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 ...

Diagonal Sums Of Doubly Substochastic Matrices, 2019 Georgian Court University

#### Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li

*Electronic Journal of Linear Algebra*

Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the sub-defect of $A$ to be the smallest integer $k$ such that there exists an $(n+k)\times(n+k)$ doubly stochastic matrix containing $A$ as a submatrix. Let $\omega_{n,k}$ denote the subset of $\omega_n$ which contains all doubly substochastic matrices with sub-defect $k$. For $\pi$ a permutation of symmetric group of degree $n$, the sequence of elements $a_{1\pi(1 ...

A Dataset Of 30-Meter Annual Vegetation Phenology Indicators (1985–2015) In Urban Areas Of The Conterminous United States, 2019 Iowa State University

#### A Dataset Of 30-Meter Annual Vegetation Phenology Indicators (1985–2015) In Urban Areas Of The Conterminous United States, Xuecao Li, Yuyu Zhou, Lin Meng, Ghassem R. Asrar, Chaoqun Lu, Qiusheng Wu

*Ecology, Evolution and Organismal Biology Publications*

Fine-resolution satellite observations show great potential for characterizing seasonal and annual dynamics of vegetation phenology in urban domains, from local to regional and global scales. However, most previous studies were conducted using coarse or moderate resolution data, which are inadequate for characterizing the spatiotemporal dynamics of vegetation phenology in urban domains. In this study, we produced an annual vegetation phenology dataset in urban ecosystems for the conterminous United States (US), using all available Landsat images on the Google Earth Engine (GEE) platform. First, we characterized the long-term mean seasonal pattern of phenology indicators of the start of season (SOS) and ...

A Note On Equity Within Differential Equations Education By Visualization, 2019 Islamic Azad University, Ahar Branch

#### A Note On Equity Within Differential Equations Education By Visualization, Younes Karimifardinpour

*CODEE Journal*

The growing importance of education equity is partly based on the premise that an individual's level of education directly correlates to future quality of life. Educational equity for differential equations (DEs) is related to achievement, fairness, and opportunity. Therefore, a pedagogy that practices DE educational equity gives a strong foundation of social justice. However, linguistic barriers pose a challenge to equity education in DEs. For example, I found myself teaching DEs either in classrooms with a low proficiency in the language of instruction or in multilingual classrooms. I grappled with a way to create an equity educational environment that ...

Kremer's Model Relating Population Growth To Changes In Income And Technology, 2019 University of Arizona

#### Kremer's Model Relating Population Growth To Changes In Income And Technology, Dan Flath

*CODEE Journal*

For thousands of years the population of Earth increased slowly, while per capita income remained essentially constant, at subsistence level. At the beginning of the industrial revolution around 1800, population began to increase very rapidly and income started to climb. Then in the second half of the twentieth century as a demographic transition began, the birth and death rates, as well as the world population growth rate, began to decline. The reasons for these transitions are hotly debated with no expert consensus yet emerging. It's the problem of economic growth. In this document we investigate a mathematical model of ...

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, 2019 Frostburg State University

#### Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

*CODEE Journal*

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem ...

Consensus Building By Committed Agents, 2019 University of Alberta

#### Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang

*CODEE Journal*

One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is ...

The Ocean And Climate Change: Stommel's Conceptual Model, 2019 Oberlin College

#### The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh

*CODEE Journal*

The ocean plays a major role in our climate system and in climate change. In this article we present a conceptual model of the Atlantic Meridional Overturning Circulation (AMOC), an important component of the ocean's global energy transport circulation that has, in recent times, been weakening anomalously. Introduced by Henry Stommel, the model results in a two-dimensional system of first order ODEs, which we explore via *Mathematica*. The model exhibits two stable regimes, one having an orientation aligned with today's AMOC, and the other corresponding to a reversal of the AMOC. This material is appropriate for a junior-level ...

Modeling The Spread And Prevention Of Malaria In Central America, 2019 Muhlenberg College

#### Modeling The Spread And Prevention Of Malaria In Central America, Michael Huber

*CODEE Journal*

In 2016, the World Health Organization (WHO) estimated that there were 216 million cases of Malaria reported in 91 countries around the world. The Central American country of Honduras has a high risk of malaria exposure, especially to United States soldiers deployed in the region. This article will discuss various aspects of the disease, its spread and its treatment and the development of models of some of these aspects with differential equations. Exercises are developed which involve, respectively, exponential growth, logistics growth, systems of first-order equations and Laplace transforms. Notes for instructors are included.

A Model Of The Transmission Of Cholera In A Population With Contaminated Water, 2019 Southwestern University

#### A Model Of The Transmission Of Cholera In A Population With Contaminated Water, Therese Shelton, Emma Kathryn Groves, Sherry Adrian

*CODEE Journal*

Cholera is an infectious disease that is a major concern in countries with inadequate access to clean water and proper sanitation. According to the World Health Organization (WHO), "cholera is a disease of inequity--an ancient illness that today sickens and kills only the poorest and most vulnerable people\dots The map of cholera is essentially the same as a map of poverty." We implement a published model (Fung, "Cholera Transmission Dynamic Models for Public Health Practitioners," *Emerging Themes in Epidemiology*, 2014) of a SIR model that includes a bacterial reservoir. Bacterial concentration in the water is modeled by the Monod ...

Sir Models: Differential Equations That Support The Common Good, 2019 Dickinson College

#### Sir Models: Differential Equations That Support The Common Good, Lorelei Koss

*CODEE Journal*

This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.

The Mathematics Of Gossip, 2019 Virginia Polytechnic Institute and State University

#### The Mathematics Of Gossip, Jessica Deters, Izabel P. Aguiar, Jacquie Feuerborn

*CODEE Journal*

How does a lie spread through a community? The purpose of this paper is two-fold: to provide an educational tool for teaching Ordinary Differential Equations (ODEs) and sensitivity analysis through a culturally relevant topic (fake news), and to examine the social justice implications of misinformation. Under the assumption that people are susceptible to, can be infected with, and recover from a lie, we model the spread of false information with the classic Susceptible-Infected-Recovered (SIR) model. We develop a system of ODEs with lie-dependent parameter values to examine the pervasiveness of a lie through a community.

The model presents the opportunity ...

An Epidemiological Math Model Approach To A Political System With Three Parties, 2019 California State University, Channel Islands

#### An Epidemiological Math Model Approach To A Political System With Three Parties, Selenne Bañuelos, Ty Danet, Cynthia Flores, Angel Ramos

*CODEE Journal*

The United States has proven to be and remains a dual political party system. Each party is associated to its own ideologies, yet work by Baldassarri and Goldberg in *Neither Ideologues Nor Agnostics* show that many Americans have positions on economic and social issues that don't fall into one of the two mainstream party platforms. Our interest lies in studying how recruitment from one party into another impacts an election. In particular, there was a growing third party presence in the 2000 and 2016 elections. Motivated by previous work, an epidemiological approach is taken to treat the spread of ...

Linking Differential Equations To Social Justice And Environmental Concerns, 2019 Claremont Colleges

#### Linking Differential Equations To Social Justice And Environmental Concerns

*CODEE Journal*

Special issue of the CODEE Journal in honor of its founder, Professor Robert Borrelli.

Point-Valued Mappings Of Sets, 2019 Missouri University of Science and Technology

#### Point-Valued Mappings Of Sets, Matt Insall

*Matt Insall*

Let X be a metric space and let CB(X) denote the closed bounded subsets of X with the Hausdorff metric. Given a complete subspace Y of CB(X), two fixed point theorems, analogues of results in [1], are proved, and examples are given to suggest their applicability in practice.

Further Properties Of An Extremal Set Of Uniqueness, 2019 Missouri University of Science and Technology

#### Further Properties Of An Extremal Set Of Uniqueness, David E. Grow, Matt Insall

*Matt Insall*

Consider the circle group T = R mod 2_ as the interval [0, 1). Then each x 2 T has a binary expansion: x =P1 k=1 xk2−k where each xk is 0 or 1. Let S be the set of x with a binary expansionsuch that the number of 1's does not exceed the number of the leading zeros by more than one. The authors prove that the countable compact set S cannot be expressed as the union of a finite number of Dirichlet sets.

Ensuring The Satisfaction Of A Temporal Specification At Run-Time, 2019 Missouri University of Science and Technology

#### Ensuring The Satisfaction Of A Temporal Specification At Run-Time, Grace Tsai, Matt Insall, Bruce M. Mcmillin

*Matt Insall*

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences can occur if the run-time behavior does not conform to the expected behavior or specifications. In this paper, we present a formal approach to ensure satisfaction of the specifications in the operational environment as follows. First we specify behavior of the systems using Interval Temporal Logic (ITL). Next we give algorithms for trace checking of programs in such systems. Finally, we present a fully distributed run-time evaluation system which causally orders the events of the system during its execution and checks ...

In-Sphere Property And Reverse Inequalities For Matrix Means, 2019 Ton Duc Thang University

#### In-Sphere Property And Reverse Inequalities For Matrix Means, Trung Hoa Dinh, Tin-Yau Tam, Bich Khue T Vo

*Electronic Journal of Linear Algebra*

The in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained.

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.

Role Of Combinatorial Complexity In Genetic Networks, 2019 Southern Methodist University

#### Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang

*SMU Journal of Undergraduate Research*

A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users ...