ? Pesquisa do estado de Minas Gerais (FAPEMIG) / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Objetivou-se com este estudo realizar a avalia??o gen?tica do crescimento de codornas de corte utilizando modelos de regress?o aleat?ria. Os dados utilizados s?o provenientes de 28.076 observa??es mensuradas em 4.507 codornas de corte de uma linhagem f?mea (LF1) pertencente ao Programa de Melhoramento Gen?tico de Codornas do Departamento de Zootecnia da Universidade Federal dos Vales do Jequitinhonha e Mucuri, em Diamantina/ MG. A caracter?stica peso corporal das codornas foi mensurada ao nascimento, aos 7, 14, 21, 28, 35 e 42 dias de idade, e avaliada por meio de modelos de regress?o aleat?ria. Nas an?lises, seis diferentes classes de vari?ncia residual, de homog?nea a heterog?nea, foram consideradas, segundo diferentes idades: Classe 1: vari?ncia residual homog?nea; Classe 2: vari?ncia residual heterog?nea em dois per?odos; Classe 3: vari?ncia residual heterog?nea em tr?s per?odos; Classe 4: vari?ncia residual heterog?nea em quatro per?odos; Classe 5: vari?ncia residual heterog?nea em cinco per?odos e, Classe 6: vari?ncia residual heterog?nea em seis per?odos. Cada classe foi testada com diferentes ordens de ajuste das fun??es polinomiais de Legendre, as quais variaram de segunda ? sexta ordem, para averiguar qual o modelo (classe de heterogeneidade de vari?ncia juntamente com a ordem de polin?mio de Legendre) apresentou o melhor ajuste para descrever as estruturas de (co)vari?ncias em fun??o do tempo (idade das codornas). De acordo com todos os crit?rios avaliados (AIC ? Crit?rio de Informa??o de Akaike, BIC ? crit?rio de Informa??o Bayesiano de Schwarz e LRT ? teste da raz?o de verossimilhan?a), o modelo com seis classes de vari?ncias residuais e de sexta ordem do polin?mio de Legendre foi o que apresentou o melhor ajuste, dado pelos menores valores de AIC e BIC, al?m de LRT significativo. Verificou-se que, com o aumento da idade das codornas, todas as vari?ncias apresentaram tend?ncia de crescimento. A estimativa de vari?ncia gen?tica aditiva aumentou do nascimento at? os 35 dias de idade, apresentando ligeira queda dos 35 aos 42 dias. As herdabilidades estimadas foram decrescentes ao longo da curva de crescimento, variando de 0,51 (1 dia) a 0,16 (42 dias). As estimativas de correla??es gen?ticas e de ambiente permanente de animal entre os pesos nas v?rias idades foram sempre altas e positivas, exceto para peso ao nascimento. No estudo do crescimento das codornas de corte, recomenda-se adotar seis classes (uma para cada semana de idade) de heterogeneidade de vari?ncia, juntamente com a utiliza??o de polin?mios de Legendre de sexta ordem. / Disserta??o (Mestrado) ? Programa de P?s-Gradua??o em Zootecnia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2011. / ABSTRACT The objective of this study was the genetic evaluation of the growth of quails using random regression models. The data used come from 28.076 observations measured in 4507 quails of a female line (LF1) belonging to the Quail Breeding program of the Animal Science Department of the University of the Jequitinhonha and Mucuri Valleys in Diamantina, MG. The characteristic of quails body weight of was measured at birth, 7, 14, 21, 28, 35 and 42 days years old. The analysis were made using random regression models, where six different classes of residual variance, heterogeneous or homogeneous, were considered, according to different age groups: Class 1: homogeneous residual variance, Class 2: heterogeneous residual variance in two periods, Class 3: heterogeneous residual variance into three periods: Class 4: heterogeneous residual variance in four periods, Class 5: heterogeneous residual variance in five periods, and Class 6: heterogeneous residual variance in six periods. Each class was tested with different orders of fit to Legendre polynomial functions, which ranged from second to sixth order, to determine which model (class of variance heterogeneity with the Legendre polynomial order) presented the best fit to describe (co)variances structures as a function of time (age of the quail). According to all five criteria (AIC - Akaike information criterion, BIC - Bayesian information criterion of Schwarz and LRT - likelihood ratio test), the model with six classes of residual variances and the sixth-order of Legendre polynomial, presented the best fit, given by the lowest values of AIC and BIC, as well as significant LRT. It was found that with increasing age of the quail, all variances tended to increase. The estimate of additive genetic variance increased from birth to 35 days old, showing a slight drop from 35 to 42 days. The estimated heritability was decreasing along the growth curve, ranging from 0.51 (one day) to 0.16 (42 days). The estimative of genetic correlations and permanent animal environment among weights in several ages have always been high and positive, except for birth weight. For study of the growth of quails it is recommended the use of six classes (one for each week of age) of variance heterogeneity, with the use of Legendre polynomials of sixth order.

Submitted by Nathália Faria da Silva (nathaliafsilva.ufv@gmail.com) on 2017-07-11T11:31:48Z No. of bitstreams: 1 texto completo.pdf: 168448 bytes, checksum: cac1c0a520e55d1c502dc8fdb8011b36 (MD5) / Made available in DSpace on 2017-07-11T11:31:48Z (GMT). No. of bitstreams: 1 texto completo.pdf: 168448 bytes, checksum: cac1c0a520e55d1c502dc8fdb8011b36 (MD5) Previous issue date: 2003-07-10 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Utilizaram-se registros de pesos do nascimento aos 196 dias de idade de 927 cordeiros filhos de 45 reprodutores e 323 matrizes de ovinos da raça Santa Inês, controlados de 1983 a 2000, pertencentes à Empresa Estadual de Pesquisa Agropecuária da Paraíba (EMEPA-PB), com os objetivos de estimar parâmetros genéticos para os efeitos aditivos direto e materno e predizer os valores genéticos dos animais, por meio de análises bicaracterísticas e regressão aleatória, para pesos em diferentes idades. Os componentes de (co)variâncias e os parâmetros genéticos direto e materno para os pesos foram estimados pelo método da máxima verossimilhança restrita, sob modelo animal, por intermédio de análises unicaracterísticas, para testar três modelos de análises, com o intuito de determinar o mais apropriado para descrever as características estudadas, o qual foi utilizado nas análises bicaracterísticas e de regressão aleatória. O modelo bicaracterística foi ajustado utilizando-se o aplicativo MTDFREML (BOLDMAN et al., 1995) e regressão aleatória, por meio de polinômios de Legendre quadráticos e cúbicos, do programa DXMRR (MEYER, 1998). De acordo com o teste de razão de verossimilhança, o modelo que incluiu o efeito aditivo mais o materno foi o que apresentou maior valor para o logaritmo da função de verossimilhança em todas as características estudadas, sendo, portanto, o escolhido. A não-inclusão do efeito materno no modelo de análise resultou em superestimação das herdabilidades para o efeito direto. A importância do efeito materno diminuiu ao longo da trajetória de crescimento, à medida que a idade dos cordeiros aumentava. As herdabilidades estimadas nas análises bicaracterísticas para o efeito genético direto foram superiores às obtidas pelas análises unicaracterísticas e tenderam a decrescer do nascimento aos 196 dias de idade, variando de 0,23 a 0,03. Já as estimadas por meio dos modelos de regressão aleatória aumentaram do nascimento aos 196 dias de idade (0,004 a 0,28), com tendência de serem mais baixas nas idades em que as estimativas do efeito materno foram mais altas. As herdabilidades para o efeito materno, obtidas por ambos os modelos, aumentaram do nascimento aos 56 dias e, então, decresceram com a idade, tendendo a apresentar o mesmo comportamento, porém as estimadas pelos modelos de regressão aleatória foram de menor magnitude. As correlações genéticas estimadas por ambos os modelos tenderam a ser altas e positivas. As correlações de Spearman e de Pearson entre os valores genéticos preditos pelos dois modelos foram baixas. As herdabilidades estimadas por meio das análises bicaracterísticas sugerem que este método permite obter estimativas mais acuradas, comparadas às obtidas nas análises unicaracterísticas. As estimativas de herdabilidade e correlações genéticas obtidas pelo modelo de regressão aleatória foram biologicamente mais coerentes quando comparadas àquelas obtidas pelo modelo bicaracterística. Entretanto, estudos adicionais envolvendo maior número de informações devem ser realizados, como também usando dados simulados, com o objetivo de avaliar com mais precisão os resultados obtidos por ambos os modelos. / Records of body weights from birth to 196 days of age of 927 lambs progeny of 45 sires and 323 dams of Santa Ines sheep, controlled from 1983 to 2000, extracted from a database of Agricultural Research Corporation of Paraiba, were used to estimate genetic parameters for the additive direct and maternal effects and to predict breeding values by two-trait and random regression analyses for weights in different ages. The (co)variance components and both direct and maternal genetic parameters were estimated by using restricted maximum likelihood methods, under animal model, by means of single-trait analyses, to test three analyses models, to establish the most appropriated to describe the studied traits, which was used in two-trait and random regression analyses. The two-traits model was fitting by using MTDFREML system (BOLDMAN et al., 1995) and the random regression by means of orthogonal Legendre polynomials, using DXMRR program (MEYER, 1998). According to the likelihood ratio test, the model that included additive direct effect and the maternal was the one that showed higher value for ln likelihood for all the studied trait. The not inclusion of maternal effect in analyses model overestimated the heritability for direct effect. The importance of maternal effect decreased along the growth trajectory, while the age of the lambs increased. The heritability estimates in two-trait analyses for genetic direct effect were higher than those obtained by single-trait analyses and tended to decrease from birth to 196 days of age, ranging from 0.23 to 0.03. However, these estimated by means of the random regression models increased from ixbirth to 196 days of age (0.004 to 0.28), tending to be lower at ages where the estimates of the maternal effects were higher. The heritability for the maternal effect obtained by both models, increased from birth to 56 days and, after, decreased with the age, tending to show the same behavior, however these estimated by random regression models were of smaller greatness. The genetic correlations estimated for both models tended to be high and positive. The Spearman and Pearson correlations among the breeding values obtained both by the models were low. The heritability estimated by means of the two-trait analyses suggest that technique allows to obtain more accurated estimates, compared to the obtained by single-trait analyses. The estimates of heritability and genetic correlations obtained by means of random regression model were biologically more consistent when compared those obtained by two-trait model. However, additional studies involving larger number of information should be accomplished, as well using simulated data, with purpose of evaluation with more accuracy the results obtained by both models.

Orientador: Nelson Callegari Júnior / Banca: Marcos Tadeu dos Santos / Banca: Renata Zotin Gomes de Oliveira / Resumo: Realizamos neste trabalho o estudo de tópicos fundamentais de Mecânica Celeste visando a aplicação em problemas de interesse atual, tal como o estudo de ressonâncias de movimentos médios em sistemas planetários extrassolares. Ênfase foi dada nos seguintes tópicos: i) formulação do problema ressonante de dois planetas em interação mútua; ii) desenvolvimento e expansão da função perturbadora; iii) solução numérica de problemas de valor inicial; iv) aplicações ao par de planetas HD10180d,e, os quais estão próximos da ressonância 3:1. A abordagem dos problemas foi realizada analítica e numericamente. Na primeira parte deste trabalho formulamos o problema geral de três corpos e reproduzimos os principais passos do desenvolvimento da função perturbadora. Na segunda parte realizamos simulações dos sistemas em questão utilizando as equações exatas de movimento (Newton) e comparamos os resultados com soluções numéricas das equações de Lagrange, i.e., equações de variação dos elementos orbitais escritas em termos da função perturbadora envolvida. Os resultados das simulações numéricas realizadas neste trabalho poderão ser aplicados para três propostas: i) comparação dos resultados entre as soluções exatas e aproximadas (Lagrange) das equações de movimento para, com isso, obter evidências numéricas do domínio de validade da aplicação da função perturbadora expandida nos problemas ressonantes; ii) estudo de dinâmica ressonante, i.e., caracterização e evolução temporal de ângulos críticos associados às ressonâncias; iii) estabilidade dinâmica de longo período dos sistemas em questão / Abstract: In this work we study a fundamental Celestial Mechanics in order to apply to problems of current interest, such as dynamics of extrasolar planetary systems. Emphasis is given on the following topics: i) formulation of the problem of two resonant planets in mutual interaction, ii) dedution and expansion of the disturbing function; iii) numerical solution of initial value problems, iv) applications to the pair of planets HD10180d,e which orbits are near to the 3:1 resonance. We adopt both, analytical and numerical approaches. In the first part, we formulate the general three-body problem, and reproduce the main steps of the expansion of the disturbing function. In the second part we show the results of a great deal of numerical simulations of the systems using both the exact equations of motion (Newton) Lagrange equations. The simulations have been done with three main goals: i) comparison of the results of the exact and approximate solutions (Lagrange) equations of motion, in order to obtain numerical evidences of the validity domain of the application of the expanded disturbing function to resonant problems, ii) study of the resonant dynamics, i.e., characterization and evolution of critical angles associated with resonances, iii) investigate long-term dynamic stability of the systems in question / Mestre