(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.
Almost Paracomplex Structures On 4-Manifolds,
2022
Department of Computing and Mathematics, South East Technological University, Waterford, Co. Waterford, Ireland
Almost Paracomplex Structures On 4-Manifolds, Nikos Georgiou, Brendan Guilfoyle
Department of Mathematics Publications
Reflection in a line in Euclidean 3-space defines an almost paracomplex structure on the space of all oriented lines, isometric with respect to the canonical neutral Kaehler metric. Beyond Euclidean 3-space, the space of oriented geodesics of any real 3-dimensional space form admits both isometric and anti-isometric paracomplex structures. This paper considers the existence or otherwise of isometric and anti-isometric almost paracomplex structures j on a pseudo-Riemannian 4-manifold (M, g), such that j is parallel with respect to the Levi-Civita connection of g. It is shown that if an isometric or anti-isometric almost paracomplex structure on a conformally flat manifold …
Thickened Surfaces, Checkerboard Surfaces, And Quantum Link Invariants,
2022
CUNY Graduate Center
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 …
(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.
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
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].
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 …
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 …
De Rham Cohomology, Homotopy Invariance And The Mayer-Vietoris Sequence,
2022
California State University - San Bernardino
De Rham Cohomology, Homotopy Invariance And The Mayer-Vietoris Sequence, Stacey Elizabeth Cox
Electronic Theses, Projects, and Dissertations
This thesis will discuss the de Rham cohomology, homotopy invariance and the Mayer-Vietoris sequence. First the necessary information for this thesis is discussed such as differential p-forms, the exterior derivative as well as pull back of a map. The de Rham cohomology is defined explicitly, some properties of the de Rham cohomology will also be discussed. It will be shown that the de Rham cohomology is in fact a homotopy invariant as well as some examples using homotopy invariance are provided. Finally the Mayer-Vietoris sequence will be established, an example of using the Mayer-Vietoris sequence to compute the de …
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 …
John Horton Conway: The Man And His Knot Theory,
2022
East Tennessee State University
John Horton Conway: The Man And His Knot Theory, Dillon Ketron
Electronic Theses and Dissertations
John Horton Conway was a British mathematician in the twentieth century. He made notable achievements in fields such as algebra, number theory, and knot theory. He was a renowned professor at Cambridge University and later Princeton. His contributions to algebra include his discovery of the Conway group, a group in twenty-four dimensions, and the Conway Constellation. He contributed to number theory with his development of the surreal numbers. His Game of Life earned him long-lasting fame. He contributed to knot theory with his developments of the Conway polynomial, Conway sphere, and Conway notation.
Slope Conjecture And Normal Surface Theory,
2022
University of South Alabama
Slope Conjecture And Normal Surface Theory, Helene Swanepoel
Graduate Theses and Dissertations (2019 - present)
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 …
How To Guard An Art Gallery: A Simple Mathematical Problem,
2022
St. John Fisher University
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
The Review: A Journal of Undergraduate Student Research
The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …
Finite N-Quandles Of Twisted Double Handcuff And Complete Graph,
2022
Loyola Marymount University and Loyola Law School
Finite N-Quandles Of Twisted Double Handcuff And Complete Graph, Veronica Backer-Peral
Honors Thesis
The Double Handcuff and K4 graphs can be generalized to a single family of spatial graphs by adding a variable number of twists between two edges. We can identify spatial graphs by calculating a quotient of the fundamental quandle, known as an N-quandle, which is a spatial graph invariant. In this paper, we prove that the N-quandle associated with this family of spatial graphs is finite when all but two edges are given a label of 2, and the remaining two edges are assigned labels from the natural numbers. To prove that the N-quandle is finite, we produce Cayley graphs …
A New Perspective On A Polynomial Time Knot Polynomial,
2022
Louisiana State University and Agricultural and Mechanical College
A New Perspective On A Polynomial Time Knot Polynomial, Robert John Quarles
LSU Doctoral Dissertations
In this work we consider the Z1(K) polynomial time knot polynomial defined and
described by Dror Bar-Natan and Roland van der Veen in their 2018 paper ”A polynomial time knot polynomial”. We first look at some of the basic properties of Z1(K), and develop an invariant of diagrams Ψm(D) related to this polynomial. We use this invariant as a model to prove how Z1(K) acts under the connected sum operation. We then discuss the effect of mirroring the knot on Z1(K), and described a geometric interpretation of some of the building blocks of the invariant. We then use these to …
Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images,
2022
University of New Mexico
Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano
Electrical and Computer Engineering ETDs
Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …
Quandles That Are Knot Quandles,
2022
Northern Michigan University
Quandles That Are Knot Quandles, Jason Haskell
All NMU Master's Theses
There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles …
Kissing The Archimedeans,
2022
Northern Michigan University
Kissing The Archimedeans, Anthony Webb
All NMU Master's Theses
In this paper the three dimensional kissing problem will be related to the Platonic and Archimedean solids. On each polyhedra presented their vertices will have spheres expanding such that the center of each of these outer spheres are the vertices of the polyhedron, and these outer spheres will continue to expand until they become tangent to each other. The ratio will be found between the radius of each outer sphere, and the radius of an inner sphere such that each inner sphere's center is the circumcenter of the polyhedron, and the inner sphere is tangent to each outer sphere. Every …
Exploration Of Piccirillo's Trick On Low Crossing Number Knots,
2022
University of Nebraska - Lincoln
Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams
Honors Program: Senior Projects (Public)
Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …
Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall,
2022
College of the Holy Cross
Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall, Thomas E. Cecil
Mathematics and Computer Science Department Faculty Scholarship
This is an unofficial translation of the original dissertation which was written in German. A few minor typographical errors have been corrected by the translator. All references should be made to the original dissertation. The classification of Dupin hypersurfaces in E4 contained in this dissertation is also contained in the journal article by Ulrich Pinkall, Dupin’sche Hyperflächen in E4, Manuscr. Math. 51 (1985), 89–119.
