Motivated by the lack of scholarship surrounding female characters in Gabriel Garcia Marquez's One Hundred Years of Solitude, I sought to examine the distinct identities of four female characters. The collapse of dualities and embodiment of hybridity in Ursula, Pilar Ternera, Amaranta, and the Remedios women reveals the hegemonic power structures that are disrupted by these empowered women. The exploration of these women and their relationships to gendered dichotomies points to the potential of their identities in enacting colonial resistance and reclaiming traditional cultural heritage.

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This thesis presents results concerning canonical extensions of bounded lattices and natural dualities for quasivarieties of default bilattices. Part I is dedicated to canonical extensions, while Part II focuses on natural duality for default bilattices. A canonical extension of a lattice-based algebra consists of a completion of the underlying lattice and extensions of the additional operations to the completion. Canonical extensions find rich application in providing an algebraic method for obtaining relational semantics for non-classical logics. Part I gives a new construction of the canonical extension of a bounded lattice. The construction is done via successive applications of functors and thus provides an elegant exposition of the fact that the canonical extension is functorial. Many existing constructions are described via representation and duality theorems. We demonstrate precisely how our new formulation relates to existing constructions as well as proving new results about complete lattices constructed from graphs. Part I ends with an analysis of the untopologised structures used in two methods of construction of canonical extensions of bounded lattices: the untopologised graphs used in our new construction, and the so-called `intermediate structure'. We provide sufficient conditions for the intermediate structure to be a lattice and, for the case of finite lattices, identify when the dual graph is not a minimal representation of the lattice. Part II applies techniques from natural duality theory to obtain dualities for quasivarieties of bilattices used in default logic. Bilattices are doubly-ordered algebraic structures which find application in reasoning about inconsistent and incomplete information. This account is the first attempt to provide dualities or representations when there is little interaction required between the two orders. Our investigations begin by using computer programs to calculate dualities for specific examples, before using purely theoretical techniques to obtain dualities for more general cases. The results obtained are extremely revealing, demonstrating how one of the lattice orders from the original algebra is encoded in the dual structure. We conclude Part II by describing a new class of default bilattices. These provide an alternative way of interpreting contradictory information. We obtain dualities for two newly-described quasivarieties and provide insights into how these dual structures relate to previously described classes of dual structures for bilattices.

The purpose of this thesis is to study a symmetry of string theory known as T-duality. We focus on a particular example establishing the equivalence between a quantized string moving in a circular space of radius R and a dual string moving in a similar space of radius 1/R . We will show that this duality implies that the momentum of the string in one picture becomes the number of times the string is wound around the circle in the dual picture. We present two proofs of T-duality. The first reflects the standard interpretation of T-duality as an isomorphism of quantum theories. The second approach is based on Hull's Double Field Theory.

Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 38-39.

In this paper, we examine responses to the conflicting institutional demands faced by an e-commerce subsidiary located in Sub-Saharan Africa and headquartered in Europe. Following an inductive approach, we gathered data from a 6-month participant-observation study and interviews with local managers. Our findings show that the subsidiary managers responded to conflicting institutional demands in a dynamic way, taking one response after the other. In some cases, the subsidiary managers responded in a way that they thought would be satisfactory but subsequent pressures from their headquarters or their local environment pushed them to adopt a new response. In other cases, the subsidiary managers intentionally adopted responses knowing that they would (have to) adopt another response later in the process.

This thesis studies the Bar-Natan skein module of the solid torus with a particular boundary curve system, and in particular a diagrammatic presentation of it due to Russell. This module has deep connections to topology and categorification: it is isomorphic to both the total homology of the (n,n)-Springer variety and the 0th Hochschild homology of the Khovanov arc ring H^n. We can also view the Bar-Natan--Russell skein module from a representation-theoretic viewpoint as an extension of the Frenkel--Khovanov graphical description of the Lusztig dual canonical basis of the nth tensor power of the fundamental U_q(sl_2)-representation. One of our primary results is to extend a dualization construction of Khovanov using Jones--Wenzl projectors from the Lusztig basis to the Russell basis. We also construct and explore several deformations of the Russell skein module. One deformation is a quantum deformation that arises from embedding the Russell skein module in a space that obeys Kauffman--Lins diagrammatic relations. Our quantum version recovers the original Russell space when q is specialized to -1 and carries a natural braid group action that recovers the symmetric group action of Russell and Tymoczko. We also present an equivariant deformation that arises from replacing the TQFT algebra A used in the construction of the rings H^n by the equivariant homology of the two-sphere with the standard action of U(2) and taking the 0th Hochschild homology of the resulting deformed arc rings. We show that the equivariant deformation has the expected rank. Finally, we consider the Khovanov two-functor F from the category of tangles. We show that it induces a surjection from the space of cobordisms of planar (2m, 2n)-tangles to the space of (H^m, H^n)-bimodule homomorphisms and give an explicit description of the kernel. We use our result to introduce a new quotient of the Russell skein module.

Recent work of Bambozzi, Ben-Bassat, and Kremnitzer suggests that derived analytic geometry over a valued field k can be modelled as geometry relative to the quasi-abelian category of Banach spaces, or rather its completion Ind(Ban_k). In this thesis we develop a robust theory of homotopical algebra in Ch(E) for E any sufficiently 'nice' quasi-abelian, or even exact, category. Firstly we provide sufficient conditions on weakly idempotent complete exact categories E such that various categories of chain complexes in E are equipped with projective model structures. In particular we show that as soon as E has enough projectives, the category Ch₊(E) of bounded below complexes is equipped with a projective model structure. In the case that E also admits all kernels we show that it is also true of Ch≥0(E), and that a generalisation of the Dold-Kan correspondence holds. Supplementing the existence of kernels with a condition on the existence and exactness of certain direct limit functors guarantees that the category of unbounded chain complexes Ch(E) also admits a projective model structure. When E is monoidal we also examine when these model structures are monoidal. We then develop the homotopy theory of algebras in Ch(E). In particular we show, under very general conditions, that categories of operadic algebras in Ch(E) can be equipped with transferred model structures. Specialising to quasi-abelian categories we prove our main theorem, which is a vast generalisation of Koszul duality. We conclude by defining analytic extensions of the Koszul dual of a Lie algebra in Ind(Ban_k).

by Leung Chi Kwan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 133-135). / Preface --- p.ii / Chapter 1 --- Introduction to Module Equivalence --- p.1 / Chapter 1.1 --- Introduction and Preliminaries --- p.1 / Chapter 2 --- Some Classical Results --- p.12 / Chapter 2.1 --- Morita Theorem --- p.12 / Chapter 2.2 --- Puller Theorem --- p.13 / Chapter 2.3 --- The Equivalence Mod-A ~Im(TP) --- p.29 / Chapter 2.4 --- The Equivalence Im(HP)~Im(Tp) --- p.33 / Chapter 3 --- *-modules and Tilting Modules --- p.39 / Chapter 3.1 --- The Equivalence Cogen(KA)~Gen(PR) --- p.39 / Chapter 3.2 --- Torsion Theories and *-modules --- p.56 / Chapter 3.3 --- The Structure of *-modules --- p.60 / Chapter 3.4 --- Characterizations of Tilting Modules --- p.65 / Chapter 4 --- Equivalences and Dualities --- p.85 / Chapter 4.1 --- The Equivalence PA~IR --- p.85 / Chapter 4.2 --- The Equivalence FGP-A ~FCI-R --- p.93 / Chapter 5 --- Torsion Theories Induced by Tilting Modules --- p.100 / Chapter 5.1 --- The Tilting Theorem --- p.100 / Chapter 5.2 --- Tilting Torsion Theories --- p.113 / Chapter 5.3 --- Isomorphisms of Endomorphism Rings of Tilting Modules --- p.122 / References --- p.133

Li, Xing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 76-80). / Abstract also in Chinese. / Introduction --- p.4 / Chapter 1 --- Preliminary --- p.6 / Chapter 1.1 --- Notations --- p.6 / Chapter 1.2 --- On Properties of Epigraphs --- p.10 / Chapter 1.3 --- Subdifferential Calculus --- p.14 / Chapter 1.4 --- Conical Approximations --- p.16 / Chapter 2 --- Duality in the Cone-convex System --- p.20 / Chapter 2.1 --- Introduction --- p.20 / Chapter 2.2 --- Various of Constraint Qualifications --- p.28 / Chapter 2.2.1 --- Slater´ةs Condition Revisited --- p.28 / Chapter 2.2.2 --- The Closed Cone Constrained Qualification --- p.31 / Chapter 2.2.3 --- The Basic Constraint Qualification --- p.38 / Chapter 2.3 --- Lagrange Multiplier and the Geometric Multiplier --- p.45 / Chapter 3 --- Stable Lagrangian Duality --- p.48 / Chapter 3.1 --- Introduction --- p.48 / Chapter 3.2 --- Stable Farkas Lemma --- p.48 / Chapter 3.3 --- Stable Duality --- p.57 / Chapter 4 --- Sequential Lagrange Multiplier Conditions --- p.63 / Chapter 4.1 --- Introduction --- p.63 / Chapter 4.2 --- The Sequential Lagrange Multiplier --- p.64 / Chapter 4.3 --- Application in Semi-Infinite Programs --- p.71 / Bibliography --- p.76 / List of Symbols --- p.80