Now showing items 55-74 of 96

    • On f-vectors of polytopes and matroids 

      Samper Casas, Jose Alejandro
      The f-vector of a simplicial complex is a fundamental invariant that counts the number of faces in each dimension. A natural question in the theory of simplicial complexes is to understand the relationship between the ...
    • On numerics and inverse problems 

      Caday, Peter Anthony
      In this thesis, two projects in inverse problems are described. The first concerns a simple mathematical model of synthetic aperture radar with undirected beam, modeled as a 2D circular Radon transform with centers restricted ...
    • On Particle Interaction Models 

      Banerjee, Sayan (2014-02-24)
      This dissertation deals with three problems in Stochastic Analysis which broadly involve interactions, either between particles (Chapters 1 and 2), or between particles and the boundary of a C2 domain (Chapter 3). In Chapter ...
    • On Selmer groups and factoring p-adic L-functions 

      Palvannan, Bharathwaj
      Samit Dasgupta has proved a formula factoring a certain restriction of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and ...
    • On singularities of generic projection hypersurfaces 

      Doherty, Davis C (2006)
      The present work studies singularities of hypersurfaces arising from generic projections of smooth projective varieties, in the context of Du Bois and semi log canonical singularities. It is demonstrated that Du Bois ...
    • On special Lagrangian equations 

      Wang, Dake (2014-02-24)
      In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1]. In subcritical phases, we construct singular ...
    • On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions 

      Van Huele, Yannick
      For certain Zp-extensions of abelian number fields, we study the Iwasawa module associated to the ideal class groups. We show that generic Zp-extensions of abelian number fields are T-semisimple. We also construct the ...
    • On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities 

      Merhej, Jessica
      A central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E. R. Reifenberg proved that if an $n$-dimensional subset $M$ of $\mathbb{R}^{n+d}$ is well ...
    • On the mod 2 general linear group homology of totally real number rings 

      Harris, Julianne S. (Julianne September) (1997)
      We study the mod 2 homology of the general linear group of rings of integers in totally real number fields. In particular, for certain such rings R, we construct a space JKR and show that the mod 2 homology of JKR is a ...
    • The Ornstein-Uhlenbeck Process In Neural Decision-Making: Mathematical Foundations And Simulations Suggesting The Adaptiveness Of Robustly Integrating Stochastic Neural Evidence 

      Wojnowicz, Michael Thomas (2013-02-25)
      This master's thesis reviews the concepts behind a stochastic process known as the Ornstein-Uhlenbeck Process, and then uses that process as a way to investigate neural decision making. In particular, MATLAB simulations ...
    • Path algebras and monomial algebras of finite GK-dimension as noncommutative homogeneous coordinate rings 

      Holdaway, Cody
      This thesis sets out to understand the categories QGr A where A is either a monomial algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: \begin{enumerate} \item What is the structure ...
    • Permutation diagrams in symmetric function theory and Schubert calculus 

      Pawlowski, Brendan
      A fundamental invariant of a permutation is its inversion set, or diagram. Natural machinery in the representation theory of symmetric groups produces a symmetric function from any finite subset of <bold>N</bold><super>2</super>, ...
    • Polynomials in Multiview Geometry 

      Aholt, Christopher (2013-04-17)
      We study multiview geometry and some of its applications through the use of polynomials. A three-dimensional world point gives rise to n ≥ 2 two-dimensional projections in n given cameras. The object of focus in this ...
    • The Positive Semidefinite Rank of Matrices and Polytopes 

      Robinson, Richard
      The positive semidefinite (psd) rank of a nonnegative <italic>p</italic> × <italic>q</italic> matrix <italic>M</italic> is defined to be the smallest integer <italic>k</italic> such that there exist <italic>k</italic> × ...
    • Problems in Algebraic Vision 

      Lee, Hon Leung
      This thesis studies several fundamental mathematical problems that arise from computer vision using techniques in algebraic geometry and optimization. Chapters 2 and 3 consider the fundamental question of the existence of ...
    • Problems in computational algebra and integer programming 

      Bogart, Tristram, 1980- (2007)
      This thesis is a compendium of several projects that span the gap between commutative algebra and geometric combinatorics: one in tropical geometry, one in computational algebra, and two in discrete geometry and integer ...
    • Qualitative stability properties of matrices 

      Bone, Terrence (1985)
      A matrix A is sign stable if some matrix with the same sign pattern of positive, negative, and zero entries has all eigenvalues with negative real parts. It is potentially stable if it is not sign unstable. The system A x ...
    • The Radiative Transfer Equation in Photoacoustic Imaging 

      Patrolia, Lee (2013-07-25)
      Photoacoustic tomography is a rapidly developing medical imaging technique that combines optical and ultrasound imaging to exploit the high contrast and high resolution of the respective individual modalities. Mathematically, ...
    • Random recursion 

      Junge, Matthew S.
      We study the limiting behavior of three stochastic processes. Two are interacting particle systems, the frog model and coalescing random walk. We work out transience and recurrence properties on various graphs. The last ...
    • The regularity of Loewner curves 

      Tran, Huy Vo
      The Loewner differential equation, a classical tool that has attracted recent attention due to Schramm-Loewner evolution (SLE), provides a unique way of encoding a simple 2-dimensional curve into a continuous 1-dimensional ...