Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
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 $\left \| \vec{x} \right \|=1$.
Extension Properties Of Asymptotic Property C And Finite Decomposition Complexity, Susan Beckhardt
Extension Properties Of Asymptotic Property C And Finite Decomposition Complexity, Susan Beckhardt
Legacy Theses & Dissertations (2009 - 2024)
We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), straight finite decomposition complexity (sFDC) which are weakenings of Gromov’s finite asymptotic dimension (FAD).
A Potential Framework For Emergent Space-Time And Geometry From Order, Newshaw Bahreyni
A Potential Framework For Emergent Space-Time And Geometry From Order, Newshaw Bahreyni
Legacy Theses & Dissertations (2009 - 2024)
This research is about seeking laws of physics and geometry from order. Anything that is measured is the result of something influencing something else. An act of influencing and the response to such influence form a pair of events. A collection of such events along with their binary ordering relation of influence which forms a