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Full-Text Articles in Physical Sciences and Mathematics
Measuring Linguistic And Cultural Evolution Using Books And Tweets, Tyler Gray
Measuring Linguistic And Cultural Evolution Using Books And Tweets, Tyler Gray
Graduate College Dissertations and Theses
Written language provides a snapshot of linguistic, cultural, and current events information for a given time period. Aggregating these snapshots by studying many texts over time reveals trends in the evolution of language, culture, and society. The ever-increasing amount of electronic text, both from the digitization of books and other paper documents to the increasing frequency with which electronic text is used as a means of communication, has given us an unprecedented opportunity to study these trends. In this dissertation, we use hundreds of thousands of books spanning two centuries scanned by Google, and over 100 billion messages, or ‘tweets’, …
Mathematical Analysis Of Some Partial Differential Equations With Applications, Kewang Chen
Mathematical Analysis Of Some Partial Differential Equations With Applications, Kewang Chen
Graduate College Dissertations and Theses
In the first part of this dissertation, we produce and study a generalized mathematical model of solid combustion. Our generalized model encompasses two special cases from the literature: a case of negligible heat diffusion in the product, for example, when the burnt product is a foam-like substance; and another case in which diffusivities in the reactant and product are assumed equal. In addition to that, our model pinpoints the dynamics in a range of settings, in which the diffusivity ratio between the burned and unburned materials varies between 0 and 1. The dynamics of temperature distribution and interfacial front propagation …