Browsing by Author "Fili, Paul"

Now showing items 1-10 of 10

    • Color symmetry in the platonic solids 

      DeHoyos, Isaiah (2019-05-10)
      Rotationally-invariant colorings of the Platonic solids are considered. Permutation representations of the symmetry groups of the Platonic solids are constructed using group actions on rotationally-invariant colorings of ...

    • Graphic matroid embeddability and Sarkaria's Theorem 

      McCoy, Wyatt (2022-05-09)
      In this paper, we intend to explore the consequences of Sarkaria's Theorem in the context of Graphic matroids. Sarkaria's Theorem states that if X is the chromatic number of the Kneser graph of a simplicial complex [Delta] ...

    • Graphs and rhythmic canons in musical composition 

      Heon, Nikole (2019-05-07)
      Musical compositions and rhythmic canons, specifically packings, are created with the use of a motif and translation set. Then undirected graphs and cliques were constructed to compare with the selection of elements for ...

    • Investigating the energy of musical chords 

      Meyer, Mitchell (2017-04-25)
      In western music, each octave is divided into 12 semitones. The number of semitones between notes played at the same time largely determines whether a chord sounds pleasing or not. In a mathematical sense, a relative energy ...

    • Mahler measure and its behavior under iteration 

      Zhang, Mingming (2021-05)
      For an algebraic number $\alpha$ we denote by $M(\alpha)$ the Mahler measure of $\alpha$. Mahler measure is a height function on polynomials with integer coefficients. Moreover, as $M(\alpha)$ is again an algebraic number ...

    • Polynomial approximation of CR singular functions 

      Fancher, Trevor (2020-05)
      We begin by recalling some basic facts about continuity and differentiability in the one real variable setting. Following a quick discussion on what classical mathematicians had in mind when dealing with continuous functions, ...

    • Polynomials having small heights on lemniscates 

      Looney, Ryan (2022-12)
      The Mahler measure of a complex polynomial is the geometric mean of that polynomial over the unit circle. By a result of Kronecker, for nonconstant integer polynomials, the Mahler measure is equal to 1 if and only if all ...

    • Polynomials with small elliptic Mahler measure via genetic algorithms 

      Clark, John Michael (2020-05)
      For a minimal polynomial $f$ we denote by $M(f)$ the Mahler measure of the roots of $f$. The classical Lehmer conjecture is concerned with finding a definitive lower bound for $M(f)$. Lehmer's polynomial is known to have ...

    • Relationship between differential intertwining operators on the indefinite orthogonal and unitary groups 

      Hader, Scott (2022-05)
      In this thesis, we will analyze degenerate principal series representations realized as smooth induced representations for the indefinite orthogonal and unitary groups G=SO_0(2p,2q) and H=U(p,q). We will induce from smooth ...

    • Using Twitter data to predict violent events 

      Hull, Kelsea (2018-05-15)