# Algebra Commons™

## All Articles in Algebra

861 full-text articles. Page 7 of 31.

Elimination For Systems Of Algebraic Differential Equations, 2017 The Graduate Center, City University of New York

#### Elimination For Systems Of Algebraic Differential Equations, Richard Gustavson

##### All Dissertations, Theses, and Capstone Projects

We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the algebraic data" of ...

On Skew-Symmetric Matrices Related To The Vector Cross Product In R^7, 2017 University of Beira Interior

#### On Skew-Symmetric Matrices Related To The Vector Cross Product In R^7, P. D. Beites, A. P. Nicolás, José Vitória

##### Electronic Journal of Linear Algebra

A study of real skew-symmetric matrices of orders $7$ and $8$, defined through the vector cross product in $\mathbb{R}^7$, is presented. More concretely, results on matrix properties, eigenvalues, (generalized) inverses and rotation matrices are established.

A Transformation That Preserves Principal Minors Of Skew-Symmetric Matrices, 2017 Faculté des Sciences Ain chock

#### A Transformation That Preserves Principal Minors Of Skew-Symmetric Matrices, Abderrahim Boussairi, Brahim Chergui

##### Electronic Journal of Linear Algebra

It is well known that two $n\times n$ symmetric matrices have equal corresponding principal minors of all orders if and only if they are diagonally similar. This result cannot be extended to arbitrary matrices. The aim of this work is to give a new transformation that preserves principal minors of skew-symmetric matrices.

The Recognition Problem For Table Algebras And Reality-Based Algebras, 2017 University of Regina

#### The Recognition Problem For Table Algebras And Reality-Based Algebras, Allen Herman, Mikhail Muzychuk, Bangteng Xu

##### EKU Faculty and Staff Scholarship

Given a finite-dimensional noncommutative semisimple algebra A over C with involution, we show that A always has a basis B for which ( A , B ) is a reality-based algebra. For algebras that have a one-dimensional representation δ , we show that there always exists an RBA-basis for which δ is a positive degree map. We characterize all RBA-bases of the 5-dimensional noncommutative semisimple algebra for which the algebra has a positive degree map, and give examples of RBA-bases of C ⊕ M n ( C ) for which the RBA has a positive degree map, for all n ≥ 2

Simple And Semi-Simple Artinian Rings, 2017 California State University - San Bernardino

#### Simple And Semi-Simple Artinian Rings, Ulyses Velasco

##### Electronic Theses, Projects, and Dissertations

The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical, Artinian rings, nilpotency, idempotency, and more. Once we reach our destination, we will examine some implications of these theorems. As a fair warning, no ring will be assumed to be commutative, or to have unity. On that note, the reader should be familiar with the basic findings from Group Theory and Ring Theory.

Elementary Abstract Algebra, 2017 Plymouth State University

#### Elementary Abstract Algebra, Emma Norbrothen Wright

##### Open Educational Resources

No abstract provided.

Projective Partitions Of Vector Spaces, 2017 Siena College

#### Projective Partitions Of Vector Spaces, Mohammad Javaheri

##### Electronic Journal of Linear Algebra

Given infinite-dimensional real vector spaces $V,W$ with $|W| \leq |V|$, it is shown that there exists a collection of subspaces of $V$ that are isomorphic to $W$, mutually intersect only at 0, and altogether cover $V$.

Note On Von Neumann And Rényi Entropies Of A Graph, 2017 Iowa State University

#### Note On Von Neumann And Rényi Entropies Of A Graph, Michael Dairyko, Leslie Hogben, Jephian C.H. Lin, Joshua Lockhart, David Roberson, Simone Severini, Michael Young

##### Mathematics Publications

We conjecture that all connected graphs of order n have von Neumann entropy at least as great as the star K1;n1 and prove this for almost all graphs of order n. We show that connected graphs of order n have Renyi 2-entropy at least as great as K1;n1 and for > 1, Kn maximizes Renyi -entropy over graphs of order n. We show that adding an edge to a graph can lower its von Neumann entropy.

Singular Value And Norm Inequalities Associated With 2 X 2 Positive Semidefinite Block Matrices, 2017 Zarqa University

#### Singular Value And Norm Inequalities Associated With 2 X 2 Positive Semidefinite Block Matrices, Aliaa Burqan, Fuad Kittaneh

##### Electronic Journal of Linear Algebra

This paper aims to give singular value and norm inequalities associated with $2\times 2$ positive semidefinite block matrices.

2017 The College at Brockport

#### A Financial Literacy Curriculum Project On Linear Functions In Algebra I Aligned With New York State Common Core State Standards, Michael T. Hughson Jr

##### Education and Human Development Master's Theses

There is a lack of financial literacy curriculum available for teachers to support students learning of mathematical skills that are needed in real life. Financial literacy curricula can support students learning real life skills needed before independent living situations in college or career. Direct mathematical modelling and application can support students comprehension of the relationship between financial literacy and algebra. This curriculum highlights the ideology of the need to know drives learning and aligns real world financial literacy problems to the Common Core State Standards (CCSS) algebra standards.

Application Of Symplectic Integration On A Dynamical System, 2017 East Tennessee State University

#### Application Of Symplectic Integration On A Dynamical System, William Frazier

##### Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic ...

On Rings Of Invariants For Cyclic P-Groups, 2017 University of Arkansas, Fayetteville

#### On Rings Of Invariants For Cyclic P-Groups, Daniel Juda

##### Theses and Dissertations

This thesis studies the ring of invariants R^G of a cyclic p-group G acting on k[x_1,\ldots, x_n] where k is a field of characteristic p >0. We consider when R^G is Cohen-Macaulay and give an explicit computation of the depth of R^G. Using representation theory and a result of Nakajima, we demonstrate that R^G is a unique factorization domain and consequently quasi-Gorenstein. We answer the question of when R^G is F-rational and when R^G is F-regular.

We also study the a-invariant for a graded ring S, that is, the maximal graded degree ...

2017 Chapman University

#### Relation Algebras, Idempotent Semirings And Generalized Bunched Implication Algebras, Peter Jipsen

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

This paper investigates connections between algebraic structures that are common in theoretical computer science and algebraic logic. Idempotent semirings are the basis of Kleene algebras, relation algebras, residuated lattices and bunched implication algebras. Extending a result of Chajda and Länger, we show that involutive residuated lattices are determined by a pair of dually isomorphic idempotent semirings on the same set, and this result also applies to relation algebras. Generalized bunched implication algebras (GBI-algebras for short) are residuated lattices expanded with a Heyting implication. We construct bounded cyclic involutive GBI-algebras from so-called weakening relations, and prove that the class of weakening ...

Six Septembers: Mathematics For The Humanist, 2017 Duquesne University

#### Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay

##### Zea E-Books

Scholars of all stripes are turning their attention to materials that represent enormous opportunities for the future of humanistic inquiry. The purpose of this book is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. This book is a primer for developing the skills to enable humanist scholars to address complicated technical material with confidence. This book, to put it plainly, is concerned with the things that the author of a technical article knows, but isn’t saying. Like any field, mathematics ...

A Game Of Monovariants On A Checkerboard, 2017 Lynchburg College

#### A Game Of Monovariants On A Checkerboard, Linwood Reynolds

##### Student Scholar Showcase

Abstract: Assume there is a game that takes place on a 20x20 checkerboard in which each of the 400 squares are filled with either a penny, nickel, dime, or quarter. The coins are placed randomly onto the squares, and there are to be 100 of each of the coins on the board. To begin the game, 59 coins are removed at random. The goal of the game is to remove each remaining coin from the board according to the following rules: 1. A penny can only be removed if all 4 adjacent squares are empty. That is, a penny cannot ...

Bridging The Gap Between College Algebra And Agronomic Math, 2017 Iowa State University

#### Bridging The Gap Between College Algebra And Agronomic Math, Haleigh Nicole Summers

##### Honors Projects and Posters

Practitioners of agronomy are often faced with scenarios involving math during their daily activities. Students studying agronomy are required to take college algebra but often miss the opportunity to bridge the gap between general algebra and agronomic math. The purpose of this research was to evaluate the effectiveness of two delivery methods for teaching agronomic math. Videos and posters were created to demonstrate: fertilizer application, unit conversions, irrigation, yield estimation, and growing degree day calculation. We predicted using videos to teach agronomic math would be more effective by providing both auditory and visual teaching methods, while posters only provide visual ...

Involutions And Total Orthogonality In Some Finite Classical Groups, 2017 College of William and Mary

#### Involutions And Total Orthogonality In Some Finite Classical Groups, Gregory K. Taylor

A group $G$ is called \emph{real} if every element is conjugate to its inverse, and $G$ is \emph{strongly real} if each of the conjugating elements may be chosen to be an involution, an element in $G$ which squares to the identity. Real groups are called as such because every irreducible character of a real group is real valued. A group $G$ is called \emph{totally orthogonal} if every irreducible complex representation is realizable over the field of real numbers. Total orthogonality is sufficient, but not necessary for reality.

Reality of representations is quantified in the Frobenius-Schur indicator. For ...

2017 The University of Western Ontario

#### Metafork: A Compilation Framework For Concurrency Models Targeting Hardware Accelerators, Xiaohui Chen

##### Electronic Thesis and Dissertation Repository

Parallel programming is gaining ground in various domains due to the tremendous computational power that it brings; however, it also requires a substantial code crafting effort to achieve performance improvement. Unfortunately, in most cases, performance tuning has to be accomplished manually by programmers. We argue that automated tuning is necessary due to the combination of the following factors. First, code optimization is machine-dependent. That is, optimization preferred on one machine may be not suitable for another machine. Second, as the possible optimization search space increases, manually finding an optimized configuration is hard. Therefore, developing new compiler techniques for optimizing applications ...

The Enhanced Principal Rank Characteristic Sequence For Hermitian Matrices, 2017 Iowa State University

#### The Enhanced Principal Rank Characteristic Sequence For Hermitian Matrices, Steve Butler, M. Catral, H. Tracy Hall, Leslie Hogben, Xavier Martinez-Rivera, Bryan L. Shader, Pauline Van Den Driessche

##### Electronic Journal of Linear Algebra

The enhanced principal rank characteristic sequence (epr-sequence) of an $n\x n$ matrix is a sequence $\ell_1 \ell_2 \cdots \ell_n$, where each $\ell_k$ is ${\tt A}$, ${\tt S}$, or ${\tt N}$ according as all, some, or none of its principal minors of order $k$ are nonzero. There has been substantial work on epr-sequences of symmetric matrices (especially real symmetric matrices) and real skew-symmetric matrices, and incidental remarks have been made about results extending (or not extending) to (complex) Hermitian matrices. A systematic study of epr-sequences of Hermitian matrices is undertaken; the differences with the case of symmetric matrices are quite ...

2017 Shanghai Jiaotong University

#### Self-Interlacing Polynomials Ii: Matrices With Self-Interlacing Spectrum, Mikhail Tyaglov

##### Electronic Journal of Linear Algebra

An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows: $$\lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0.$$ A method for constructing sign definite matrices with self-interlacing spectrum from totally nonnegative ones is presented. This method is applied to bidiagonal and tridiagonal matrices. In particular, a result by O. Holtz on the spectrum of real symmetric anti-bidiagonal matrices with positive nonzero entries is generalized.