Browsing University of Waterloo by Title
Now showing items 7605-7624 of 18922
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A Generalization of Roth's Theorem in Function Fields
(University of Michigan, Department of Mathematics, 2012-11)For n ∈ N = {1, 2, ...}, let D3([1, n]) denote the maximal cardinality of an integer subset of [1, n] containing no nontrivial 3-term arithmetic progression. In a fundamental paper [9], Roth proved that D3([1, n]) n/log ... -
A generalization of Roth's theorem in function fields
(World Scientific Publishing, 2009-11)Let 𝔽q[t] denote the polynomial ring over the finite field 𝔽q, and let formula denote the subset of 𝔽q[t] containing all polynomials of degree strictly less than N. For non-zero elements r1, …, rs of 𝔽q satisfying r1 ... -
A Generalization of the Discounted Penalty Function in Ruin Theory
(University of Waterloo, 2008-08-21)As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each ... -
A Generalization of the Erdös-Kac Theorem and its Applications
(Cambridge University Press, 2004-12-01)We axiomatize the main properties of the classical Erdös-Kac Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties ... -
A Generalization of the Turán Theorem and Its Applications
(Cambridge University Press, 2004-12-01)We axiomatize the main properties of the classical Turan Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties ... -
Generalization on Text-based Games using Structured Belief Representations
(University of Waterloo, 2020-12-23)Text-based games are complex, interactive simulations where a player is asked to process the text describing the underlying state of the world to issue textual commands for advancing in a game. Playing these games can be ... -
A Generalization to Signed Graphs of a Theorem of Sergey Norin and Robin Thomas
(University of Waterloo, 2019-12-19)In this thesis we characterize the minimal non-planar extensions of a signed graph. We consider the following question: Given a subdivision of a planar signed graph (G, Σ), what are the minimal structures that can be added ... -
Generalizations and Applications of the Stochastic Block Model to Basketball Games and Variable Selection Problems
(University of Waterloo, 2017-01-24)Over the past decade, there has been an explosion of network data in a vast number of circumstances, such as the World Wide Web, social networks, gene interactions, economic networks, etc. Scientific analysis of networks ... -
Generalizations of All-or-Nothing Transforms and their Application in Secure Distributed Storage
(University of Waterloo, 2021-01-26)An all-or-nothing transform is an invertible function that maps s inputs to s outputs such that, in the calculation of the inverse, the absence of only one output makes it impossible for an adversary to obtain any information ... -
Generalizations of the Gap Principle and the Thue-Siegel Principle, with Applications to Diophantine Equations
(University of Waterloo, 2019-07-16)In this thesis we develop generalizations of two well-known principles from the theory of Diophantine approximation, namely the gap principle and the Thue-Siegel principle. Our results find their applications in the theory ... -
Generalizations to Corrections of Measurement Error Effects for Dynamic Treatment Regimes
(University of Waterloo, 2022-08-19)Measurement error is a pervasive issue in questions of estimation and inference. Generally, any data which are measured with error will render the results of an analysis which ignores this error unreliable. This is a ... -
A Generalized 2-D Multiport Model for Planar Circuits with Slots in Ground Plane
(University of Waterloo, 2005)With increasing complexity of microwave integrated circuits and tendency towards building integrated modules, real estate in printed circuit boards becomes more at premium. On the other hand, building MIC's on a ... -
A Generalized Adversary Method for Quantum Query Complexity
(University of Waterloo, 2022-05-20)Quantum query complexity measures the minimum number of queries a quantum algorithm needs to make to some input string to compute a function of that input. Query complexity models are widely used throughout quantum computing, ... -
A Generalized Blending Scheme for Arbitrary Order of Continuity
(University of Waterloo, 2023-03-20)In this thesis, new templates and formulas of blending functions, schemes, and algorithms are derived for solving the scattered data interpolation problem. The resulting data fitting scheme interpolates the positions and ... -
Generalized coherent states and classical limits in quantum mechanics
(University of Waterloo, 2000) -
Generalized Complex Structures on Kodaira Surfaces
(University of Waterloo, 2014-08-05)In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized ... -
Generalized GCDs as Applications of Vojta’s Conjecture
(University of Waterloo, 2023-08-31)Starting with an analysis of the result that for any coprime integers a and b, and some ϵ > 0, we have eventually that gcd(a^n − 1,b^n − 1) < a^ϵn holds for all n, we are motivated to look for geometric reasons why this ... -
Generalized holographic dualities for metric gravity & Quantum geometry based on area variables
(University of Waterloo, 2020-09-18)Holography holds promise for simplifying computations in quantum gravity. In part I of this thesis, we construct holographic boundary theories for linearized gravity, for a general family of finite or quasi-local boundaries, ... -
The Generalized Method of Moments for Mixture and Mixed Models
(University of Waterloo, 2015-09-28)Mixture models can be found in a wide variety of statistical applications. However, undertaking statistical inference in mixture models, especially non-parametric mixture models, can be challenging. A general, or nonparametric, ... -
A Generalized Optimal Planning Platform for Microgrids of Remote Communities Considering Frequency and Voltage Regulation Constraints
(University of Waterloo, 2017-10-24)Access to electricity is a key factor behind development and expansion of modern societies, and electric power systems are the backbone infrastructure for economic growth of nations and communities. However, more than a ...