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Articles 1  30 of 1266
FullText Articles in Algebra
Noncommutative Tensor Triangular Geometry And Its Applications To Representation Theory, Kent Barton Vashaw
Noncommutative Tensor Triangular Geometry And Its Applications To Representation Theory, Kent Barton Vashaw
LSU Doctoral Dissertations
One of the cornerstones of the representation theory of Hopf algebras and finite tensor categories is the theory of support varieties. Balmer introduced tensor triangular geometry for symmetric monoidal triangulated categories, which united various support variety theories coming from disparate areas such as homotopy theory, algebraic geometry, and representation theory. In this thesis a noncommutative version will be introduced and developed. We show that this noncommutative analogue of Balmer's theory can be determined in many concrete situations via the theory of abstract support data, and can be used to classify thick tensor ideals. We prove an analogue of prime ...
On The Generalization Of Interval Valued Fuzzy Generalized BiIdeals In Ordered Semigroups, Muhammad S. Ali Khan, Saleem Abdullah, Kostaq Hila
On The Generalization Of Interval Valued Fuzzy Generalized BiIdeals In Ordered Semigroups, Muhammad S. Ali Khan, Saleem Abdullah, Kostaq Hila
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new general form than interval valued fuzzy generalized biideals in ordered semigroups is introduced. The concept of interval valued fuzzy generalized biideals is initiated and several properties and characterizations are provided. A condition for an interval valued fuzzy generalized biideal to be an interval valued fuzzy generalized biideal is obtained. Using implication operators and the notion of implicationbased an interval valued fuzzy generalized biideal, characterizations of an interval valued fuzzy generalized biideal and an interval valued fuzzy generalized biideal are considered.
Hamacher Operations Of Fermatean Fuzzy Matrices, I. Silambarasan
Hamacher Operations Of Fermatean Fuzzy Matrices, I. Silambarasan
Applications and Applied Mathematics: An International Journal (AAM)
The purpose of this study is to extend the Fermatean fuzzy matrices to the theory of Hamacher operations. In this paper, the concept of Hamacher operations of Fermatean fuzzy matrices are introduced and some desirable properties of these operations, such as commutativity, idempotency, and monotonicity are discussed. Further, we prove DeMorgan’s laws over complement for these operations. Furthermore, the scalar multiplication and exponentiation operations of Fermatean fuzzy matrices are constructed and their algebraic properties are investigated. Finally, some properties of necessity and possibility operators of Fermatean fuzzy matrices are proved.
Developing Mathematical Flexible Thinking In Students With Disabilities, Bridget Sadler
Developing Mathematical Flexible Thinking In Students With Disabilities, Bridget Sadler
Education and Human Development Master's Theses
This curriculum project was designed to improve mathematical flexible thinking skills, with a focus on students with disabilities. This is achieved through the integration of inquirybased learning activities and mathematical discourse throughout each lesson. This collection of lessons is not a unit, rather it is a collection of exemplar lessons which detail how to embed these strategies to develop students mathematical fleible thinking skills. Hoever, all lessons are from Alegbra I and Geometry. Teachers can use this curriculum as it is, or as a model of how to support the development of flexible thinking skills for all students ...
Streaming Down The SternBrocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), Marcus L. Shell
Streaming Down The SternBrocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), Marcus L. Shell
Theses
This paper explores and elaborates on a method of solving Pell’s equation as introduced by Norman Wildberger. In the first chapters of the paper, foundational topics are introduced in expository style including an explanation of Pell’s equation. An explanation of continued fractions and their ability to express quadratic irrationals is provided as well as a connection to the SternBrocot tree and a convenient means of representation for each in terms of 2×2 matrices with integer elements. This representation will provide a useful way of navigating the SternBrocot tree computationally and permit us a means of computing continued ...
Frobenius And Homological Dimensions Of Complexes, Taran Funk
Frobenius And Homological Dimensions Of Complexes, Taran Funk
Dissertations, Theses, and Student Research Papers in Mathematics
Much work has been done showing how one can use a commutative Noetherian local ring R of prime characteristic, viewed as algebra over itself via the Frobenius endomorphism, as a test for flatness or projectivity of a finitely generated module M over R. Work on this dates back to the famous results of Peskine and Szpiro and also that of Kunz. Here I discuss what work has been done to push this theory into modules which are not necessarily finitely generated, and display my work done to weaken the assumptions needed to obtain these results.
Adviser: Tom Marley
Algebraic Structures And Variations: From Latin Squares To Lie Quasigroups, Erik Flinn
Algebraic Structures And Variations: From Latin Squares To Lie Quasigroups, Erik Flinn
All NMU Master's Theses
In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider various mappings between such algebraic objects and utilize matrix representations to give a negative conclusion to a question concerning isotopies in the case of quasigroups.
Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody
Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody
Undergraduate Honors Theses
A graph has quantum symmetry if the algebra associated with its quantum automorphism group is noncommutative. We study what quantum symmetry means and outline one specific method for determining whether a graph has quantum symmetry, a method that involves studying planar algebras and manipulating planar tangles. Modifying a previously used method, we prove that the 5cycle has no quantum symmetry by showing it has the generating property.
A Survey Of Methods To Determine Quantum Symmetry Of Graphs, Samantha Phillips
A Survey Of Methods To Determine Quantum Symmetry Of Graphs, Samantha Phillips
Undergraduate Honors Theses
We introduce the theory of quantum symmetry of a graph by starting with quantum permutation groups and classical automorphism groups. We study graphs with and without quantum symmetry to provide a comprehensive view of current techniques used to determine whether a graph has quantum symmetry. Methods provided include specific tools to show commutativity of generators of algebras of quantum automorphism groups of distancetransitive graphs; a theorem that describes why nontrivial, disjoint automorphisms in the automorphism group implies quantum symmetry; and a planar algebra approach to studying symmetry.
Symmetric Presentation Of Finite Groups, And Related Topics, Marina Michelle Duchesne
Symmetric Presentation Of Finite Groups, And Related Topics, Marina Michelle Duchesne
Electronic Theses, Projects, and Dissertations
We have discovered original symmetric presentations for several finite groups, including 2^{2}:^{.}(2^{4}:(2^{.}S_{3})), M_{11}, 3:(PSL(3,3):2), S_{8}, and 2^{.}M_{12}. We have found homomorphic images of several progenitors, including 2^{*18}:((6x2):6), 2^{*24}:(2^{.}S_{4}), 2^{*105}:A_{7}, 3^{*3}:_{m}(2^{3}:3), 7^{*8}:_{m}(PSL(2,7):2), 3^{*4}:_{m}(4^{2}:2^{2}), 7^{*5}:(2xA_{5}), and 5^{*6}:_{m}S_{5}. We have provided the isomorphism type of all of the finite images that we have discovered. We ...
On The Hamiltonicity Of Subgroup Lattices, Nicholas Charles Fleece
On The Hamiltonicity Of Subgroup Lattices, Nicholas Charles Fleece
MSU Graduate Theses
In this paper we discuss the Hamiltonicity of the subgroup lattices of
different classes of groups. We provide sufficient conditions for the
Hamiltonicity of the subgroup lattices of cubefree abelian groups. We also
prove the nonHamiltonicity of the subgroup lattices of dihedral and
dicyclic groups. We disprove a conjecture on nonabelian pgroups by
producing an infinite family of nonabelian pgroups with Hamiltonian
subgroup lattices. Finally, we provide a list of the Hamiltonicity of the
subgroup lattices of every finite group up to order 35 barring two groups.
On Elliptic Curves, Montana S. Miller
On Elliptic Curves, Montana S. Miller
MSU Graduate Theses
An elliptic curve over the rational numbers is given by the equation y^{2} = x^{3}+Ax+B. In our thesis, we study elliptic curves. It is known that the set of rational points on the elliptic curve form a finitely generated abelian group induced by the secanttangent addition law. We present an elementary proof of associativity using Maple. We also present a relatively concise proof of the MordellWeil Theorem.
Proper Sum Graphs, Austin Nicholas Beard
Proper Sum Graphs, Austin Nicholas Beard
MSU Graduate Theses
The Proper Sum Graph of a commutative ring with identity has the prime ideals as vertices, with two ideals adjacent if their sum is a proper ideal. This thesis expands upon the research of Dhorajia. We will cover the groundwork to understanding the basics of these graphs, and gradually narrow our efforts into the minimal prime ideals of the ring.
Classification Of Cayley Rose Window Graphs, Angsuman Das, Arnab Mandal
Classification Of Cayley Rose Window Graphs, Angsuman Das, Arnab Mandal
Theory and Applications of Graphs
Rose window graphs are a family of tetravalent graphs, introduced by Steve Wilson. Following it, Kovacs, Kutnar and Marusic classified the edgetransitive rose window graphs and Dobson, Kovacs and Miklavic characterized the vertex transitive rose window graphs. In this paper, we classify the Cayley rose window graphs.
Normality Properties Of Composition Operators, Grace Weeks, Hallie Kaiser, Katy O'Malley
Normality Properties Of Composition Operators, Grace Weeks, Hallie Kaiser, Katy O'Malley
Celebration of Scholarship 2021
We explore two main concepts in relation to truncated composition matrices: the conditions required for the binormal and commutative properties. Both of these topics are important in linear algebra due to their connection with diagonalization.
We begin with the normal solution before moving onto the more complex binormal solutions. Then we cover conditions for the composition matrix to commute with the general matrix. Finally, we end with ongoing questions for future work.
Factoring: Difference Of Squares, Thomas Lauria
Factoring: Difference Of Squares, Thomas Lauria
Open Educational Resources
This lesson plan will explain how to factor basic difference of squares problems
Matrix Product Structure Of A Permuted Quasi Cyclic Code And Its Dual, Perian Perdhiku
Matrix Product Structure Of A Permuted Quasi Cyclic Code And Its Dual, Perian Perdhiku
Dissertations
In my Dissertation I will work mostly with Permuted Quasi Cyclic Codes. They are a generalization of Cyclic Codes, one of the most important families of Linear Codes in Coding Theory. Linear Codes are very useful in error detection and correction. Error Detection and Correction is a technique that first detects the corrupted data sent from some transmitter over unreliable communication channels and then corrects the errors and reconstructs the original data. Unlike linear codes, cyclic codes are used to correct errors where the pattern is not clear and the error occurs in a short segment of the message.
The ...
C5 Is Almost A Fractalizer, Bernard Lidicky, Connor Mattes, Florian Pfender
C5 Is Almost A Fractalizer, Bernard Lidicky, Connor Mattes, Florian Pfender
Mathematics Publications
We determine the maximum number of induced copies of a 5cycle in a graph on n vertices for every n. Every extremal construction is a balanced iterated blowup of the 5cycle with the possible exception of the smallest level where for n=8, the Möbius ladder achieves the same number of induced 5cycles as the blowup of a 5cycle on 8 vertices.
This result completes work of Balogh, Hu, Lidický, and Pfender [Eur. J. Comb. 52 (2016)] who proved an asymptotic version of the result. Similarly to their result, we also use the flag algebra method but we extend its ...
Some Model Theory Of Free Groups, Christopher James Natoli
Some Model Theory Of Free Groups, Christopher James Natoli
Dissertations, Theses, and Capstone Projects
There are two main sets of results, both pertaining to the model theory of free groups. In the first set of results, we prove that nonabelian free groups of finite rank at least 3 or of countable rank are not Ahomogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely generated free groups and finitely generated elementary free groups, fail to form AFraisse classes and that the class of nonabelian limit groups fails to form a strong AFraisse class.
The second main result is that if a countable group is elementarily ...
Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, I. Sabadini, Daniele C. Struppa
Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, I. Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.
A Gentle Introduction To Inequalities: A Casebook From The Fullerton Mathematical Circle, Adam Glesser, Matt Rathbun, Bogdan Suceavă
A Gentle Introduction To Inequalities: A Casebook From The Fullerton Mathematical Circle, Adam Glesser, Matt Rathbun, Bogdan Suceavă
Journal of Math Circles
Run for nearly a decade, the Fullerton Mathematical Circle at California State University, Fullerton prepares middle and high school students for mathematical research by exposing them to difficult problems whose solutions require only ageappropriate techniques and background. This work highlights one of the avenues of study, namely inequalities. We cover Engel's lemma, the CauchySchwartz inequality, and the AMGM inequality, as well as providing a wealth of problems where these results can be applied. Full solutions or hints, several written by Math Circle students, are given for all of the problems, as well as some commentary on how or when ...
Mathematical Magic: A Study Of Number Puzzles, Nicasio M. Velez
Mathematical Magic: A Study Of Number Puzzles, Nicasio M. Velez
RoseHulman Undergraduate Mathematics Journal
Within this paper, we will briefly review the history of a collection of number puzzles which take the shape of squares, polygons, and polyhedra in both modular and nonmodular arithmetic. Among other results, we develop construction techniques for solutions of both Modulo and regular Magic Squares. For other polygons in nonmodular arithmetic, specifically of order 3, we present a proof of why there are only four Magic Triangles using linear algebra, disprove the existence of the Magic Tetrahedron in two ways, and utilizing the infamous 3SUM combinatorics problem we disprove the existence of the Magic Octahedron.
Maximums Of Total Betti Numbers In Hilbert Families, Jay White
Maximums Of Total Betti Numbers In Hilbert Families, Jay White
Theses and DissertationsMathematics
Fix a family of ideals in a polynomial ring and consider the problem of finding a single ideal in the family that has Betti numbers that are greater than or equal to the Betti numbers of every ideal in the family. Or decide if this special ideal even exists. Bigatti, Hulett, and Pardue showed that if we take the ideals with a fixed Hilbert function, there is such an ideal: the lexsegment ideal. Caviglia and Murai proved that if we take the saturated ideals with a fixed Hilbert polynomial, there is also such an ideal. We present a generalization of ...
Counting Conjugacy Classes Of Elements Of Finite Order In Compact Exceptional Groups, Qidong He
Counting Conjugacy Classes Of Elements Of Finite Order In Compact Exceptional Groups, Qidong He
Honors Theses
Given a compact exceptional group $G$ and $m,s\in\mathbb{N}$, let $N(G,m)$ be the number of conjugacy classes of elements of order $m$ in $G$, and $N(G,m,s)$ the number of such classes whose elements have $s$ distinct eigenvalues. In string theory, the problem of enumerating certain classes of vacua in the string landscape can be rephrased in terms of the study of these quantities. We develop unified combinatorial algorithms based on Burnside's Lemma that can be used to compute both quantities for each of the five compact exceptional groups. Thus, we provide ...
On Properties Of Positive Semigroups In Lattices And Totally Real Number Fields, Siki Wang
On Properties Of Positive Semigroups In Lattices And Totally Real Number Fields, Siki Wang
CMC Senior Theses
In this thesis, we give estimates on the successive minima of positive semigroups in lattices and ideals in totally real number fields. In Chapter 1 we give a brief overview of the thesis, while Chapters 2 – 4 provide expository material on some fundamental theorems about lattices, number fields and height functions, hence setting the necessary background for the original results presented in Chapter 5. The results in Chapter 5 can be summarized as follows. For a fullrank lattice L ⊂ Rd, we are concerned with the semigroup L+ ⊆ L, which denotes the set of all vectors with nonnegative coordinates in L ...
The Complexity Of Symmetry, Matthew Lemay
The Complexity Of Symmetry, Matthew Lemay
HMC Senior Theses
One of the main goals of theoretical computer science is to prove limits on how efficiently certain Boolean functions can be computed. The study of the algebraic complexity of polynomials provides an indirect approach to exploring these questions, which may prove fruitful since much is known about polynomials already from the field of algebra. This paper explores current research in establishing lower bounds on invariant rings and polynomial families. It explains the construction of an invariant ring for whom a succinct encoding would imply that NP is in P/poly. It then states a theorem about the circuit complexity partial ...
The Beautiful Math Of Everything And You Included, E. Ozie
The Beautiful Math Of Everything And You Included, E. Ozie
The STEAM Journal
This a reflection on how there is beautiful math to everything. An author's interpretation of matrices and mechanics in its relationship to someone's identity.
Adaptive Analytics: It’S About Time, Charles Dziuban, Colm Howlin, Patsy Moskal, Tammy Muhs, Connie Johnson, Rachel Griffin, Carissa Hamilton
Adaptive Analytics: It’S About Time, Charles Dziuban, Colm Howlin, Patsy Moskal, Tammy Muhs, Connie Johnson, Rachel Griffin, Carissa Hamilton
Current Issues in Emerging eLearning
This article describes a cooperative research partnership among a large public university, a forprofit private institution and their common adaptive learning platform provider. The focus of this work explored adaptive analytics that uses data the investigators describe as metaphorical “digital learning dust” produced by the platform as a matter of course. The information configured itself into acquired knowledge, growth, baseline status and engagement. Two complimentary models evolved. The first, in the public university, captured endofcourse data for predicting success. The second approach, in the private university, formed the basis of a dynamic realtime data analytic algorithm. In both cases the ...
Behavior And Dynamics Of The Set Of Absolute Nilpotent And Idempotent Elements Of Chain Of Evolution Algebras Depending On The Time, Anvar Imomkulov
Behavior And Dynamics Of The Set Of Absolute Nilpotent And Idempotent Elements Of Chain Of Evolution Algebras Depending On The Time, Anvar Imomkulov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper we construct some families of threedimensional evolution algebras which satisfies ChapmanKolmogorov equation. For all of these chains we study the behavior of the baric property, the behavior of the set of absolute nilpotent elements and dynamics of the set of idempotent elements depending on the time.
Using Desmos To Support Conceptual Understanding Of Quadratic Equations And Their Graphs, Shannon Bromley
Using Desmos To Support Conceptual Understanding Of Quadratic Equations And Their Graphs, Shannon Bromley
Education and Human Development Master's Theses
When teaching secondary mathematics, there is often a struggle to distinguish true understanding versus the ability to follow a memorized procedure. This commonly occurs in Algebra I content of solving and graphing quadratic equations. Engaging students in Desmos interactive graphing learning activities has been shown to help deepen students’ understanding of such concepts. This curriculum project is designed to deepen students’ understanding and fluency of quadratic equations by including handson activities that support students discovering relationships and patterns between quadratic equations and their corresponding graphs. The unit plan aligns to the New York State Common Core State Standards.