Upper Bounds For Inverse Domination In Graphs,
2021
Clayton State University
Upper Bounds For Inverse Domination In Graphs, Elliot Krop, Jessica Mcdonald, Gregory J. Puleo
Theory and Applications of Graphs
In any graph G, the domination number \gamma(G) is at most the independence number \alpha(G). The Inverse Domination Conjecture says that, in any isolate-free G, there exists pair of vertex-disjoint dominating sets D, D' with |D|=\gamma(G) and |D'| \leq \alpha(G). Here we prove that this statement is true if the upper bound \alpha(G) is replaced by \frac{3}{2}\alpha(G) – 1 (and G is not a clique). We also prove that the conjecture holds whenever \gamma(G)\leq 5 or |V(G)|\leq 16.
Skolem Number Of Cycles And Grid Graphs,
2021
Southern Connecticut State University
Skolem Number Of Cycles And Grid Graphs, Braxton Carrigan, John Asplund
Theory and Applications of Graphs
A Skolem sequence can be thought of as a labelled path where two vertices with the same label are that distance apart. This concept has naturally been generalized to labellings of other graphs, but always using at most two of any integer label. Given that more than two vertices can be mutually distance d apart, we define a new generalization of a Skolem sequences on graphs that we call proper Skolem labellings. This brings rise to the question; ``what is the smallest set of consecutive positive integers we can use to proper Skolem label a graph?'' This will be known …
Ergodicity Of Burgers' System,
2021
Jagiellonian University, Lojasiewicza 6, 30-348 Kraków, Poland
Ergodicity Of Burgers' System, Szymon Peszat, Krystyna Twardowska, Jerzy Zabczyk
Journal of Stochastic Analysis
No abstract provided.
Two Of Kunita's Papers On Stochastic Flows In Early 1980s,
2021
Kyushu University, Fukuoka 819-0395, Japan
Two Of Kunita's Papers On Stochastic Flows In Early 1980s, Setsuo Taniguchi
Journal of Stochastic Analysis
No abstract provided.
Some Progress On Random Matrix Theory (Rmt),
2021
Western University
Some Progress On Random Matrix Theory (Rmt), Feiying Yang
Undergraduate Student Research Internships Conference
This is a research report about Random Matrix Theory (RMT), which studies Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE) and Gaussian Symplectic Ensemble (GSE), the purpose is to prove Wigner’s semicircle law.
Rigid Connections On The Projective Line With Elliptic Toral Singularities,
2021
Louisiana State University and Agricultural and Mechanical College
Rigid Connections On The Projective Line With Elliptic Toral Singularities, Alisina Azhang
LSU Doctoral Dissertations
We generalize two studies of rigid $G$-connections on $\pp$ which have an irregular singularity at origin and a regular singularity at infinity with unipotent monodromy: one is the work of Kamgarpour-Sage which classifies rigid homogeneous Coxeter $G$-connections with slope $\frac{r}{h}$, where $h$ is the Coxeter number of $G$, and the other is the work of Chen, which proves the existence of rigid homogeneous elliptic regular $G$-connections with slope $\frac{1}{m}$, where $m$ is an elliptic number for $G$. In our work, similar to Chen, we look for rigid homogeneous elliptic regular $G$-connections, but we allow the slope to have a numerator …
Conjunctive Join-Semilattices,
2021
Louisiana State University at Baton Rouge
Conjunctive Join-Semilattices, Charles N. Delzell, Oghenetega Ighedo, James J. Madden
Mathematics, Physics, and Computer Science Faculty Articles and Research
A join-semilattice L with top is said to be conjunctive if every principal ideal is an intersection of maximal ideals. (This is equivalent to a first-order condition in the language of semilattices.) In this paper, we explore the consequences of the conjunctivity hypothesis for L, and we define and study a related property, called “ideal conjunctivity,” which is applicable to join-semilattices without top. Results include the following: (a) Every conjunctive join-semilattice is isomorphic to a join-closed subbase for a compact T1-topology on max L, the set of maximal ideals of L, and under weak hypotheses …
Domino Circles,
2021
Bard College
Domino Circles, Lauren L. Rose, A. Gwinn Royal, Amanda Serenevy, Anna Varvak
Journal of Math Circles
Creating a circle with domino pieces has a connection with complete graphs in Graph Theory. We present a hands-on activity for all ages, using dominoes to explore problem solving, pattern recognition, parity, graph theory, and combinatorics. The activities are suitable for elementary school students, the graph theory interpretations are suitable for middle and high school students, and the underlying mathematical structures will be of interest to college students and beyond.
Error Estimates For Discrete Approximations Of Game Options With Multivariate Diffusion Asset Prices,
2021
The Hebrew University, Jerusalem 91904, Israel
Error Estimates For Discrete Approximations Of Game Options With Multivariate Diffusion Asset Prices, Yuri Kifer
Journal of Stochastic Analysis
No abstract provided.
An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent,
2021
Nova Southeastern University
An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent, Killian J. Hitsman, Vehbi E. Paksoy
Mako: NSU Undergraduate Student Journal
No abstract provided.
Searching For New Relations Among The Eilenberg-Zilber Maps,
2021
Western University
Searching For New Relations Among The Eilenberg-Zilber Maps, Owen T. Abma
Undergraduate Student Research Internships Conference
The goal of this project was to write a computer program that would aid in the search for relations among the Eilenberg-Zilber maps, which relate to simplicial objects in algebraic topology. This presentation outlines the process of writing this program, the challenges faced along the way, and the final results of the project.
Contemporary Mathematical Approaches To Computability Theory,
2021
Western University
Contemporary Mathematical Approaches To Computability Theory, Luis Guilherme Mazzali De Almeida
Undergraduate Student Research Internships Conference
In this paper, I present an introduction to computability theory and adopt contemporary mathematical definitions of computable numbers and computable functions to prove important theorems in computability theory. I start by exploring the history of computability theory, as well as Turing Machines, undecidability, partial recursive functions, computable numbers, and computable real functions. I then prove important theorems in computability theory, such that the computable numbers form a field and that the computable real functions are continuous.
Profiling Mathematical Procedural And Problem-Solving Skills Of Undergraduate Students Following A New Mathematics Curriculum,
2021
Technological University Dublin
Profiling Mathematical Procedural And Problem-Solving Skills Of Undergraduate Students Following A New Mathematics Curriculum, Fiona Faulkner, Mark Prendergast, Cormac Breen, Michael Carr
Articles
In 2010 a mathematics curriculum was introduced in Irish second level schools entitled ‘Project Maths’ (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. https://www.education.ie/en/Publications/Policy-Reports/Report-of-the-Project-Maths-Implementation-Group.pdf]. This paper aims to examine the performance of 1st year undergraduate students’ procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students’ skills in each area and findings demonstrated that students perform statistically significantly …
Categorical Aspects Of Graphs,
2021
Western University
Categorical Aspects Of Graphs, Jacob D. Ender
Undergraduate Student Research Internships Conference
In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.
Spectral Graph Theory And Research,
2021
Western University
Spectral Graph Theory And Research, Nathan H. Kershaw, Lewis Glabush
Undergraduate Student Research Internships Conference
Our topic of study was Spectral Graph Theory. We studied the algebraic methods used to study the properties of graphs (networks) and became familiar with the applications of network analysis. We spent a significant amount of time studying the way virus’s spread on networks, with particular applications to Covid-19. We also investigated the relationship between graph spectra and structural properties.
College Algebra Through Problem Solving (2021 Edition),
2021
CUNY Queensborough Community College
College Algebra Through Problem Solving (2021 Edition), Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Stelmach
Open Educational Resources
This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.
Incomplete? Or Indefinite? Intuitionism On Gödel’S First Incompleteness Theorem,
2021
Yale University
Incomplete? Or Indefinite? Intuitionism On Gödel’S First Incompleteness Theorem, Quinn Crawford
The Yale Undergraduate Research Journal
This paper analyzes two natural-looking arguments that seek to leverage Gödel’s first incompleteness theorem for and against intuitionism, concluding in both cases that the argument is unsound because it equivocates on the meaning of “proof,” which differs between formalism and intuitionism. I argue that this difference explains why “proof” has definite extension for the formalist but not for the intuitionist. Sections 1-3 summarize various philosophies of mathematics and Gödel’s result. Section 4 argues that, because the Gödel sentence of a formal system is provable to the intuitionist, they are neither aided nor attacked by Gödel’s first incompleteness theorem. Section 5 …
Studies Of Subvarieties Of Classical Complex Algebraic Geometry,
2021
Western University
Studies Of Subvarieties Of Classical Complex Algebraic Geometry, Wenzhe Wang
Undergraduate Student Research Internships Conference
My project in this USRI program is to study subvariety of classical complex algebraic geometry. I observed the orbit of elements in the unit sphere in space ℂ² ⊗ ℂ², the structure of unit sphere of ℂ² ⊗ ℂ². After this, I tried to generalize the result to ℂ^n ⊗ ℂ^n.
Bernstein-Sato Polynomials In Commutative
Algebra,
2021
Universitat Politècnica de Catalunya
Bernstein-Sato Polynomials In Commutative Algebra, Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez-Betancourt
Department of Mathematics: Faculty Publications
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.
Euler's De Serie Lambertina, Translated From Latin To English With Supplementary Notes,
2021
Individual
Euler's De Serie Lambertina, Translated From Latin To English With Supplementary Notes, Sam Gallagher
Euleriana
Originally published in 1779, Euler's De Serie Lambertina provides one of the early examples of the Lambert W function, a special function used in the solution to certain transcendental equations. Following the work of Johann Heinrich Lambert in 1759, who discussed a series solution to the general polynomial in series, and then particularly the solution of the general trinomial, Euler describes a symmetric form of the trinomial and its series solution. Euler investigates the series' special cases and general properties, and its use in solving certain transcendental equations. He provides several proofs of the validity of the series expansion to …
