Loop Homology Of Bi-Secondary Structures, 2019 Illinois State University

#### Loop Homology Of Bi-Secondary Structures, Andrei Bura

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

The Energy-Spectrum Of Bicompatible Sequences, 2019 Illinois State University

#### The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Diffusion And Consensus On Weakly Connected Directed Graphs, 2019 Portland State University

#### Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel

*Mathematics and Statistics Faculty Publications and Presentations*

Let G be a weakly connected directed graph with asymmetric graph Laplacian L. Consensus and diffusion are dual dynamical processes defined on G by x˙=−Lx for consensus and p˙=−pL for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors {γ¯i}ki=1 of the left null-space of L and a basis of column vectors {γi}ki=1 of the right null-space of L in terms of the partition of G into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and ...

Torsors Over Simplicial Schemes, 2019 The University of Western Ontario

#### Torsors Over Simplicial Schemes, Alexander S. Rolle

*Electronic Thesis and Dissertation Repository*

Let X be a simplicial object in a small Grothendieck site C, and let G be a sheaf of groups on C. We define a notion of G-torsor over X, generalizing a definition of Gillet, and prove that there is a bijection between the set of isomorphism classes of G-torsors over X, and the set of maps in the homotopy category of simplicial presheaves on C, with respect to the local weak equivalences, from X to BG. We prove basic results about the resulting non-abelian cohomology invariant, including an exact sequence associated to a central extension of sheaves of groups ...

Classification Of Minimal Separating Sets In Low Genus Surfaces, 2019 Portland State University

#### Classification Of Minimal Separating Sets In Low Genus Surfaces, J. J. P. Veerman, William Maxwell, Victor Rielly, Austin K. Williams

*J. J. P. Veerman*

Consider a surface *S* and let *M* ⊂ *S*. If *S* \ *M* is not connected, then we say *M* separates *S*, and we refer to *M* as a separating set of *S*. If *M* separates *S*, and no proper subset of *M* separates *S*, then we say *M* is a minimal separating set of *S*. In this paper we use computational methods of combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus *g* = 2 and *g* = 3. The classification for genus 0 and 1 was done in earlier work, using methods of algebraic topology.

The T3,T4-Conjecture For Links, 2019 University of Nebraska - Lincoln

#### The T3,T4-Conjecture For Links, Katie Tucker

*Dissertations, Theses, and Student Research Papers in Mathematics*

An oriented *n*-component link is a smooth embedding of *n* oriented copies of *S*^{1} into *S*^{3}. A diagram of an oriented link is a projection of a link onto **R**^{2} such that there are no triple intersections, with notation at double intersections to indicate under and over strands and arrows on strands to indicate orientation. A local move on an oriented link is a regional change of a diagram where one tangle is replaced with another in a way that preserves orientation. We investigate the local moves *t*_{3} and *t*_{4}, which are conjectured to ...

Introduction To Classical Field Theory, 2019 Department of Physics, Utah State University

#### Introduction To Classical Field Theory, Charles G. Torre

*All Complete Monographs*

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

Mathematics And Programming Exercises For Educational Robot Navigation, 2019 Loyola University Chicago

#### Mathematics And Programming Exercises For Educational Robot Navigation, Ronald I. Greenberg

*Computer Science: Faculty Publications and Other Works*

This paper points students towards ideas they can use towards developing a convenient library for robot navigation, with examples based on Botball primitives, and points educators towards mathematics and programming exercises they can suggest to students, especially advanced high school students.

Properties Of Functionally Alexandroff Topologies And Their Lattice, 2019 Western Kentucky University

#### Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix

*Masters Theses & Specialist Projects*

This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set.

The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies ...

Localization Theory In An Infinity Topos, 2019 The University of Western Ontario

#### Localization Theory In An Infinity Topos, Marco Vergura

*Electronic Thesis and Dissertation Repository*

We develop the theory of *reflective subfibrations* on an ∞-topos E. A reflective subfibration L on E is a pullback-compatible assignment of a reflective subcategory D_X ⊆ E/X with associated localization functor L_X, for every X in E. Reflective subfibrations abound in homotopy theory, albeit often disguised, e.g., as stable factorization systems. The added properties of a reflective *subfibration* L on E compared to a mere reflective subcategory of E are crucial for most of our results. For example, we can prove that L-local maps (i.e., those maps p in D_X for some X in E) admit a ...

Dehn Functions Of Bestvina-Brady Groups, 2019 Louisiana State University and Agricultural and Mechanical College

#### Dehn Functions Of Bestvina-Brady Groups, Yu-Chan Chang

*LSU Doctoral Dissertations*

In this dissertation, we prove that if the flag complex on a finite simplicial graph is a 2-dimensional triangulated disk, then the Dehn function of the associated Bestvina--Brady group depends on the maximal dimension of the simplices in the interior of the flag complex. We also give some examples where the flag complex on a finite simplicial graph is not 2-dimensional, and we establish a lower bound for the Dehn function of the associated Bestvina--Brady group.

Euler Entertainments, 2019 Butler University

#### Euler Entertainments, Jeremiah Farrell, Karen Farrell

*Jeremiah Farrell*

No abstract provided.

The White Rabbit 12-Puzzle, 2019 Butler University

#### The White Rabbit 12-Puzzle, Chris Morgan, Jeremiah Farrell

*Jeremiah Farrell*

Martin Gardner's fondness for the characters and themes of Lewis Carroll's "Alice" is well-known and to honor Gardner we offer two word puzzles to be played on the 12-node diagram of the WHITE RABBIT.

Kate Jones – A Tribute, 2019 Butler University

#### Kate Jones – A Tribute, Karen Farrell, Jeremiah Farrell

*Jeremiah Farrell*

Kate is also an accomplished recreational mathematician and poet. To try to match in a small way her creative ability, we offer three puzzle-games in her honor: O'BEIRNE's TRI-HEX, PAPPUS and "KATe JONES". These three are specific examples of (9,3) symmetric configurations. More generally an (n,r) configuration is a collection of n "points"and n "lines" subject to the following requirements:

Rl: Any two points belong to at most one line.

R2: Each line has r points, and each point belongs to r lines.

Martin Gardner Puzzle-Games, 2019 Butler University

#### Martin Gardner Puzzle-Games, Stephen Bloom, Lacey Echols, Jeremiah Farrell, Shannon Lieb

*Jeremiah Farrell*

No abstract provided.

Paul Swinford – A Tribute, 2019 Butler University

The Jin And Jang Of Quantum Physics Truth Tables, 2019 Butler University

#### The Jin And Jang Of Quantum Physics Truth Tables, Shannon Lieb, Jeremiah Farrell

*Jeremiah Farrell*

No abstract provided.

The Tea Party, 2019 Butler University

A Gathering For Gardner Puzzle-Game, 2019 Butler University

#### A Gathering For Gardner Puzzle-Game, Jeremiah Farrell, Chris Morgan

*Jeremiah Farrell*

Each different letter of "GATHERING FOR GARDNER" is used exactly three times in the following words: DIE, FAD, FIT, FOG, GIN, HAG, HER, HOD, NOR, RAT, TEN.

Alice In Wonderland For G4g13, 2019 Butler University

#### Alice In Wonderland For G4g13, Jeremiah Farrell, Emmanuelle Malte Salvatore, Todd Wilk Estroff

*Jeremiah Farrell*

Each of the ten different letters in the title is used exactly three times to form the words in the circles. Martin Gardner's famous work *The Annotated Alice *was first published in 1960 and we honor him in this essay.