Using pencils of quadrics, we study a construction of torsors of Jacobians of hyperelliptic curves twice of which is Pic^1. We then use this construction to study the arithmetic invariant theory of the actions of SO2n+1 and PSO2n+2 on self-adjoint operators and show how they facilitate in computing the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational Weierstrass point, and the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational non-Weierstrass point, over arbitrary number fields. / Mathematics

The artist discusses her Master of Fine Arts exhibition at East Tennessee State University, Slocumb Galleries, Johnson City, Tennessee, October 28-November 8, 2002. Her exhibition was a personal narrative of her southern upbringing in small town Appalachia as well as a reflection of her inner thoughts and feelings towards feminism, adolescence, sexuality and Barbie. She chose to reference the female form, void of an actual body, implied through clothing. Works are figurative and sculptural and are constructed of copper, sterling and fine silver. They are sculptural hollow vessels, raised, formed, and colored with gesso and prismacolor pencils. Topics discussed: the artist's experiences as a woman, development in graduate school, casting versus raising, a detailed technical discussion on each piece, the influences of Marilyn da Silva’s use of the narrative and color on metal, and Judith Shea’s use of clothing to reference the human form. Includes images and discussions of twenty-six works and images of the exhibition.

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Made available in DSpace on 2010-04-20T20:20:01Z (GMT). No. of bitstreams: 1 149577.pdf: 249444 bytes, checksum: 0886870205bbb58b6dd47f087f3d36ce (MD5) Previous issue date: 2007-10-10T00:00:00Z / A competição acirrada no mercado têm obrigado os varejistas a avaliar produtos com bastante critério antes de adquiri-los. Nas papelarias, o mesmo ocorre com a compra de instrumentos de escrita. Nesta dissertação é analisado o processo de compra de lapiseiras. Atualmente existe uma infinidade de modelos de lapiseiras com diferentes cores, estampas, cheiros, preços e fornecedores. Como escolher para que tenham alto giro no ponto-de-venda, minimizando os custos e maximizando os ganhos, torna-se o grande desafio para a organização que pretende continuar competitiva. Para aumentar o conhecimento sobre esse processo, esta dissertação teve como propósito investigar as variáveis que influenciam a decisão do comprador varejista, dono de papelaria. Foram realizados dois estudos de caso com papelarias. Por fim, descobriu-se que a decisão do comprador de lapiseiras não se restringe ao produto. Existem diversas variáveis que podem influenciar a sua decisão, como o representante, a distribuição efetiva, a garantia e o marketing (comunicação).

Cette thèse porte sur certains aspects symboliques-numériques du problème des paires invariantes pour les polynômes de matrices. Les paires invariantes généralisent la définition de valeur propre / vecteur propre et correspondent à la notion de sous-espaces invariants pour le cas nonlinéaire. Elles trouvent leurs applications dans le calcul numérique de plusieurs valeurs propres d’un polynôme de matrices; elles présentent aussi un intérêt dans le contexte des systèmes différentiels. En utilisant une approche basée sur les intégrales de contour, nous déterminons des expressions du nombre de conditionnement et de l’erreur rétrograde pour le problème du calcul des paires invariantes. Ensuite, nous adaptons la méthode des moments de Sakurai-Sugiura au calcul des paires invariantes et nous étudions le comportement de la version scalaire et par blocs de la méthode en présence de valeurs propres multiples. Le résultats obtenus à l’aide des approches directes peuvent éventuellement être améliorés numériquement grâce à une méthode itérative: nous proposons ici une comparaison de deux variantes de la méthode de Newton appliquée aux paires invariantes. Le problème des solvants de matrices est très proche de celui des paires invariants. Le résultats présentés ci-dessus sont donc appliqués au cas des solvants pour obtenir des expressions du nombre de conditionnement et de l’erreur, et un algorithme de calcul basé sur la méthode des moments. De plus, nous étudions le lien entre le problème des solvants et la transformation des polynômes de matrices en forme triangulaire. / In this thesis, we study some symbolic-numeric aspects of the invariant pair problem for matrix polynomials. Invariant pairs extend the notion of eigenvalue-eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. They have applications in the numeric computation of several eigenvalues of a matrix polynomial; they also present an interest in the context of differential systems. Here, a contour integral formulation is applied to compute condition numbers and backward errors for invariant pairs. We then adapt the Sakurai-Sugiura moment method to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues, and we analyze the behavior of the scalar and block versions of the method in presence of different multiplicity patterns. Results obtained via direct approaches may need to be refined numerically using an iterative method: here we study and compare two variants of Newton’s method applied to the invariant pair problem. The matrix solvent problem is closely related to invariant pairs. Therefore, we specialize our results on invariant pairs to the case of matrix solvents, thus obtaining formulations for the condition number and backward errors, and a moment-based computational approach. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials.