Totally Positive Completable Matrix Patterns And Expansion, 2019 College of William and Mary

#### Totally Positive Completable Matrix Patterns And Expansion, David Allen

*Undergraduate Honors Theses*

Though some special cases are now understood, the characterization of TP-completable patterns is far from complete. Here, a new idea is developed: the \underline{expansion} of a pattern. It is used to explain some recent results, such as border patterns. The effects of expansion on certain cases of non-completable and completable patterns is examined, as well as an attempt to characterize $3$-by-$n$ TP-completable patterns. While many TP-completable patterns remain so under expansion, a counterExample shows that this is not always so. In the process, some new results about TP-completability are given.

Taking Notes: Generating Twelve-Tone Music With Mathematics, 2019 East Tennessee State University

#### Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder

*Electronic Theses and Dissertations*

There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of diﬀerent musical notes, each of which has diﬀerent sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.

Median Energy Imaging Of Supernova Remnants With Chandra X-Ray Observatory, 2019 College of William and Mary

#### Median Energy Imaging Of Supernova Remnants With Chandra X-Ray Observatory, Anne Blackwell

*Undergraduate Honors Theses*

Supernova remnants (SNRs) play an important role in shaping the energy density, chemical enrichment, and interstellar medium (ISM) of galaxies, and in our understanding of stellar evolution. Due to the high plasma temperatures of SNRs, they primarily emit X-rays. Using data collected with the Chandra observatory, we study a novel statistical imaging analysis technique to probe the underlying structure and physical properties of DEM L71, a SNR in the Large Magellanic Cloud. We used the statistical properties of the photons within an image pixel, such as the median energy, to make images of the energetics across the SNR. We have ...

Understanding The Impact Of Peer-Led Workshops On Student Learning, 2019 CUNY New York City College of Technology

#### Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Armando Cosme, Nadia Kennedy

*Publications and Research*

As students we often wonder why some subjects are easy to understand and requires not much effort in terms of re-reading the material, for us to grasp what it entails. One subject seems to remain elusive and uneasy for a vast majority of learners at all levels of education; that subject is Mathematics, it is one subject that most learners finds difficult even after doubling the amount of time spent on studying the material. My intention is to explore ways to make Mathematics easier for other students using feedback from students enrolled in NSF mathematics peer leading workshops, and use ...

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, 2019 University of Lynchburg

#### Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

*Undergraduate Theses and Capstone Projects*

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, 2019 Chapman University

#### A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

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

The classical unconditional exact *p*-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact *p*-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate ...

Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, 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 ...

Monoidal Supercategories And Superadjunction, 2019 University of Ottawa

#### Monoidal Supercategories And Superadjunction, Dene Lepine

*Rose-Hulman Undergraduate Mathematics Journal*

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.

Heterogeneous Boolean Networks With Two Totalistic Rules, 2019 University of Nebraska at Omaha

#### Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

*Student Research and Creative Activity Fair*

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet ...

Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, 2019 University of Nebraska at Omaha

#### Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller

*Student Research and Creative Activity Fair*

**Description**: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my general ...

Forensics Analysis For Bone Pair Matching Using Bipartite Graphs In Commingled Remains, 2019 University of Nebraska at Omaha

#### Forensics Analysis For Bone Pair Matching Using Bipartite Graphs In Commingled Remains, Ryan Ernst

*Student Research and Creative Activity Fair*

Identification of missing prisoners of war is a complex and time consuming task. There are many missing soldiers whose remains have yet to be returned to their families and loved ones. This nation has a solemn obligation to its soldiers and their families who have made the ultimate sacrifice for their country. There are currently over 82,000 unidentified prisoners of war which are identified at a rate of 100+ per year. At this rate it would take 300+ years to complete the identification process. Previously, anthropologists used excel spreadsheets to sort through skeletal data. This project aims to streamline ...

Operator Algebras Generated By Left Invertibles, 2019 University of Nebraska - Lincoln

#### Operator Algebras Generated By Left Invertibles, Derek Desantis

*Dissertations, Theses, and Student Research Papers in Mathematics*

Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*-algebras. Representations of such algebras encode the dynamics of orthonormal sets in a Hilbert space.We instigate a research program on concrete operator algebras that model the dynamics of Hilbert space frames.

The primary object of this thesis is the norm-closed operator algebra generated by a left invertible $T$ together with its Moore-Penrose inverse $T^\dagger$. We denote this algebra by $\mathfrac{A}_T$. In the isometric case, $T^\dagger = T^*$ and $\mathfrac{A}_T$ is a representation ...

Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, 2019 Universidad Católica del Norte

#### Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao

*Electronic Journal of Linear Algebra*

The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, which has played an important role in the study of certain nonnegative inverse spectral problems. A number of partial results about the problem have been published by several authors, mainly by H. \v{S}migoc. In this paper, the relevance of a Brauer's result, and its implication for the nonnegative inverse eigenvalue problem with prescribed diagonal entries is emphasized. As a consequence, given a list of complex ...

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.

Extending Set Functors To Generalised Metric Spaces, 2019 University Politehnica of Bucharest

#### Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

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

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_{V} on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and we ...

Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, 2019 Louisiana State University, Baton Rouge, LA USA

#### Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar

*Communications on Stochastic Analysis*

No abstract provided.

Composition Of Gaussian Noises From Successive Convex Integrations, 2019 Indian Statistical Institute

#### Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta

*Communications on Stochastic Analysis*

No abstract provided.

Random Matrices, Continuous Circular Systems And The Triangular Operator, 2019 Wrocław University of Science and Technology, Wrocław, Poland

#### Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski

*Communications on Stochastic Analysis*

No abstract provided.

Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, 2019 Indian Statistical Institute

#### Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan

*Communications on Stochastic Analysis*

No abstract provided.

Limiting Means For Spherical Slices, 2019 University of Connecticut, Storrs, CT USA

#### Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta

*Communications on Stochastic Analysis*

No abstract provided.