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Full-Text Articles in Physical Sciences and Mathematics
First Order Approximation On The Basilica Julia Set, Xintan Xia, Taryn Flock
First Order Approximation On The Basilica Julia Set, Xintan Xia, Taryn Flock
Mathematics, Statistics, and Computer Science Honors Projects
We consider the basilica Julia set of the quadratic polynomial P (z) = z^2 - 1, with its successive graph approximations defined in terms of the external ray parametrization of the set. Following the model of Kigami and later Strichartz, we exploit these graph approximations to define derivatives of functions defined on the fractal, an endeavor complicated by asymmetric neighborhood behaviors at approximated vertex points across levels, and by the topology of these vertices. We hence differentiate even and odd levels of approximations of the Julia set and construct, accordingly, normal derivatives corresponding to each level category at the vertices, …
A Brascamp-Lieb–Rary Of Examples, Anina Peersen
A Brascamp-Lieb–Rary Of Examples, Anina Peersen
Mathematics, Statistics, and Computer Science Honors Projects
This paper focuses on the Brascamp-Lieb inequality and its applications in analysis, fractal geometry, computer science, and more. It provides a beginner-level introduction to the Brascamp-Lieb inequality alongside re- lated inequalities in analysis and explores specific cases of extremizable, simple, and equivalent Brascamp-Lieb data. Connections to computer sci- ence and geometric measure theory are introduced and explained. Finally, the Brascamp-Lieb constant is calculated for a chosen family of linear maps.