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  • Trace forms and self-dual normal bases in Galois field extensions

    Creator:
    Kang, Dong Seung
    Abstract:
    Let G be a finite group, G₂ be a Sylow 2-subgroup of G, and L/K be a G-Galois extension. We study the trace form qL/K of L/K and the question of existence of a self-dual normal basis. Our main results are as follows: (1) If G₂ is not abelian and...
    Resource Type:
    Dissertation

  • New methods for finite field arithmetic

    Creator:
    Yanik, Tuğrul
    Abstract:
    We describe novel methods for obtaining fast software implementations of the arithmetic operations in the finite field GF(p) and GF(p[superscript k]). In GF(p) we realize an extensive speedup in modular addition and subtraction routines and some small speedup in the modular multiplication routine with an arbitrary prime modulus p which...
    Resource Type:
    Dissertation
    Full Text:
    reviews, par- ticularly to Dr. Thomas A. Schmidt from the Mathematics Department. At various stages in

  • An inner product on adelic measures

    Creator:
    Oberly, Peter J.
    Abstract:
    We define an inner product on a vector space of adelic measures over a number field $K$. We find that the norm induced by this inner product governs weak convergence at each place of $K$. The canonical adelic measure associated to a rational map is in this vector space, and...
    Resource Type:
    Dissertation
    Full Text:
    Tom Schmidt, who preformed an exceptionally close read of a previous draft of this dissertation. His

  • Fourier Analysis and Equidistribution on the p-adic Integers

    Creator:
    Somasunderam, Naveen
    Abstract:
    In this dissertation, we use Fourier-analytic methods to study questions of equidistribution on the compact abelian group Zp of p-adic integers. In particu- lar, we prove a LeVeque-type Fourier analytic upper bound on the discrepancy of sequences. We establish p-adic analogues of the classical Dirichlet and Fejér kernels on R/Z,...
    Resource Type:
    Dissertation
    Full Text:
    1.4. Let T be the circle group under multiplication, T = {z ∈ C | |z| = 1}. Given a compact abelian

  • Overpartition Ranks, Cranks, and Frobenius Representations

    Creator:
    Morrill, Thomas
    Abstract:
    We generalize overpartition rank and crank generating functions to obtain k-fold variants, and give a combinatorial interpretation for each. The k-fold crank generating function is interpreted by extending the first and second residual cranks to a natural infinite family. The k-fold rank generating functions generate two families of buffered Frobenius...
    Resource Type:
    Dissertation
    Full Text:
    : Adding a staircase to λ = (2, 0, 0). Proof of Lemma 2.7.1. Fix integers 0 ≤ s ≤ t. Similarly to the

  • Feedback in multiple antenna wireless communication systems

    Creator:
    Xu, Tao
    Abstract:
    Multiple-input multiple-output wireless systems promise significant capacity gain and/or diversity gain over single antenna systems. If channel state information (CSI) is available at both the transmitter and the receiver, the performance can be further improved. In this thesis, first, we study binary index feedback problem in beamforming systems when the...
    Resource Type:
    Dissertation
    Full Text:
    expectation Tr(·) the trace of a matrix (·)T the transpose (·)∗ the conjugate (·)H the conjugate transpose

  • Enumeration Problems on Symmetries of Riemann Surfaces

    Creator:
    Camacho, Charles A.
    Abstract:
    We describe two combinatorial problems in the theory of automorphism groups of compact Riemann surfaces of genus two or greater: enumerate the topological actions of a finite group on surfaces and determine the set of genera of surfaces admitting such a group action, called the genus spectrum. We illustrate results...
    Resource Type:
    Dissertation
    Full Text:
    thank William Bogley for suggesting I study a family of finite groups; Thomas Schmidt for connecting me

  • Periodicity and Partition Congruences

    Creator:
    Al-Saedi, Ali Hammood
    Abstract:
    In this note, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our extended technique could be a useful tool to prove congruences for certain types of combinatorial...
    Resource Type:
    Dissertation
    Full Text:
    divisible by `N . The following identity is a more general version of (1.2), s∑ i=1 λ(n`N + ai) ≡ t∑ j=1

  • The structure of E6

    Creator:
    Wangberg, Aaron D.
    Abstract:
    A fundamental question related to any Lie algebra is to know its subalgebras. This is particularly true in the case of E6, an algebra which seems just large enough to contain the algebras which describe the fundamental forces in the Standard Model of particle physics. In this situation, the question...
    Resource Type:
    Dissertation
    Full Text:
    of E6 Abstract approved: Tevian Dray A fundamental question related to any Lie algebra is to know

  • You are What, When, Where, and How you Eat : Mercury in Avian Food Webs across Multiple Spatial Scales

    Creator:
    Jackson, Allyson K.
    Abstract:
    Human alterations of landscapes take many forms, one of which is anthropogenic pollution. Mercury (Hg) is a complex contaminant because its uptake into the food web is not driven entirely by loading to the system; methylation is necessary to make Hg bioavailable and toxic to fish and wildlife. Because methylation...
    Resource Type:
    Dissertation
    Full Text:
    . N. Alpers, and J. T. Ackerman. 2016. Mercury in western North America: A synthesis of