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 ...

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 ...

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.

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.

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.

Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, 2019 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

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

*Communications on Stochastic Analysis*

No abstract provided.

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.

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

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

*Wojciech Budzianowski*

No abstract provided.

Exploring Flag Matroids And Duality, 2018 California State University, San Bernardino

#### 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, 2018 California State University, San Bernardino

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

*Electronic Theses, Projects, and Dissertations*

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, 2018 P.h.D student

#### 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, 2018 Charles University, Prague, Czech Republic

#### 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 ...

Partial Sum Trigonometric Identities And Chebyshev Polynomials, 2018 Colorado Mesa University

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

*Rose-Hulman Undergraduate Mathematics Journal*

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