PHD, Kent State University, 2023, College of Arts and Sciences / Department of Mathematical Sciences

In 1903, Hermann Minkowski started the modern theory of convex geometry, the study of convex bodies in n-dimensional Euclidean space. The foundation for convex geometry is the so-called Brunn-Minkowski Theory. There are a few core facts in this theory: the Brunn-Minkowski inequality, which asserts that volume is (1/n)-concave over compact sets; that the volume of Minkowski sums of convex bodies is a homogeneous polynomial of degree n, whose coefficients are the mixed volumes; that there exist a class of operators on convex bodies, the so-called Minkowski valuations, which create "more symmetric versions" of a given convex body; and that the surface area measure of a convex body is a Borel measure on the sphere, and, in fact, Minkowski's existence theorem states every Borel measure on the sphere (up to some minor constraints) is the surface area measure of a convex body. In this dissertation, we will discuss extensions of these concepts beyond from volume (the Lebesgue measure) to measures with density. The standard Gaussian measure will serve as our prototypical example. We work on extensions of mixed volumes, the so-called mixed measures, and prove a series of inequalities for them. We also establish a weighted version of Minkowski's existence theorem, and studied weighted analogues of Minkowski valuations. Applications to information theory are also shown. Along the way, we establish a weighted extension of a reverse Hölder-type inequality, known as Berwald's inequality.

Committee: Artem Zvavitch (Advisor); Matthieu Fradelizi (Advisor); Dmitry Ryabogin (Committee Member); Volodymyr Andriyevskyy (Committee Member); Fedor Dragan (Committee Member); Maxim Dzero (Committee Member) Subjects: Mathematics

Honors Theses, Ohio Dominican University, 2018, Honors Theses

A consideration of faith and courage in the works of Ellie Wiesel, Soren Kierkegaard and Josef Pieper are used to define faith and courage. These definitions are employed to place Wiesel in the tradition of western humanism. Wiesel's humanism, however, is unlike the atheist or the Christian. His work, especially the Night Trilogy (Night, Dawn, The Accident), illustrates a unique faith in humanity and the human person based on the passionate search for God and the courage to believe.

Committee: R. W. Carstens Ph.D. (Advisor); Joan Franks O.P., Ph.D. (Other); John Marazita Ph.D. (Other) Subjects: Ethics; Philosophy; Political Science

MFA, Kent State University, 2018, College of the Arts / School of Art

In my thesis, I am investigating an understanding of self by using the unique language of textiles to translate digital photography. We construct identity via the mind-body connection, which is the mind's processing of the body's physical experience. As human experience is based on linear time, our notions of self depend on a constant cycle of perception, storage, and recollection. However, as memory is an unreliable source, our definitions of inner identity become highly variable. The disconnect between past and present is at the heart of the disconnect between mind and body. The imagery used of the body in the box references interior and exterior forces of influence that contribute to the fluctuation of memory and therefore self- understanding. The box is also symbolic of storage, of something meant be kept, as the picture is used to hold on to an experience or memory. Compartmentalization means an attempt at order. Thus, the imagery of containment connects to the binary nature of both weaving and digital information: the relationship of pixel and thread. Each exists due to their respective systems of order. The digitally designed weave structure both defines through its binary system and obscures through its visual effect. As the proximity to origin affects the clarity or accuracy of memory, so the physical proximity to the weavings determines the clarity of the image. This leads to a question of looking at the imagery and experiencing the sensation of tactility present in textile—looking and touching. Here lies a presentation of embodied cognition—the crux of the mind-body connection. The image/mind is held within the cloth/body.

Committee: Janice Lessman-Moss MFA (Advisor); Davin Ebanks MFA (Committee Member); Andrew Kuebeck MFA (Committee Member) Subjects: Design; Fine Arts; Language; Metaphysics; Optics; Philosophy; Systems Design; Technology; Textile Research

Master of Arts, The Ohio State University, 2018, Arts Policy and Administration

This thesis is a self-reflective autoethnographic exploration of the philosophy of Martin Heidegger, Herbert Marcuse, Theodor Adorno & Max Horkheimer, Marshall McLuhan, Neil Postman, Andrew Feenberg, Franco Berardi, et al. The inspiration for this study came from my experience managing a crowdfunding campaign for a community-based program and is a personal exercise in reconciling the use of technology with the desire for human interaction and connection. The investigation is centered on the phenomenology of Martin Heidegger, the critical theory of culture of Herbert Marcuse, and the work of both these philosophers – and their intellectual peers – to explain the interconnected relationships of people, technology, and art. This document serves as an artifact of personal examination and development through the reading, analysis, and application of philosophy in personal and professional contexts.

Committee: James H. Sanders III (Advisor); Jennifer T. F. (Eisenhauer) Richardson (Committee Member) Subjects: Aesthetics; Arts Management; Behavioral Sciences; Communication; Fine Arts; Language; Mass Communications; Mass Media; Museum Studies; Personal Relationships; Philosophy; Sociology; Technology; Web Studies

Doctor of Philosophy (PhD), Ohio University, 2017, Mathematics (Arts and Sciences)

A paper by Shelah that established the consistency of i < u gave an independent family with a host of properties. This dissertation investigates how these properties give rise to different varieties of independent families. We explore the connection between independent families and ultrafilters. We us Martins Axiom as a guide for looking at the generic existence of independent families. We show that selective independent families are preserved in both Iterated Sacks Forcing and Side-by-side Sacks Forcing.

Committee: Todd Eisworth (Advisor); Vladimir Uspenskiy (Committee Member); Sergio Lopez (Committee Member); Philip Ehrlich (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 1976, Graduate School

Committee: Not Provided (Other) Subjects: Mathematics

Master of Fine Arts in Creative Writing, Cleveland State University, 2016, College of Liberal Arts and Social Sciences

This thesis consists of ten short stories that are structured, formatted and thematically aligned with the yamas and niyamas, the ten moral tenants of yoga philosophy. The yamas and niyamas are the first two limbs of Patinjali's eightfold path, or the path to enlightenment through yogic practices. The yamas account for five principles that guide ethical living and instruct followers on how to interact with others and the world. The yamas consist of: ahimsa (non-violence), satya (truthfulness), asteya (non-stealing), brahmacharya (non-excess), and aparigraha (non-possessiveness). The niyamas are guidelines for personal practices that relate to, develop, and enhance one's relationship with self. The niyamas are: saucha (purity), santosha (contentment), tapas (self-discipline), svadhyaya (self-study), and ishvara prandihana (surrender). Each story in this collection loosely correlates with and comments on its assigned yama or niyama. As a collection, the stories function as glimpses of being—fractal pieces of life from inside differing existential or personal crises. The characters face moral, personal and spiritual dilemmas, often grappling with ghosts from the past, striving to make sense of what is through varying tools and coping mechanisms. The highest goal for this thesis is to act as commentary on the modern condition by using the spiritual and existential lens to diagnose and categorize modern afflictions. Some characters reach towards being—towards harmony or enlightenment—as dressing for their wounds. Others merely grapple with their conditions of dis-ease. Still others contribute to, and worsen, the disharmony. Guided by ten moral principles, these stories stand alone and work together to lead readers into the depths of varying states of being, while shedding light on modernity's inherent conflict with ancient spiritual practices.

Committee: Imad Rahman MFA (Committee Chair); Caryl Pagel MFA (Committee Member); Christopher Barzak MFA (Committee Member); David Lardner PhD (Committee Member) Subjects: Fine Arts; Language Arts; Literature; Modern Literature; Religion; Spirituality; Theology

Master of Arts (MA), Ohio University, 2014, Philosophy (Arts and Sciences)

Immanuel Kant speaks of human sensation in the Transcendental Aesthetic as occurring only on the condition that an object be "given to us" by way of affecting the mind. Some commentators think there is problem with Kant's account of affection in that they read Kant to be illegitimately applying some of the categories of the understanding, e.g., causality and existence, beyond the realm of possible experience. This is problematic in that Kant repeatedly states that the categories (including causality and existence) have application only to objects of experience and thus have no application to things in themselves or noumena. This reading holds Kant's philosophy to be internally inconsistent. In this essay, I try to save Kant from inconsistency and offer a solution to the problem of affection that is supported by a specific interpretation of transcendental philosophy. Specifically, I argue that the solution to the problem of affection is given by considering the relation obtaining between affecting object and the senses to be logical. This logical relation is found in the hypothetical form of antecedent and consequent where the antecedent grounds the consequent. I will also argue that we must think of this grounding relation in analogy to a causal one, that is, we think of the affecting object as if it were the cause of the matter of sensibility. In the process of expounding this solution, I will also be arguing for a "one world" interpretation of transcendental idealism.

Committee: James Petrik (Advisor); John Bender (Committee Member); Alfred Lent (Committee Member) Subjects: Philosophy

PhD, University of Cincinnati, 2005, Arts and Sciences : Mathematical Sciences

In this dissertation we studied nonlinear partial differential equations in two different directions. We apply the bifurcation theory to investigate a number of positive solutions of the semilinear Dirichlet boundary value problem on a n-dimensional ball for the second order elliptic equation with periodic nonlinearity containing a positive parameter. Our approach appeals to the well known results of B. Gidas, W.-M. Ni, L. Nirenberg, the bifurcation theorems of M. G. Crandall and P. H. Rabinowitz, and the stationary phase method. Further, we investigate the issue of global existence of the solutions of the Cauchy problem for the semilinear Tricomi-type equations, appearing in the boundary value problems problems of gas dynamics. We study Cauchy problem trough integral equation and give some sufficient conditions for the existence of the global weak solutions. We prove necessity of these conditions. We obtain necessary condition for the existence of the self-similar solutions for the semilinear Tricomi-type equation. In our approach we employ the fundamental solution and the Lp-Lq estimates for the linear Tricomi-type equations.

Committee: Dr. Philip Korman (Advisor) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2009, English

The purpose of my dissertation is to illuminate the depth of Herman Melville's philosophical and aesthetical inquiries into the fundamental questions about human existence and possibilities in his novel Moby-Dick. I investigate the ways in which the novel interrogates the basic tenets of Platonism and Christianity and explores a positive alternative to the limitations of the existing system of knowledge by reading the novel in relation to Arthur Schopenhauer's and Friedrich Nietzsche's revision of the traditional understanding of human will, epistemology, and religion of the West. In his views of human life and the world, Melville's remarkable affinities with Schopenhauer have drawn much critical attention, but not many critics have paid attention to the import of the similarities between Melville and Nietzsche. My analysis of Melville's intellectual relationship with these two German philosophers contributes to current scholarship not only by bringing to light Melville's position in the larger intellectual tradition beyond his immediate cultural milieu, but also by exploring how Moby-Dick provides an answer to whether literature has a positive power especially when literature seems to undermine its own credibility and authority by questioning the validity of narrative and truth. I contend that Schopenhauer's differentiation between the veil of appearance and an inner reality of every natural phenomenon can elucidate Ahab's investigation of the incongruities between seems and is, while the concept of will as “merely a blind, irresistible impulse” can throw light on Ahab's “will determinate” and “madness maddened” in his pursuit of Moby Dick. Regarding Ahab's rejection of conventional religious doctrines in his attempt to give meaning to his life, I argue that Ahab's self-overcoming does not extend to examining the implications of his mad pursuit of Moby Dick, ultimately differentiating him from the Nietzschean Overman despite their similarities. My analysis of Ishma (open full item for complete abstract)

Committee: Steven Fink PhD (Advisor); Elizabeth Hewitt PhD (Committee Member); Susan Williams PhD (Committee Member) Subjects: English literature