Extending an explicit result from Bridson–Conder–Reid, this work provides an algorithm for distinguishing finite quotients between cocompact triangle groups Δ ?and lattices Γ of constant curvature symmetric 2-spaces. Much of our attention will be on when these lattices are Fuchsian groups. We prove that it will suffice to take a finite quotient that is Abelian, dihedral, a subgroup of PSL(<i>n</i>,<b>F</b>_<i>q</i>) (for an odd prime power q), or an Abelian extension of one of these 3 groups. For the latter case, we will require and develop an approach for creating group extensions upon a shared finite quotient of Δ? and Γ which between them have differing degrees of smoothness. Furthermore, on the order of a finite quotient that distinguishes between ?Δ and Γ, we are able to establish an effective upperbound that is superexponential depending on the cone orders appearing in each group.<br>

After becoming interested in the beauty of numbers and the intricate patterns of their behavior, the author concluded that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in combinatorics, namely Fundamental Principles, Permutations, Combinations, and Pascal's Triangle, which are appropriate for third grade level.

The central focus of this dissertation study is to understand the impact of the Sarbanes-Oxley Act and the factors that contribute to increased risk of fraud in order to determine why fraud may occur despite the imposed regulation of the Sarbanes-Oxley Act. The main premise of the study tests the application of the fraud triangle framework constructs to publicly traded restaurant companies during the time period of 2002-2014, using proxy variables defined through literature. Essentially, the study seeks to identify the factors that may provide the optimal criteria to engage in fraudulent or opportunistic behavior. The fraud triangle theoretical framework is comprised of the constructs of pressure, opportunity and rationalization, and has mostly been utilized by external auditors to assess the fraud risk of various companies. It has never been applied to the restaurant industry, and the proxy variables selected have never before been tested in a comprehensive model. Thus, a major contribution of this study may enable executive managers to assess the fraud triangle conditions according to the model in order to afford conclusions regarding increased risk of fraud. The study first hypothesized that the Sarbanes-Oxley Act has had a significant impact on detecting increased risk of fraud for publicly traded restaurant companies. Additionally, the study controlled for and tested the proxy variables of the fraud triangle constructs to determine if any of the variables had a significant impact on detecting increased risk of fraud for publicly traded restaurant companies. The variables tested included company size, debt, employee turnover, organizational structure, international sales growth, executive stock compensation, return on assets, the Recession, and macro-economic factors of interest, inflation, and unemployment rates. The research study adopted an exploratory research design using the case of publicly traded United States restaurant companies in order to provide a better understanding of the characteristics that may contribute to increased fraud risk. The study assumed a binary distribution of the dependent variable, increased fraud risk, measured by the incidence of a reported internal control deficiency over the testable time period. Specifically, the study employed a probit model to estimate the probability that an entity or company will be at an increased risk of fraud based on the independent variables that support and are linked to the fraud triangle framework. Additionally, the model assumes equal weight to the variables of the fraud triangle framework. Through use of the probit model, the major findings of the study were as follows: First, the Sarbanes-Oxley Act does have a significant impact on highlighting areas of increased fraud risk for publicly traded restaurant companies. Second, for the total population of restaurant companies, only the Recession, interest rates, inflation rates and unemployment rates are significant indicators of increased fraud risk. None of the internal variables were significant. However, once the data was segmented by type of restaurant, the results revealed significance of both internal and external variables. These results imply a couple of theoretical notions: first, that the Sarbanes-Oxley Act is an effective means for detecting risk of fraud for publicly traded restaurant companies when considering variables that support the fraud triangle; second, that the fraud triangle is contextual when applied to the restaurant industry because only the variables that are outside of managements control were significant. Finally, from a managerial perspective, the study provides evidence that macro-economic conditions that might affect consumer demand may increase the risk of fraud for publicly traded restaurant companies.

The constant development of new plays is vital for theatre to stay relevant. There is a desire, a yearning, a need to see the issues we face in our lives on stage in current contexts, and to watch characters living with them. The ability, as an Actor, to be an asset to the process of creating new works is invaluable. For my thesis, I discuss the role of the Actor in the process of developing new plays for the stage. I say “discuss” because I venture to guess that this role is constantly evolving. There may be as many ways to approach the process as there are collaborative teams. Therefore, I do not suggest there is one right way in which an Actor can play a part in the process of new play development, nor do I intend this to be a comprehensive look at all the roles an Actor can play. However, I discovered some best practices, which I put into a list and seized this opportunity to cultivate my skills in these areas. My intent was to work and speak with Playwrights and Directors, learning from them what they value in an Actor at the various phases of new play development, and to nurture these skills within myself. I utilized my discoveries in the World Premiere of Triangle Logic by Debbie Lamedman. As theatre is a collaborative art, I learned to shift and adapt my role, depending on the other collaborators. While Triangle Logic was the larger focus of my thesis work, I also sought additional smaller projects, such as the workshop productions of Steven Christopher Yockey’s play, Heavier Than…, part of Orlando Shakespeare Theater’s PlayFest 2010, and Orlando Repertory Theatre’s devised play Writes of Spring, I thinK his NamE Was rick. I applied iii techniques I learned while working on Triangle Logic to the other new projects, where appropriate. I endeavored to evaluate each experience objectively, while recognizing that they were, by nature, subjective experiences.

Ray tracing is a graphical technique that provides realistic simulation of light sources and complex lighting effects within three-dimensional scenes, but it is a time-consuming process that requires a tremendous amount of compute power. In order to reduce the number of calculations required to render an image, many different algorithms and techniques have been developed. One such development is the use of tree-like data structures to partition space for quick traversal when finding intersection points between rays and primitives. Even with this technique, ray-primitive intersection for large datasets is still the bottleneck for ray tracing. This thesis proposes the use of a specific spatial data structure, the K-D tree, for faster ray casting of primary rays and enables a ray-triangle culling technique that compliments view frustum and backface culling. The proposed method traverses the entire tree structure to mark nodes to be inactive if it is outside of the view frustum and skipped if the triangle is a backface. In addition, a ray frustum is calculated to test the spatial coherency of the primary ray. The combination of these optimizations reduces the average number of intersection tests per ray from 98% to 99%, depending on the data size.

The extraction of lithium, a crucial mineral for the production of batteries in the rapidlyexpanding electric vehicle and renewable energy sectors, has gained significant attention due toits environmental and social implications. This thesis provides a comprehensive literature reviewon the environmental and social challenges associated with lithium extraction from the LithiumTriangle countries, namely Argentina, Bolivia, and Chile, through the lens of political ecology.Drawing upon a wide range of scholarly articles, reports, and case studies, this research examinesthe complex interplay between ecological dynamics and sociopolitical factors in the context oflithium extraction. The literature review explores key themes including land use conflicts, waterscarcity and pollution, indigenous rights and participation, governance and regulation, and globalmarket dynamics. The literature review reveals that lithium extraction in the Lithium Trianglecountries presents various environmental challenges. These include the large-scale use of waterresources, potential water contamination from mining activities, and the disruption of fragileecosystems. From a political ecology perspective, the review highlights the power dynamics andpolitical-economic structures that shape the governance of lithium extraction. It criticallyanalyzes the role of multinational corporations, government policies, and international marketforces in influencing the environmental and social outcomes of lithium mining operations.Furthermore, the review emphasizes the importance of recognizing and incorporating theperspectives and rights of local communities and indigenous groups in decision-makingprocesses. By adopting a political ecology perspective, it underscores the need for sustainable andsocially just approaches to lithium mining that prioritize environmental conservation, communityengagement, and equitable distribution of benefits. The findings of this literature review caninform future research, policy development, and advocacy efforts aimed at promoting responsibleand inclusive practices in the lithium industry. / Lithium utvinning, en nyckelkomponent i elbils- och förnybar energisektorns framväxt, haruppmärksammats för dess påverkan på miljö och samhälle. Denna avhandling utför enomfattande litteraturgenomgång om miljö- och samhällsutmaningar vid litiumutvinning i LitiumTriangel-länderna: Argentina, Bolivia och Chile. Genom att analysera en bred samlingvetenskapliga artiklar, rapporter och fallstudier utforskar studien det komplexa samspelet mellanekologi och sociopolitisk vid litiumutvinning. Litteraturgenomgången utforskar centrala ämnensom markkonflikter, vattenbrist och föroreningar, ursprungsbefolkningars rättigheter ochdeltagande, styrning och globala marknadskrafter. Resultaten avslöjar miljöutmaningar vidlitiumutvinning i Triangel-länderna, inklusive vattenanvändning, förorening ochekosystemstörningar. Genom ett politiskt ekologiskt perspektiv belyser översikten maktstruktureroch påverkan från multinationella företag, regeringspolitik och internationella marknadskrafter.Översikten understryker även vikten av att inkludera lokalbefolkningens ochursprungsbefolkningars perspektiv och rättigheter i beslutsprocesser. Studien främjar hållbara ochrättvisa tillvägagångssätt för litiumutvinning och visar att resultaten kan påverka framtidaforskning, policyutveckling och påverkansarbete för ansvarsfulla och inkluderande metoder inomlitiumindustrin.

Despite being the prefered approach for still-image compression for nearly a decade, wavelet-based coding for video has been slow to emerge, due primarily to the fact that the shift variance of the discrete wavelet transform hinders motion estimation and compensation crucial to modern video coders. Recently it has been recognized that a redundant, or overcomplete, wavelet transform is shift invariant and thus permits motion prediction in the wavelet domain. In this dissertation, other uses for the redundancy of overcomplete wavelet transforms in video coding are explored. First, it is demonstrated that the redundant-wavelet domain facilitates the placement of an irregular triangular mesh to video images, thereby exploiting transform redundancy to implement geometries for motion estimation and compensation more general than the traditional block structure widely employed. As the second contribution of this dissertation, a new form of multihypothesis prediction, redundant wavelet multihypothesis, is presented. This new approach to motion estimation and compensation produces motion predictions that are diverse in transform phase to increase prediction accuracy. Finally, it is demonstrated that the proposed redundant-wavelet strategies complement existing advanced video-coding techniques and produce significant performance improvements in a battery of experimental results.

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Regulation Crowdfunding, enacted in May 2016, is intended to facilitate capital formation in startups and small businesses funded primarily by small investors (Securities and Exchange Commission (SEC), 2016b). This dissertation investigates (1) the risk of fraud in equity crowdfunding offerings and (2) whether investors respond to fraud signals by selecting (rejecting) offers with low (high) fraud risk. Because equity crowdfunding is quite new, no frauds have yet been identified. Therefore, I employ a predictive analytics tool, Benford’s Law, to assess the fraud risk of the offering. I select observable indicators to represent the Fraud Triangle dimensions—incentives, opportunities and rationalization—and test if they predict fraud risk. I also compare offer funding outcomes to my fraud risk assessments to identify if investors’ selections consider fraud risk appropriately. The relaxed auditor assurance and disclosure requirements attracts both honest and dishonest founders, but I find that the risk of fraud is higher in equity crowdfunding offers than in public offerings as reported by other studies. I find that there are several individual fraud indicators and models that explain fraud risk, but these do not predict whether the offer is funded or not (funding outcomes) or the amount that is raised if funded. This dissertation is the first to apply Benford’s Law to equity crowdfunding offers and map fraud attributes to fraud risk and funding outcomes. My dissertation can inform investors, issuers, regulators, intermediaries and practitioners of the high risk of fraud in equity crowdfunding offerings and of several noteworthy fraud indicators. / Business Administration/Accounting