# Algebra Commons™

## All Articles in Algebra

979 full-text articles. Page 1 of 36.

Patterns, Symmetries, And Mathematical Structures In The Arts, 2020 Georgia Southern University

#### Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach

##### University Honors Program Theses

Mathematics is a discipline of academia that can be found everywhere in the world around us. Mathematicians and scientists are not the only people who need to be proficient in numbers. Those involved in social sciences and even the arts can benefit from a background in math. In fact, connections between mathematics and various forms of art have been discovered since as early as the fourth century BC. In this thesis we will study such connections and related concepts in mathematics, dances, and music.

An Anatomical And Functional Analysis Of Digital Arteries, 2019 University of Lynchburg

#### An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith

##### Student Scholar Showcase

Blood flow to the tissue of the hands and digits is efficiently regulated by vasoconstriction and vasodilation. Through a series of cadaveric dissection, we examined arteries in the hands and digits, including ulnar artery, radial artery, palmar arteries, and digital arteries, for their distribution (branching) patterns and morphological parameters (e.g., thickness, length between branches, external and internal diameters). Using data directly collected from three female cadavers as input variables to our mathematical model, we simulated vasoconstriction (-20% and -10% diameter) and vasodilation (+10% and +20 diameter) to evaluate the extent of changes in blood volume and flow within the ...

2019 University of Lynchburg

#### Group Theoretical Analysis Of Arbitrarily Large, Colored Square Grids, Brett Ehrman

##### Student Scholar Showcase

In this research, we examine n x n grids whose individual squares are each colored with one of k distinct colors. We seek a general formula for the number of colored grids that are distinct up to rotations, reflections, and color reversals. We examine the problem using a group theoretical approach. We define a specific group action that allows us to incorporate Burnside’s Lemma, which leads us to the desired general results

2019 Central Washington University

#### How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve

##### Pre-calculus and Trigonometry

No abstract provided.

Greatest Common Divisor: Algorithm And Proof, 2019 University of St. Thomas - Houston

#### Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

##### Number Theory

No abstract provided.

2019 Otterbein University

#### Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell

##### Honors Thesis Projects

This research will study the effect teaching the history of mathematics in a high school classroom has on student understanding. To accomplish this, lessons both including and excluding historical background on different topics were taught in an Honors Algebra 2 class in the high school setting. This research aims to engage student learning and investigation of topics that normally do not draw a lot of student focus and spark a new or revived interest in mathematics for students by broadening lessons to include material of which students would not otherwise be exposed. The lessons themselves aim to engage other current ...

Integrating Mathematics And Educational Robotics: Simple Motion Planning, 2019 Loyola University Chicago

#### Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg

##### Computer Science: Faculty Publications and Other Works

This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics.

Monoidal Supercategories And Superadjunction, 2019 University of Ottawa

#### Monoidal Supercategories And Superadjunction, Dene Lepine

We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.

Strengthening Relationships Between Neural Ideals And Receptive Fields, 2019 Texas A&M University

#### Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant

Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code C can be represented by its neural ideal JC. In turn, the polynomials in JC can be used to determine the relationships among the receptive fields of the neurons. In a paper by Curto et al., three such relationships, known as the Type 1-3 relations, were linked to the neural ideal by three if-and-only-if statements. Later, Garcia et al. discovered the Type 4-6 relations. These new relations differed from the first three in that they were related ...

Dissertation_Davis.Pdf, 2019 University of Kentucky

#### Dissertation_Davis.Pdf, Brian Davis

##### brian davis

Simplices are the simplest" examples of polytopes, and yet they exhibit much of the rich and subtle combinatorics and commutative algebra of their more general cousins. In this way they are sufficiently complicated --- insights gained from their study can inform broader research in Ehrhart theory and associated fields.

In this dissertation we consider two previously unstudied properties of lattice simplices; one algebraic and one combinatorial. The first is the Poincare series of the associated semigroup algebra, which is substantially more complicated than the Hilbert series of that same algebra. The second is the partial ordering of the elements of the ...

Enhanced Koszulity In Galois Cohomology, 2019 The University of Western Ontario

#### Enhanced Koszulity In Galois Cohomology, Marina Palaisti

##### Electronic Thesis and Dissertation Repository

Despite their central role in Galois theory, absolute Galois groups remain rather mysterious; and one of the main problems of modern Galois theory is to characterize which profinite groups are realizable as absolute Galois groups over a prescribed field. Obtaining detailed knowledge of Galois cohomology is an important step to answering this problem. In our work we study various forms of enhanced Koszulity for quadratic algebras. Each has its own importance, but the common ground is that they all imply Koszulity. Applying this to Galois cohomology, we prove that, in all known cases of finitely generated pro-$p$-groups, Galois ...

Parametric Natura Morta, 2019 Independent researcher, Palermo, Italy

#### Parametric Natura Morta, Maria C. Mannone

##### The STEAM Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

Diagonal Sums Of Doubly Substochastic Matrices, 2019 Georgian Court University

#### Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li

Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the sub-defect of $A$ to be the smallest integer $k$ such that there exists an $(n+k)\times(n+k)$ doubly stochastic matrix containing $A$ as a submatrix. Let $\omega_{n,k}$ denote the subset of $\omega_n$ which contains all doubly substochastic matrices with sub-defect $k$. For $\pi$ a permutation of symmetric group of degree $n$, the sequence of elements $a_{1\pi(1 ... In-Sphere Property And Reverse Inequalities For Matrix Means, 2019 Ton Duc Thang University #### In-Sphere Property And Reverse Inequalities For Matrix Means, Trung Hoa Dinh, Tin-Yau Tam, Bich Khue T Vo ##### Electronic Journal of Linear Algebra The in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained. Surjective Additive Rank-1 Preservers On Hessenberg Matrices, 2019 Walailak University #### Surjective Additive Rank-1 Preservers On Hessenberg Matrices, Prathomjit Khachorncharoenkul, Sajee Pianskool ##### Electronic Journal of Linear Algebra Let$H_{n}(\mathbb{F})$be the space of all$n\times n$upper Hessenberg matrices over a field~$\mathbb{F}$, where$n$is a positive integer greater than two. In this paper, surjective additive maps preserving rank-$1$on$H_{n}(\mathbb{F})$are characterized. 2019 Faculty of Sciences and Mathematics, University of Niš #### Solving The Sylvester Equation Ax-Xb=C When$\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, Nebojša Č. Dinčić ##### Electronic Journal of Linear Algebra The method for solving the Sylvester equation$AX-XB=C$in complex matrix case, when$\sigma(A)\cap\sigma(B)\neq \emptyset$, by using Jordan normal form is given. Also, the approach via Schur decomposition is presented. Resolution Of Conjectures Related To Lights Out! And Cartesian Products, 2019 University of Wyoming #### Resolution Of Conjectures Related To Lights Out! And Cartesian Products, Bryan A. Curtis, Jonathan Earl, David Livingston, Bryan L. Shader ##### Electronic Journal of Linear Algebra Lights Out!\ is a game played on a$5 \times 5$grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration of lit lights and reach a state where all lights are out. Two conjectures posed in a recently published paper about Lights Out!\ on Cartesian products of graphs are resolved. A Note On Linear Preservers Of Semipositive And Minimally Semipositive Matrices, 2019 Indian Institute of Science, Bengaluru #### A Note On Linear Preservers Of Semipositive And Minimally Semipositive Matrices, Projesh Nath Choudhury, Rajesh Kannan, K. C. Sivakumar ##### Electronic Journal of Linear Algebra Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipositive) are well studied in matrix theory. In this short note, the structure of linear maps which preserve the set of all semipositive/minimally semipositive matrices is studied. An open problem is solved, and some ambiguities in the article [J. Dorsey, T. Gannon, N. Jacobson, C.R. Johnson and M. Turnansky. Linear preservers of semi-positive matrices. {\em Linear and Multilinear Algebra}, 64:1853--1862, 2016.] are clarified. Vector Cross Product Differential And Difference Equations In R^3 And In R^7, 2019 University of Beira Interior #### Vector Cross Product Differential And Difference Equations In R^3 And In R^7, Patrícia D. Beites, Alejandro P. Nicolás, Paulo Saraiva, José Vitória ##### Electronic Journal of Linear Algebra Through a matrix approach of the$2$-fold vector cross product in$\mathbb{R}^3$and in$\mathbb{R}^7$, some vector cross product differential and difference equations are studied. Either the classical theory or convenient Drazin inverses, of elements belonging to the class of index$1\$ matrices, are applied.

Equivalence Of Classical And Quantum Codes, 2019 University of Kentucky

#### Equivalence Of Classical And Quantum Codes, Tefjol Pllaha

##### Theses and Dissertations--Mathematics

In classical and quantum information theory there are different types of error-correcting codes being used. We study the equivalence of codes via a classification of their isometries. The isometries of various codes over Frobenius alphabets endowed with various weights typically have a rich and predictable structure. On the other hand, when the alphabet is not Frobenius the isometry group behaves unpredictably. We use character theory to develop a duality theory of partitions over Frobenius bimodules, which is then used to study the equivalence of codes. We also consider instances of codes over non-Frobenius alphabets and establish their isometry groups. Secondly ...