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  • 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
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    , and New Demonstrations of, the Borel Normal Number Theorem Abstract approved: Robert M. Burton The

  • Zeros of Certain Combinations of Products of Eisenstein Series

    Creator:
    Klangwang, Jetjaroen
    Abstract:
    In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...
    Resource Type:
    Dissertation
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    determining the number of zeros of Eisenstein series which is the focus of this dissertation. Since Ek(τ) is

  • On Small Heights of Totally p-adic Numbers

    Creator:
    Stacy, Emerald T.
    Abstract:
    The height of an algebraic number A is a measure of how arithmetically complicated A is. We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height...
    Resource Type:
    Dissertation
    Full Text:
    number α is a measure of how arithmetically compli- cated α is. We say α is totally p-adic if the

  • Estimation of the order of an autoregressive time series : a Bayesian approach

    Creator:
    Robb, Loretta J.
    Abstract:
    Finite order autoregressive models for time series are often used for prediction and other inferences. Given the order of the model, the parameters of the models can be estimated by least squares, maximum likelihood, or the Yule-Walker method. The basic problem is estimating the order of the model. A number...
    Resource Type:
    Dissertation
    Full Text:
    Estimation of the order of an autoregressive time series

  • Weak-supervision Time-series Analysis

    Creator:
    You, Zeyu
    Abstract:
    Efficient time-series analysis can impact multiple application domains such as motif discovery in gene analysis or music data, extracting spectro-temporal patterns in acoustic scene analysis, or annotating and classifying electrical bio-signals (such as ECG, EEG, and EMG) for medical applications. Time-series analysis involves a variety of tasks. To predict future...
    Resource Type:
    Dissertation
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    12, 2019. Title: Weak-supervision Time-series Analysis Abstract approved: Raviv Raich E�cient

  • Performance evaluation and design of multiple time series based forecasting systems

    Creator:
    Chen, Kuei-Lin
    Abstract:
    The study evaluates performances of three multiple time series (MTS) forecasting methods; investigates possible improvements in MTS forecasting operations, and proposes a multiple time series based forecasting system. Time series considered are finite, linear, covariance stationary, and discrete. Specific objectives for the thesis were: (a) conducting comparative studies of MTS...
    Resource Type:
    Dissertation
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    included to indicate the number of time series. Thus, MMA(s, q) represents an s-variate moving average

  • Heat transfer in magnetic fluids at low Reynolds number

    Creator:
    Choi, Sang Hyouk
    Abstract:
    This study was concerned with the flow of a magnetic self-propelled ferrohydrodynamic fluid in a horizontal circular tube subjected to axially varying temperature and magnetic field. The first phase of the study involved the analytical solution to the governing equations for the velocity and temperature profiles within the fully developed...
    Resource Type:
    Dissertation
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    Heat transfer in magnetic fluids at low Reynolds number

  • Bilinear stochastic processes and time series

    Creator:
    Tang, Zhigiang
    Abstract:
    In engineering, biology, ecology, medicine, economics and social science, some processes are essentially bilinear, and some could be approximated accurately by bilinear processes under certain conditions. In this thesis the bilinear stochastic process and bilinear time series are discussed. Bilinear models essentially are nonlinear; the superposition rule is not valid....
    Resource Type:
    Dissertation
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    Bilinear stochastic processes and time series AN

  • 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
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    consider how well a given transcendental number can be approximated by algebraic numbers, or if there

  • Arithmetic dynamical questions with local rationality conditions

    Creator:
    Noytaptim, Chatchai
    Abstract:
    We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
    Resource Type:
    Dissertation
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    algebraic number is totally real (respectively, totally p-adic) if its minimal polynomial over Q splits