The Alexander polynomial is a well understood classical knot invariant with interesting symmetry properties and recent applications in knot Floer homology. There are many different ways to compute the Alexander polynomia ...
Just as prime numbers can be thought of as the building blocks of the natural numbers, in a similar fashion, simple groups may be considered the building blocks of finite groups. Burnside considered the following
quest ...
In this paper we examine some of the developments concerning the Gauss class number problems and build a solid understanding of the class number. First we will develop some background knowledge necessary to understand th ...
In this paper we explore the eight geometries of Thurston's geometrization conjecture. We begin by discussing group actions, covering space topology, fiber bundles, and Seifert fiber spaces. We make precise the notion ...
We consider wide bandwidth electromagnetic pulse interrogation problems for the determination of
dielectric response parameters in complex dispersive materials. We couple Maxwell's equations with an
auxiliary ODE model ...
The first published notion that the j-function was in any way related to the Monster came in 1979, when Conway and Norton noted in [CN79] that each coefficient in the q- expansion of the j-function could be written as a ...
In probability and statistics, Simpson’s paradox is an apparent paradox in which a trend is present in different groups, but is reversed when the groups are combined. Joel Cohen (1986) has shown that continuously distrib ...
The study into specific properties of the partition function has been a rich topic for number theorists for many years. Much of the current work involving the arithmetic properties of the partition function and their see ...
The paper reviews percolation and some of its important properties, particularly
on the 2-D square lattice. A bilevel lattice is introduced, with a percolation model
representing the spread of a forest fire according t ...
We consider numerical methods for finding approximate solutions
to Ordinary Differential Equations (ODEs) with parameters distributed
with some probability by the Generalized Polynomial Chaos (GPC)
approach. In partic ...
We introduce a model for the surplus of nonprofit organizations (NPO).
We assume two types of spending schemes for an NPO. Type I is a constant spending rate and Type II is a variable rate above and below a cut-off rese ...