Inaug.-diss.--Leipzig. / Lebenslauf.

Thesis (M. Div.)--Emmanuel School of Religion, Johnson City, Tenn., 1999. / Vita. Includes bibliographical references (leaves 122-132).

Thesis (M.A.)--Abilene Christian University, 1990. / Includes bibliographical references (leaves 139-156).

Esta tese estuda a geometria de problemas variacionais através da linearização e projetivização das suas equações de Euler - Lagrange. O processo de linearização fornece a passagem das equações de Euler - Lagrange para as equações de Jacobi; a minimalidade (local) de extremais está determinada pelo conceito de ponto conjugado, que tem natureza projetiva. Propriedades de minimalidade local são transformadas em propriedades de auto-interseção de uma curva na variedade de Grassmann adequada. Desenvolvemos este processo em duas aplicações: 1) O estudo da minimalidade local de extremais de problemas variacionais de ordem superior. Neste caso, encontramos uma curva não degenerada de planos isotrópicos num espaço vetorial simplético, que, após prolongamento por derivadas, fornece uma curva degenerada de planos Lagrangeanos cujas auto-interseções determinam a minimalidade. 2) No caso mais clássico de problemas de ordem um, estudamos a versão linear - projetiva do problema inverso: dada uma equação diferencial de ordem dois, quando ela é a equação de Euler - Lagrange de um problema variacional? Veremos que as condições do problema inverso linear - projetivo fornecem informações sobre os possíveis Lagrangianos, por exemplo a assinatura. / In this work we study the geometry of high order calculus of variations through the linearization and projectivization of their Euler Lagrange equations. The linearization process provides the passage from the Euler Lagrange equations to the Jacobi equations; the (local) minimality properties of the extremal is determined by conjugate points, which is a projective concept. Minimaltiy properties of the extremals are transformed into self-intersection propertie of curves in the appropriate Grassmann manifold. We develop this process in two instances: 1) The study of minimality properties of extremals of higher-order variational problems. In this case, we find a non-degenerate curve of isotropic subspaces, that, after prolongation by derivatives, gives a degenerate curve of Lagrangian planes whose self-intersections determine minimality. 2) In the classical case of order one variational problems, we study a projective-linear version of the inverse problem: given a second order differential equation, when is it the Euler-Lagrange equation of a variational problem? We will see that the conditions given by the linear projective inverse problem provides information about the possible Lagrangians, for example, its signature.

This thesis surveys the major works on the topic of verbal aspect. Chapter 1 provides an introduction, giving the background to the issue and listing some of the major contributors to the topic, Stanley Porter, Rodney Decker, Buist Fanning, and Constantine Campbell. Chapter 2 reviews and analyzes the contributions of these authors in this area of study. Further, this thesis seeks to clarify the topic, by exposing each author's views concerning the major matters of debate and by listing some subjects in verbal aspect that are in need of further study; in particular, the issue of the aspect of the perfect verb form, the aspect of the future verb form, and the historical present. Finally, chapter 3 demonstrates the importance of this issue for the study of Scripture, specifically, the study of the New Testament, and it gives suggestions for further study in this area.

Esta tese estuda a geometria de problemas variacionais através da linearização e projetivização das suas equações de Euler - Lagrange. O processo de linearização fornece a passagem das equações de Euler - Lagrange para as equações de Jacobi; a minimalidade (local) de extremais está determinada pelo conceito de ponto conjugado, que tem natureza projetiva. Propriedades de minimalidade local são transformadas em propriedades de auto-interseção de uma curva na variedade de Grassmann adequada. Desenvolvemos este processo em duas aplicações: 1) O estudo da minimalidade local de extremais de problemas variacionais de ordem superior. Neste caso, encontramos uma curva não degenerada de planos isotrópicos num espaço vetorial simplético, que, após prolongamento por derivadas, fornece uma curva degenerada de planos Lagrangeanos cujas auto-interseções determinam a minimalidade. 2) No caso mais clássico de problemas de ordem um, estudamos a versão linear - projetiva do problema inverso: dada uma equação diferencial de ordem dois, quando ela é a equação de Euler - Lagrange de um problema variacional? Veremos que as condições do problema inverso linear - projetivo fornecem informações sobre os possíveis Lagrangianos, por exemplo a assinatura. / In this work we study the geometry of high order calculus of variations through the linearization and projectivization of their Euler Lagrange equations. The linearization process provides the passage from the Euler Lagrange equations to the Jacobi equations; the (local) minimality properties of the extremal is determined by conjugate points, which is a projective concept. Minimaltiy properties of the extremals are transformed into self-intersection propertie of curves in the appropriate Grassmann manifold. We develop this process in two instances: 1) The study of minimality properties of extremals of higher-order variational problems. In this case, we find a non-degenerate curve of isotropic subspaces, that, after prolongation by derivatives, gives a degenerate curve of Lagrangian planes whose self-intersections determine minimality. 2) In the classical case of order one variational problems, we study a projective-linear version of the inverse problem: given a second order differential equation, when is it the Euler-Lagrange equation of a variational problem? We will see that the conditions given by the linear projective inverse problem provides information about the possible Lagrangians, for example, its signature.

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<p>In the fifteen-spined stickleback, <i>Spinachia spinachia</i>, males provide females with direct benefits by fanning, cleaning and guarding the offspring. Males announce their parental skills through intense body shakes during courtship. Females preferred to mate with more intensely shaking males. As a result, females got better fathers for their offspring, as such males achieved a higher hatching success. Not only did male behavioural cues attract females, but males also used their nests as extrabodily ornaments. The nest is held together with shiny secretional threads consisting of a glycoprotein. Females chose to spawn in nests with more secretional threads. A likely reason for this is that the threads are metabolically costly for the male to produce and the amount of secretion indicates a male's nutritional status, which is of great importance as parental duties are energetically costly. Moreover, females preferred nests built high up in the vegetation, as such nests were safer from egg predators. Competition with other males for females favoured males building higher nests than did their neighbours, probably because females preferred high nests. Male-male interactions, such as sneaking and egg stealing, caused decreased paternity among males in nature as assessed by a microsatellite analysis. Males adjusted their paternal effort according to their previous investment in the brood, but not according to paternity. Thus, female choice is based on multiple cues and results in better paternal care. Males invest in courtship, male-male competition, nest construction and paternal care, the outcome determining their success in mate attraction.</p>

In the fifteen-spined stickleback, Spinachia spinachia, males provide females with direct benefits by fanning, cleaning and guarding the offspring. Males announce their parental skills through intense body shakes during courtship. Females preferred to mate with more intensely shaking males. As a result, females got better fathers for their offspring, as such males achieved a higher hatching success. Not only did male behavioural cues attract females, but males also used their nests as extrabodily ornaments. The nest is held together with shiny secretional threads consisting of a glycoprotein. Females chose to spawn in nests with more secretional threads. A likely reason for this is that the threads are metabolically costly for the male to produce and the amount of secretion indicates a male's nutritional status, which is of great importance as parental duties are energetically costly. Moreover, females preferred nests built high up in the vegetation, as such nests were safer from egg predators. Competition with other males for females favoured males building higher nests than did their neighbours, probably because females preferred high nests. Male-male interactions, such as sneaking and egg stealing, caused decreased paternity among males in nature as assessed by a microsatellite analysis. Males adjusted their paternal effort according to their previous investment in the brood, but not according to paternity. Thus, female choice is based on multiple cues and results in better paternal care. Males invest in courtship, male-male competition, nest construction and paternal care, the outcome determining their success in mate attraction.

This dissertation investigates the ways in which Philadelphia artists and architects visualized, comprehended, and reformed the city's rapidly changing urban environment in the early republic, prior to the modern articulation of "ecology" as a scientific concept by late nineteenth-century naturalists such as Ernst Haeckel. I consider a variety of different media--including popular depictions and manifestations of Penn's Treaty Elm, fireplace and stove models by Charles Willson Peale, architectural designs for the Philadelphia Waterworks by Benjamin Henry Latrobe, and a self-portrait bust by the sculptor William Rush--in order to demonstrate that the human body served as a powerful creative metaphor in Philadelphia circa 1800, not only for understanding and representing natural processes in political or aesthetic terms, but also for framing critical public discourse about the city's actual environmental conditions. Specifically, I reveal how this metaphorical framework produced a variety of effects in art and architecture of the period, sometimes facilitating and at other times obscuring an understanding about the natural world as an arena of dynamic transformation. By revealing the previously unexplored environmental significance of the objects in question, my dissertation asserts that ecological change played an instrumental role in shaping artistic production and urban development in the decades following United States independence. / Art History