Η παρούσα διατριβή εντάσσεται ερευνητικά στην περιοχή της στατιστικής θεωρίας αποφάσεων. Αντικείμενο της είναι η μελέτη προβλημάτων εκτίμησης ποσοστιαίου σημείου για το μοντέλο της παραμετρικής εκθετικής κατανομής. Στο πρώτο κεφάλαιο περιέχονται κάποιοι ορισμοί και παρουσιάζονται γνωστά αποτελέσματα. Στο δεύτερο κεφάλαιο παρατίθεται το μοντέλο της διπ. εκθετικής κατανομής και κατασκευάζονται γνωστοί εκτιμητές για το ποσοστιαίο σημείο της. Στο τρίτο κεφάλαιο εξετάζονται οι εκτιμητές τύπου stein, στο τέταρτο κεφάλαιο οι εκτιμητές τύπου bayes, ενώ στο τελευταίο κεφάλαιο δίνονται οι γραφικές παραστάσεις οι οποίες δείχνουν το ποσοστό βελτίωσης που πετυχαίνεται με την χρήση των πιο πάνω εκτιμητών. / This paper is enlisted in the area of the statistical decision theory. Its objective is the problem of estimation of the fraction point in the model of the exponential distribution with two parameters. In the first chapter, we propose simple and well known theorems, the second chapter comprises of the model of the exponential distribution and well known estimators for her fraction point, in the third chapter the stein estimators are presented, the fourth chapter has the bayes estimators and finally we present the graphical presentations.

In this thesis, we study two problems focusing on the interplay between geometric properties of differential equations and their invariants. / For the first project, we study the validity of the principle of symmetric criticality (PSC) in the context of invariant gauge fields over the four-dimensional non-reductive pseudo-Riemannian homogeneous spaces G/K recently classified by Fels & Renner (2006). Given H compact semi-simple, classification results are obtained for principal H-bundles over G/K admitting: (1) a G-action (by bundle automorphisms) projecting to left multiplication on the base, and (2) at least one G-invariant connection. There are two cases which admit nontrivial examples of such bundles and all G-invariant connections on these bundles are Yang--Mills. Using the invariant criteria obtained by Anderson--Fels--Torre, the validity of PSC is investigated for the bundle of connections and is shown to fail for all but one of the Fels--Renner cases. This failure arises from degeneracy of the scalar product on pseudo-tensorial forms restricted to the space of symmetric variations of an invariant connection. In the exceptional case where PSC is valid, there is a unique G-invariant connection which is moreover universal, i.e. it is a solution of the Euler--Lagrange equations associated to any G-invariant Lagrangian on the bundle of connections. This solution is a canonical connection associated with a weaker notion of reductivity which we introduce. / The second project is a study of the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge--Ampere (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric equations are derived and explicit symmetry algebras are presented. Moreover, all such equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional) structures is also given.

The matrix exponential is a very important subclass of functions of matrices that has been studied extensively in the last 50 years. In this thesis, we discuss some of the more common matrix functions and their general properties, and we specifically explore the matrix exponential. In principle, the matrix exponential could be computed in many ways. In practice, some of the methods are preferable to others, but none are completely satisfactory. Computations of the matrix exponential using Taylor Series, Scaling and Squaring, Eigenvectors, and the Schur Decomposition methods are provided.

No description available.

Statistical analysis of network data is an active field of study, in which researchers inves- tigate graph-theoretic concepts and various probability models that explain the behaviour of real networks. This thesis attempts to combine two of these concepts: an exponential random graph and a centrality index. Exponential random graphs comprise the most useful class of probability models for network data. These models often require the assumption of a complex dependence structure, which creates certain difficulties in the estimation of unknown model parameters. However, in the context of dynamic networks the exponential random graph model provides the opportunity to incorporate a complex network structure such as centrality without the usual drawbacks associated with parameter estimation. The thesis employs this idea by proposing probability models that are equivalent to the logistic regression models and that can be used to explain behaviour of both static and dynamic networks.

Thesis (Ph. D.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves 165-173). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Hong Kong, 1990.

abstract: There have been a number of studies that have examined students’ difficulties in understanding the idea of logarithm and the effectiveness of non-traditional interventions. However, there have been few studies that have examined the understandings students develop and need to develop when completing conceptually oriented logarithmic lessons. In this document, I present the three papers of my dissertation study. The first paper examines two students’ development of concepts foundational to the idea of logarithm. This paper discusses two essential understandings that were revealed to be problematic and essential for students’ development of productive meanings for exponents, logarithms and logarithmic properties. The findings of this study informed my later work to support students in understanding logarithms, their properties and logarithmic functions. The second paper examines two students’ development of the idea of logarithm. This paper describes the reasoning abilities two students exhibited as they engaged with tasks designed to foster their construction of more productive meanings for the idea of logarithm. The findings of this study provide novel insights for supporting students in understanding the idea of logarithm meaningfully. Finally, the third paper begins with an examination of the historical development of the idea of logarithm. I then leveraged the insights of this literature review and the first two papers to perform a conceptual analysis of what is involved in learning and understanding the idea of logarithm. The literature review and conceptual analysis contributes novel and useful information for curriculum developers, instructors, and other researchers studying student learning of this idea. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2018

Submitted by Rodrigo Felipe da Silva null (rodrigofelipeww@hotmail.com) on 2016-08-29T00:06:15Z No. of bitstreams: 1 dissertacao final.pdf: 3098255 bytes, checksum: 38c69f33c20861a5bc6a8a6953fa8352 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-08-30T16:52:00Z (GMT) No. of bitstreams: 1 silva_rf_me_sjrp.pdf: 3098255 bytes, checksum: 38c69f33c20861a5bc6a8a6953fa8352 (MD5) / Made available in DSpace on 2016-08-30T16:52:00Z (GMT). No. of bitstreams: 1 silva_rf_me_sjrp.pdf: 3098255 bytes, checksum: 38c69f33c20861a5bc6a8a6953fa8352 (MD5) Previous issue date: 2016-07-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No ensino da matemática um dos assuntos mais desa adores aos alunos do Ensino Médio é o de funções exponenciais e logarítmicas, sendo que grande parte dos alunos possuem difi culdades de compreensão e resolução dos exercícios propostos. Dessa maneira o trabalho em tela tem como objetivo precípuo o ensino de funções exponenciais e logarítmicas, visando apresentar aos docentes a possibilidade de ensinar o conteúdo de maneira mais atrativa e acessível aos seus alunos. Para tanto, a pesquisa se valeu de levantamento bibliográ fico e documental acerca da temática abordada. Salienta-se que ao iniciar o ensino de funções é preciso fazer um resgate histórico do conteúdo, buscando desvelar suas origens. Posteriormente o trabalho traz as concepções do tema segundo os documentos o ciais. A m de concretizar o estudo trabalha-se com o uso das defi nições aritméticas e geométricas, pois são fundamentais para o entendimento das funções, e também com situações problema contextualizadas, buscando envolver os alunos no processo de ensino aprendizagem promovendo o levantamento de hipóteses e consolidando a aprendizagem. Essas situações problemas serão difundidas por meio de atividades propostas nas quais pretende-se explorar a caracterização da função logarítmica e exponencial, buscando relacioná-las ao contexto do educando, em situações que poderiam ocorrer em seu cotidiano, para isso propomos alguns exemplos de atividades, como: a utilização do BRO ce Calc no Ensino de potenciação com números irracionais, o jogo de xadrez, mágica do baralho e a resolução de problemas da OBMEP e do ENEM. / In teaching mathematics one of most challenging subjects to middle school students is of exponential and logarithmic functions, being that most of the students have difficulties in understanding and addressing the proposed exercises. In this way the work on canvas aims foremost teaching of exponential and logarithmic functions, n order to present to teachers the possibility to teach the content more attractive and accessible to his students. To this end, the research used for bibliographical and documental about the theme addressed.It should be noted that the starting teaching duties must make a historic rescue of the contents, looking for their origins unveiling. In order to implement the study works with the use of arithmetic and geometric definitions, because they are fundamental to the understanding of the functions, and also with contextualized problem situations, seeking to engage students in teaching learning process promoting the survey of hypotheses and consolidating learning. These problems will be disseminated through activities in which it is intended to explore the characterization of logarithmic and exponential function, seeking to relate them to the context of educating, in situations that could occur in their daily lives, for this we propose some examples of activities, such as: libreoffice Calc use in teaching empowerment with irrational numbers, the game of chess, magic of the deck and the troubleshooting of OBMEP and ENEM.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-20T11:17:09Z No. of bitstreams: 1 carlosaugustoribeiro.pdf: 530796 bytes, checksum: 03aec0a60c8d7351265389f4be1436fa (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T13:07:34Z (GMT) No. of bitstreams: 1 carlosaugustoribeiro.pdf: 530796 bytes, checksum: 03aec0a60c8d7351265389f4be1436fa (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T14:08:06Z (GMT) No. of bitstreams: 1 carlosaugustoribeiro.pdf: 530796 bytes, checksum: 03aec0a60c8d7351265389f4be1436fa (MD5) / Made available in DSpace on 2017-02-07T14:08:06Z (GMT). No. of bitstreams: 1 carlosaugustoribeiro.pdf: 530796 bytes, checksum: 03aec0a60c8d7351265389f4be1436fa (MD5) Previous issue date: 2013-08-16 / Nesse trabalho apresentamos uma proposta para introduzir, já no 1o ano do Ensino Médio, a idéia de Taxa de Variação de uma Função tanto do ponto de vista algébrico como geométrico e caracterizar as funções elementares (a m, quadrática e exponencial) a partir de suas variabilidades ( a forma como uma função cresce ou decresce). Nesse sentido, é muito importante uma certa conexão com a disciplina de Física, onde a Cinemática é um ambiente valioso para esse estudo. Finalmente, propomos um estudo intuitivo de Limite de Sequência o que permitirá uma abordagem mais consistente do importante número de Euler que aparece naturalmente em situações onde a variação de uma certa grandeza num certo instante é proporcional ao seu valor naquele instante. / In this work we have presented a proposal to introduce, early in the rst year of High School Education, the idea of the Rate of Variation of a Function either from the algebraic or geometric point of view and characterize the elementary functions (a ne, quadratic and exponential) from their variabilities (the form as a function increase and decrease). In this sense, it is very important to have a certain connection with the discipline of Physics, where the kinematics is a rich environment for this study. To conclude, we proposed an intuitive study of Limit of Sequence, which will allow us a more consistent approach of the important number of Euler that appears naturally in situations where the variation of a certain grandeur in a speci c moment is proportional to its value at that moment.