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Full-Text Articles in Physical Sciences and Mathematics
The Characterization Of Graphs With Small Bicycle Spectrum, Bette Catherine Putnam
The Characterization Of Graphs With Small Bicycle Spectrum, Bette Catherine Putnam
Electronic Theses and Dissertations
Matroids designs are defined to be matroids in which the hyperplanes all have the same size. The dual of a matroid design is a matroid with all circuits of the same size, called a dual matroid design. The connected bicircular dual matroid designs have been characterized previously. In addition, these results have been extended to connected bicircular matroids with circuits of two sizes in the case that the associated graph is a subdivision of a 3-connected graph. In this dissertation, we will use a graph theoretic approach to discuss the characterizations of bicircular matroids with circuits of two and three …
Rank-Based Two Sample Tests Under A General Alternative, Jamye Curry
Rank-Based Two Sample Tests Under A General Alternative, Jamye Curry
Electronic Theses and Dissertations
The problem of testing whether two samples come from the same or different population is a classical one in statistics. In this dissertation, I first study rank based formulation of univariate two-sample distribution-free tests. One form of the test statistic is the average of between-group distances of ranks. The other form of the test statistic is the difference between the average of between-group distances of ranks and the average of within-group distances of ranks. Although they are different in formulation, they are closely related to the two-sample Cramer-von Mises criterion. The first one is a linear transformation of Cramer-von Mises …
(Visible) Tilings Of Squares And Hypercubes, John Randall Burt
(Visible) Tilings Of Squares And Hypercubes, John Randall Burt
Electronic Theses and Dissertations
More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit square.Here we consider various classes of tilings , this is, packings where there is no empty space inside the unit square. Several types of questions will be explored here. Various construction techniques are introduced, especially methods of generating tilings from tilings with fewer tiles. For some small values of n, I determine all tilings of the unit square with n tiles. I have found a best possible upper bound for a visible tiling, that is a tiling which every tile shares a …
Ramsey Theory Using Matroid Minors, Dixie Smith Horne
Ramsey Theory Using Matroid Minors, Dixie Smith Horne
Electronic Theses and Dissertations
This thesis considers a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified minors. However, there are results from the literature for which the number N exists for certain collections of minors. We first encode totally unimodular matrix representations of certain matroids. We use the computer program MACEK to investigate this question for certain classes of specified minors.
Moments Of Products Of L-Functions, Caroline Laroche Turnage-Butterbaugh
Moments Of Products Of L-Functions, Caroline Laroche Turnage-Butterbaugh
Electronic Theses and Dissertations
We first consider questions on the distribution of the primes. Using the recent advancement towards the Prime k-tuple Conjecture by Maynard and Tao, we show how to produce infinitely many strings of consecutive primes satisfying specified congruence conditions. We answer an old question of Erdös and Turán by producing strings of consecutive primes whose successive gaps form an increasing (respectively decreasing) sequence. We also show that such strings exist whose successive gaps follow a certain divisibility pattern. Finally, for any coprime integers a and D ≥ 1, we refine a theorem of D. Shiu and find strings of consecutive primes …