Now showing items 21-40 of 91

• #### An electrodynamic inverse problem in chiral media ﻿

(1998)
We consider the inverse problem of determining the electromagnetic material parameters of a body from information obtainable only at the boundary of the body; such information comes in the form of a boundary map which we ...
• #### Elliptic Inverse Problems ﻿

Inverse problems arise in various areas of science and engineering including medical imaging, computer vision, geophysics, solid mechanics, astronomy, and so forth. A wide range of these problems involve elliptic operators. ...
• #### Essential spanning forests and electric networks in groups ﻿

(1997)
Let $\Gamma$ be a Cayley graph of a finitely generated group G. Subgraphs which contain all vertices of $\Gamma ,$ have no cycles, and no finite connected components are called essential spanning forests. The set \${\cal ...
• #### Estimating Norms of Matrix Functions using Numerical Ranges ﻿

(2013-11-14)
We study Crouzeix's conjecture: for any polynomial p and any square matrix A, the spectral norm of the matrix p(A) is at most double of the supremum norm of the polynomial p on the numerical range of the matrix A.
• #### Finite-Difference Methods for Second-Order Wave Equations with Reduced Dispersion Errors ﻿

Finite Difference (FD) schemes have been used widely in computing approximations for partial differential equations for wave propagation, as they are simple, flexible and robust. However, even for stable and accurate ...
• #### 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 ...
• #### 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 ...
• #### 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 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.
• #### 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 ...
• #### 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 ...
• #### Inverse Boundary-Value Problems on an Infinite Slab ﻿

In this work, we study the stability aspect of two inverse boundary-value problems (IBVPs) on an infinite slab with partial data. The uniqueness aspects of these IBVPs were considered and studied by Li and Uhlmann for the ...
• #### Inverse Problems for Scalar Elliptic Equations and Systems ﻿

In this thesis, we discuss inverse boundary value problems for scalar equations and for systems. First we introduce the famous Calder\'on problem and its recent developments. We focus on deriving the stability estimate of ...