Now showing items 1-5 of 5
The Analysis of Quasi-Continuous Functions
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
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
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 ...
Closed Geodesics on the Punctured Torus
We examine the behavior of geodesics on the punctured torus. We first consider simple geodesics and the results of . In particular, it can be shown that the lifts of these geodesics into the upper half plane are ...
The Characteristic Polynomial of Multi-Rooted, Directed Trees
We define the characteristic polynomial for single-rooted trees and begin with a theorem about this polynomial, derived from the known contrac- tion/deletion formula. We expand our scope to include multi-rooted, directed ...