Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, 2017 Colorado State University-Pueblo

#### Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, Janet Heine Barnett

*Calculus*

No abstract provided.

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 ...

Constructing A Square An Ancient Indian Way Activity, 2017 Pittsburg State University

#### Constructing A Square An Ancient Indian Way Activity, Cynthia J. Huffman Ph.D.

*Open Educational Resources - Math*

In this activity students use string to model one of the ways that was used in ancient India for constructing a square. The construction was used in building a temporary fire altar. The activity is based on a translation by Sen and Bag of the Baudhāyana-śulba-sūtra.

Constructing A Square Indian Fire Altar Activity, 2017 Pittsburg State University

#### Constructing A Square Indian Fire Altar Activity, Cynthia J. Huffman Ph.D.

*Open Educational Resources - Math*

In this activity, we will model constructing a square fire altar with a method similar to one used by people in ancient India. The fire altars, which were made of bricks, had various shapes. Instructions for building the altars were in Vedic texts called *Śulba-sūtras*. We will follow instructions for constructing a square *gārhapatya *fire altar* *from the *Baudhāyana-śulba-sūtra*, which was written during the Middle Vedic period, about 800-500 BC.

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 ...

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 ...

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.

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 ...

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 ...

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 Lidický, Cory Palmer

*Bernard Lidický*

For positive integers k and d such that 4≤k4in a k-edge-coloring of the d-dimensional hypercube Qd. Interestingly, the k-edge-colorings of Qd yielding the maximum number of rainbow copies of C4 also have the property that every copy of C4 which is not rainbow is monochromatic.

Mixed Strategies For Deterministic Differential Games, 2017 Brown University

#### Mixed Strategies For Deterministic Differential Games, Wendell H. Fleming, Daniel Hernandez-Hernandez

*Communications on Stochastic Analysis*

No abstract provided.

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.

Spatial Ergodicity Of The Harris Flows, 2017 Institute of Mathematics NAS of Ukraine

#### Spatial Ergodicity Of The Harris Flows, E.V. Glinyanaya

*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.

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 ...