Some Generalizations Of Classical Integer Sequences Arising In Combinatorial Representation Theory, 2020 Western Kentucky University

#### Some Generalizations Of Classical Integer Sequences Arising In Combinatorial Representation Theory, Sasha Verona Malone

*Masters Theses & Specialist Projects*

There exists a natural correspondence between the bases for a given finite-dimensional representation of a complex semisimple Lie algebra and a certain collection of finite edge-colored ranked posets, laid out by Donnelly, et al. in, for instance, [Don03]. In this correspondence, the Serre relations on the Chevalley generators of the given Lie algebra are realized as conditions on coeﬀicients assigned to poset edges. These conditions are the so-called diamond, crossing, and structure relations (hereinafter DCS relations.) New representation constructions of Lie algebras may thus be obtained by utilizing edge-colored ranked posets. Of particular combinatorial interest are those representations whose corresponding ...

On Product Of Smooth Neutrosophic Topological Spaces, 2020 University of New Mexico

#### On Product Of Smooth Neutrosophic Topological Spaces, Florentin Smarandache, Kalaivani Chandran, Swathi Sundari Sundaramoorthy, Saeid Jafari

*Mathematics and Statistics Faculty and Staff Publications*

In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.

Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, 2020 University of New Mexico

#### Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Madad Khan, Seok-Zun Song

*Mathematics and Statistics Faculty and Staff Publications*

the notion of (i, j, k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

A General Model Of Neutrosophic Ideals In Bck/Bci-Algebras Based On Neutrosophic Points, 2020 University of New Mexico

#### A General Model Of Neutrosophic Ideals In Bck/Bci-Algebras Based On Neutrosophic Points, Florentin Smarandache, Hashem Bordbar, Rajab Ali Borzooei, Young Bae Jun

*Mathematics and Statistics Faculty and Staff Publications*

More general form of (∈, ∈∨q)-neutrosophic ideal is introduced, and their properties are investigated.

Universal Localizations Of Certain Noncommutative Rings, 2020 Utah State University

#### Universal Localizations Of Certain Noncommutative Rings, Tyler B. Bowles

*All Graduate Theses and Dissertations*

A common theme throughout algebra is the extension of arithmetic systems to ones over which new equations can be solved. For instance, someone who knows only positive numbers might think that there is no solution to *x* + 3 = 0, yet later learns *x *= ‚àí3 to be a feasible solution. Likewise, when faced with the equation 2*x *= 3, someone familiar only with integers may declare that there is no solution, but may later learn that *x *= 3/2 is a reasonable answer. Many eventually learn that the extension of real numbers to complex numbers unlocks solutions to previously unsolvable equations ...

Transitioning From The Abstract To The Concrete: Reasoning Algebraically, 2020 Missouri State University

#### Transitioning From The Abstract To The Concrete: Reasoning Algebraically, Andrea Lynn Martin

*MSU Graduate Theses*

Why are students not making a smooth transition from arithmetic to algebra? The purpose of this study was to understand the nature of students’ algebraic reasoning through tasks involving generalizing. After students’ algebraic reasoning had been analyzed, the challenges they encountered while reasoning were analyzed. The data was collected through semi-structured interviews with six eighth grade students and analyzed by watching recorded interviews while tracking algebraic reasoning. Through data analysis of students’ algebraic reasoning, three themes emerged: 1) it was possible for students to reach stage two (informal abstraction) and have an abstract understanding of the mathematical pattern even if ...

Hadamard Diagonalizable Graphs Of Order At Most 36, 2020 Ontario Tech University

#### Hadamard Diagonalizable Graphs Of Order At Most 36, Jane Breen, Steve Butler, Melissa Fuentes, Bernard Lidicky, Michael Phillips, Alexander W. N. Riasanovsky, Sung-Yell Song, Ralihe R. Villagrán, Cedar Wiseman, Xiaohong Zhang

*Mathematics Publications*

If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries ±1, then the matrix formed by taking the columns as the eigenvectors is a Hadamard matrix and the graph is said to be Hadamard diagonalizable.

In this article, we prove that if n=8k+4 the only possible Hadamard diagonalizable graphs are Kn, Kn/2,n/2, 2Kn/2, and nK1, and we develop an efficient computation for determining all graphs diagonalized by a given Hadamard matrix of any order. Using these two tools, we determine and present all Hadamard diagonalizable graphs up to ...

Maximizing Five-Cycles In Kr-Free Graphs, 2020 Iowa State University

#### Maximizing Five-Cycles In Kr-Free Graphs, Bernard Lidicky, Kyle Murphy

*Mathematics Publications*

The Erdos Pentagon problem asks to find an n-vertex triangle-free graph that is maximizing the number of 5-cycles. The problem was solved using flag algebras by Grzesik and independently by Hatami, Hladky, Kral, Norin, and Razborov. Recently, Palmer suggested the general problem of maximizing the number of 5-cycles in K_{k+1}-free graphs. Using flag algebras, we show that every K_{k+1}-free graph of order n contains at most 110k4(k4−5k3+10k2−10k+4)n5+o(n5)

copies of C_5 for any k≥3, with the Turan graph begin the extremal graph for large enough n.

A Real World Example Of Solving A Quadratic Equation In Movie Cgi, 2020 Pittsburg State University

#### A Real World Example Of Solving A Quadratic Equation In Movie Cgi, Cynthia J. Huffman Ph.D.

*Faculty Submissions*

It is important to expose students to the beauty and usefulness of mathematics. Since computer graphics are familiar to most students due to video games and movies, they make a great source for motivating topics in mathematics. This activity shows students an application of solving quadratic equations to computing the line of sight to spherical objects in computer graphics.

Topics In Gravitational Wave Physics, 2020 University of Arkansas, Fayetteville

#### Topics In Gravitational Wave Physics, Aaron David Johnson

*Theses and Dissertations*

We begin with a brief introduction to gravitational waves. Next we look into the origin of the Chandrasekhar transformations between the different equations found by perturbing a Schwarzschild black hole. Some of the relationships turn out to be Darboux transformations. Then we turn to GW150914, the first detected black hole binary system, to see if the nonlinear memory might be detectable by current and future detectors. Finally, we develop an updated code for computing equatorial extreme mass ratio inspirals which will be open sourced as soon as it has been generalized for arbitrary inclinations.

Families Of Homogeneous Licci Ideals, 2020 University of Arkansas, Fayetteville

#### Families Of Homogeneous Licci Ideals, Jesse Keyton

*Theses and Dissertations*

This thesis is concered with the graded structure of homogeneous CI-liaison. Given two homogeneous ideals in the same linkage class, we want to understand the ways in which you can link from one ideal to the other. We also use homogeneous linkage to study the socles and Hilbert functions of Artinian monomial ideals.

First, we build off the work of C. Huneke and B. Ulrich on monomial liaison. They provided an algorithm to check the licci property of Artinian monomial ideals and we use their method to characterize when two Artinian monomial ideals can be linked by monomial regular sequences ...

Harmony Amid Chaos, 2020 Olivet Nazarene University

#### Harmony Amid Chaos, Drew Schaffner

*Pence-Boyce STEM Student Scholarship*

We provide a brief but intuitive study on the subjects from which Galois Fields have emerged and split our study up into two categories: harmony and chaos. Specifically, we study finite fields with elements where is prime. Such a finite field can be defined through a logarithm table. The Harmony Section is where we provide three proofs about the overall symmetry and structure of the Galois Field as well as several observations about the order within a given table. In the Chaos Section we make two attempts to analyze the tables, the first by methods used by Vladimir Arnold as ...

College Algebra Notes And Exercises (Gcsu), 2020 Georgia Gwinnett College

#### College Algebra Notes And Exercises (Gcsu), Rabia Shahbaz, Janice Alves

*Mathematics Ancillary Materials*

Developed as part of a Round 13 Mini-Grant, these updated supplementary materials for Stitz-Zeager Open Source Mathematics and the LibGuides Open Course for College Algebra at GCSU include notes and exercises on equations, inequalities, functions, polynomial and rational functions, and exponential and logarithmic functions are included in one .zip file.

On The Extension Of Positive Definite Kernels To Topological Algebras, 2020 Chapman University

#### On The Extension Of Positive Definite Kernels To Topological Algebras, Daniel Alpay, Ismael L. Paiva

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, 2020 Belmont University

#### Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, Ryan D. Fox

*Colorado Mathematics Teacher*

I present how transformations can be applied to support students’ solving linear inequalities involving absolute value. In particular, the horizontal dilations/compressions and translations of graphical representations of distances from zero along a number line are important tools to emphasize a visual representation of the solutions to absolute value inequalities.

Equivariant Cohomology For 2-Torus Actions And Torus Actions With Compatible Involutions, 2020 The University of Western Ontario

#### Equivariant Cohomology For 2-Torus Actions And Torus Actions With Compatible Involutions, Sergio Chaves Ramirez

*Electronic Thesis and Dissertation Repository*

The Borel equivariant cohomology is an algebraic invariant of topological spaces with actions of a compact group which inherits a canonical module structure over the cohomology of the classifying space of the acting group. The study of syzygies in equivariant cohomology characterize in a more general setting the torsion-freeness and freeness of these modules by topological criteria. In this thesis, we study the syzygies for elementary 2-abelian groups (or 2- tori) in equivariant cohomology with coefficients over a field of characteristic two. We approach the equivariant cohomology theory by an equivalent approach using group cohomology, that will allow us to ...

Ideal Theory In Bck/Bci-Algebras In The Frame Of Hesitant Fuzzy Set Theory, 2020 University of Tabuk

#### Ideal Theory In Bck/Bci-Algebras In The Frame Of Hesitant Fuzzy Set Theory, G. Muhiuddin, Habib Harizavi, Young Bae Jun

*Applications and Applied Mathematics: An International Journal (AAM)*

Several generalizations and extensions of fuzzy sets have been introduced in the literature, for example, Atanassov’s intuitionistic fuzzy sets, type 2 fuzzy sets and fuzzy multisets, etc. Using the Torra’s hesitant fuzzy sets, the notions of Sup-hesitant fuzzy ideals in BCK/BCI-algebras are introduced, and its properties are investigated. Relations between Sup-hesitant fuzzy subalgebras and Sup-hesitant fuzzy ideals are displayed, and characterizations of Sup-hesitant fuzzy ideals are discussed.

Model Theory Of Groups And Monoids, 2020 The Graduate Center, City University of New York

#### Model Theory Of Groups And Monoids, Laura M. Lopez Cruz

*Dissertations, Theses, and Capstone Projects*

We first show that arithmetic is bi-interpretable (with parameters) with the free monoid and with partially commutative monoids with trivial center. This bi-interpretability implies that these monoids have the QFA property and that finitely generated submonoids of these monoids are definable. Moreover, we show that any recursively enumerable language in a finite alphabet X with two or more generators is definable in the free monoid. We also show that for metabelian Baumslag-Solitar groups and for a family of metabelian restricted wreath products, the Diophantine Problem is decidable. That is, we provide an algorithm that decides whether or not a given ...

Assessing Student Understanding While Solving Linear Equations Using Flowcharts And Algebraic Methods, 2020 California State University, San Bernardino

#### Assessing Student Understanding While Solving Linear Equations Using Flowcharts And Algebraic Methods, Edima Umanah

*Electronic Theses, Projects, and Dissertations*

Solving linear equations has often been taught procedurally by performing inverse operations until the variable in question is isolated. Students do not remember which operation to undo first because they often memorize operations with no understanding of the underlying meanings. The study was designed to help assess how well students are able to solve linear equations. Furthermore, the lesson is designed to help students identify solving linear equations in more than one-way. The following research questions were addressed in this study: Does the introduction of multiple ways to think about linear equations lead students to flexibly incorporate appropriate representations/strategies ...

Hyperbolic Triangle Groups, 2020 California State University, San Bernardino

#### Hyperbolic Triangle Groups, Sergey Katykhin

*Electronic Theses, Projects, and Dissertations*

This paper will be on hyperbolic reflections and triangle groups. We will compare hyperbolic reflection groups to Euclidean reflection groups. The goal of this project is to give a clear exposition of the geometric, algebraic, and number theoretic properties of Euclidean and hyperbolic reflection groups.