Index Catalog // ScholarsArchive@OSU

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

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
Full Text:: algebraic number is totally real (respectively, totally p-adic) if its minimal polynomial over Q splits

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

A general theory of density in additive number theory

Creator:: Freedman, Allen Roy
Abstract:: See PDF for abstract.
Resource Type:: Dissertation
Full Text:: GENERAL THEORY OF DENSITY IN ADDITIVE NUMBER THEORY Abstract approved (Major pr fessor) L

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
Full Text:: Heat transfer in magnetic fluids at low Reynolds number

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

A numerical study of inertial flow features in moderate Reynolds number flow through packed beds of spheres

Creator:: Finn, Justin Richard
Abstract:: In this work, flow through synthetic arrangements of contacting spheres is studied as a model problem for porous media and packed bed type flows. Direct numerical simulations are performed for moderate pore Reynolds numbers in the range, 10 ≤ Re ≤ 600, where non-linear porescale flow features are known to...
Resource Type:: Dissertation
Full Text:: : A Numerical Study of Inertial Flow Features in Moderate Reynolds Number Flow Through Packed Beds of

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
Full Text:: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5 Two-parameters families of modular forms

Students' Understanding of Complex Numbers in Middle-Division Physics

Creator:: Smith, Emily M.
Abstract:: Mathematical sophistication increases rapidly as students transition from lower- to upper-division physics courses. Complex algebra is one of the mathematical tools that is not introduced or used in lower-division physics courses but is pervasive throughout upper-division courses. In this dissertation, I study middle-division physics students' developing fluency with complex number...
Resource Type:: Dissertation
Full Text:: physics students’ developing fluency with complex number algebra as they transition from lower- to upper

An analysis of the effect of mathematics readiness education at the kindergarten level on the growth of conceptual ability of number as measured by Piaget's stages of the development of number

Creator:: Anderson, Doloris Gerkewicz
Abstract:: The purpose of this study was to test two assumptions. They are that factors in a child's background correlate with the notion of conservation and that additional mathematical instruction will result in a higher level of maturity of the notion of conservation as well as increased achievement in mathematical skills....
Resource Type:: Dissertation
Full Text:: education at the kindergarten level on the growth of conceptual ability of number as measured by Piaget's

ScholarsArchive@OSU

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

Arithmetic dynamical questions with local rationality conditions

On Small Heights of Totally p-adic Numbers

A general theory of density in additive number theory

Heat transfer in magnetic fluids at low Reynolds number

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

A numerical study of inertial flow features in moderate Reynolds number flow through packed beds of spheres

Zeros of Certain Combinations of Products of Eisenstein Series

Students' Understanding of Complex Numbers in Middle-Division Physics

An analysis of the effect of mathematics readiness education at the kindergarten level on the growth of conceptual ability of number as measured by Piaget's stages of the development of number

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