Browsing by Department "Mathematics"
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(20100114)This dissertation is devoted to various aspects of groups generated by automata. We study particular classes and examples of such groups from different points of view. It consists of four main parts. In the first part we ...

(20210415)In this dissertation, we give two main results. First, we use the BruinierOno formula to give an asymptotic formula for the partition function $p(n)$ with an effective bound on the error term. Second, we give an asymptotic ...

(20100116)This dissertation is devoted to the groups generated by automata. The first part of the dissertation deals with Lpresentations for such groups. We describe the sufficient condition for an essentially free automaton group ...

(Texas A&M University, 20070425)We study behavior for negative times t of the 2D periodic NavierStokes equations and Burgers' original model for turbulence. Both systems are proved to have rich sets of solutions that exist for all t  R and increase ...

(20210629)Let $L^2_h(\Omega,\mu)$ denote the space of holomorphic functions on $\Omega$ which are squareintegrable with respect to the weight $\mu:\Omega\to [0,\infty)$, where $\Omega$ is a domain in $\mathbb{C}^n$. When $\mu$ is ...

(20180413)We derive a lower and an upper bound for the rank of the finite part of operator Ktheory groups of maximal and reduced C*algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing ...

(20090515)In 1998, J. P. Hansen introduced the construction of an errorcorrecting code over a finite field Fq from a convex integral polytope in R2. Given a polytope P ⊂ R2, there is an associated toric variety XP , and Hansen used ...

(20160408)The Hochschild cohomology of an associative algebra is a Gerstenhaber algebra, having a graded ring structure given by the cup product and a compatible graded Lie algebra structure given by the Gerstenhaber bracket. The ...

(20121030)The classical theory of linear elastic fracture mechanics for a quasistatic crack in an infinite linear elastic body has two significant mathematical inconsistencies: it predicts unbounded cracktip stresses and an ...

(20210503)Signature plays an important role in geometry and topology. In the space with singularity, Goresky and MacPherson extend the signatures to oriented pseudomanifolds with only even codimensional stratums by using generalized ...

(20210824)An open educational resource (OER) textbook covering calculus for business and social sciences. Topics covered include limits and continuity, The Derivative, curve sketching and optimization, and antidifferentiation, . ...

(Texas A&M University, 20061030)Frames have recently become popular in the area of applied mathematics known as digital signal processing. Frames offer a level of redundancy that bases do not provide. In a subarea of signal processing known as data ...

(20130813)In this thesis, we study timedependent empirical processes, which extend the classical empirical processes to have a time parameter; for example the empirical process for a sequence of independent stochastic processes {Yi ...

(20160805)In this thesis we start by giving a quick review of the classical ChowlaSelberg formula. We then recall a conjecture of Colmez which relates the Faltings height of an abelian variety with complex multiplication by the ...

(20140805)In this dissertation we study cluster value problems for Banach algebras H(B) of analytic functions on the open unit ball B of a Banach space X that contain X* and 1. Solving cluster value problems requires understanding ...

(20190403)In this paper, we first introduce the RSK algorithm, which gives a correspondence between integer sequences and standard tableaux. Then we introduce Schensted’s theorem and Greene’s theorem that describe how the shape of ...

(20101012)A natural problem that arises in the study of derivations on a Banach algebra is to classify the commutators in the algebra. The problem as stated is too broad and we will only consider the algebra of operators acting on ...

(Texas A&M University, 20060816)This dissertation consists of two parts. In the first part we show that for 1 k 1, a complex manifold M of dimension at least k in the boundary of a smooth bounded pseudoconvex domain in Cn is an obstruction to compactness ...

(20140710)In this dissertation we are concerned with a problem which asks whether the compactness of the ∂ ̅Neumann operator is preserved under the intersection of two bounded pseudoconvex domains in ℂ^(n) with the mild assumption ...

(20200702)In this dissertation we consider methods from complex analysis to solve inverse spectral problems for Schroedinger operators on finite intervals and semiinfinite Jacobi operators. After discussing necessary background ...