ResearchWorks Archive

Browsing Mathematics by Title

Browsing Mathematics by Title

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  • 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 ...
  • 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, ...
  • 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 ...
  • Drugan, Gregory
    We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows ...
  • Mailhot, James Michael (2003)
    The Mordell-Weil theorem states that the points of an elliptic curve defined over a number field form a finitely generated, abelian group. The rank of this group, generally referred to as the rank of the elliptic curve, ...
  • Deines, Alyson Laurene
    A crowning achievement of Number theory in the 20th century is a theorem of Wiles which states that for an elliptic curve E over <bold>Q</bold> of conductor N, there is a non-constant map from the modular curve of level N ...
  • Wong, Chun Wai Carto (2013-02-25)
    In this dissertation, we show that the chordal Loewner differential equation with C^{beta} driving function generates a C^{beta + 1/2} slit for 1/2 < beta <= 2, except when beta = 3/2 the slit is only proved to be weakly C^{1,1}.
  • Wright, James M., 1960- (1996)
    A strong Markov process, $W\sp0$, is constructed by a natural linking together of two independent stable processes of type ($\alpha,\ \beta\sb1$) and ($\alpha,\ \beta\sb2$). The drift for a stable process X of type ($\alpha,\ ...
  • Duarte Espinoza, Mauricio Andres (2012-09-13)
    This dissertation studies two different types of interaction of diffusion processes with the boundary of a domain $DsubRR^n$, which is assumed to be bounded, and of class $C^2(RR^n)$. The first process that is studied is ...
  • Blair, Matthew D (2005)
    Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. In this work, such methods are used to show Strichartz inequalities for ...
  • Wolcott, Frank Lucas (2012-09-13)
    We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending previous work done under a Noetherian hypothesis. Maps between rings R → S induce adjoint functors between ...
  • Tittelfitz, Justin Jeffrey (2013-11-14)
    We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0, T ] × boundary of Omega, where Omega in R3 ...
  • Slivken, Erik Dustin
    In this thesis we present three problems. The first problem is to find a good description of the number of fixed points of a 231-avoiding permutation. We use a bijection from Dyck paths to 231-avoiding permutations that ...
  • Tadic, Tvrtko
    We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical ...
  • Dochtermann, Anton, 1978- (2007)
    In this thesis we consider topological aspects of graph homomorphisms. Our main object of study is the Hom complex of graphs, a space first introduced by Lovasz to obtain lower bounds on chromatic number, and more recently ...
  • Chiecchio, Alberto
    In this thesis we do the first steps towards a non-Q-Gorenstein Minimal Model Program. We extensively study non-Q-factorial singularities, using the techniques introduced by [dFH09]. We introduce a new class of singularities, ...
  • Kirson, Antonio (2010)
    An automorphism $\sigma$ of a projective variety $X$ is said to be \textit{wild} if $\sigma(Y)\neq Y$ for every non-empty subvariety $Y\subsetneq X$. In MR2227726 Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that ...

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