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2021

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Articles 241 - 270 of 1314

Full-Text Articles in Mathematics

Upper Bounds For Inverse Domination In Graphs, Elliot Krop, Jessica Mcdonald, Gregory J. Puleo Aug 2021

Upper Bounds For Inverse Domination In Graphs, Elliot Krop, Jessica Mcdonald, Gregory J. Puleo

Theory & 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.

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Skolem Number Of Cycles And Grid Graphs, Braxton Carrigan, John Asplund Aug 2021

Skolem Number Of Cycles And Grid Graphs, Braxton Carrigan, John Asplund

Theory & 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 …

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Ergodicity Of Burgers' System, Szymon Peszat, Krystyna Twardowska, Jerzy Zabczyk Aug 2021

Ergodicity Of Burgers' System, Szymon Peszat, Krystyna Twardowska, Jerzy Zabczyk

Journal of Stochastic Analysis

No abstract provided.

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Two Of Kunita's Papers On Stochastic Flows In Early 1980s, Setsuo Taniguchi Aug 2021

Two Of Kunita's Papers On Stochastic Flows In Early 1980s, Setsuo Taniguchi

Journal of Stochastic Analysis

No abstract provided.

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Rigid Connections On The Projective Line With Elliptic Toral Singularities, Alisina Azhang Aug 2021

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 …

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Conjunctive Join-Semilattices, Charles N. Delzell, Oghenetega Ighedo, James J. Madden Aug 2021

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 …

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Domino Circles, Lauren L. Rose, A. Gwinn Royal, Amanda Serenevy, Anna Varvak Aug 2021

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.

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Error Estimates For Discrete Approximations Of Game Options With Multivariate Diffusion Asset Prices, Yuri Kifer Aug 2021

Error Estimates For Discrete Approximations Of Game Options With Multivariate Diffusion Asset Prices, Yuri Kifer

Journal of Stochastic Analysis

No abstract provided.

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An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent, Killian J. Hitsman, Vehbi E. Paksoy Aug 2021

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.

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Profiling Mathematical Procedural And Problem-Solving Skills Of Undergraduate Students Following A New Mathematics Curriculum, Fiona Faulkner, Mark Prendergast, Cormac Breen, Michael Carr Aug 2021

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 …

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A Method For Characterizing Daily Physiology From Widely Used Wearables, Clark Bowman, Yitong Huang, Olivia J. Walch, Yu Fang, Elena Frank, Jonathan Tyler, Caleb Mayer, Christopher Stockbridge, Cathy Goldstein, Srijan Sen, Daniel B. Forger Aug 2021

A Method For Characterizing Daily Physiology From Widely Used Wearables, Clark Bowman, Yitong Huang, Olivia J. Walch, Yu Fang, Elena Frank, Jonathan Tyler, Caleb Mayer, Christopher Stockbridge, Cathy Goldstein, Srijan Sen, Daniel B. Forger

Mathematics Sciences: Faculty Publications

Millions of wearable-device users record their heart rate (HR) and activity. We introduce a statistical method to extract and track six key physiological parameters from these data, including an underlying circadian rhythm in HR (CRHR), the direct effects of activity, and the effects of meals, posture, and stress through hormones like cortisol. We test our method on over 130,000 days of real-world data from medical interns on rotating shifts, showing that CRHR dynamics are distinct from those of sleep-wake or physical activity patterns and vary greatly among individuals. Our method also estimates a personalized phase-response curve of CRHR to activity …

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College Algebra Through Problem Solving (2021 Edition), Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Stelmach Aug 2021

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.

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Incomplete? Or Indefinite? Intuitionism On Gödel’S First Incompleteness Theorem, Quinn Crawford Aug 2021

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 …

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Bernstein-Sato Polynomials In Commutative Algebra, Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez-Betancourt Aug 2021

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.

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Euler's De Serie Lambertina, Translated From Latin To English With Supplementary Notes, Sam Gallagher Aug 2021

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 …

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Translation Of Euler's Paper E421, Alexander Aycock Aug 2021

Translation Of Euler's Paper E421, Alexander Aycock

Euleriana

This is paper is the result of Euler’s findings on the Eulerian integral of second kind, i.e. the Γ-function: It summarises results and formulas on and properties of the integral in the title that Euler had obtained up to this point in his career and offers more elegant proofs of those before-mentioned results, formulas and properties. The results include a derivation of the integral in the title from an algebraic integral, the reflection formula for the Γ-function and finally a formula equivalent to the Gaußian multiplication formula for the Γ-function, expressed by Euler using mere integrals of algebraic functions.

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Euler And The Multiplication Formula For The Gamma Function, Alexander Aycock Aug 2021

Euler And The Multiplication Formula For The Gamma Function, Alexander Aycock

Euleriana

We show that an apparently overlooked result of Leonhard Euler (1707-1783) from [E421] is essentially equivalent to the general multiplication for- mula for the Γ-function that was proven by Carl Friedrich Gauss (1777-1855) in [Ga28].

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On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa Aug 2021

On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa

Euleriana

This is an annotated translation from Latin of E327 -- De motu rectilineo trium corporum se mutuo attrahentium (“On the rectilinear motion of three bodies mutually attracting each other”). In this publication, Euler considers three bodies lying on a straight line, which are attracted to each other by central forces inversely proportional to the square of their separation distance (inverse-square law). Here Euler finds that the parameter that controls the relative distances among the bodies is given by a quintic function.

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Euler's Miracle, William Dunham Aug 2021

Euler's Miracle, William Dunham

Euleriana

This article features some genuine Eulerian magic. In 1748, Leonhard Euler considered a modification of the harmonic series in which negative signs were attached to various terms by a rule that was far from self-evident. With his accustomed flair, he determined its sum, and the result was utterly improbable. There are a few occasions in mathematics when the term “breathtaking” is not too strong. This is one of them.

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Ed Sandifer: An Eulerian Marathoner, Robert E. Bradley Aug 2021

Ed Sandifer: An Eulerian Marathoner, Robert E. Bradley

Euleriana

Ed Sandifer was the founding secretary of the Euler Society. He published a remarkable quantity of Euler scholarship at the time of Euler’s Tercentenary in 2007.

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Spotlight On The Euler Archive, Cynthia J. Huffman Ph.D. Aug 2021

Spotlight On The Euler Archive, Cynthia J. Huffman Ph.D.

Euleriana

A spotlight on the Euler Archive with a special emphasis on contributions by Dr. C. Edward Sandifer.

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Review: A History Of Mathematics In The United States And Canada (Vol. 1), By David Zitarelli, Lawrence D'Antonio Aug 2021

Review: A History Of Mathematics In The United States And Canada (Vol. 1), By David Zitarelli, Lawrence D'Antonio

Euleriana

This is a review of the 2019 text by David ZItarelli, A History of Mathematics in the United States and Canada. Volume 1: 1492 - 1900

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Sharing Contributions To Euler Scholarship, Erik R. Tou, Christopher Goff Aug 2021

Sharing Contributions To Euler Scholarship, Erik R. Tou, Christopher Goff

Euleriana

A summary of this issue's contents.

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Hessian Formulas And Estimates For Parabolic Schrödinger Operators, Xue-Mei Li Aug 2021

Hessian Formulas And Estimates For Parabolic Schrödinger Operators, Xue-Mei Li

Journal of Stochastic Analysis

No abstract provided.

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Remembering Kunita-San, Ken-Iti Sato Aug 2021

Remembering Kunita-San, Ken-Iti Sato

Journal of Stochastic Analysis

No abstract provided.

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On \Delta^(K)-Colouring Of Powers Of Paths And Cycles, Merlin Thomas Ellumkalayil Ms, Sudev Naduvath Aug 2021

On \Delta^(K)-Colouring Of Powers Of Paths And Cycles, Merlin Thomas Ellumkalayil Ms, Sudev Naduvath

Theory & Applications of Graphs

In an improper vertex colouring of a graph, adjacent vertices are permitted to receive same colours. An edge of an improperly coloured graph is said to be a bad edge if its end vertices have the same colour. A near-proper colouring of a graph is a colouring which minimises the number of bad edges by restricting the number of colour classes that can have adjacency among their own elements. The δ (k) - colouring is a near-proper colouring of G consisting of k given colours, where 1 ≤ k ≤ χ(G) – 1, which minimises the number of bad …

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On The Application Of Principal Component Analysis To Classification Problems, Jianwei Zheng, Cyril Rakovski Aug 2021

On The Application Of Principal Component Analysis To Classification Problems, Jianwei Zheng, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

Principal Component Analysis (PCA) is a commonly used technique that uses the correlation structure of the original variables to reduce the dimensionality of the data. This reduction is achieved by considering only the first few principal components for a subsequent analysis. The usual inclusion criterion is defined by the proportion of the total variance of the principal components exceeding a predetermined threshold. We show that in certain classification problems, even extremely high inclusion threshold can negatively impact the classification accuracy. The omission of small variance principal components can severely diminish the performance of the models. We noticed this phenomenon in …

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An Adaptive Cryptosystem On A Finite Field, Awnon Bhowmik, Unnikrishnan Menon Aug 2021

An Adaptive Cryptosystem On A Finite Field, Awnon Bhowmik, Unnikrishnan Menon

Publications and Research

Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information. This paper introduces an adaptive block encryption scheme. This system is based on product, exponent, and modulo operation on a finite field. At the heart of this algorithm lies an innovative and robust trapdoor function that operates in the Galois Field and is responsible for the superior speed and security offered by it. Prime number theorem plays a fundamental role in this system, to keep unwelcome adversaries at bay. This is a …

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Chemistry Card Games - Games For Learning And Enjoying Chemistry, Michelle M. Clark Aug 2021

Chemistry Card Games - Games For Learning And Enjoying Chemistry, Michelle M. Clark

Sabbatical Projects

Many chemistry students struggle due to a lack of basic math skills. My goal over sabbatical is to develop active learning modules that improve math literacy. I will be collaborating with Dr. Joan Cotter, a renowned math curriculum author whose comprehensive math program utilizes an innovative approach that could benefit chemistry students who have poor math literacy.

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Globally Conservative Solutions For The Modified Camassa–Holm (Moch) Equation, Zhaonan Luo, Zhijun Qiao, Zhaoyang Yin Aug 2021

Globally Conservative Solutions For The Modified Camassa–Holm (Moch) Equation, Zhaonan Luo, Zhijun Qiao, Zhaoyang Yin

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we present the globally conservative solutions to the Cauchy problem for the modified Camassa–Holm (MOCH) equation. First, we transform the equation into an equivalent semi-linear system under new variables. Second, according to the standard ordinary differential equation theory with the aid of the conservation law, we give the global solutions of the semi-linear system. Finally, returning to the original variables, we obtain the globally conservative solutions to the MOCH equation.

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