# Other Mathematics Commons™

Articles 1 - 30 of 1112

## Full-Text Articles in Other Mathematics

May 2019

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

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, Nathan Molder May 2019

#### 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.

Apr 2019

#### 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, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski Apr 2019

#### 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 ...

Apr 2019

#### 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, Dene Lepine Mar 2019

#### 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.

Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh Mar 2019

#### 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, 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, 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, Derek Desantis Mar 2019

#### 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, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao Feb 2019

#### 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, Prathomjit Khachorncharoenkul, Sajee Pianskool Feb 2019

#### 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, Adriana Balan, Alexander Kurz, Jiří Velebil Jan 2019

#### 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 TV 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, Po-Han Hsu, Padamanbhan Sundar Jan 2019

#### 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, Amites Dasgupta Jan 2019

#### 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, Romuald Lenczewski Jan 2019

#### 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, Manil T. Mohan

##### Communications on Stochastic Analysis

No abstract provided.

Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta Jan 2019

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

##### Communications on Stochastic Analysis

No abstract provided.

Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas Jan 2019

#### Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas

##### Communications on Stochastic Analysis

No abstract provided.

Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri Jan 2019

#### Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri

##### Communications on Stochastic Analysis

No abstract provided.

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski Dec 2018

#### Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Exploring Flag Matroids And Duality, Zachary Garcia Dec 2018

#### Exploring Flag Matroids And Duality, Zachary Garcia

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

Matroids capture an abstraction of independence in mathematics, and in doing so, connect discrete mathematical structures that arise in a variety of contexts. A matroid can be defined in several cryptomorphic ways depending on which perspective of a matroid is most applicable to the given context. Among the many important concepts in matroid theory, the concept of matroid duality provides a powerful tool when addressing difficult problems. The usefulness of matroid duality stems from the fact that the dual of a matroid is itself a matroid. In this thesis, we explore a matroid-like object called a flag matroid. In particular ...

Symmetric Presentations And Double Coset Enumeration, Charles Seager Dec 2018

#### Symmetric Presentations And Double Coset Enumeration, Charles Seager

In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut ... Commutators Involving Matrix Functions, Osman Kan, Süleyman Solak Nov 2018 #### Commutators Involving Matrix Functions, Osman Kan, Süleyman Solak ##### Electronic Journal of Linear Algebra Some results are obtained for matrix commutators involving matrix exponentials$\left(\left[e^{A},B\right],\left[e^{A},e^{B}\right]\right)\$ and their norms.

Determinants Of Interval Matrices, Jaroslav Horáček, Milan Hladík, Josef Matějka Nov 2018

#### Determinants Of Interval Matrices, Jaroslav Horáček, Milan Hladík, Josef Matějka

##### Electronic Journal of Linear Algebra

In this paper we shed more light on determinants of real interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the state-of-the-art method, however, it is less consuming regarding computational time. Other methods transferable from real matrices (e.g., the Gerschgorin circles, Hadamard's inequality ...

A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr Nov 2018

#### A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr

##### Doctoral Dissertations

A graph is outer-planar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outer-planar (NOP) if it is edgeless or has an edge whose deletion results in an outer-planar graph. An edge of a non outer-planar graph whose removal results in an outer-planar graph is a vulnerable edge. This dissertation focuses on near outer-planar (NOP) graphs. We describe the class of all such graphs in terms of a ﬁnite list of excluded graphs, in a manner similar to the well-known Kuratowski Theorem for planar ...

Oct 2018

#### Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller

Using Euler’s theorem, geometric sums and Chebyshev polynomials, we prove trigonometric identities involving sums and multiplications of cosine.

Oct 2018

#### Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

#### A Decomposition Of A Space Of Multiple Wiener Integrals By The Difference Of Two Independent Lévy Processes In Terms Of The Lévy Laplacian, Atsushi Ishikawa

##### Communications on Stochastic Analysis

No abstract provided.

A Stochastic Integral By A Near-Martingale, Shinya Hibino, Hui-Hsiung Kuo, Kimiaki Saitô Oct 2018

#### A Stochastic Integral By A Near-Martingale, Shinya Hibino, Hui-Hsiung Kuo, Kimiaki Saitô

##### Communications on Stochastic Analysis

No abstract provided.