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ThesisVo, Anh DuyCircular Nim is a twoplayer impartial combinatorial game consisting of n stacks of tokens placed in a circle. A move consists of choosing k consecutive stacks and taking at least one token from one or more stacks. The last player able to make a move . . .

ThesisCollister, DanielConsider D to be a finite set of positive integers. This thesis focuses on two parameters of D. The first parameter treats the elements of D as being the speeds of runners. This parameter, denoted kappa(D), is the value of the maximum possible distanc . . .

ThesisVu, MinhLet G be a graph and let dG(u; v) be the distance between two vertices u and v in G. Let j and k be positive real numbers. An L(j; k)labeling of G is a function, f : V (G) > R+ U {0}, such that f(u)f(v) > j if d(u; v) = 1; and f(u)f(v) > k if . . .

ThesisRamirez, JeannetteLet G be a simple connected graph. For any two vertices u and v, let d(u,v) denote the distance between u and v in G. A radio klabeling of G for a fixed positive integer k, is a function f which assigns to each vertex a nonnegative integer label such . . .

ThesisTran, DanielPricing stock market data is difficult because it is inherently noisy and prone to unexpected events. However, stock market data generally exhibits trends in the medium and long term. A typical successful stock index exhibits an initiation phase, rapi . . .

ThesisYang, James SzufuIn set theory, the Axiom of Choice (AC) was formulated in 1904 by Ernst Zermelo. It is an addition to the older ZermeloFraenkel (ZF) set theory. We call it ZermeloFraenkel set theory with the Axiom of Choice and abbreviate it as ZFC. This paper star . . .

ThesisVoskanian, Edward K.We calculate the Kazhdan constant for the Paley graph of order p, where p is an odd prime. We provide a formula for the best possible lower bound in the limit. We obtain explicit formulas that are valid for particular classes of primes.

ThesisHu, ZiyuA strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they have adjacent endpoints. The strong chromatic index of a graph G, denoted by χs′(G), is the minimu . . .

ThesisHayes, TravisIn this thesis, we will explore the Kazhdan constant of finite cyclic groups and generating sets associated with Cayley graphs. It has been previously shown that a specific pair of groups and generating sets with isomorphic Cayley graphs yield the sam . . .

ThesisALOTAIBI, IBRAHIM JABERIf you have a polynomial f with real coefficients and want to know about the number and values of its real roots, there is no better tool than a Sturm sequence. This is a sequence of polynomials f0; f1; f2; : : : ; fn = f with the property that the va . . .

ThesisSzijjarto, Leslie J.Mathematical modeling is an important tool in epidemiology. It provides a way to understand the primary forces in disease dynamics, and to conduct theoretical experiments that are not possible in practice. In this paper, we study mathematical models t . . .

ThesisTellez, IsraelMathematical modeling is an essential tool in epidemiology. Models are constructed to describe the spread of an infectious disease in a population. This thesis focuses on deterministic compartmental models in which population is divided into distinct . . .

ThesisSmith, Preston ThomasIn this thesis, we will recursively construct a sequence of groups using semidirect products. Using it, we will then construct a sequence of symmetric multisubsets to generate a sequence of 3regular Cayley graphs with logarithmic diameter. We will t . . .

ThesisChyau, Sam ZiMingA multidistance labeling (or radio labeling) of a graph G is a function f that assigns each vertex a nonnegative integer label such that the separation of labels between distinct vertices u,v is at least diam(G) + 1−d(u,v), where the distance d(u,v) . . .

ThesisReyes, Marcos AntonioIn this thesis, we investigate the Kazhdan constant of groups and generating sets associated with Cayley graphs. In particular, we look at groups and generating sets that yield isomorphic Cayley graphs and compute their Kazhdan constants–in other word . . .

ThesisRobinson, GrantLet $D$ be a fixed set of prime numbers. In this thesis we investigate the chromatic number of graphs with vertex set of the integers and edges between any pair of vertices whose distance is in $D$. Such a graph is called a prime distance graph, and t . . .

ThesisGrassi, Jayson FrankBy mapping the rows/columns of a matrix, M, to a set of polynomials, and then calculating the Wronskian of that set we can deterimine whether or not the rows/columns of M are linearly independent. However, if the rows/columns of M are linearly depende . . .

ThesisAl Fares, Ahmed SaeedThis thesis concerns the existence of 2groups with certain derived length, with a specified order of the quotient subgroups. Let a, b, c be positive integers. We will show that there exists a finite 2group G of derived length 3 such that G/G  = 2 . . .

ThesisSzijjarto, Leslie J.Mathematical modeling is an important tool in epidemiology. It provides a way to understand the primary forces in disease dynamics, and to conduct theoretical experiments that are not possible in practice. In this paper, we study mathematical models t . . .

ThesisGranados Del Cid, Jorge DimasThis thesis provides an overview of various partial dierential equations, in cluding their applications, classications, and methods of solving them. We show the reduction (change of variables process) of an elliptic equation to the Laplace equa tion . . .

ThesisParsanian, ArtinA new parameterization of all integer triangles through a simple diagram enables the generation of all the Primitive Pythagorean Triples (PPTs), the alignment of the major approaches regarding the treatment and production of the set of such triples, a . . .

ThesisLower bounds on the orders of the terms of the derived series of finite 2groups of derived length 3Golvin, Ezekiel DanielLet G be a finite group with derived length three, such that the number of elements in G is a power of 2, and G, G', and G''' form the derived (commutator subgroup) series of G, where G''' is the trivial group. Let the order of G/G' be 2^a, and the or . . .

ThesisChen, Ronald Y.This thesis discusses the reducibility of homogeneous trivariate polynomials of degree 2 and 3. In the degree 2 case, we give necessary and sufficient conditions for the reducibility of such a polynomial. When a factorization exists, we show how to fi . . .

ThesisReynoso, Eduardo YovanyThis thesis investigates the reducibility of trivariate homogeneous symmetric polynomials. For polynomials of degrees 2, 3, 4 and 5 we have complete results. Specifically, we classify all the possible factorizations of such polynomials and give condit . . .

ThesisAvetisyan, Misha MichaelThe purpose of this paper is to describe some applications of the theory of Hilbert spaces to integral equations. The main goal is to illustrate possible applications of techniques developed in theory and to include the standard classification of the . . .

ThesisCao Ying, AlexandraThe Dutch artist M.C Escher became known to the mathematical community in 1954, at the time the British mathematician Sir Roger Penrose came up with the idea of the impossible triangle after seeing Escher’s lithograph Relativity. From 1937 to 1941, M. . . .