Extending Difference Of Votes Rules On Three Voting Models., 2017 University of Louisville

#### Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King

*Electronic Theses and Dissertations*

In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer *k*, the difference of votes rule M_{k} outputs the alternative that beats the competing alternative by more than *k* votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. In ...

Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., 2017 University of Louisville

#### Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., M. Ryan Luke

*Electronic Theses and Dissertations*

In this dissertation, we will examine residuated mappings on a function lattice and how they behave with respect to the way-below relation. In particular, which residuated $\phi$ has the property that $F$ is way-below $\phi(F)$ for $F$ in appropriate sets. We show the way-below relation describes the separation of two functions and how this corresponds to contraction mappings on probabilistic metric spaces. A new definition for contractions is considered using the way-below relation.

Dependence Structures In Lévy-Type Markov Processes, 2017 University of Tennessee, Knoxville

#### Dependence Structures In Lévy-Type Markov Processes, Eddie Brendan Tu

*Doctoral Dissertations*

In this dissertation, we examine the positive and negative dependence of infinitely divisible distributions and Lévy-type Markov processes. Examples of infinitely divisible distributions include Poissonian distributions like compound Poisson and α-stable distributions. Examples of Lévy-type Markov processes include Lévy processes and Feller processes, which include a class of jump-diffusions, certain stochastic differential equations with Lévy noise, and subordinated Markov processes. Other examples of Lévy-type Markov processes are time-inhomogeneous Feller evolution systems (FES), which include additive processes. We will provide a tour of various forms of positive dependence, which include association, positive supermodular association (PSA), positive supermodular dependence (PSD), and positive ...

Π-Operators In Clifford Analysis And Its Applications, 2017 University of Arkansas, Fayetteville

#### Π-Operators In Clifford Analysis And Its Applications, Wanqing Cheng

*Theses and Dissertations*

In this dissertation, we studies Π-operators in different spaces using Clifford algebras. This approach generalizes the Π-operator theory on the complex plane to higher dimensional spaces. It also allows us to investigate the existence of the solutions to Beltrami equations in different spaces.

Motivated by the form of the Π-operator on the complex plane, we first construct a Π-operator on a general Clifford-Hilbert module. It is shown that this operator is an L^2 isometry. Further, this can also be used for solving certain Beltrami equations when the Hilbert space is the L^2 space of a measure space. This ...

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, 2017 Utah State University

#### Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

*All Graduate Plan B and other Reports*

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log_{2}(α)^{3} + 16.5log_{2}(α)^{2} + 6log ...

Vertex Weighted Spectral Clustering, 2017 East Tennessee State University

#### Vertex Weighted Spectral Clustering, Mohammad Masum

*Electronic Theses and Dissertations*

Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to ...

Cayley Graphs Of Groups And Their Applications, 2017 Missouri State University

#### Cayley Graphs Of Groups And Their Applications, Anna Tripi

*MSU Graduate Theses*

Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the ...

Disciple, 2017 Pacific Lutheran University

#### Disciple, Jessica K. Sklar

*Journal of Humanistic Mathematics*

This is a love poem for mathematics.

Discrete And Continuous: A Fundamental Dichotomy In Mathematics, 2017 University of New South Wales

#### Discrete And Continuous: A Fundamental Dichotomy In Mathematics, James Franklin

*Journal of Humanistic Mathematics*

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.

Some Thoughts On The Epicurean Critique Of Mathematics, 2017 American University of Kuwait

#### Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou

*Journal of Humanistic Mathematics*

In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a 'mathematical atomism' was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not.

Quantitative Literacy In The Affective Domain: Computational Geology Students’ Reactions To Devlin’S The Math Instinct, 2017 University of South Florida

#### Quantitative Literacy In The Affective Domain: Computational Geology Students’ Reactions To Devlin’S The Math Instinct, Victor J. Ricchezza, H. L. Vacher

*Numeracy*

Building on suggestions from alumni from a recent interview project, students in Computational Geology at the University of South Florida were tasked with reading a popular non-fiction book on mathematics and writing about the book and their feelings about math. The book, *The Math Instinct* by Keith Devlin, was chosen because we believed it would give the students something interesting to write about and not because we had any expectations in particular about what it might reveal about or do for their math anxiety. The nature of the responses received from the students led to the performance of a post-hoc ...

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, 2017 Ithaca College

#### Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

*Numeracy*

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added ...

An Optimal Execution Problem With S-Shaped Market Impact Functions, 2017 Association of Mathematical Finance Laboratory

#### An Optimal Execution Problem With S-Shaped Market Impact Functions, Takashi Kato

*Communications on Stochastic Analysis*

No abstract provided.

Shrinkage Function And Its Applications In Matrix Approximation, 2017 University of Florida, Gainesville

#### Shrinkage Function And Its Applications In Matrix Approximation, Toby Boas, Aritra Dutta, Xin Li, Katie Mercier, Eric Niderman

*Electronic Journal of Linear Algebra*

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are demonstrated in solving several well-known problems, together with a new result in matrix approximation.

Rainbow Copies Of C4 In Edge-Colored Hypercubes, 2017 University of Illinois at Urbana-Champaign

#### Rainbow Copies Of C4 In Edge-Colored Hypercubes, József Balogh, Michelle Delcourt, Bernard Lidicky, Cory Palmer

*Bernard Lidický*

For positive integers k and d such that 4 <= k < d and k not equal 5, we determine the maximum number of rainbow colored copies of C-4 in a k-edge-coloring of the d-dimensional hypercube Q(d). Interestingly, the k-edge-colorings of Q(d) yielding the maximum number of rainbow copies of C-4 also have the property that every copy of C-4 which is not rainbow is monochromatic.

Entropy In Topological Groups, Part 2, 2017 University of Udine

#### Entropy In Topological Groups, Part 2, Dikran Dikranjan

*Summer Conference on Topology and Its Applications*

Entropy was introduced first in thermodynamics and statistical mechanics, as well as information theory. In the last sixty years entropy made its way also in topology, ergodic theory, as well as other branches of mathematics as algebra, geometry and number theory where dynamical systems appear in one way or another.

Roughly speaking, entropy is a non-negative real number or infinity assigned to a "selfmap" T of a "space" X, where the "space" X can be a topological or uniform space, a measure space, an abstract or topological group (or vector space) or just a set. The "selfmap" T can be ...

Stationary Solutions Of Stochastic Partial Differential Equations In The Space Of Tempered Distributions, 2017 Tata Institute of Fundamental Research

#### Stationary Solutions Of Stochastic Partial Differential Equations In The Space Of Tempered Distributions, Suprio Bhar

*Communications on Stochastic Analysis*

No abstract provided.

Fractal Behavior Of Multivariate Operator-Self-Similar Stable Random Fields, 2017 Heinrich-Heine-Universität Düsseldorf

#### Fractal Behavior Of Multivariate Operator-Self-Similar Stable Random Fields, Ercan Sönmez

*Communications on Stochastic Analysis*

No abstract provided.

On Infinite Stochastic And Related Matrices, 2017 Volterra Center, Roma

#### On Infinite Stochastic And Related Matrices, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

*Communications on Stochastic Analysis*

No abstract provided.

Statistical Analysis Of The Non-Ergodic Fractional Ornstein–Uhlenbeck Process Of The Second Kind, 2017 Cadi Ayyad University

#### Statistical Analysis Of The Non-Ergodic Fractional Ornstein–Uhlenbeck Process Of The Second Kind, Brahim El Onsy, Khalifa Es-Sebaiy, Ciprian A. Tudor

*Communications on Stochastic Analysis*

No abstract provided.