A Mathematical Model For The Upper Limits Of Thyroid Volume In Adolescents, 2019 University of South Florida

#### A Mathematical Model For The Upper Limits Of Thyroid Volume In Adolescents, Jacob Treanor

*Undergraduate Journal of Mathematical Modeling: One + Two*

This paper describes a mathematical model that relates age to the volume of the thyroid gland, given in milliliters, of adolescents based on data from a 1997 study by the World Health Organization (W.H.O.) (World Health Organization, 1997). Using the upper limit per age group provided by the data, a model was constructed through integration of the second derivative of the data for males and females, ages 6-15. It was concluded that the upper limit for the thyroid volume could be expressed by one of two second order polynomial equations, depending on gender, with any values significantly larger ...

Assimilating Mathematical Thinking To The Learning Of Shadows, 2019 Montclair State University

#### Assimilating Mathematical Thinking To The Learning Of Shadows, Taheeda Shwana Street-Conaway

*Theses, Dissertations and Culminating Projects*

This study focuses on a teaching experiment with 33 six-graders in a Kearny public school in Hudson County, New Jersey, during the 2017-2018 academic year. More specifically, this study explored a) the types of tasks and tools that can be used to develop students’ covariational and correspondence reasoning in learning about shadows and b) the nature of students’ reasoning about covariation and correspondence relationships as students engage in the use of tools and tasks. The results showed that the simulation and the tasks I designed had the students engaged in the learning process. Students were able to reason about the ...

Equivalence Of Classical And Quantum Codes, 2019 University of Kentucky

#### Equivalence Of Classical And Quantum Codes, Tefjol Pllaha

*Theses and Dissertations--Mathematics*

In classical and quantum information theory there are different types of error-correcting codes being used. We study the equivalence of codes via a classification of their isometries. The isometries of various codes over Frobenius alphabets endowed with various weights typically have a rich and predictable structure. On the other hand, when the alphabet is not Frobenius the isometry group behaves unpredictably. We use character theory to develop a duality theory of partitions over Frobenius bimodules, which is then used to study the equivalence of codes. We also consider instances of codes over non-Frobenius alphabets and establish their isometry groups. Secondly ...

Three Formative Questions In The Quantitative Literacy Movement, 2019 Dartmouth College

#### Three Formative Questions In The Quantitative Literacy Movement, Dorothy Wallace

*Numeracy*

In this essay we remember early discussions attempting to answer three questions that played a formative role in our understanding of and approach to numeracy, quantitative literacy, and quantitative reasoning: (1) What is numeracy? (2) Should the QL movement promote any specific kind of pedagogy? (3) What organizational structure will best support QL?

As the QL movement has progressed, these three questions continue to be difficult to answer. As a result, they have been useful formative guides for institutions and organizations seeking to improve the quantitative reasoning of students. Now that the quantitative literacy movement has a firmer standing in ...

On The Determination Of The Number Of Positive And Negative Polynomial Zeros And Their Isolation, 2019 Technological University Dublin

#### On The Determination Of The Number Of Positive And Negative Polynomial Zeros And Their Isolation, Emil Prodanov

*Articles*

A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real co-efficients and degree $n$ can be restricted with significantly better determinacy than that provided by the Descartes' rule of signs and also isolate quite successfully the zeros of the polynomial. The method relies on solving equations of degree smaller than that of the given polynomial. One can determine analytically the exact number of positive and negative zeros of a polynomial of degree up to and including five and also fully isolate the zeros of the polynomial analytically and ...

Van Der Waals Universe With Adiabatic Matter Creation, 2019 Technological University Dublin

#### Van Der Waals Universe With Adiabatic Matter Creation, Emil Prodanov, Rossen Ivanov

*Articles*

A FRWL cosmological model with perfect fluid comprising of van der Waals gas and dust has been studied in the context of dynamical analysis of a three-component autonomous non-linear dynamical system for the particle number density $n$, the Hubble parameter $H$, and the temperature $T$. Perfect fluid isentropic particle creation at rate proportional to an integer power $\alpha$ of $H$ has been incorporated. The existence of a global first integral allows the determination of the temperature evolution law and hence the reduction of the dynamical system to a two-component one. Special attention is paid to the cases of $\alpha = 2 ...

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.

Umsl Faculty Expertise, 2018 Selected Works

#### Umsl Faculty Expertise

*Adrian Clingher*

Gershgorin Type Sets For Eigenvalues Of Matrix Polynomials, 2018 National Technical University of Athens

#### Gershgorin Type Sets For Eigenvalues Of Matrix Polynomials, Christina Michailidou, Panayiotis Psarrakos

*Electronic Journal of Linear Algebra*

New localization results for polynomial eigenvalue problems are obtained, by extending the notions of the Gershgorin set, the generalized Gershgorin set, the Brauer set and the Dashnic-Zusmanovich set to the case of matrix polynomials.

Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, 2018 Utah State University

#### Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, John R. Stevens, Jennifer S. Herrick, Roger K. Wolff, Martha L. Slattery

*Mathematics and Statistics Faculty Publications*

**Background:** When genomics researchers design a high-throughput study to test for differential expression, some biological systems and research questions provide opportunities to use paired samples from subjects, and researchers can plan for a certain proportion of subjects to have paired samples. We consider the effect of this paired samples proportion on the statistical power of the study, using characteristics of both count (RNA-Seq) and continuous (microarray) expression data from a colorectal cancer study.

**Results:** We demonstrate that a higher proportion of subjects with paired samples yields higher statistical power, for various total numbers of samples, and for various strengths of ...

Ordering Cacti With Signless Laplacian Spread, 2018 China University of Mining and Technology

#### Ordering Cacti With Signless Laplacian Spread, Zhen Lin, Shu-Guang Guo

*Electronic Journal of Linear Algebra*

A cactus is a connected graph in which any two cycles have at most one vertex in common. The signless Laplacian spread of a graph is defined as the difference between the largest eigenvalue and the smallest eigenvalue of the associated signless Laplacian matrix. In this paper, all cacti of order n with signless Laplacian spread greater than or equal to n − 1/2 are determined.

Two Linear Preserver Problems On Graphs, 2018 Hunan University

#### Two Linear Preserver Problems On Graphs, Yanan Hu, Zhenhua Lyu

*Electronic Journal of Linear Algebra*

Let n, t, k be integers such that 3 ≤ t,k ≤ n. Denote by G_n the set of graphs with vertex set {1,2,...,n}. In this paper, the complete linear transformations on G_n mapping K_t-free graphs to K_t-free graphs are characterized. The complete linear transformations on G_n mapping C_k-free graphs to C_k-free graphs are also characterized when n ≥ 6.

Regularity Radius: Properties, Approximation And A Not A Priori Exponential Algorithm, 2018 Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Prague, Czech Republic and Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

#### Regularity Radius: Properties, Approximation And A Not A Priori Exponential Algorithm, David Hartman, Milan Hladik

*Electronic Journal of Linear Algebra*

The radius of regularity, sometimes spelled as the radius of nonsingularity, is a measure providing the distance of a given matrix to the nearest singular one. Despite its possible application strength this measure is still far from being handled in an efficient way also due to findings of Poljak and Rohn providing proof that checking this property is NP-hard for a general matrix. There are basically two approaches to handle this situation. Firstly, approximation algorithms are applied and secondly, tighter bounds for radius of regularity are considered. Improvements of both approaches have been recently shown by Hartman and Hlad\'{i ...

Modeling The Spread Of Disease, 2018 University of North Dakota

#### Modeling The Spread Of Disease, James Hollister

*Essential Studies UNDergraduate Showcase*

Mathematically modeling the spread of disease in a population is a focus among epidemiologists. Using an SIR model (susceptible, infected, and recovered), we can create a system of differential equations to help better understand how a disease spreads in a simple environment. However, if we are to create a more realistic environment, computer simulations may be necessary. We can use the results from these simulations to try and find ways to eradicate the disease as efficiently as possible. In this poster, we will present the SIR model, present a system of differential equations that describe the movement of disease in ...

A New Trend In Human Reproduction - Women In The Usa, 2018 University of North Dakota

#### A New Trend In Human Reproduction - Women In The Usa, Abby Rokke

*Essential Studies UNDergraduate Showcase*

The control a woman is allowed to have over her own reproductive system has been a recent popular topic of debate. Since the 1950's, women have made up over half of the total United States population. With women making up the majority of the country's citizens, it would be quite the contradiction for them to not have the right to make decisions about their own bodies. Over the last two decades many contraceptive and medical advances have assisted in a woman's ability to make her own choice. An interesting trend in childbearing has occurred from this new ...

Equations Of Motion In A Rotating Noninertial Reference Frame, 2018 University of North Dakota

#### Equations Of Motion In A Rotating Noninertial Reference Frame, Nicholas L. Sponsel

*Essential Studies UNDergraduate Showcase*

Measurement is an essential part of empirical research. As such, understanding whether the frame of reference in which a measurement occurs is inertial is essential for accurate data. As a rotating sphere, Earth is a non-inertial frame of reference and gives rise to fictitious forces. These forces are derived through vector algebra and further solved through matrix differential equations. The final solution for how velocity evolves over time results in sinusoidal functions with a period of 24 hours for Earth. To test the equations further, rational scenarios are proposed for different locations on the surface of Earth involving different initial ...

Subsets Of Vertices Of The Same Size And The Same Maximum Distance, 2018 Karlsruhe Institute of Technology

#### Subsets Of Vertices Of The Same Size And The Same Maximum Distance, Maria Axenovich, Dominik Duerrschnabel

*Theory and Applications of Graphs*

For a simple connected graph $G=(V,E)$ and a subset $X$ of its vertices, let $$d^*(X) = \max\{{\rm dist}_G(x,y): x,y\in X\}$$ and let

$h^*(G)$ be the largest $k$ such that there are disjoint vertex subsets $A$ and $B$ of $G$, each of size $k$ such that $d^*(A) = d^*(B).$

Let $h^*(n) = \min \{h^*(G): |V(G)|=n\}$. We prove that $h^*(n) = \lfloor (n+1)/3 \rfloor,$ for $n\geq 6.$ This solves the homometric set problem restricted to the largest distance exactly. In addition we compare $h^*(G)$ with ...

Context Is Critical: K-5th Grade Three-Act Math Tasks, 2018 Illinois Mathematics and Science Academy

#### Context Is Critical: K-5th Grade Three-Act Math Tasks, Lindsey Herlehy

*Publications & Research*

Mathematicians view mathematics within interesting and natural contexts. In this session, participants will engage and explore Three-Act Math Tasks; a story-telling pedagogical strategy that elicits student curiosity, collaboration, and questioning while redefining the term “real-world context” and the role that students play in the learning process. Resources will be provided

Equilibrium Analysis For An Epidemic Model With A Reservoir For Infection, 2018 University of Wisconsin - Milwaukee

#### Equilibrium Analysis For An Epidemic Model With A Reservoir For Infection, Istvan Lauko, Gabriella Pinter, Rachel Elizabeth Tewinkel

*Mathematical Sciences Student Articles*

We consider a system of non-linear differential equations describing the spread of an epidemic in two interacting populations. The model assumes that the epidemic spreads within the first population, which in turn acts as a reservoir of infection for the second population. Weexplore the conditions under which the epidemic is endemic in both populations and discuss the global asymptotic stability of the endemic equilibrium using a Lyapunov function and results established for asymptotically autonomous systems. We discuss monkeypox as an example of an emerging disease that can be modelled in this way and present some numerical results representing the model ...

Pentagons In Triangle-Free Graphs, 2018 Iowa State University

#### Pentagons In Triangle-Free Graphs, Bernard Lidicky, Florian Pfender

*Mathematics Publications*

For all n≥9, we show that the only triangle-free graphs on n vertices maximizing the number 5-cycles are balanced blow-ups of a 5-cycle. This completely resolves a conjecture by Erd\H{o}s, and extends results by Grzesik and Hatami, Hladky, Kral, Norin and Razborov, where they independently showed this same result for large n and for all n divisible by 5.