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Full-Text Articles in Physical Sciences and Mathematics
Fuchsian Groups, Bob Anaya
Fuchsian Groups, Bob Anaya
Electronic Theses, Projects, and Dissertations
Fuchsian groups are discrete subgroups of isometries of the hyperbolic plane. This thesis will primarily work with the upper half-plane model, though we will provide an example in the disk model. We will define Fuchsian groups and examine their properties geometrically and algebraically. We will also discuss the relationships between fundamental regions, Dirichlet regions and Ford regions. The goal is to see how a Ford region can be constructed with isometric circles.
Unifications Of Pythagorean Triple Schema, Emily Hammes
Unifications Of Pythagorean Triple Schema, Emily Hammes
Undergraduate Honors Theses
Euclid’s Method of finding Pythagorean triples is a commonly accepted and applied technique. This study focuses on a myriad of other methods behind finding such Pythagorean triples. Specifically, we discover whether or not other ways of finding triples are special cases of Euclid’s Method.
Coarse Geometric Coherence, Jonathan Lee Grossman
Coarse Geometric Coherence, Jonathan Lee Grossman
Legacy Theses & Dissertations (2009 - 2024)
This dissertation establishes three coarse geometric analogues of algebraic coherence: geometric coherence, coarse coherence, and relative coarse coherence. Each of these coarse geometric coherence notions is a coarse geometric invariant. Several permanence properties of these coarse invariants are demonstrated, elementary examples are computed, and the relationships that these properties have with one another and with other previously established coarse geometric invariants are investigated. Significant results include that the straight finite decomposition complexity of A. Dranishnikov and M. Zarichnyi implies coarse coherence, and that M. Gromov’s finite asymptotic dimension implies coherence, coarse coherence, and relative coarse coherence. Further, as a consequence …
Applications Of Jeu De Taquin To Representation Theory And Schubert Calculus, Daniel Stephen Hono
Applications Of Jeu De Taquin To Representation Theory And Schubert Calculus, Daniel Stephen Hono
Legacy Theses & Dissertations (2009 - 2024)
We describe some applications of the \emph{jeu de taquin} algorithm on standard Young tableaux of skew shape $\lambda/\mu$ for $\lambda$ and $\mu$ partitions. We first briefly survey the relevant background on symmetric functions with a focus on the \emph{Schur functions}. We then introduce the Littlewood-Richardson coefficients in terms of Schur functions and survey some of the applications of the corresponding Littlewood-Richardson rule to representation theory and Schubert calculus on the Grassmannian. A reformulation of the Littlewood-Richardson rule in terms of the jeu de taquin algorithm and \emph{growth diagrams} is then surveyed. We illustrate this formulation with some examples. Finally, we …
Non-Euclidean Metric On The Resolvent Set, Mai Thi Thuy Tran
Non-Euclidean Metric On The Resolvent Set, Mai Thi Thuy Tran
Legacy Theses & Dissertations (2009 - 2024)
For a bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$, the Douglas-Yang metric on the resolvent set $\rho(A)$ is defined by the metric function $g_{\vec{x}}(z)=\left \| \big(A -z I\big)^{-1} \vec{x} \right \|^2$, where $\vec{x} \in \mathcal{H}$ with $\left \| \vec{x} \right \|=1$.