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Investigating the Lavrentiev Phenomenon
No full textThe calculus of variations is a field of mathematical analysis that provides methods for finding optimizing functions of functionals. This research investigated the Lavrentiev Phenomenon, an important problem in the calculus of variations, which occurs when there is a gap in the infimum of the functional as the space of admissible functions is restricted. Specifically, we examine functionals for which the infimum is strictly greater in the space of Lipschitz functions than in the space of continuous and integrable functions. This poster introduces the classical example of a Lavrentiev Gap and proposes a generalization of this example. The research also includes a translation from French to English of M. Lavrentiev’s seminal 1926 paper, “Sur Quelques Problèmes du Calcul des Variations.
1. “What Border? Where?” Mapping Border Patrol Actions in Northern Ohio
No full textSocial scientists know little about the methods of collaboration between the United States Border Patrol (USBP) and local and state law enforcement agencies (e.g. Armenta 2017, Boyce 2023). The unregulated and unrecorded nature of these collaborations raises questions about the efficacy and constitutionality of these multifaceted enforcement efforts. This project seeks to contribute to ongoing conversations aimed at shining light on these interagency relationships along the northern border
What Makes an Emotionally Compelling Novel? A Sentiment Analysis of Science Fiction Novels 1984 and We
Get PDFThe purpose of this project is to compare the Soviet novel We by Yevgeny Zamyatin (1924) to the English novel 1984 by George Orwell (1949). Many have previously drawn comparisons between the two works, but the focus of this research is to find dissimilarities in their respective emotional arcs using sentiment analysis, a computational tool used for processing large bodies of text. The findings of this research were twofold. Firstly, the novel We suffers from an undeveloped emotional arc due to a weak narrative voice and a lack of emotionally varied events. This is especially notable when compared to 1984, which despite having a similar plot, has a strongly developed emotional arc that fluctuates in proportion to the events of the novel. Secondly, this research suggests that emotional arcs are an essential quality of a successful work, equal perhaps, to the importance of a robust plot. This research is relevant to the fields of literary criticism and publishing as sentiment analysis becomes increasingly used as a tool for understanding quality stories and predicting successful sales
