Mathematics Commons^™

The Complete Classification Of Five-Dimensional Dirichlet–Voronoi Polyhedra Of Translational Lattices, Mathieu Dutour Sikiric, Alexey Garber, Achill Schürmann, Clara Waldmann

School of Mathematical & Statistical Sciences Faculty Publications

This paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.

Computing Closed Forms For The Convergent Series $\Displaystyle\Sum_{N \In \Mathbb{Z}}\Frac{1}{(N^3+Bn^2+Cn+D)^K}$, Gagandeep K. Virk

Theses and Dissertations (Comprehensive)

In this thesis we discuss the various approaches that will be taken to evaluate and find a finite closed form for the sum $$\sum_{n \in \mathbb{Z}} \frac{1}{(n^3+Bn^2+Cn+D)^k}$$ where $B, C, D \in \mathbb{C}$ and $k$ is a positive integer. We begin this thesis by studying the cubic equations and discussing briefly various methods of finding their roots. Cardano's method (1545) for finding the roots of cubic polynomials is explored in detail as this method is used in later parts of the thesis to make calculations while evaluating the sums. Various tools and techniques from Fourier analysis are reviewed for these …

An Application Of The Spectral Theorem To The Laplacian On A Riemannian Manifold, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

There continues to be great interest in the study of the heat equation on Riemannian manifolds. This may be due to the remarkable more recent work of Patodi [1]. It may also be due in part to the asymptotic expansion of Minakshisundaram and Pleijel. The heat equation involves a parabolic partial differential equation that describes the distribution of heat in a given region over time. This equation has also appears in probability theory to describe random walks. The heat equation is also of importance in Riemannian geometry, topology and applied mathematics.

The Prominence Of Affect In Creativity: Expanding The Conception Of Creativity In Mathematical Problem Solving, Eric L. Mann, Scott A. Chamberlin, Amy K. Graefe

Faculty Publications

Constructs such as fluency, flexibility, originality, and elaboration have been accepted as integral components of creativity. In this chapter, the authors discuss affect (Leder GC, Pehkonen E, Törner G (eds), Beliefs: a hidden variable in mathematics education? Kluwer Academic Publishers, Dordrecht, 2002; McLeod DB, J Res Math Educ 25:637–647, 1994; McLeod DB, Adams VM, Affect and mathematical problem solving: a new perspective. Springer, New York, 1989) as it relates to the production of creative outcomes in mathematical problem solving episodes. The saliency of affect in creativity cannot be underestimated, as problem solvers require an appropriate state of mind in order …

On An Iteration Method For Solving A Class Of Nonlinear Matrix Equations, Mohamed Illafe

Open Access Theses & Dissertations

In this thesis, I looked at the most recent extension of the Banach Contraction Principle [1]. Then I show that a concept of Sorgenfrey space may be used to explain this extension as well as Ran and Reurings fixed point theorem.

Complex Gleason Measures And The Nemytsky Operator, Miguel Angel Valles

Open Access Theses & Dissertations

This Thesis is devoted to generalize previous results on Gleason measures

to complex Gleason measures, and to develop a functional calculus

for complex measures in relation to the Nemytsky operator. Furthermore

we present the interpretation of our results in the field of quantum

mechanics, some concrete examples and further extensions of several

theorems.

Combining Interval And Probabilistic Uncertainty In Engineering Applications, Andrew Martin Pownuk

Open Access Theses & Dissertations

In many practical application, we process measurement results and expert estimates. Measurements and expert estimates are never absolutely accurate, their result are slightly different from the actual (unknown) values of the corresponding quantities. It is therefore desirable to analyze how this measurement and estimation inaccuracy affects the results of data processing. There exist numerous methods for estimating the accuracy of the results of data processing under different models of measurement and estimation inaccuracies: probabilistic, interval, and fuzzy. To be useful in engineering applications, these methods should provide accurate estimate for the resulting uncertainty, should not take too much computation time, …

A Hierarchical Statistical Engineering Modeling Methodology, Teddy Steven Cotter

Engineering Management & Systems Engineering Faculty Publications

In the ASEM-IAC 2015, Cotter (2015) proposed a systemic joint deterministic-stochastic dynamic causal Bayesian statistical engineering model that addressed the knowledge gap needed to integrate deterministic mathematical engineering models within a stochastic framework. However, Cotter did not specify the modeling methodology through which statistical engineering models could be developed, diagnosed, and applied to predict systemic mission performance. This paper updates research into the development a hierarchical statistical engineering modeling methodology and sets forth the initial theoretical foundation for the methodology.

Secondary Mathematics Teachers' Disposition Toward Challenge And Its Impact On Teaching Practice, Yirah Mariana Valverde

Open Access Theses & Dissertations

This two phase, sequential exploratory study focused on mathematics teachers' disposition toward challenge and its impact in their teaching practice and students' performance. This heavily qualitative study employed a mixed methodology to answer the following guiding research question: how do teachersâ?? disposition towards challenge affect teaching practice and what is the nature of that relationship?

During the initial phase (quantitative), two teachers who were enrolled in a graduate mathematics at a University in the southwestern U.S. were selected for the study (N=5). The goal of the class was to increase the participants' mathematical knowledge for teaching. The purposive selection was …