ResearchWorks Archive

Browsing Mathematics by Issue Date

Browsing Mathematics by Issue Date

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  • 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 ...
  • 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 ...
  • Hubenthal, John Mark (2013-02-25)
    We consider the inverse source problem for the radiative transfer equation, under various assumptions on the scattering and absorption parameters, as well as on the accessible data. In such a setup, we measure the outgoing ...
  • 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 ...
  • Wang, Wenhan (2013-02-25)
    We introduce the notion of isolated genus two curves. There is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap. Thus there is no known way of transporting ...
  • 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}.
  • An, Yajun (2013-04-17)
    A new methodology was proposed in Finkelstein and Kastner (2007,2008) to derive finite-difference (FD) schemes in the joint time-space domain to reduce dispersion error. The key idea is that the true dispersion relation ...
  • 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 ...
  • Blair-Stahn, Nathaniel Deveroux (2013-04-17)
    We study the macroscopic geometry of first-passage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ...
  • Ning, Weiyang (2013-07-25)
    The mixing time of a Markov chain describes how fast the Markov chain converges to its stationary distribution. In this thesis, we survey some of the knowledge and main tools available in this field by looking at examples. ...
  • Grigg, Nathan (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 ...
  • 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, ...
  • Choi, Daeshik (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.
  • Paquette, Elliot (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 ...
  • Solbrig, Mary Katherine (2013-11-14)
    Every 10 years the United States performs a census, and this census determines how many members of congress will represent each state. Then begins an unfortunate battle, as cartographers manipulate the boundaries for ...
  • 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 ...
  • Chen, Jie (2013-11-14)
    Inverse problems arise in different disciplines including exploration geophysics, medical imaging and nondestructive evaluation. In some settings, a single modality displays either high contrast or high resolution but not ...
  • Zhuang, Guangbin (2013-11-14)
    We study Hopf algebras of finite Gelfand-Kirillov dimension. By analyzing the free pointed Hopf algebra F(t), we show the existence of certain Hopf subalgebras of pointed Hopf domains H whose GK-dimension are finite and ...
  • Kocyigit, Ilker (2013-11-14)
    We study hybrid imaging techniques that aim to overcome the ill-posedness of the Electric Impedance Tomography using the acousto-electric coupling. For the isotropic case, we consider the problem of reconstructing the ...
  • 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 ...

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