Left-Separation Of Ω1, 2022 University of Northern Iowa
Left-Separation Of Ω1, Lukas Stuelke, Adrienne Stanley Ph.D.
Summer Undergraduate Research Program (SURP) Symposium
A topological space is left-separated if it can be well-ordered so that every initial segment is closed. Here, we show that all countable ordinal numbers are left-separated. We then prove that a similar method could not work for ω1 , using the pressing-down lemma1 . We finish by showing that a left-separating well-ordering on ω1 necessarily leads to a contradiction.
Rendezvous Numbers Of Compact And Connected Spaces, 2022 University of Northern Iowa
Rendezvous Numbers Of Compact And Connected Spaces, Kevin Demler, Bill Wood Ph.D.
Summer Undergraduate Research Program (SURP) Symposium
The concept of a rendezvous number was originally developed by O. Gross in 1964, and was expanded upon greatly by J. Cleary, S. Morris, and D. Yost in 1986. This number exists for every metric space, yet very little is known about it, and it’s exact value for most spaces is not known. Furthermore, it’s exact value is difficult to calculate, and in most cases we can only find bounds for the value. We focused on their arguments using convexity and applied it to shapes in different metrics and graphs. Using sets of points that stood out (vertices, midpoints) as …
Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, 2022 East Tennessee State University
Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill
STEM Guitar Project’s BBT Acoustic Kit
This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.
The CADD data set for each of the three (3) top bracing designs includes …
Finding Approximate Pythagorean Triples (And Applications To Lego Robot Building), 2022 Loyola University Chicago
Finding Approximate Pythagorean Triples (And Applications To Lego Robot Building), Ronald I. Greenberg, Matthew Fahrenbacher, George K. Thiruvathukal
Computer Science: Faculty Publications and Other Works
This assignment combines programming and data analysis to determine good combinations of side lengths that approximately satisfy the Pythagorean Theorem for right triangles. This can be a standalone exercise using a wide variety of programming languages, but the results are useful for determining good ways to assemble LEGO pieces in robot construction, so the exercise can serve to integrate three different units of the Exploring Computer Science high school curriculum: "Programming", "Computing and Data Analysis", and "Robotics". Sample assignment handouts are provided for both Scratch and Java programmers. Ideas for several variants of the assignment are also provided.
On A Relation Between Ado And Links-Gould Invariants, 2022 Louisiana State University and Agricultural and Mechanical College
On A Relation Between Ado And Links-Gould Invariants, Nurdin Takenov
LSU Doctoral Dissertations
In this thesis we consider two knot invariants: Akutsu-Deguchi-Ohtsuki(ADO) invariant and Links-Gould invariant. They both are based on Reshetikhin-Turaev construction and as such share a lot of similarities. Moreover, they are both related to the Alexander polynomial and may be considered generalizations of it. By experimentation we found that for many knots, the third order ADO invariant is a specialization of the Links-Gould invariant. The main result of the thesis is a proof of this relation for a large class of knots, specifically closures of braids with five strands.
General Covariance With Stacks And The Batalin-Vilkovisky Formalism, 2022 University of Massachusetts Amherst
General Covariance With Stacks And The Batalin-Vilkovisky Formalism, Filip Dul
Doctoral Dissertations
In this thesis we develop a formulation of general covariance, an essential property for many field theories on curved spacetimes, using the language of stacks and the Batalin-Vilkovisky formalism. We survey the theory of stacks, both from a global and formal perspective, and consider the key example in our work: the moduli stack of metrics modulo diffeomorphism. This is then coupled to the Batalin-Vilkovisky formalism–a formulation of field theory motivated by developments in derived geometry–to describe the associated equivariant observables of a theory and to recover and generalize results regarding current conservation.
The Local Cohomology Spectral Sequence For Topological Modular Forms, 2022 Wayne State University
The Local Cohomology Spectral Sequence For Topological Modular Forms, Robert Bruner, John Greenlees, John Rognes
Mathematics Faculty Research Publications
We discuss proofs of local cohomology theorems for topological modular forms, based on Mahowald–Rezk duality and on Gorenstein duality, and then make the associated local cohomology spectral sequences explicit, including their differential patterns and hidden extensions.
Unomaha Problem Of The Week (2021-2022 Edition), 2022 University of Nebraska at Omaha
Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs
UNO Student Research and Creative Activity Fair
The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.
Now there are three difficulty tiers to POW problems, roughly corresponding to …
Introduction To Classical Field Theory, 2022 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.
Van Kampen Diagrams And Small Cancellation Theory, 2022 California Polytechnic State University, San Luis Obispo
Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey
Master's Theses
(R1956) Neutrosophic Soft E-Compact Spaces And Application Using Entropy Measure, 2022 Government Polytechnic College for Women, Annamalai University
(R1956) Neutrosophic Soft E-Compact Spaces And Application Using Entropy Measure, P. Revathi, K. Chitirakala, A. Vadivel
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the concept of neutrosophic soft e-compactness is presented on neutrosophic soft topological spaces using the definition of e-open cover and its types. In addition, neutrosophic soft e-compactness and neutrosophic soft e-separation axioms are associated. Also, the concept of neutrosophic soft locally e-compactness is introduced in neutrosophic soft topological spaces and some of its properties are discussed. Added to that, an application in decision making problem is given using entropy.
(R1961) On Fuzzy Upper And Lower Theta Star Semicontinuous Multifunctions, 2022 J. J. College of Arts and Science (Autonomous)
(R1961) On Fuzzy Upper And Lower Theta Star Semicontinuous Multifunctions, A. Mughil, A. Vadivel, O. Uma Maheswari
Applications and Applied Mathematics: An International Journal (AAM)
This work introduces the concepts of fuzzy upper and lower theta star (respectively theta)- semicontinuous multifunction on fuzzy topological spaces in the Sostak sense. In L-fuzzy topological spaces, the mutual relationships of these fuzzy upper (resp. fuzzy lower) theta star (resp. theta)-semicontinuous multifunctions are established, as well as several characterizations and properties. Later, researchers looked at the composition and union of these multifunctions.
Thickened Surfaces, Checkerboard Surfaces, And Quantum Link Invariants, 2022 The Graduate Center, City University of New York
Thickened Surfaces, Checkerboard Surfaces, And Quantum Link Invariants, Joseph W. Boninger
Dissertations, Theses, and Capstone Projects
This dissertation has two parts, each motivated by an open problem related to the Jones polynomial. The first part addresses the Volume Conjecture of Kashaev, Murakami, and Murakami. We define a polynomial invariant, JTn, of links in the thickened torus, which we call the nth toroidal colored Jones polynomial, and we show JTn satisfies many properties of the original colored Jones polynomial. Most significantly, JTn exhibits volume conjecture behavior. We prove a volume conjecture for the 2-by-2 square weave, and provide computational evidence for other links. We also give two equivalent constructions …
(R1898) A Study On Inextensible Flows Of Polynomial Curves With Flc Frame, 2022 Ordu University
(R1898) A Study On Inextensible Flows Of Polynomial Curves With Flc Frame, Süleyman Şenyurt, Kemal Eren, Kebire Hilal Ayvacı
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we investigate the inextensible flows of polynomial space curves in R3. We calculate that the necessary and sufficient conditions for an inextensible curve flow are represented as a partial differential equation involving the curvatures. Also, we expressed the time evolution of the Frenet like curve (Flc) frame. Finally, an example of the evolution of the polynomial curve with Flc frame is given and graphed.
The Adams Spectral Sequence For The Image-Of-J Spectrum, 2022 Wayne State University
The Adams Spectral Sequence For The Image-Of-J Spectrum, Robert R. Bruner, John Rognes
Mathematics Faculty Research Publications
We show that if we factor the long exact sequence in cohomology of a cofiber sequence of spectra into short exact sequences, then the d_2-differential in the Adams spectral sequence of any one term is related in a precise way to Yoneda composition with the 2-extension given by the complementary terms in the long exact sequence. We use this to give a complete analysis of the Adams spectral sequence for the connective image-of-J spectrum, finishing a calculation that was begun by D. Davis [Bol. Soc. Mat. Mexicana (2) 20 (1975), pp. 6–11].
Slope Conjecture And Normal Surface Theory, 2022 University of South Alabama
Slope Conjecture And Normal Surface Theory, Helene Swanepoel
<strong> Theses and Dissertations </strong>
In this thesis we explore the relationship between quantum link invariants and the geometric and topological properties for a family of pretzel knots P(−2r, 2r + 1, 2r + s), r ≥ 1 and s ≥ 3, as predicted by the Slope conjecture. This conjecture asserts a connection between the degree of the colored Jones polynomial and boundary slopes of these knots. We introduce fundamentals of knot theory and prove that the minimum degree of the Jones polynomial for the family of pretzel knots P(−2r, 2r + 1, 2r + s), r ≥ 1 and s ≥ 3, is −6r …
Sangaku In Multiple Geometries: Examining Japanese Temple Geometry Beyond Euclid, 2022 Murray State University
Sangaku In Multiple Geometries: Examining Japanese Temple Geometry Beyond Euclid, Nathan Hartmann
Honors College Theses
When the country of Japan was closed from the rest of the world from 1603 until
1867 during the Edo period, the field of mathematics developed in a different way
from how it developed in the rest of the world. One way we see this development
is through the sangaku, the thousands of geometric problems hung in various Shinto and Buddhist temples throughout the country. Written on wooden tablets by people from numerous walks of life, all these problems hold true within Euclidean geometry. During the 1800s, while Japan was still closed, non-Euclidean geometries began to develop across the …
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, 2022 University of Arkansas, Fayetteville
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, Minh Lam Nguyen
Graduate Theses and Dissertations
The Rarita-Schwinger operator Q was initially proposed in the 1941 paper by Rarita and Schwinger to study wave functions of particles of spin 3/2, and there is a vast amount of physics literature on its properties. Roughly speaking, 3/2−spinors are spinor-valued 1-forms that also happen to be in the kernel of the Clifford multiplication. Let X be a simply connected Riemannian spin 4−manifold. Associated to a fixed spin structure on X, we define a Seiberg-Witten-like system of non-linear PDEs using Q and the Hodge-Dirac operator d∗ + d+ after suitable gauge-fixing. The moduli space of solutions M contains (3/2-spinors, purely …
The Examination Of The Arithmetic Surface (3, 5) Over Q, 2022 California State University - San Bernardino
The Examination Of The Arithmetic Surface (3, 5) Over Q, Rachel J. Arguelles
Electronic Theses, Projects, and Dissertations
This thesis is centered around the construction and analysis of the principal arithmetic surface (3, 5) over Q. By adjoining the two symbols i,j, where i2 = 3, j2 = 5, such that ij = -ji, I can produce a quaternion algebra over Q. I use this quaternion algebra to find a discrete subgroup of SL2(R), which I identify with isometries of the hyperbolic plane. From this quaternion algebra, I produce a large list of matrices and apply them via Mobius transformations to the point (0, 2), which is the center of my Dirichlet domain. This …
A Coarse Approach To The Freudenthal Compactification And Ends Of Groups, 2022 University of Tennessee, Knoxville
A Coarse Approach To The Freudenthal Compactification And Ends Of Groups, Hussain S. Rashed
Doctoral Dissertations
The main purpose of this work is to present a coarse counterpart to the Freudenthal compactification and its corona (the space of ends) that generalizes the Freudenthal compactification of a Freudenthal topological space X (connected, locally connected, locally compact and σ-compact) and its corona; then applying it to groups as coarse space to obtain generalizations to many well-known results in the theory of ends of groups. To this end, we present two constructions:
1. The Coarse Freudenthal compactification of a proper metric space which is a coarse compactification that coincides with the Freudenthal compactification when the metric space is geodesic. …