The evaluation of infinite series plays an important part in numerical calculation. In hand calculation whenever a transcendental function is involved, one usually consults a table. Not only do the construction of the tables require the evaluation of transcendental functions, but with the advent of the electronic computer it is usually more convenient to have such evaluation carried out by the computer than to try to store a table of the necessary values to carry out the intended calculation. / Advisor: H. C. Griffith, Professor Directing Study. / Typescript. / "August 1960." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 37).

"The purpose of this paper is to study methods by which a value can be assigned to an infinite series. The reason for studying about these methods lies in the fact that infinite series often appear as the end result of a calculation or computation. A desire to obtain a usable end result leads us to the investigation of methods for evaluating infinite series"--Introduction. / "August, 1955." / Typescript. / Advisor: Howard E. Taylor, Professor Directing Paper. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 40).

MacMahon's Master Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. We give a complete proof of MacMahon's Master Theorem based on MacMahon's original 1960 proof. We also study a specific infinite dimensional matrix inverse due to C. Krattenthaler.

In der vorliegenden Arbeit wird ein Programmcode zur numerischen Modalanalyse dreidimensionaler Fluide in komplexen akustischen Systemen, speziell in Resonatoren, entwickelt. Mit diesem Code ist es möglich, turbulente Strömungen im Rahmen der Modalanalyse zu berücksichtigen. Hierzu wird ein realistisches Strömungsprofil, ermittelt mithilfe eines 3D-Navier-Stokes-Lösers, verwendet. Der Hauptteil der Arbeit befasst sich mit der Herleitung der für die Berechnung notwendigen Galbrun-Gleichung und deren Aufbereitung zur numerischen Analyse. Für die numerische Umsetzung kommt die Methode der finiten Elemente in Verbindung mit komplex konjugierten, infiniten Astley-Leis Elementen zur Anwendung. Die infiniten Elemente werden genutzt, um in den betrachteten Außenraumproblemen die Abstrahlung in das Fernfeld abzubilden. Nach der Anwendung des entwickelten Programmcodes auf einfachere Modelle erfolgen Untersuchungen zur Intonation einer Blockflöte. Hierzu wird das Fluid innerhalb und im Nahfeld des Instruments unter Berücksichtigung des turbulenten Strömungsprofils, welches sich beim Spielen der Blockflöte ausbildet, betrachtet. Im Ergebnis stehen die Eigenwerte des Instruments in Abhängigkeit von der gewählten Griffkombination. Zur Evaluierung der Ergebnisse und zur Untersuchung des Einflusses der Strömung auf den Klang erfolgt der Vergleich mit den exakten Eigenfrequenzen. Die Galbrun-Gleichung wurde bereits von anderen Autoren untersucht und auf akustische Problemstellungen angewendet. Im Rahmen dieser Arbeit erfolgt jedoch erstmalig die Anwendung der Galbrun-Gleichung auf Eigenwertprobleme. Darüber hinaus sind der Autorin keine Arbeiten bekannt, die sich mit dreidimensionalen Modellen befassen. In der vorliegenden Arbeit werden somit erstmals komplexe dreidimensionale Modelle unter Anwendung der Galbrun-Gleichung untersucht.

Les principaux sujets d'intérêt de cette thèse concerneront deux notions de la complexité d'un mot infini : la complexité abélienne et la complexité de permutation. La complexité abélienne a été étudiée durant les dernières décennies. La complexité de permutation est, elle, une forme de complexité des mots relativement nouvelle qui associe à chaque mot apériodique de manière naturelle une permutation infinie. Nous nous pencherons sur deux sujets dans le domaine de la complexité abélienne. Dans un premier temps, nous nous intéresserons à une notion abélienne de la maximal pattern complexity définie par T. Kamae. Deuxièmement, nous analyserons une limite supérieure de cette complexité pour les mots C-équilibré. Dans le domaine de la complexité de permutation des mots apériodiques binaires, nous établissons une formule pour la complexité de permutation du mot de Thue-Morse, conjecturée par Makarov, en étudiant la combinatoire des sous-permutations sous l'action du morphisme de Thue-Morse. Par la suite, nous donnons une méthode générale pour calculer la complexité de permutation de l'image de certains mots sous l'application du morphisme du doublement des lettres. Finalement, nous déterminons la complexité de permutation de l'image du mot de Thue-Morse et d'un mot Sturmien sous l'application du morphisme du doublement des lettres. / The main topics of interest in this thesis will be two types of complexity, abelian complexity and permutation complexity. Abelian complexity has been investigated over the past decades. Permutation complexity is a relatively new type of word complexity which investigates lexicographical ordering of shifts of an aperiodic word. We will investigate two topics in the area of abelian complexity. Firstly we will consider an abelian variation of maximal pattern complexity. Secondly we consider an upper bound for words with the C-balance property. In the area of permutation complexity, we compute the permutation complexity function for a number of words. A formula for the complexity of Thue-Morse word is established by studying patterns in subpermutations and the action of the Thue-Morse morphism on the subpermutations. We then give a method to calculate the complexity of the image of certain words under the doubling map. The permutation complexity function of the image of the Thue-Morse word under the doubling map and the image of a Sturmian word under the doubling map are established.

This thesis is devoted to investigating some properties of the sequence (Wn) of the denominators. This is a divisibility sequence; that is, Wm | Wn whenever m | n. Our task here is to examine a conjecture on the number of prime terms in (Wn), well known as the Primality conjecture. We will prove that there is a uniform lower bound on n beyond such that all terms Wn have at least two distinct prime factors. In some cases, the bound is as low as n = 2.

The representation theory of infinite dimensional groups is in its infancy. This paper is an attempt to apply the orbit method to a particular infinite dimensional group, the spin extension of the restricted unitary group. Our main contribution is in showing that various homogeneous spaces for this group admit measures which can be used to realize the unitary structure for the standard modules.

In concurrency theory—the branch of (theoretical) computer science that studies the logical and mathematical foundations of parallel computation—there are two main formal ways of modelling the behaviour of systems where multiple actions or events can happen independently and at the same time: either with interleaving or with partial order semantics. On the one hand, the interleaving semantics approach proposes to reduce concurrency to the nondeterministic, sequential computation of the events the system can perform independently. On the other hand, partial order semantics represent concurrency explicitly by means of an independence relation on the set of events that the system can execute in parallel; following this approach, the so-called ‘true concurrency’ approach, independence or concurrency is a primitive notion rather than a derived concept as in the interleaving framework. Using interleaving or partial order semantics is, however, more than a matter of taste. In fact, choosing one kind of semantics over the other can have important implications—both from theoretical and practical viewpoints—as making such a choice can raise different issues, some of which we investigate here. More specifically, this thesis studies concurrent systems with partial order semantics and focuses on their bisimulation and model-checking problems; the theories and techniques herein apply, in a uniform way, to different classes of Petri nets, event structures, and transition system with independence (TSI) models. Some results of this work are: a number of mu-calculi (in this case, fixpoint extensions of modal logic) that, in certain classes of systems, induce exactly the same identifications as some of the standard bisimulation equivalences used in concurrency. Secondly, the introduction of (infinite) higher-order logic games for bisimulation and for model-checking, where the players of the games are given (local) monadic second-order power on the sets of elements they are allowed to play. And, finally, the formalization of a new order-theoretic concurrent game model that provides a uniform approach to bisimulation and model-checking and bridges some mathematical concepts in order theory with the more operational world of games. In particular, we show that in all cases the logic games for bisimulation and model-checking developed in this thesis are sound and complete, and therefore, also determined—even when considering models of infinite state systems; moreover, these logic games are decidable in the finite case and underpin novel decision procedures for systems verification. Since the mu-calculi and (infinite) logic games studied here generalise well-known fixpoint modal logics as well as game-theoretic decision procedures for analysing concurrent systems with interleaving semantics, this thesis provides some of the groundwork for the design of a logic-based, game-theoretic framework for studying, in a uniform manner, several concurrent systems regardless of whether they have an interleaving or a partial order semantics.

Published from 1985 to 1986, DC Comics’ Crisis on Infinite Earths created the expectation that each crossover will result in numerous deaths and alter the structure or history of the DC Universe. Since many of these changes, such as the death of a popular or iconic character, cannot be sustained long term, the success and influence of Crisis on Infinite Earths led to the erosion of the very elements that made it shocking. Entire worlds can be destroyed, but superreaders eventually suspect that no change is ever permanent and, as more iconic characters are revived or rebooted, death is no longer meaningful.

We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)