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Filtering by: Creator Corwith, Holly L. Remove constraint Creator: Corwith, Holly L. Committee Member Swisher, Holly Remove constraint Committee Member: Swisher, Holly

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  • Classifying Octonionic-Linear Operators

    Creator:
    Putnam, Alexander
    Abstract:
    The goal of this paper is to classify linear operators with octonionic coefficients and octonionic variables. While building up to the octonions we also classify linear operators over the quaternions and show how to relate the linear operators over the quaternions and octonions to matrices. We also construct a basis...
    Resource Type:
    Capstone Project
    Full Text:
    ∈ C. To check, assume m,n, l ∈ C and consider x→ mxn+ lx = (mn)x+ lx = (mn+ l)x. (2.5) Thus, our set

  • Explicit Dynamical Systems on the Sierpiński Curve

    Creator:
    Homsomboon, Worapan
    Resource Type:
    Dissertation
    Full Text:
    Escher, Prof. Ren Guo and Prof. Holly Swisher for their comments and suggestions. I acknowledge

  • Classifying seven dimensional manifolds of fixed cohomology type

    Creator:
    Montagantirud, Pongdate
    Abstract:
    Finding new examples of compact simply connected spaces admitting a Riemannian metric of positive sectional curvature is a fundamental problem in differential geometry. Likewise, studying topological properties of families of manifolds is very interesting to topologists. The Eschenburg spaces combine both of those interests: they are positively curved Riemannian manifolds...
    Resource Type:
    Dissertation
    Full Text:
    sectional curvature. In 1997, L. Astey, E. Micha and G. Pastor [AMP97] used classification theorem II to

  • Connections between combinatorics of permutations and algorithms and geometry

    Creator:
    Wills, Dean Connable
    Abstract:
    Geometric Problems become increasingly intractable and difficult to visualize as the number of dimensions increases beyond three. Inductions from lower dimensional spaces are possible yet often awkward. This thesis shows how elementary linear algebra, vector calculus, and combinatorics offer improved methods for calculating the dihedral angles of n-simplicies and proving...
    Resource Type:
    Dissertation
    Full Text:
    determined bulb strength s, when we find the largest floor l ≤ N such that the bulb survives a drop from l

  • Continued fractions and the divisor at infinity on a hyperelliptic curve : examples and order bounds

    Creator:
    Daowsud, Katthaleeya
    Abstract:
    We use the theory of continued fractions over function fields in the setting of hyperelliptic curves of equation y²=f(x), with deg(f)=2g+2. By introducing a new sequence of polynomials defined in terms of the partial quotients of the continued fraction expansion of y, we are able to bound the sum of...
    Resource Type:
    Dissertation
    Full Text:
    formal sum of points on C. That is, D = l∑ i=1 niPi, ni ∈ Z, Pi ∈ C, where the degree of D is

  • A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

    Creator:
    Rockwell, Daniel Luke
    Abstract:
    The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the...
    Resource Type:
    Dissertation
    Full Text:
    , and fifjfkfl with i, j, k, l all distinct. Since we have as- sumed the fi’s are independent and have

  • The density signature

    Creator:
    Migler-VonDollen, Theresa
    Abstract:
    In real networks, identifying dense regions is of great importance. For example, in a network that represents academic collaboration, authors within the densest component of the graph tend to be the most prolific. Dense subgraphs often identify communities in social networks. And dense subgraphs can be used to discover regulatory...
    Resource Type:
    Dissertation
    Full Text:
    GF C J L I N M D H E A B K GF C J L I N M D H E A B K GF C J L I N M D H E

  • New Families of pseudo-Anosov Homeomorphisms with Vanishing Sah-Arnoux-Fathi Invariant

    Creator:
    Do, Hieu Trung
    Abstract:
    Translation surfaces can be viewed as polygons with parallel and equal sides identified. An affine homeomorphism φ from a translation surface to itself is called pseudo-Anosov when its derivative is a constant matrix in SL₂(R) whose trace is larger than 2 in absolute value. In this setting, the eigendirections of...
    Resource Type:
    Dissertation
    Full Text:
    interval exchange transformations. We follow closely the notation presented in [Fi, L, Vi]. The idea of

  • Algebraic Pappus Curves

    Creator:
    Hatase, Tatsuhiko
    Abstract:
    We show that Pappus Curves, introduced by R. Schwartz to study his dynamical system in the real projective plane generated by iterated applications of the classical Pappus Theorem, are algebraic exactly in the linear case. Our approach is to use properties of projective curves such as singular points, genus, number...
    Resource Type:
    Dissertation
    Full Text:
    Its Transverse Linefield L. . . . . . . . . . . . . . . . . . . . . . . . . . 77 ALGEBRAIC PAPPUS

  • Mahler's order functions and algebraic approximation of p-adic numbers

    Creator:
    Dietel, Brian Christopher
    Abstract:
    If P is an integer polynomial denote the degree of P by ∂(P) and let H(P) be the maximum of the absolute value of the coefficients of P. Define Λ(P)=2[superscript ∂(P)]H(P) and for a fixed prime p let C[subscript p] denote the completion of the algebraic closure of the p-adic...
    Resource Type:
    Dissertation
    Full Text:
    committee members, David Finch, Dennis Garity, Thomas Schmidt, Holly Swisher, and Todd Palmer. Personal I