Browsing by Department "Mathematics"

Now showing items 21-39 of 340

    • The Arveson-Douglas Conjecture 
      Wang, Yi (2018-05-31)
      The Arveson-Douglas Conjecture states that, closures of polynomial ideals in some analytic Hilbert modules, such as the Drury-Arveson module, Bergman module or Hardy module, are essentially normal. The conjecture has ...
    • Asymptotic expansions of the regular solutions to the 3D Navier-Stokes equations and applications to the analysis of the helicity 
      Hoang, Luan Thach (Texas A&M University, 2005-08-29)
      A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type ...
    • Asymptotic, Algorithmic and Geometric Aspects of Groups Generated by Automata 
      Savchuk, Dmytro M. (2010-01-14)
      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 ...
    • Asymptotics for Traces of Weak Maass Forms and Applications 
      Khaochim, Narissara (2021-04-15)
      In this dissertation, we give two main results. First, we use the Bruinier-Ono 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 ...
    • Asymptotics of the Relative Reshetikhin-Turaev Invariants 
      Wong, Ka Ho (2023-04-28)
      In this dissertation, we study the asymptotic expansion conjecture of the relative Reshetikhin-Turaev invariants proposed by T. Yang and the author in [65] for all pairs (M, L) satisfying the property that M∖L is homeomorphic ...
    • Automata groups 
      Muntyan, Yevgen (2010-01-16)
      This dissertation is devoted to the groups generated by automata. The first part of the dissertation deals with L-presentations for such groups. We describe the sufficient condition for an essentially free automaton group ...
    • Backward time behavior of dissipative PDE 
      Dascaliuc, Radu (Texas A&M University, 2007-04-25)
      We study behavior for negative times t of the 2D periodic Navier-Stokes 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 ...
    • Bergman Kernels, Hartogs Domains, and the Wiegerinck Problem 
      Boudreaux, Blake Joseph (2021-06-29)
      Let $L^2_h(\Omega,\mu)$ denote the space of holomorphic functions on $\Omega$ which are square-integrable with respect to the weight $\mu:\Omega\to [0,\infty)$, where $\Omega$ is a domain in $\mathbb{C}^n$. When $\mu$ is ...
    • Bounds for the Rank of the Finite Part of Operator K-Theory and Polynomially Full Groups 
      Samurkas, Suleyman Kagan (2018-04-13)
      We derive a lower and an upper bound for the rank of the finite part of operator K-theory groups of maximal and reduced C*-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing ...
    • Bounds on codes from smooth toric threefolds with rank(pic(x)) = 2 
      Kimball, James Lee (2009-05-15)
      In 1998, J. P. Hansen introduced the construction of an error-correcting 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 ...
    • Brackets on Hochschild cohomology of Noncommutative Algebras 
      Grimley, Lauren Elizabeth (2016-04-08)
      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 ...
    • Brittle Fracture Modeling with a Surface Tension Excess Property 
      Ferguson, Lauren (2012-10-30)
      The classical theory of linear elastic fracture mechanics for a quasi-static crack in an infinite linear elastic body has two significant mathematical inconsistencies: it predicts unbounded crack-tip stresses and an ...
    • C algebraic Higher Signatures on Non-Witt Spaces 
      Liu, Mingyu (2021-05-03)
      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 ...
    • Calculus for Business & Social Sciences OER Textbook 
      Allen, Angela J.; Orchard, Patrick J. (2021-08-24)
      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, . ...
    • Causal equivalence of frames 
      Henderson, Troy Lee, IV (Texas A&M University, 2006-10-30)
      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 sub-area of signal processing known as data ...
    • Central Limit Theorems for Empirical Processes Based on Stochastic Processes 
      Yang, Yuping (2013-08-13)
      In this thesis, we study time-dependent 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 ...
    • The Chowla-Selberg Formula for CM Fields and the Colmez Conjecture 
      Barquero Sanchez, Adrian Alberto (2016-08-05)
      In this thesis we start by giving a quick review of the classical Chowla-Selberg formula. We then recall a conjecture of Colmez which relates the Faltings height of an abelian variety with complex multiplication by the ...
    • Classification of Tripartite Tensors with Small Geometric Ranks 
      Geng, Runshi (2023-03-06)
      Geometric Rank of tensors was introduced by Kopparty et al. as a useful tool to study algebraic complexity theory, extremal combinatorics and quantum information theory. This dissertation studies the classification of ...
    • Cluster Value Problems in Infinite-Dimensional Spaces 
      Ortega Castillo, Sofia (2014-08-05)
      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 ...