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...
This thesis brings together under one cover a survey
of the history of the real number e along with a study
of the present state of its theory and calculation.
This white paper gives an overview of the software applications used by university presses to publish digital monographs. In addition, we will look at routes taken by university presses to move from all print to some e-publishing and list the supplemental online content that is typically offered for a fee.
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...
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...
By using continued fractions the set of positive
irrationals can be put in one to one correspondence
with the set of sequences of positive integers. The
entries of an arbitrary sequence of integers can be any
subset of Z and each integer appearing can occur once,
infinitly often, or anything...
Let A and B be two subsets of the set of all non-negative
integers with 0 ε A and O ε B. The sum of the sets A and B is
the set C = A + B = {a + b: a ε A, b ε B). For n...
In 1932 A. Ya. Khinchin gave the first partial solution of the celebrated 1931 αβ Conjecture of L.G. Schnirelmann and E. Landau of the density of sums of sets on integers, which was completely proved in 1942 by H.B. Mann.
Khinchin's theorem is proved along with theorems of P. Scherk...
In this thesis, we study conditions not involving density which
guarantee that a given positive integer is contained in a sum of sets
of nonnegative integers. We survey the literature, give more detailed
proofs of some known theorems, develop some new theorems,
and make some conjectures.
The Rainbow hydrothermal plume was
discovered during a recent geophysical survey along
200km of the Mid-Atlantic Ridge (MAR), SW of the
Azores Triple Junction, in which at least seven new sites
of hydrothermal activity were identified. Here, we present
the first hydrographic study of the Rainbow plume, 36°
15'N, the...
A study of the running time of several known algorithms and several new algorithms to compute the n[superscript th] element of the Fibonacci sequence is presented. Since the size of the n[superscript th] Fibonacci number grows exponentially with n, the number of bit operations, instead of the number of integer...
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...
It is well known that the Fibonacci numbers can be expressed in the
form Round {1/√5 λ₀[superscript n]} where λ₀ = (1 + √5)/2. [Knu75] We look at integer sequences which are solutions to non-negative difference equations and show that if the equation is 1-Bounded then the solution can be...
The Euler-MacLaurin sum formula has appeared in the titles
of two quite recent papers whose authors were primarily interested
in certain applications. In this paper a somewhat different approach
to the myriad of formulas for summation, integration, differentiation,
etc. , is based on the simple identity which defines the set...
Four cell lines derived from embryonic tissues of four species
of salmonid fishes, and one from a hepatoma in rainbow trout have
been established in this laboratory. The species represented are
chinook, coho, and sockeye salmon; and steelhead and rainbow trout.
All of these lines have been cultivated for approximately...
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...
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...
Random number generation is important in many fields today. It is particularly important in the field of cryptography when generating nonce values, cryptographic keys, and other data required in many cryptographic applications. The proliferation of small, handheld devices that are typically connected to large networks via a wireless connection requires...
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...
Wright's Point, a 250-foot-high, sinuous, flat-topped ridge, projects eastward into Harney Basin, Harney County, Oregon. This 6-mile-long feature ranges from 200 to 600 yards wide and merges with a broad mesa at its western end. The nearest topographic highs are Dog Mountain, 2 miles southwest, and foothills of the Blue...
Bold, rocky headlands alternating with long curved beaches, sand spits, and bays -- these are the dominant landforms that make up the more than 40 miles of scenic coastline between Roads End and Tillamook Bay. With the exception of Cape Kiwanda, which is composed of sandstone, the headlands are made...