Acoustic Versus Electromagnetic Field Theory: Scalar, Vector, Spinor Representations And The Emergence Of Acoustic Spin, 2020 Chapman University

#### Acoustic Versus Electromagnetic Field Theory: Scalar, Vector, Spinor Representations And The Emergence Of Acoustic Spin, Lucas Burns, Konstantin Y. Bliokh, Franco Nori, Justin Dressel

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

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether ...

"Fireworks And Quadratic Functions”, 2020 Illinois Mathematics and Science Academy

#### "Fireworks And Quadratic Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

Evolution Of Computational Thinking Contextualized In A Teacher-Student Collaborative Learning Environment., 2020 Louisiana State University and Agricultural and Mechanical College

#### Evolution Of Computational Thinking Contextualized In A Teacher-Student Collaborative Learning Environment., John Arthur Underwood

*LSU Doctoral Dissertations*

The discussion of Computational Thinking as a pedagogical concept is now essential as it has found itself integrated into the core science disciplines with its inclusion in all of the Next Generation Science Standards (NGSS, 2018). The need for a practical and functional definition for teacher practitioners is a driving point for many recent research endeavors. Across the United States school systems are currently seeking new methods for expanding their students’ ability to analytically think and to employee real-world problem-solving strategies (Hopson, Simms, and Knezek, 2001). The need for STEM trained individuals crosses both the vocational certified and college degreed ...

"Sheet Metal And Polynomials At Work”, 2020 Illinois Mathematics and Science Academy

#### "Sheet Metal And Polynomials At Work”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

Semilattice Sums Of Algebras And Mal’Tsev Products Of Varieties, 2020 Iowa State University

#### Semilattice Sums Of Algebras And Mal’Tsev Products Of Varieties, Clifford Bergman, T. Penza, A. B. Romanowska

*Mathematics Publications*

The Mal’tsev product of two varieties of similar algebras is always a quasivariety. We consider when this quasivariety is a variety. The main result shows that if V is a strongly irregular variety with no nullary operations, and S is a variety, of the same type as V, equivalent to the variety of semilattices, then the Mal’tsev product V ◦ S is a variety. It consists precisely of semilattice sums of algebras in V. We derive an equational basis for the product from an equational basis for V. However, if V is a regular variety, then the Mal’tsev ...

"Dancing Fountains”, 2020 Illinois Mathematics and Science Academy

"American Football: Field Goals And Quadratic Functions”, 2020 Illinois Mathematics and Science Academy

#### "American Football: Field Goals And Quadratic Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

“Product Development: Model Rockets As Toys”, 2020 Illinois Mathematics and Science Academy

#### “Product Development: Model Rockets As Toys”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Crash Reconstruction: Stopping Distance”, 2020 Illinois Mathematics and Science Academy

#### "Crash Reconstruction: Stopping Distance”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

The Distribution Of The Greatest Common Divisor Of Elements In Quadratic Integer Rings, 2020 CUNY Bernard M Baruch College

#### The Distribution Of The Greatest Common Divisor Of Elements In Quadratic Integer Rings, Asimina S. Hamakiotes

*Student Theses*

For a pair of quadratic integers *n* and *m* chosen randomly, uniformly, and independently from the set of quadratic integers of norm *x* or less, we calculate the probability that the greatest common divisor of (*n,m*) is *k*. We also calculate the expected norm of the greatest common divisor (*n,m*) as *x* tends to infinity, with explicit error terms. We determine the probability and expected norm of the greatest common divisor for quadratic integer rings that are unique factorization domains. We also outline a method to determine the probability and expected norm of the greatest common divisor of ...

"Tracker Software And Matchbox Car Jumps”, 2020 Illinois Mathematics and Science Academy

#### "Tracker Software And Matchbox Car Jumps”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Human Cannonball Stunts And Quadratic Functions”, 2020 Illinois Mathematics and Science Academy

#### "Human Cannonball Stunts And Quadratic Functions”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Car Darts And Parabolas”, 2020 Illinois Mathematics and Science Academy

"Matchbox Stunts And Simulations”, 2020 Illinois Mathematics and Science Academy

#### "Matchbox Stunts And Simulations”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

"Straw Rockets And Parabolas”, 2020 Illinois Mathematics and Science Academy

#### "Straw Rockets And Parabolas”, Kelly W. Remijan

*Teacher Resources*

No abstract provided.

Singular Value Decomposition, 2020 Coastal Carolina University

#### Singular Value Decomposition, Krystal Bonaccorso, Andrew Incognito

*Honors Theses*

A well-known theorem is Diagonalization, where one of the factors is a diagonal matrix. In this paper we will be describing a similar way to factor/decompose a non-square matrix. The key to both of these ways to factor is eigenvalues and eigenvectors.

Structure Theorems For Idempotent Residuated Lattices, 2020 University of Bern

#### Structure Theorems For Idempotent Residuated Lattices, José Gil-Férez, Peter Jipsen, George Metcalfe

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

In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in various subclasses. We also establish the finite embeddability property for certain varieties generated by classes of residuated lattices that are conservative in the sense that monoid multiplication always yields one of its arguments. We then make use of a more symmetric version of Raftery’s characterization theorem for totally ordered commutative idempotent residuated lattices to prove that the variety generated by this class ...

Two-Outcome Synchronous Correlation Sets And Connes' Embedding Problem, 2020 Army Cyber Institute

#### Two-Outcome Synchronous Correlation Sets And Connes' Embedding Problem, Travis Russell

*West Point Research Papers*

We show that Connes' embedding problem is equivalent to the weak Tsirelson problem in the setting of two-outcome synchronous correlation sets. We further show that the extreme points of two-outcome synchronous correlation sets can be realized using a certain class of universal C*-algebras. We examine these algebras in the three-experiment case and verify that the strong and weak Tsirelson problems have affirmative answers in that setting.

Gray Codes In Music Theory, 2020 University of Maine

#### Gray Codes In Music Theory, Isaac L. Vaccaro

*Electronic Theses and Dissertations*

In the branch of Western music theory called serialism, it is desirable to construct chord progressions that use each chord in a chosen set exactly once. We view this problem through the scope of the mathematical theory of Gray codes, the notion of ordering a finite set X so that adjacent elements are related by an element of some specified set R of involutions in the permutation group of X. Using some basic results from the theory of permutation groups we translate the problem of finding Gray codes into the problem of finding Hamiltonian paths and cycles in a Schreier ...

Beginning Algebra Made Useful, 2020 Grand Valley State University

#### Beginning Algebra Made Useful, Charlene E. Beckmann

*Open Textbooks*

*Beginning Algebra Made Useful* addresses the needs of learners to make sense of algebra by quantifying and generalizing everyday occurrences such as commuting to work, buying gas or pizza, and determining the better deal. It requires learners to actively engage with algebraic concepts through physical and thought experiments in ways that help them connect ideas, representations, and contexts, and solve problems that arise in their daily lives. The text* *helps learners grow their brains and develop growth mindsets as they learn algebra conceptually. Problem sets continue the process, extending work begun in each lesson, applying new understandings to new contexts ...