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Now showing items 1-10 of 13

#### Projective Collineations in Perspective Art

(2012)

In this paper, we show that any projective collineation is equivalent to the
composition of four perspective collineations. In addition, we give our equivalence an
interpretation from perspective art. A projective ...

#### A Classification of Nonstandard Models of Peano Arithmetic by Goodstein’s Theorem

(2012)

In this paper I intend to outline a method for finding nonstandard models of Peano Arithmetic (PA) that satisfy Goodstein's theorem. Goodstein's Theorem is an
interesting result because, though it is expressible completely ...

#### The Hyperbolic Structure of the Complements of Rational Links with Conway Notation mn for m,n≥2

(2011)

We use a specific application of Adams algorithm to investigate the hyper-
bolic structure of rational links composed of two tangles. The investigation
begins with the gure-eight knot (the simplest hyperbolic knot), and ...

#### An Introduction to Classical Modular Forms with Kohnen’s Proof of the Product Expansion of the Delta Function

(2010)

This pro ject studies modular forms, a certain family of complex analytic
functions which have an invariance property making them very useful in
analytic number theory. The particular focus of this paper is on a speciﬁc ...

#### The Analysis of Quasi-Continuous Functions

(2007)

We give examples of quasi-continuous functions whose second iterates are discontinuous everywhere in the domain. A function is quasi-continuous if the inverse image of every open set in the codomain is quasi-open in the ...

#### A Variation of Arrow's Impossibility Theorem

(2009)

In this paper I will relax Arrow’s original assumptions (monotonicity and non-imposition) and replace them a new assumption that we will call Minimally Responsive Range. This new assumption is weaker than the original ...

#### Dynamics of Piecewise Continuous Functions

(2007)

In our paper, we explore the chaotic behavior of a class of piecewise continuous functions defined on an interval X in the real line. A function or curve is piecewise continuous if it is continuous at all but a finite ...

#### Hyperbolic 3-Manifolds: Dehn Surgery Approach to the Figure-Eight Knot Complement

(2011)

This project provides an examination of knot complements and their relationship to hyperbolic 3-manifolds. It begins with the study of knot theory, specifically knot complements in S. The knots we will be focusing on are ...

#### Reflections and Their Images

(2013)

This paper investigates the applications of linear algebra in the field of projective geometry, using Coxeter’s “Projective Geometry” as a source material. It examines the relationship between reflections in Euclidean ...

#### Closed Geodesics on the Punctured Torus

(2007)

We examine the behavior of geodesics on the punctured torus. We first consider simple geodesics and the results of [1]. In particular, it can be shown that the lifts of these geodesics into the upper half plane are ...