Thesis (Ph. D.)--State University of New York at Binghamton, of Department of Mathematical Sciences, 2007. / Includes bibliographical references.

Thesis (M. S.)--Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Evans Harrell; Committee Member: Guillermo Goldsztein; Committee Member: Mohammad Ghomi

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (p. 85-91).

We develop the mathematical theory of the open/closed correspondence, proposed by Mayr in physics as a class of dualities between open strings on Calabi-Yau 3-folds and closed strings on Calabi-Yau 4-folds. Given an open geometry on a toric Calabi-Yau 3-orbifold relative to a framed Aganagic-Vafa outer brane, we construct a closed geometry on a toric Calabi-Yau 4-orbifold and establish the correspondence between the two geometries on the following levels across both the A- and B-sides of mirror symmetry: numerical Gromov-Witten invariants; generating functions of Gromov-Witten invariants; B-model hypergeometric functions and Givental-style mirror theorems; Picard-Fuchs systems and solutions; integral cycles on Hori-Vafa mirrors and periods; mixed Hodge structures.

A boundedness structure (bornology) on a topological space is an ideal of subsets containing all singletons, that is, closed under taking subsets and unions of finitely many elements. In this paper we deal with the structure of the whole family of bounded subsets rather than the specific properties of them by means of certain functions that we define on a metrizable topological group. Our motivation is twofold: on the one hand, we obtain useful information about the structural features of certain remarkable classes of bounded systems, cofinality, local properties, etc. For example, we estimate the cofinality of these boundedness notions. In the second part of the paper, we apply duality methods in order to obtain estimations of the size of a local base for an important class of groups. This translation, which has been widely exhibited in the Pontryagin-van Kampen duality theory of locally compact abelian groups, is often very relevant and has been extended by many authors to more general classes of topological groups. In this work we follow basically the pattern and terminology given by Vilenkin in 1998.

Adaptive resource allocation in wireless communication systems is crucial in order to support the diverse QoS needs of the services and optimize resource utilization. The design of resource allocation schemes should consider the service type for which it is intended. Moreover, due to feedback delay and channel estimation error, the Channel Quality Indicator (CQI) reported to the transmitter may not be a perfect measure of the channel quality and its use for resource allocation may severely degrade the systems performance. In this thesis, we study resource allocation and CQI reporting for wireless networks while taking the aforementioned factors into consideration. First, we consider resource allocation and adaptive modulation in uplink SC-FDMA systems. This is a combinatorial problem whose optimal solution is exponentially complex. We use canonical duality theory to derive a polynomial complexity resource allocation algorithm that provides a nearly optimal solution to the problem. Then, we focus on resource allocation for video streaming in wireless networks with time-varying interference. To this end, by using risk-sensitive control approach, we develop a cross-layer optimization framework that performs power control at the PHY/MAC layer and rate adaptation at the APPLICATION layer jointly and provides fairness among nodes. Finally, by using stochastic control and game theory, we design a robust best-M CQI reporting scheme for multi-carrier and multi-user systems which takes into account the impact of feedback delay and error in CQI computation. Performing resource allocation on the basis of the proposed CQI reporting can significantly improve the system performance.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2007. / Includes bibliographical references.

Orientador: Roberto Andreani / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-22T06:15:13Z (GMT). No. of bitstreams: 1 BaygorreaCusihuallpa_Nancy_M.pdf: 1656614 bytes, checksum: 036b8eeb6a7f3e461c7ca051fed6fd3d (MD5) Previous issue date: 2013 / Resumo: Esta dissertação desenvolve um estudo detalhado da convergência local do método de ponto proximal para resolver o problema de encontrar zeros de operadores maximais sem a condição de monotonicidade. Em particular, é estudada a convergência dos métodos de multiplicadores proximais para resolver problemas de otimização não linear sem a condição de convexidade. Para obter os resultados desejados apresentaremos ferramentas de análise variacional para substituir a condição de monotonicidade maximal do operador como também, a teoria de dualidade generalizada para a aplicação do método de multiplicadores proximais. Apresentamos também uma aplicação do algoritmo do ponto proximal aos métodos dos multiplicadores para uma classe de problemas gerais baseados num esquema de dualidade generalizada / Abstract: In this dissertation we will develop a detailed study of local convergence of proximal point method for finding a root of maximal operators without monotonicity. In particular, it is studied the convergence for proximal method of multipliers by solving nonlinear optimization problems without convexity conditions. In order to obtain the desired results we will study some variational analysis tools to replace maximal monotonicity condition of operators as well as general duality theory which is t reacted to study an application to proximal method of multipliers. Also, we show an application of the proximal point algorithm to the multipliers methods for a class of problems which is based in general duality scheme / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

Moll (1991) has criticised the proposal that demand restructuring should act as the impetus for economic growth in a post-apartheid South Africa on the grounds of, a lack of empirical support. The demand restructuring thesis is premised on two empirically testable assertions: firstly that realisable economies of scale are greater in labour-intensive wage goods sectors than in luxury goods and secondly that in manufacturing as a whole labour can easily substitute for capital. While a number of studies employing either the Cobb-Douglas (Cobb & Douglas, 1948) or Constant Elasticity of Substitution (CES) ( Arrow, Chenery, Minhas & Solow, 1961) functions have attempted to quantify these features of technology, their conclusions are potentially invalid. Both functions impose the maintained hypotheses of homotheticity, homogeneity and seperability a priori. As primary hypothesis tests regarding the magnitude of parameters depend on the validity of both the hypothesis being tested and the underlying maintained hypotheses, the plausibility of maintained hypotheses is an important consideration when choosing a functional form for econometric analysis. Homotheticity and homogeneity constrain the theoretical determinants of economies of scale and seperability. The theoretical determinants of substitution thus limit the contexts in which functions which embody these hypotheses are likely to be appropriate. The mathematical concept of duality has permitted the development of flexible, general functions, such as the Transcendental Logarithmic Cost Function (Christensen, Jorgensen and Lau, 1971, 1973), which rather than imposing, permits the testing of the most commonly imposed maintained hypotheses. By applying this function to three sub-sectors of South African manufacturing both the validity of the commonly imposed maintained hypotheses and the empirical premises of the demand restructuring position are assessed in this dissertation. This application indicates that not only are the hypotheses of homotheticity, homogeneity and seperability invalid but that the inappropriate imposition of homotheticity, homogeneity and seperability invalid but that the inappropriate imposition of homotheticity biases estimates of scale downwards. Evidence also emerges to challenge Moll's (1991) assertions regarding the empirical validity of demand restructuring. / Thesis (M.Com.)-University of Natal, Durban, 1995.

This thesis examines the elegant theory of polar and Legendre duality, and its potential use in convex geometry and geometric analysis. It derives a theorem of polar - Legendre duality for all convex bodies, which is captured in a commutative diagram. A geometric flow on a convex body induces a distortion on its polar dual. In general these distortions are not flows defined by local curvature, but in two dimensions they do have similarities to the inverse flows on the original convex bodies. These ideas can be extended to higher dimensions. Polar - Legendre duality can also be used to examine Mahler's Conjecture in convex geometry. The theory presents new insight on the resolved two-dimensional problem, and presents some ideas on new approaches to the still open three dimensional problem.