Thesis (Ph. D.)--University of Notre Dame, 2003. / Thesis directed by Stephen H. Watson for the Department of Philosophy. "December 2003." Includes bibliographical references (leaves 297-303).

We consider various infinite series and examine their arithmetic nature. Series of interest are of the form $$\sum_{n =0}^{\infty} \frac{f(n)A(n)}{B(n)}, \;\;\;\; \sum_{n \in \mathbb{Z}}\frac{f(n)A(n)}{B(n)}, \;\;\;\; \sum_{n=0}^{\infty} \frac{z^n A(n)}{B(n)}$$ where $f$ is algebraic valued periodic function, $A(x), B(x) \in \overline{\mathbb{Q}}[x]$ and $z$ is an algebraic number with $|z| \leq 1$. We also examine multivariable extensions $$\sum_{n_1, \ldots, n_k = 0}^{\infty} \frac{f(n_1, \ldots, n_k)A_1(n_1) \cdots A_k(n_k)}{B_1(n_1) \cdots B_k(n_k)}$$ and $$\sum_{n_1, \ldots, n_k \in \mathbb{Z}} \frac{f(n_1, \ldots, n_k)A_1(n_1) \cdots A_k(n_k)}{B_1(n_1) \cdots B_k(n_k)}.$$ These series are all very natural things to write down and we would like to understand them better. We calculate closed forms using various techniques. For example, we use relations between Hurwitz zeta functions, digamma functions, polygamma functions, Fourier analysis, discrete Fourier transforms, among other objects and techniques. Once closed forms are found, we make use of some of the well-known transcendental number theory including the theorem of Baker regarding linear forms in logarithms of algebraic numbers to determine their arithmetic nature. In one particular setting, we extend the work of Bundschuh \cite{bundschuh} by proving the following series are all transcendental for positive $c \in \mathbb{Q} \setminus \mathbb{Z}$ and $k$ a positive integer: $$\sum_{n \in \mathbb{Z}} \frac{1}{(n^2 + c)^k}, \;\;\; \sum_{n \in \mathbb{Z}} \frac{1}{(n^4 - c^4)^{2k}}, \;\;\; \sum_{n \in \mathbb{Z}} \frac{1}{(n^6 - c^6)^{2k}}, \;\;\; \sum_{n \in \mathbb{Z}} \frac{1}{(n^3 \pm c^3)^{2k}}$$ $$\sum_{n \in \mathbb{Z}} \frac{1}{n^3 \pm c^3}, \;\;\; \sum_{|n| \geq 2} \frac{1}{n^3 -1}, \;\;\; \sum_{|n| \geq 2} \frac{1}{n^4 -1}, \;\;\; \sum_{|n| \geq 2} \frac{1}{n^6 -1}.$$ Bundschuh conjectured that the last three series are transcendental, but we offer the first unconditional proofs of transcendence. We also show some conditional results under the assumption of some well-known conjectures. In particular, for $A_i(x), B_i(x) \in \overline{\mathbb{Q}}[x]$ with each $B_i(x)$ has only simple rational roots, if Schanuel's conjecture is true, the series (avoiding roots of the denominator) $$\mathop{{\sum}}_{n_1, \ldots, n_k =0}^{\infty} \frac{f(n_1, \ldots, n_k)A_1(n_1) \cdots A_k(n_k)}{B_1(n_1) \cdots B_k(n_k)}$$ is either an effectively computable algebraic number or transcendental. We also show that Schanuel's conjecture implies that the series $$\sum_{n \in \mathbb{Z}} \frac{A(n)}{B(n)}$$ is either zero or transcendental, when $B(x)$ has non-integral roots. We develop a general theory, analyzing various infinite series throughout. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-04-23 10:45:19.735

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This thesis offers an interpretative framework of Italo Calvino’s later work (the cosmicomic stories, Le città invisibili, and Palomar), based on the notions of myth, desire, utopia and science. Its aim is to suggest a reading of these texts as a common literary project best described as being deeply influenced by mythological elements and structures, while clearly bearing the mark of enlightened thought. The study exposes both the intellectual implications of such a project, and the aesthetic mechanisms by which it takes its form. The research was informed by Calvino’s own relevant critical work, a network of secondary criticism approaching either the texts which were of interest to this particular work or the themes and notions that were to be explored, and a set of tertiary texts, which helped to consolidate pivotal notions. The latter include the work of thinkers who had a major influence on Calvino as it is known from his essays and his letters (like Charles Fourier or Giorgio de Santillana), but also other figures, such as Anton Chekhov or Albert Camus, who emerged as interesting comparative opportunities for our study. The analysis of the cosmicomic stories explores the relationship between myth-making and individual responsibility. It draws parallels between intellectual commitment and literary projection, and defines Calvino’s utopian project, including it in a reflection on knowledge, myth and the tyranny of abstract thought. Individual responsibility emerges as a prospective and a retrospective activity, which is explained alongside the idea of ‘poetics in the making’. Le città invisibili is studied as an illustration of Calvino’s precise poetics using the image of the city. The notions of the episode and the frame are the central concepts around which the inquiry is articulated. Discussing the ideas of desire and the search for the ideal, it is possible to draw solid links with the cosmological project of the cosmicomics and Calvino’s idea of utopia and myth. With an examination of characterisation in Palomar and a close analysis of the quest for meaning, this thesis also attempts a definition of Calvino’s aesthetics as the ‘aesthetics of earthly transcendence’. It moves on to a comparative study of Palomar and Le Mythe de Sisyphe by Albert Camus, in order to suggest an interpretation of the main character, as a man who lives and observes his life in the face of the absurd; the literary consequence being the immediate confrontation between writing and death, and the presence of silence threatening understanding and communication.

Thesis (Ph.D.)--Ohio University, June, 2007. / Includes bibliographical references (leaves 190-208)

Thesis (Ph. D.)--University of California, Santa Cruz. / Typescript. Includes bibliographical references (leaves [247]-253).

M. Phil. (Personal, Interpersonal and Professional Leadership) / Orientation: Personal experience of the phenomenon of transcendence and a preliminary literature review indicates that the phenomenon of transcendence can be better integrated within the Personal, Interpersonal and Professional Leadership (PPL) framework as well as within other leadership theories. Research purpose: The aim of the study is to conceptualise transcendence within PPL and leadership in general using auto-ethnography research methodology. Motivation for the study: Current leadership literature within PPL does not include the integration of the phenomenon of transcendence as a model towards spirituality and leadership. This gap can contextualise spirituality and leadership through transcendence. Research design: The research approach within this study was based a postmodernist qualitative philosophy. Auto-ethnography was used as methodology and also included a life history of another person to verify the auto-ethnographic data. Main findings: The study yielded an auto-ethnographic story with a rich and varied description of how a person can experience transcendence within the personal leadership field. The analysis of the collected data has revealed themes that can possibly contribute towards spirituality and leadership. Practical implications: The findings of this study might bring insight into the human ability of transcendence despite difficulty or suffering, and that can contribute to spirituality and leadership. Anticipated contribution: The study provides some understanding of how a person can still develop into a leader despite difficulties or hardship. This understanding can contribute to leadership development interventions, which can also be explored further in future.

M.Phil. / The hypothesis of the research essay was that people experience a lack of meaning or purpose in their lives. The general aim of this research essay was to define why self-transcendence is an important component in a balanced person's life and how it can contribute to adding meaning to a person's life. The contribution of Personal and Professional Leadership to the development and/or improvement of self-transcendence, was also investigated. The research methodology used in the research essay includes hermeneutic and descriptive strategies. The research methods that were used include a word and concept analysis, in order to clarify concepts central to the title of the research essay. A literature study was also conducted, to clarify self-transcendence from the perspective of various philosophers and their theories, within an existential and Personal and Professional Leadership paradigm. The following were important findings of the research essay: • Self-transcendence refers to the desire within a person to give more of himself to others. This will not only have an influence on the legacy that he leaves behind, but also on his own perceptions, self-awareness and potential platform. • The key elements of self-transcendence are: the ability to make a free choice with one's own free will, self-awareness, true north values, selfactualisation; and to have service-orientated relationships with others. • Self-transcendence plays a very important role in a person's life, by influencing a person's quality of life, legacy and ultimately the meaning of his life. • Personal and Professional Leadership plays a very important role in improving and developing self-transcendence, by creating an awareness of the continuous growth process towards enhancing selftranscendence. This could assist a person in becoming more proactive, by wanting to become more self-transcendent. • Servant Leadership can play an important role in self-transcendence. • Self-transcendence can enable a person to gain greater control over his life, which in turn will create a sense of meaning. • Self-transcendence can give a person a sense of belonging and purpose in his life, and also give a feeling that after his death, a part of him will continue to live on. • The research essay concludes by indicating that self-transcendence can, therefore, play a very important role in giving meaning to a person's life.

The thesis deals with the topic of a relation of the human being to transcendence through the concept of metaphor and metaphorical representation. It begins with the comparison of two philosophical systems, namely the ones of Immanuel Kant and Friedrich Nietzsche, whose conceptions are in thesis connected through the question of the limits of human understanding and the relation between the process of thinking and language. The thesis deals with those questions from the point of view of the philosophical concept of the metaphor. This concept, its history and implications are the main topics for the last two chapters. The conclusion will offer two opposite positions, symbolism and idealism. We can find those positions retrospectively in the mentioned works of Kant and Nietzsche thanks to the theory of Jacques Derrida in the final part of the thesis, but we also come to the assumption that their opposition will remain undecided.

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