Thesis (Ph. D.)--University of Oregon, 2002. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 118-120). Also available for download via the World Wide Web; free to University of Oregon users.

Let x be a real reflexive separable locally uniformly convex banach space with locally uniformly convex dual spacex *. Let t:x\supset d(t)\rightarrow 2 {x *} be maximal monotone with 0\in t(0), 0\in intd(t) and c:x\supset d(c)\rightarrow x *. Assume that $l\subset d(c)$ is a dense linear subspace of x, c is of class (s_+)_l and \langle cx,x\rangle\geq-\psi(\lx\l), x\in d(c), where \psi:\mathbb{r} +\rightarrow\mathbb{r} + is nondecreasing. a new topological degree is developed for the sum t+c in chapter one. This theory extends the recent degree theory for the operators c of type (s_+)_{0,l} in [15]. unlike such a recent extension to multivalued (s_+)_{0,l}-type operators, the current approach utilizes the approximate degree d(t_t+c,g,0), t\downarrow 0, where t_t = (T {-1}+tJ {-1}) {-1}and G is an open bounded subset of X and is such that $0\in G$, for the single-valued mapping $T_t+C$. The subdifferential\partial\varphi, for \varphi belonging to a large class of proper c onvex lower semicontinuous functions, gives rise to operators T to which this degree theory applies. Theoretical applications to problems of Nonlinear Analysis are included, as well as applications from the field of partial differential equations. Let T:X\supset D(T)\rightarrow 2 {X *} be maximal monotone with compact resolvents, i.e, the operator $(T+\epsilonJ) {-1}:X *\rightarrow X is compact for every \in 0. We present a relevant result in chapter 2 that says there exists an open ball around zero in the image of a relatively open set by a continuous and bounded perturbation of a maximal monotone operator with compact resolvents. The generalized degree function for compact perturbations of m-accretive operators established by Y. -Z Chen in [7] isextended to the case of a multivalued compact perturbations of maximal monotone maps by appealing to the topological degree forset-valued compact fields in locally convex spaces introduced by Tsoy Wo-Ma in [25]. Such is the content of the thi rd chapter. A unified eigen value theory is developed for the pair(T,S), where T:X\supset D(T)\rightarrow 2 {X *} is aquasimonotone-type operator which belong to the so-called A_G(QM) class introduced by Arto Kittila in [23] and S is abounded demicontinuous mapping of class (S)_+. Conditions are given for the existence of a pair (x,\lambda)\in (0,\infty)\times(D(T+S)\cap\partial G)$ such that Tx+\lambda Sx\ni 0$. This is the content of Chapter 4.

Thesis (Ph. D.)--Duke University, 2007. / Includes bibliographical references.

Thesis (M.Sc.) -- Memorial University of Newfoundland. 1973. / Typescript. Bibliography : leaves 45. Also available online.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1991. / Includes bibliographical references (p. 96-98).

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (p. 101-104 ).

Thesis (doctoral)--Bonn, 1997. / On t.p. x̲ and y̲ are superscript. Includes bibliographical references (p. 117-119).

Thesis (Ph. D.)--University of Oregon, 2006. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves - ). Also available for download via the World Wide Web; free to University of Oregon users.

Le but principal de cette thèse est de définir une extension de la traduction de double-négation de Gödel à tous les types tronqués, dans le contexte de la théorie des types homotopique. Ce but utilisera des théories déjà existantes, comme la théorie des faisceaux de Lawvere-Tierney, quenous adapterons à la théorie des types homotopiques. En particulier, on définira le fonction de faisceautisation de Lawvere-Tierney, qui est le principal théorème présenté dans cette thèse.Pour le définir, nous aurons besoin de concepts soit déjà définis en théorie des types, soit non existants pour l’instant. En particulier, on définira une théorie des colimits sur des graphes, ainsi que leur version tronquée, et une notion de modalités tronquées basée sur la définition existante de modalité.Presque tous les résultats présentés dans cette thèse sont formalisée avec l’assistant de preuve Coq, muni de la librairie [HoTT/Coq] / The main goal of this thesis is to define an extension of Gödel not-not translation to all truncated types, in the setting of homotopy type theory. This goal will use some existing theories, like Lawvere-Tierney sheaves theory in toposes, we will adapt in the setting of homotopy type theory. In particular, we will define a Lawvere-Tierney sheafification functor, which is the main theorem presented in this thesis.To define it, we will need some concepts, either already defined in type theory, either not existing yet. In particular, we will define a theory of colimits over graphs as well as their truncated version, and the notion of truncated modalities, based on the existing definition of modalities.Almost all the result presented in this thesis are formalized with the proof assistant Coq together with the library [HoTT/Coq]

vii, 54 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We investigate the existence of a stable homotopy category (SHC) associated to the category of p -complete abelian groups [Special characters omitted]. First we examine [Special characters omitted] and prove [Special characters omitted] satisfies all but one of the axioms of an abelian category. The connections between an SHC and homology functors are then exploited to draw conclusions about possible SHC structures for [Special characters omitted]. In particular, let [Special characters omitted] denote the category whose objects are chain complexes of [Special characters omitted] and morphisms are chain homotopy classes of maps. We show that any homology functor from any subcategory of [Special characters omitted] containing the p-adic integers and satisfying the axioms of an SHC will not agree with standard homology on free, finitely generated (as modules over the p -adic integers) chain complexes. Explicit examples of common functors are included to highlight troubles that arrise when working with [Special characters omitted]. We make some first attempts at classifying small objects in [Special characters omitted]. / Committee in charge: Hal Sadofsky, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Daniel Dugger, Member, Mathematics; Sergey Yuzvinsky, Member, Mathematics; Elizabeth Reis, Outside Member, Womens and Gender Studies