Browsing Mathematics by Title
Now showing items 60-79 of 188
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Finite-Difference Methods for the Wave Equation with Reduced Dispersion Errors
(2013-04-17)A new methodology was proposed in Finkelstein and Kastner (2007,2008) to derive finite-difference (FD) schemes in the joint time-space domain to reduce dispersion error. The key idea is that the true dispersion relation ... -
Flavors of the Fubini-Bruhat Order
Fubini words are generalized permutations, allowing for repeated letters, and theyare in one-to-one correspondence with ordered set partitions. Brendan Pawlowski and Brendon Rhoades extended permutation matrices to pattern ... -
Formal group laws and hypergraph colorings
This thesis demonstrates a connection between formal group laws and chromatic symmetric functions of hypergraphs, two seemingly unrelated topics in the theory of symmetric functions. A formal group law is a symmetric ... -
Four Problems in Probability and Optimization
(2014-02-24)This thesis studies bootstrap percolation, a problem in probability, as well as several topics in the application of sums of squares to combinatorial optimization. In the chapter on percolation, we bound the critical ... -
Gaps of saddle connection directions for some branched covers of tori
We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the ... -
Geodesic X-Ray Transform on Asymptotically Hyperbolic Manifolds
This dissertation contains work of the author and joint work with C. Robin Graham concerning the geodesic X-ray transform in the setting of asymptotically hyperbolic manifolds. It is divided into three self contained ... -
A Geometric Perspective on First-Passage Competition
(2013-04-17)We study the macroscopic geometry of first-passage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ... -
Geometry and algorithms for signal recovery: from convex duality to non-convex formulations
Structured signal recovery is a central task in a variety of scientific applications, and naturally leads to non-linear and non-convex optimization problems that present many interesting mathematical and algorithmic ... -
Geometry and Optimization of Relative Arbitrage
This thesis is devoted to the mathematics of volatility harvesting, the idea that extra portfolio growth may be created by systematic rebalancing. First developed by E. R. Fernholz in the late 90s and the early 2000s, ... -
Graded group schemes
We define graded group schemes and graded group varieties and develop their theory. We give a generalization of the result that connected graded bialgebras are graded Hopf algebra. Our result is given for a broader class ... -
Grothendieck Duality on Diagrams of Schemes
The Du Bois complex and Du Bois singularities, which extend results of Hodge theory to singular complex varieties, can be defined in terms of a cubical hyperresolution. In this dissertation I further develop the language ... -
The Grothendieck Groups of Module Categories over Coherent Algebras
Let <italic>k</italic> be a field and <italic>B</italic> either a finitely generated free <italic>k</italic>-algebra, or a regular <italic>k</italic>-algebra of global dimension two with at least three generators, generated ... -
Heat Kernel Estimates for Markov Processes Associated with Time-Dependent Dirichlet Forms
In this paper, time-inhomogeneous stable-like processes are investigated. We establish the relation between the transition operators and time-dependent parabolic equations, as well as upper heat kernel estimates. -
Higher direct images of ideal sheaves, correspondences in log Hodge cohomology and globally F-full varieties
This document consists of three mathematically independent and more or less thematically independent parts. Chapter 1 concerns invariance of the cohomology groups of divisorial ideal sheaves under (a restricted class of) ... -
Homological algebra of Stanley-Reisner rings and modules
Associated to each simplicial complex $\Delta$ and each field $\field$ is the Stanley--Reisner ring $\field[\Delta]$. The answers to a multitude of questions related to simplicial complexes have historically been found ... -
Hopf algebras of finite Gelfand-Kirillov dimension
(2013-11-14)We study Hopf algebras of finite Gelfand-Kirillov dimension. By analyzing the free pointed Hopf algebra F(t), we show the existence of certain Hopf subalgebras of pointed Hopf domains H whose GK-dimension are finite and ... -
How to weld: Energies, weldings, and driving functions
We prove a variant of the welding zipper algorithm converges for curves $\gamma \subset \nH \cup \{0\}$ that have Loewner driving functions $\xi \in C^{3/2+\epsilon}$. Convergence holds whether one ``zips up'' with straight ... -
Hybrid inverse problems
(2013-11-14)Inverse problems arise in different disciplines including exploration geophysics, medical imaging and nondestructive evaluation. In some settings, a single modality displays either high contrast or high resolution but not ... -
Hybrid Inverse Problems Arising from Acousto-Electric Coupling
(2013-11-14)We study hybrid imaging techniques that aim to overcome the ill-posedness of the Electric Impedance Tomography using the acousto-electric coupling. For the isotropic case, we consider the problem of reconstructing the ... -
Interacting particle systems with partial annihilation through membranes
This thesis studies the <italic>hydrodynamic limit</italic> and the <italic>fluctuation limit</italic> for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive ...