Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 270-272. / by Stephen Kinyon Young. / Ph.D.

Matroids capture an abstraction of independence in mathematics, and in doing so, connect discrete mathematical structures that arise in a variety of contexts. A matroid can be defined in several cryptomorphic ways depending on which perspective of a matroid is most applicable to the given context. Among the many important concepts in matroid theory, the concept of matroid duality provides a powerful tool when addressing difficult problems. The usefulness of matroid duality stems from the fact that the dual of a matroid is itself a matroid. In this thesis, we explore a matroid-like object called a flag matroid. In particular, we suggest a notion of duality for flag matroids and we investigate the implications of this notion.

Fundamentally, creative endeavors are affected by the personal philosophy of artists which are greatly concerned with their perception and interpretation of life and death. These two concepts form a reality which consists of this dichotomy. As `unity' has been an underlying goal in the work of many artists, it challenges the polarity conveyed in this viewpoint causing contemplation and conversation around the framing of their own existence through their work.

Orientador: Horatiu Nastase / Resumo: Nesta tese, discutimos três modelos cosmológicos que são baseados direta ou indiretamente em ideias advindas de teoria das cordas. Depois de uma revisão geral de cosmologia em teoria das cordas, um resumo de cosmologia e teoria das cordas é apresentado, com ênfase nos conceitos fundamentais e teóricos. Então descrevemos como o acoplamento camaleônico pode potencialmente afetar as predições de inflação cósmica com campo único, com tratamento cuidadoso dos modos de perturbação cosmológica adiabáticos e de entropia. Além disso uma nova abordagem para a dualidade-T em soluções cosmológicas de supergravidade bosônica é discutida no contexto de teoria dupla de campos. Por fim, propomos uma nova prescrição para o mapa holográfico em cosmologia que pode ser usado para conectar modelos fundamentais de cosmologia holográfica com outras abordagens fenomenológicas. / Doutor

A prop profile of a differential geometric structure is a minimal resolution of an algebraic prop such that representations of this resolution are in one-to-one correspondence with structures of the given type. We begin this thesis with a detailed account of the algebraic tools necessary to construct prop profiles; we treat operads and props, and resolutions of these through Koszul duality. Our main results can be summarized as follows. Firstly, we contribute to the work of S.A. Merkulov on the prop profiles of Poisson and Nijenhuis structures. We prove that the operad of the latter prop profile is Koszul by showing that it has a PBW-basis, and we provide a geometrical interpretation of the former in terms of an L-infinity structure on the structure sheaf of a manifold. Secondly, we construct prop profiles of compatible Poisson and Nijenhuis structures. Representations of minimal resolutions of props correspond to Maurer-Cartan elements of certain Lie algebras associated to the resolved props. Also the differential geometric structures are defined as solutions of Maurer-Cartan equations. We show the correspondence between props and differential geometry by providing explicit isomorphisms between these Lie algebras. Thirdly, in order to construct the prop profiles of compatible Poisson and Nijenhuis structures we study operads of compatible algebraic structures. By studying Cohen-Macaulay properties of posets associated to such operads we prove the Koszulness of a large class of operads of compatible structures.

Reciprocal processes, whose concept can be traced back to E. Schrödinger, form a class of stochastic processes constructed as mixture of bridges, that satisfy a time Markov field property. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This presentation is based on joint works with M. Thieullen, R. Murr and C. Léonard.

This paper tests the relationship between ownership/leadership structures and stock returns for firms listed in Taiwan. A ¡§Governance Index¡¨ is built based on four different aspects of the company¡¦s governance structure: 1.) CEO duality, 2.) Size of the board of directors, 3.) Managements¡¦ shareholdings and 4.) Block shareholders¡¦ holding. This index is used as a proxy measure of the effectiveness of corporate governance mechanism. I show that firms identified by the governance index as under sounding governance outperform those under poor governance. The results indicate that the corporate governance index built in this study is a valid measure in evaluating the effectiveness of corporate governance of firms in Taiwan. I demonstrate one additional application of the governance index constructed in this dissertation by showing that firms (identified by the governance index) with strong corporate governance mechanism effectively constrain the propensity of managers to engage in earnings management and improve the quality of reported earnings. Corporate governance is an effective monitoring device of the quality of financial reporting. Firms with poor governance structure are more likely to avoid reporting small losses by reporting small positive earnings. Furthermore, the magnitude of abnormal accruals is significantly related to governance level. Firms with weak corporate governance structures are more likely to use discretionary accruals to raise reported earnings.

The aim of this work is to make some investigations concerning duality for multiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, under some appropriate assumptions, the existence of strong duality. Closely related to the strong duality we derive the optimality conditions for each of these three duals. By means of these considerations, we study the duality for two vector optimization problems, namely, a convex multiobjective problem with cone inequality constraints and a special fractional programming problem with linear inequality constraints. To each of these vector problems we associate a scalar primal and study the duality for it. The structure of both scalar duals give us an idea about how to construct a multiobjective dual. The existence of weak and strong duality is also shown. We conclude our investigations by making an analysis over different duality concepts in multiobjective optimization. To a general multiobjective problem with cone inequality constraints we introduce other six different duals for which we prove weak as well as strong duality assertions. Afterwards, we derive some inclusion results for the image sets and, respectively, for the maximal elements sets of the image sets of these problems. Moreover, we show under which conditions they become identical. A general scheme containing the relations between the six multiobjective duals and some other duals mentioned in the literature is derived. / Das Ziel dieser Arbeit ist die Durchführung einiger Untersuchungen bezüglich der Dualität für Mehrzieloptimierungsaufgaben. Zu diesem Zweck wird als erstes mit Hilfe des so genannten konjugierten Verfahrens die Dualität für skalare Optimierungsaufgaben untersucht. Das erlaubt uns zu einer primalen Aufgabe drei unterschiedliche duale Aufgaben zuzuordnen. Wir betrachten die Beziehungen zwischen den optimalen Zielfunktionswerten der drei Dualaufgaben und untersuchen die Existenz der starken Dualität unter naheliegenden Annahmen. Im Zusammenhang mit der starken Dualität leiten wir für jede dieser Dualaufgaben die Optimalitätsbedingungen her. Die obengenannten Ergebnisse werden beim Studium der Dualität für zwei Vektoroptimierungsaufgaben angewandt, und zwar für die konvexe Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen und für eine spezielle Quotientenoptimierungsaufgabe mit linearen Ungleichungen als Nebenbedingungen. Wir assoziieren zu jeder dieser vektoriellen Aufgaben eine skalare Aufgabe für welche die Dualität betrachtet wird. Die Formulierung der beiden skalaren Dualaufgaben führt uns zu der Konstruktion der Mehrzieloptimierungsaufgabe. Die Existenz von schwacher und starker Dualität wird bewiesen. Wir schliessen unsere Untersuchungen ab, indem wir eine Analyse von verschiedenen Dualitätskonzepten in der Mehrzieloptimierung durchführen. Zu einer allgemeinen Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen werden sechs verschiedene Dualaufgaben eingeführt, für die sowohl schwache als auch starke Dualitätsaussagen gezeigt werden. Danach leiten wir verschiedene Beziehungen zwischen den Bildmengen, bzw., zwischen den Mengen der maximalen Elemente dieser Bildmengen der sechs Dualaufgaben her. Dazu zeigen wir unter welchen Bedingungen werden diese Mengen identisch. Ein allgemeines Schema das die Beziehungen zwischen den sechs dualen Mehrzieloptimierungsaufgaben und andere Dualaufgaben aus der Literatur enthält, wird dargestellt.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 79-80).

This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize with respect to the given topology play an important role in the existence of minimizers of integral problems. We will introduce the important concepts of quasiconvexity and polyconvexity. Inspired by finite element methods from Numerical Analysis, we introduce a perturbed problem which has some surprising uniqueness properties.