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 ...

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 ...

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 ...

Singular Ramsey And Turán Numbers, 2019 University of Haifa-Oranim

#### Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza

*Theory and Applications of Graphs*

We say that a subgraph F of a graph G is singular if the degrees d_G(v) are all equal or all distinct for the vertices v of F. The singular Ramsey number Rs(F) is the smallest positive integer n such that, for every m at least n, in every edge 2-coloring of K_m, at least one of the color classes contains F as a singular subgraph. In a similar flavor, the singular Turán number Ts(n,F) is defined as the maximum number of edges in a graph of order n, which does not contain F as a ...

Solving The Sylvester Equation Ax-Xb=C When $\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, 2019 Faculty of Sciences and Mathematics, University of Niš

#### Solving The Sylvester Equation Ax-Xb=C When $\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, Nebojša Č. Dinčić

*Electronic Journal of Linear Algebra*

The method for solving the Sylvester equation $AX-XB=C$ in complex matrix case, when $\sigma(A)\cap\sigma(B)\neq \emptyset$, by using Jordan normal form is given. Also, the approach via Schur decomposition is presented.

When Revolutions Happen: Algebraic Explanation, 2019 University of Texas at El Paso

#### When Revolutions Happen: Algebraic Explanation, Julio Urenda, Vladik Kreinovich

*Departmental Technical Reports (CS)*

At first glance, it may seem that revolutions happen when life becomes really intolerable. However, historical analysis shows a different story: that revolutions happen not when life becomes intolerable, but when a reasonably prosperous level of living suddenly worsens. This empirical observation seems to contradict traditional decision theory ideas, according to which, in general, people's happiness monotonically depends on their level of living. A more detailed model of human behavior, however, takes into account not only the current level of living, but also future expectations. In this paper, we show that if we properly take these future expectations into ...

Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, 2019 California Polytechnic State University - San Luis Obispo

#### Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing

*Mathematics*

Based on properties of *n*-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymptotic boundary at infinity of at most two points. Moreover, the presence of two points in the asymptotic boundary is a rigidity condition that forces the hypersurface to be an equidistant hypersurface about a geodesic line in hyperbolic space. This gives an affirmative answer to the question raised by Alexander and Currier (Proc Symp Pure Math 54(3):37–44, 1993).

Decision Theory Explains "Telescoping Effect" -- That Our Time Perception Is Biased, 2019 University of Texas at El Paso

#### Decision Theory Explains "Telescoping Effect" -- That Our Time Perception Is Biased, Laxman Bokati, Vladik Kreinovich

*Departmental Technical Reports (CS)*

People usually underestimate time passed since distant events, and overestimate time passed since recent events. There are several explanations for this "telescoping effect", but most current explanations utilize specific features of human memory and/or human perception. We show that the telescoping effect can be explained on a much basic level of decision theory, without the need to invoke any specific ways we perceive and process time.

How To Generate "Nice" Cubic Polynomials -- With Rational Coefficients, Rational Zeros And Rational Extrema: A Fast Algorithm, 2019 University of Texas at El Paso

#### How To Generate "Nice" Cubic Polynomials -- With Rational Coefficients, Rational Zeros And Rational Extrema: A Fast Algorithm, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

Students feel more comfortable with rational numbers than with irrational ones. Thus, when teaching the beginning of calculus, it is desirable to have examples of simple problems for which both zeros and extrema point are rational. Recently, an algorithm was proposed for generating cubic polynomials with this property. However, from the computational viewpoint, the existing algorithm is not the most efficient one: in addition to applying explicit formulas, it also uses trial-and-error exhaustive search. In this paper, we propose a computationally efficient algorithm for generating all such polynomials: namely, an algorithm that uses only explicit formulas.

Analysis Of Feast Spectral Approximations Using The Dpg Discretization, 2019 Portland State University

#### Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker

*Mathematics and Statistics Faculty Publications and Presentations*

A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of ...

Special Issue Call For Papers: Creativity In Mathematics, 2019 University of Oklahoma

#### Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey

*Journal of Humanistic Mathematics*

*The Journal of Humanistic Mathematics* is pleased to announce a call for papers for a special issue on Creativity in Mathematics. Please send your abstract submissions via email to the guest editors by March 1, 2019. Initial submission of complete manuscripts is due August 1, 2019. The issue is currently scheduled to appear in July 2020.

What The Wasp Said, 2019 Independent scholar

#### What The Wasp Said, Hugh C. Culik

*Journal of Humanistic Mathematics*

On a bright spring day, the ancient building housing the English and Logic Departments begins to slowly collapse on itself, trapping McMann (an inept English professor) and Lucy Curt (a logician) in the office they share. As the Fibonacci repetitions of the building’s brickwork slowly peel away, McMann seizes the moment to tell Lucy stories about skunks, stories whose recurrent pattern finally leads to the unrecognized connection between a “message” burned into his ear by a wasp and the orderly universe for which he cannot find a language. At last, he looks up only to see Lucy descending a ...

An 1883 Faery Tale, 2019 Claremont Colleges

#### An 1883 Faery Tale, Scott W. Williams

*Journal of Humanistic Mathematics*

A poem about the construction of Georg Cantor's famous set.

Irrational Infinity, 2019 Claremont Colleges

#### Irrational Infinity, Ricky Chen

*Journal of Humanistic Mathematics*

A short whimsical poem on the cardinality of irrational numbers.

Cosmology, 2019 Edinboro University

A Mathematician's Travel Memories, 2019 University of Pikeville

#### A Mathematician's Travel Memories, Michael Holcomb

*Journal of Humanistic Mathematics*

No abstract provided.