The Riemann Curvature Tensor, 2019 Louisiana Tech University

#### The Riemann Curvature Tensor, Jennifer Cox

*Mathematics Senior Capstone Papers*

A tensor is a mathematical object that has applications in areas including physics, psychology, and artificial intelligence. The Riemann curvature tensor is a tool used to describe the curvature of n-dimensional spaces such as Riemannian manifolds in the field of differential geometry. The Riemann tensor plays an important role in the theories of general relativity and gravity as well as the curvature of spacetime. This paper will provide an overview of tensors and tensor operations. In particular, properties of the Riemann tensor will be examined. Calculations of the Riemann tensor for several two and three dimensional surfaces such as that ...

Mathematical Analysis Of The Duck Migration To Louisiana, 2019 Louisiana Tech University

#### Mathematical Analysis Of The Duck Migration To Louisiana, Brandon Garcia

*Mathematics Senior Capstone Papers*

The purpose of this project is to research the relationship between duck migration and weather patterns, more specifically trying to determine if the rainfall and temperature in a given year affects the migration patterns of ducks. Duck hunters and conservation- ists alike have observed an overall decrease in the duck population in Louisiana over the past 70 years. Though some years have seen an increase, the population has not recovered to the level from the 1950s. These observations have led to many questions about what have happened to the ducks or where have the ducks gone. Using differ- ent forms ...

Solving The Traveling Salesman Problem Using Ordered-Lists, 2019 Air Force Institute of Technology

#### Solving The Traveling Salesman Problem Using Ordered-Lists, Petar D. Jackovich

*Theses and Dissertations*

The arc-greedy heuristic is a constructive heuristic utilized to build an initial, quality tour for the Traveling Salesman Problem (TSP). There are two known sub-tour elimination methodologies utilized to ensure the resulting tours are viable. This thesis introduces a third novel methodology, the Greedy Tracker (GT), and compares it to both known methodologies. Computational results are generated across multiple TSP instances. The results demonstrate the GT is the fastest method for instances below 400 nodes while Bentley's Multi-Fragment maintains a computational advantage for larger instances. A novel concept called Ordered-Lists is also introduced which enables TSP instances to be ...

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 ...

Second Order Stochastic Partial Integro Differential Equations With Delay And Impulses, 2019 Department of Mathematics, UCEK, JNTUK, Kakinada, A.P. -533003, India

#### Second Order Stochastic Partial Integro Differential Equations With Delay And Impulses, M.V.S.S.B.B.K. Sastry, G.V.S.R. Deekshitulu

*Communications on Stochastic Analysis*

No abstract provided.

On A Stochastic 2d Cahn-Hilliard-Navier-Stokes System Driven By Jump Noise, 2019 Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, USA

#### On A Stochastic 2d Cahn-Hilliard-Navier-Stokes System Driven By Jump Noise, G. Deugoué, T. Tachim Medjo

*Communications on Stochastic Analysis*

No abstract provided.

Some Properties Of The Inhomogeneous Panjer Process, 2019 Department of Industrial Engineering, Pontificia Universidad Javeriana, Bogotá D.C., Colombia

#### Some Properties Of The Inhomogeneous Panjer Process, Ana María Beltrán Cortés, José Alfredo Jiménez Moscoso

*Communications on Stochastic Analysis*

No abstract provided.

On The Adjoint Markov Policies In Stochastic Differential Games, 2019 University of Minnesota, Minneapolis, MN 55455, USA

#### On The Adjoint Markov Policies In Stochastic Differential Games, Nicolai V. Krylov

*Communications on Stochastic Analysis*

No abstract provided.

Regularity Of The Local Time Of Diffusions On The Positive Real Line With Reflection At Zero, 2019 University of the Ryukyus, Department of Mathematical Sci- ences, Faculty of Science, Nishihara-cho, Okinawa 903-0213, Japan

#### Regularity Of The Local Time Of Diffusions On The Positive Real Line With Reflection At Zero, Masafumi Hayashi

*Communications on Stochastic Analysis*

No abstract provided.

A Nonlocal Approach To The Quantum Kolmogorov Backward Equation And Links To Noncommutative Geometry, 2019 Investec Bank PLC, 30 Gresham Street, London EC2V 7QP, United Kingdom

#### A Nonlocal Approach To The Quantum Kolmogorov Backward Equation And Links To Noncommutative Geometry, Will Hicks

*Communications on Stochastic Analysis*

No abstract provided.

On The Spectrum Of Self-Adjoint Lévy Generators, 2019 School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, England

#### On The Spectrum Of Self-Adjoint Lévy Generators, David Applebaum

*Communications on Stochastic Analysis*

No abstract provided.

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 ...

A Strength Test For The Borda Count, 2019 Bard College

#### A Strength Test For The Borda Count, Jade Monroe Waring

*Senior Projects Spring 2019*

When running an election with more than two candidates, there are many ways to choose the winner. A famous theorem of Arrow states that the only mathematically fair way to choose is to do so at random. Because this is not a desirable way to choose a winner of an election, many mathematicians have devised alternate ways of aggregating ballots. In my project I consider one of these ways -- the Borda Count, considered to be one of the most desirable from both the point of view of mathematics and economics -- and came up with a method to test the mathematical ...

Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, 2019 Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

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

*Communications on Stochastic Analysis*

No abstract provided.