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Department of Mathematics and Statistics

Department of Mathematics and Statistics

 

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  • Sneiderman, Robert (2021-01-13)
    Standard sampling and monitoring of fish populations are invasive and time- consuming techniques. The ongoing development of statistical techniques to analyze environmental DNA (eDNA) introduces a possible solution to these ...
  • Manke, Kurtis (2021-01-05)
    The effective degree model has been applied to both SIR and SIS type diseases (those which confer permanent immunity and those which do not, respectively) with great success. The original model considers a large system ...
  • Preissl, Dayton (2021-01-04)
    This master thesis is devoted to the kinetic description in phase space of strongly magnetized plasmas. It addresses the problem of stability near equilibria for magnetically confined plasmas modeled by the relativistic ...
  • Dore-Hall, Skye (2020-12-22)
    In 2019, Adams, Ehlting, and Edwards developed a four-variable system of ordinary differential equations modelling phenylalanine metabolism in plants according to Michaelis-Menten kinetics. Analysis of the model suggested ...
  • Niezen, Joanna (2020-09-30)
    A design is a set of points, V, together with a set of subsets of V called blocks. A classic type of design is a balanced incomplete block design, where every pair of points occurs together in a block the same number of ...
  • Hsu, Kevin (2020-08-23)
    The orientation completion problem for a hereditary class C of oriented graphs asks whether a given partially oriented graph can be completed to a graph belonging to C. This problem was introduced recently and is a ...
  • Bai, Kuang (2020-07-18)
    The main purpose of this dissertation is to investigate directional constraint qualifications and necessary optimality conditions for nonsmooth set-constrained mathematical programs. First, we study sufficient conditions ...
  • Carr, MacKenzie (2020-07-18)
    Given a finite set V, a convexity, C, is a collection of subsets of V that contains both the empty set and the set V and is closed under intersections. The elements of C are called convex sets. We can define several different ...
  • Johnson, Jesse T. (2020-05-08)
    Circular words, also known as necklaces, are combinatorial objects closely related to linear words. A brief history of circular words is given, from their early conception to present results. We introduce the concept of a ...
  • Horan, Joseph Anthony (2020-05-06)
    At its core, a dynamical system is a set of things and rules for how they change. In the study of dynamical systems, we often ask questions about long-term or average phenomena: whether or not there is an equilibrium for ...
  • Parker, Matthew R. P. (2020-04-29)
    The key results of this thesis are (1) an extension of N-mixture models to incorporate the additional layer of obfuscation brought by observing counts from a related auxiliary population (rather than the target population), ...
  • Xie, Rongzheng (2020-04-29)
    In 2007, Modolo and colleagues derived a population density equation for a population of Izhekevich neurons. This population density equation can describe oscillations in the brain that occur in Parkinson’s disease. ...
  • Bruce, Chris (2020-04-20)
    We initiate the study of a new class of semigroup C*-algebras arising from number-theoretic considerations; namely, we generalize the construction of Cuntz, Deninger, and Laca by considering the left regular C*-algebras ...
  • Duwenig, Anna (2020-04-09)
    The irrational rotation algebra A_θ is known to be Poincaré self-dual in the KK-theoretic sense. The spectral triple representing the required K-homology fundamental class was constructed by Connes out of the Dolbeault ...
  • Yang, Feiran (2020-01-03)
    Let G = (V,E) be a graph and f be a function such that f : V -> {0,1,2,..., k}. Let V_f^+ = {v : f(v) > 0}. If for every vertex v not in V_f^+ there exists a vertex w in V_f^+ such that d(v,w) ≤ f(w) then f is called ...
  • Halliday, Felicia (2020-01-02)
    This thesis is partitioned into three parts: improving pre-calculus skills of students in an introductory calculus course, the game of Cops and Robber on oriented graphs, and the generalized game of Cops and Robber. In the ...
  • Bowditch, Flora Caroline (2019-12-20)
    Let v ∈ Z+ and G be a simple graph. A G-decomposition of Kv is a collection F={F1,F2,...,Ft} of subgraphs of Kv such that every edge of Kv occurs in exactlyone of the subgraphs and every graph Fi ∈ F is isomorphic to G. A ...
  • Hyungeun, Shin (2019-10-03)
    The movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model, using a previously developed non-oscillatory balanced scheme. The model of TC used here takes an exponential form, ...
  • Neilson, Linda (2019-08-29)
    The usual graph parameters related to independent and dominating sets can be adapted to broadcasts on graphs. We examine some possible definitions for an inde- pendent broadcast. We determine the minimum maximal and the ...
  • Ye, Ying Ying (2019-08-29)
    Chordal graphs are an important class of perfect graphs. The beautiful theory surrounding their study varies from natural applications to elegant characterizations in terms of forbidden subgraphs, subtree representations, ...

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