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Browsing Mathematics by Title
Now showing items 37-56 of 188
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Connections Between Lanczos Iteration and Orthogonal Polynomials
(2010-01-10)In this thesis we examine the connections between orthogonal polynomials and the Lanczos algorithm for tridiagonalizing a Hermitian matrix. The Lanczos algorithm provides an easy way to calculate and to estimate the ... -
Convergence and approximation for primal-dual methods in large-scale optimization
(1990)Large-scale problems in convex optimization often can be reformulated in primal-dual (minimax) representations having special decomposition properties. Approximation of the resulting high-dimensional problems by restriction ... -
Convex Optimization over Probability Measures
The thesis studies convex optimization over the Banach space of regular Borel measures on a compact set. The focus is on problems where the variables are constrained to be probability measures. Applications include ... -
Convexity, convergence and feedback in optimal control
(2000)The results of this thesis are oriented towards the study of convex problems of optimal control in the extended piecewise linear-quadratic format. Such format greatly extends the classical linear-quadratic regulator problem ... -
Cornered Asymptotically Hyperbolic Metrics
This thesis considers asymptotically hyperbolic manifolds that have a finite boundary in addition to the usual infinite boundary – cornered asymptotically hyperbolic manifolds. A theorem of Cartan-Hadamard type near infinity ... -
Counting social interactions for discrete subsets of the plane
We will use dynamical, geometric, and analytic techniques to study translation surfaces. A translation surface is, informally, a collection of polygons in the plane with parallel sides identified by translation to form a ... -
Cubes, Codes, and Graphical Designs
Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical ... -
Cycle type factorizations in the finite general linear groups
Recent work by Huang, Lewis, Morales, Reiner, and Stanton suggests that the regular elliptic elements of $\mathrm{GL}_n \mathbb{F}_q$ are somehow analogous to the $n$-cycles of the symmetric group. In 1981, Stanley enumerated ... -
Deformation invariance of rational pairs
Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the ... -
Deformations of Categories of Coherent Sheaves and Fourier-Mukai Transforms
(2013-07-25)In modern algebraic geometry, an algebraic variety is often studied by way of its category of coherent sheaves or derived category. Recent work by Toda has shown that infinitesimal deformations of the category of coherent ... -
Designing Scheduling Algorithms via a Mathematical Perspective
This document will discuss three problems that I worked on during my Ph.D. Chapter \ref{chapter: SC} contains my work on the Santa Claus problem, and Chapters \ref{chapter: S1} and \ref{chapter: S2} contain my work on ... -
Determinantal Representations and the Image of the Principal Minor Map
Research in algebraic geometry has interfaces with other fields, such as matrix theory, combinatorics, and convex geometry. It is a branch of mathematics that studies solution to systems of polynomial equations and ... -
Dual Equivalence Graphs and their Applications
In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's ... -
Eigenvalue fluctuations for random regular graphs
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are <italic>universal</italic>. We probe the edges of universality by studying ... -
Eigenvalue Fluctuations of Random Matrices beyond the Gaussian Universality Class
(2013-11-14)The goal of this thesis is to develop one of the threads of what is known in random matrix theory as universality, which essentially is that a large class of matrices generalizing the Gaussian matrices (certain Wigner ... -
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. ... -
Epidemics on critical random graphs: limits and continuum descriptions
Understanding how diseases spread through populations is vital for mitigation efforts. For any disease at hand, the specifics of how a disease spreads through a community depends on many factors: how the disease is ... -
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.