An Enticing Study Of Prime Numbers Of The Shape 𝑝 = 𝑥^2 + 𝑦^2, 2020 CUNY New York City College of Technology

#### An Enticing Study Of Prime Numbers Of The Shape 𝑝 = 𝑥^2 + 𝑦^2, Xiaona Zhou

*Publications and Research*

We will study and prove important results on primes of the shape 𝑥^{2} + 𝑦^{2} using number theoretic techniques. Our analysis involves maps, actions over sets, fixed points and involutions. This presentation is readily accessible to an advanced undergraduate student and lay the groundwork for future studies.

Get The News Out Loudly And Quickly: Modeling The Influence Of The Media On Limiting Infectious Disease, 2020 Marshall University

#### Get The News Out Loudly And Quickly: Modeling The Influence Of The Media On Limiting Infectious Disease, Anna Mummert, Howard Weiss

*Mathematics Faculty Research*

During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of ...

Some Examples Of The Liouville Integrability Of The Banded Toda Flows, 2020 Utah State University

#### Some Examples Of The Liouville Integrability Of The Banded Toda Flows, Zachary Youmans

*All Graduate Theses and Dissertations*

The Toda lattice is a famous integrable system studied by Toda in the 1960s. One can study the Toda lattice using a matrix representation of the system. Previous results have shown that this matrix of dimension *n* with 1 band and *n*−1 bands is Liouville integrable. In this paper, we lay the foundation for proving the general case of the Toda lattice, where we consider the matrix representation with dimension *n* and a partially filled lower triangular part. We call this the banded Toda flow. The main theorem is that the banded Toda flow up to dimension 10 is ...

Analyzing The Von Neumann Entropy Of Contact Networks, 2020 Utah State University

#### Analyzing The Von Neumann Entropy Of Contact Networks, Thomas J. Brower

*All Graduate Theses and Dissertations*

When modeling the spread of disease, ecologists use ecological or contact networks to model how species interact with their environment and one another. The structure of these networks can vary widely depending on the study, where the nodes of a network can be defined as individuals, groups, or locations among other things. With this wide range of definition and with the difficulty of collecting samples, it is difficult to capture every factor of every population. Thus ecologists are limited to creating smaller networks that both fit their budget as well as what is reasonable within the population of interest. With ...

"A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", 2020 University Of New Mexico

#### "A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen 4785403, Paul-Yvann Djamen

*Mathematics & Statistics ETDs*

In this thesis, I studied a newly developed variable selection method SODA, and three customarily used variable selection methods: LASSO, Elastic net, and Random forest for environmental mixture data. The motivating datasets have neuro-developmental status as responses and metal measurements and demographic variables as covariates. The challenges for variable selections include (1) many measured metal concentrations are highly correlated, (2) there are many possible ways of modeling interactions among the metals, (3) the relationships between the outcomes and explanatory variables are possibly nonlinear, (4) the signal to noise ratio in the real data may be low. To compare these methods ...

Connecting Ancient Philosophers’ Math Theory To Modern Fractal Mathematics, 2020 College of the Holy Cross

#### Connecting Ancient Philosophers’ Math Theory To Modern Fractal Mathematics, Colin Mccormack

*Parnassus: Classical Journal*

No abstract provided.

Laplacian Spectral Properties Of Signed Circular Caterpillars, 2020 University of Naples `Federico II' Italy

#### Laplacian Spectral Properties Of Signed Circular Caterpillars, Maurizio Brunetti

*Theory and Applications of Graphs*

A circular caterpillar of girth $n$ is a graph such that the removal of all pendant vertices yields a cycle $C_n$ of order $n$.

A signed graph is a pair $\Gamma=(G, \sigma)$, where $G$ is a simple graph and $\sigma: E(G) \rightarrow \{+1, -1\}$ is the sign function defined on the set $E(G)$ of edges of $G$. The signed graph $\Gamma$ is said to be balanced if the number of negatively signed edges in each cycle is even, and it is said to be unbalanced otherwise.

We determine some bounds for the first $n$ Laplacian eigenvalues of ...

Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, 2020 West Chester University of Pennsylvania

#### Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci

*Mathematics Faculty Publications*

Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover a method for producing infinite sets of solutions and almost solutions of the equation N M reversal N M ⋅= ⋅ ( ) , our results are valid in a general numeration base b > 2 .

Superposed Ornstein-Uhlenbeck Processes, 2020 University of Mary Washington

#### Superposed Ornstein-Uhlenbeck Processes, Julius Esunge, Auguste Muhau

*Journal of Stochastic Analysis*

No abstract provided.

Von Neumann's Minimax Theorem For Continuous Quantum Games, 2020 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### Von Neumann's Minimax Theorem For Continuous Quantum Games, Luigi Accardi, Andreas Boukas

*Journal of Stochastic Analysis*

No abstract provided.

On The Extension Of Positive Definite Kernels To Topological Algebras, 2020 Chapman University

#### On The Extension Of Positive Definite Kernels To Topological Algebras, Daniel Alpay, Ismael L. Paiva

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

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, 2020 Belmont University

#### Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, Ryan D. Fox

*Colorado Mathematics Teacher*

I present how transformations can be applied to support students’ solving linear inequalities involving absolute value. In particular, the horizontal dilations/compressions and translations of graphical representations of distances from zero along a number line are important tools to emphasize a visual representation of the solutions to absolute value inequalities.

Taylor Expansions And Castell Estimates For Solutions Of Stochastic Differential Equations Driven By Rough Paths, 2020 University of Southern California, Los Angeles, CA 90089-2532, USA

#### Taylor Expansions And Castell Estimates For Solutions Of Stochastic Differential Equations Driven By Rough Paths, Qi Feng, Xuejing Zhang

*Journal of Stochastic Analysis*

No abstract provided.

Graphs That Are Cospectral For The Distance Laplacian, 2020 Rice University

#### Graphs That Are Cospectral For The Distance Laplacian, Boris Brimkov, Ken Duna, Leslie Hogben, Kate Lorenzen, Carolyn Reinhart, Sung-Yell Song, Mark Yarrow

*Mathematics Publications*

The distance matrix D(G) of a graph G is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is D^{L}(G)=T(G)−D(G), where T(G) is the diagonal matrix of row sums of D(G). We establish several general methods for producing DL-cospectral graphs that can be used to construct infinite families. We provide examples showing that various properties are not preserved by D^{L}-cospectrality, including examples of D^{L}-cospectral strongly regular and circulant graphs. We establish that the absolute values of coefficients of the distance Laplacian characteristic polynomial ...

Equivariant Cohomology For 2-Torus Actions And Torus Actions With Compatible Involutions, 2020 The University of Western Ontario

#### Equivariant Cohomology For 2-Torus Actions And Torus Actions With Compatible Involutions, Sergio Chaves Ramirez

*Electronic Thesis and Dissertation Repository*

The Borel equivariant cohomology is an algebraic invariant of topological spaces with actions of a compact group which inherits a canonical module structure over the cohomology of the classifying space of the acting group. The study of syzygies in equivariant cohomology characterize in a more general setting the torsion-freeness and freeness of these modules by topological criteria. In this thesis, we study the syzygies for elementary 2-abelian groups (or 2- tori) in equivariant cohomology with coefficients over a field of characteristic two. We approach the equivariant cohomology theory by an equivalent approach using group cohomology, that will allow us to ...

Convex And Nonconvex Optimization Techniques For Multifacility Location And Clustering, 2020 Portland State University

#### Convex And Nonconvex Optimization Techniques For Multifacility Location And Clustering, Tuyen Dang Thanh Tran

*Dissertations and Theses*

This thesis contains contributions in two main areas: calculus rules for generalized differentiation and optimization methods for solving nonsmooth nonconvex problems with applications to multifacility location and clustering. A variational geometric approach is used for developing calculus rules for subgradients and Fenchel conjugates of convex functions that are not necessarily differentiable in locally convex topological and Banach spaces. These calculus rules are useful for further applications to nonsmooth optimization from both theoretical and numerical aspects. Next, we consider optimization methods for solving nonsmooth optimization problems in which the objective functions are not necessarily convex. We particularly focus on the class ...

The Burning Number Of Directed Graphs: Bounds And Computational Complexity, 2020 Delft University of Technology

#### The Burning Number Of Directed Graphs: Bounds And Computational Complexity, Remie Janssen

*Theory and Applications of Graphs*

The burning number of a graph was recently introduced by Bonato et al. Although they mention that the burning number generalizes naturally to directed graphs, no further research on this has been done. Here, we introduce graph burning for directed graphs, and we study bounds for the corresponding burning number and the hardness of finding this number. We derive sharp bounds from simple algorithms and examples. The hardness question yields more surprising results: finding the burning number of a directed tree with one indegree-0 node is NP-hard, but FPT; however, it is W[2]-complete for DAGs. Finally, we give ...

How Mathematics And Computing Can Help Fight The Pandemic: Two Pedagogical Examples, 2020 University of Texas at El Paso

#### How Mathematics And Computing Can Help Fight The Pandemic: Two Pedagogical Examples, Julio Urenda, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

*Departmental Technical Reports (CS)*

With the 2020 pandemic came unexpected mathematical and computational problems. In this paper, we provide two examples of such problems -- examples that we present in simplified pedagogical form. The problems are related to the need for social distancing and to the need for fast testing. We hope that these examples will help students better understand the importance of mathematical models.

Convexity And Curvature In Hierarchically Hyperbolic Spaces, 2020 The Graduate Center, City University of New York

#### Convexity And Curvature In Hierarchically Hyperbolic Spaces, Jacob Russell-Madonia

*All Dissertations, Theses, and Capstone Projects*

Introduced by Behrstock, Hagen, and Sisto, hierarchically hyperbolic spaces axiomatized Masur and Minsky's powerful hierarchy machinery for the mapping class groups. The class of hierarchically hyperbolic spaces encompasses a number of important and seemingly distinct examples in geometric group theory including the mapping class group and Teichmueller space of a surface, virtually compact special groups, and the fundamental groups of 3-manifolds without Nil or Sol components. This generalization allows the geometry of all of these important examples to be studied simultaneously as well as providing a bridge for techniques from one area to be applied to another.

This thesis ...

Towards Realism Interpretation Of Wave Mechanics Based On Maxwell Equations In Quaternion Space And Some Implications, Including Smarandache’S Hypothesis, 2020 University of New Mexico

#### Towards Realism Interpretation Of Wave Mechanics Based On Maxwell Equations In Quaternion Space And Some Implications, Including Smarandache’S Hypothesis, Florentin Smarandache, Victor Christianto, Yunita Umniyati

*Mathematics and Statistics Faculty and Staff Publications*

No abstract provided.