Physical Sciences and Mathematics Commons^™

Image-Based Microbiome Profiling Differentiates Gut Microbial Metabolic States, Sarwesh Rauniyar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Rippled Almost Periodic Behavior In An Epilepsy Model, David Chan, Candace Kent

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Topology And Ecology: Deducing States Of The Upper Mississippi River System, Killian Davis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Connecting People To Food: A Network Approach To Alleviating Food Deserts, Anna Sisk

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Identification Of Control Targets In Boolean Networks Via Computational Algebra, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Integral Projection Model For Gizzard Shad That Includes Density-Dependent Age-0 Survival, James Peirce, Greg Sandland

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model, Michael Kerckhove, Shuheng Chen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden

Mathematics

Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.

Examining Middle School Students' Methods Of Justification, Leslie Reyes- Hernandez

Mathematics

Researching students’ thinking is imperative to improving the education system throughout the world. From extensive research, it is noted that students are unaccustomed and struggle with providing valid mathematical justifications (e.g. Inglis & Alcock 2012). The National Council of Teachers of Mathematics (NCTM, 2000) and Common Core State Standards of Mathematics (CCSSM, 2010) suggest that students should have several opportunities to construct mathematical arguments across all grade levels. To take a closer look at this educational phenomenon, we prompt fifth to eighth-grade students with nine mathematical tasks. Within our research, we focus on tasks based on number properties, algebraic thinking, …

Towards Constructing Vertex Algebroids, Nicholas J. Klecki

Theses and Dissertations

The notion of vertex algebroids were introduced in the late 1990's as a crucial tool for the study of chiral differential operators and chiral de Rham complex. Vertex algebroids play vital role in the study of N-graded vertex algebra. Also, they have deep connection with representation theory of Leibniz algebras. However, the classification of irreducible modules of vertex algebroids is not completed.

The aim of this thesis is to investigate the possibility of using the simple Lie algebra G_2 and its irreducible modules to construct vertex A-algebroids B that contain G_2 as their Levi factor. Under very mild and natural …

Lie Groups And Euler-Bernoulli Beam Equation, Medeu Amangeldi

Theses and Dissertations

Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.

Embedding Factorizations, Anna Johnsen

Theses and Dissertations

Let $V$ be a set of $n$ vertices for some $n\in\mathbb{N}$ and let $E$ be a collection of $h$-subsets of $V$. Then $\mathscr G = (V,E)$ is an $h$-unifrom hypergraph and we refer to $V$ as its vertex set and to $E$ as its edge set. We say that $\mathscr G$ is complete and denote it by $K_n^h$ if every $h$-subset of $V$ is contained in $E$. If every edge in $E$ is repeated $\lambda$ times, we say $G$ is $\lambda$-fold. Specifically, $\lambda K_n^h$ is the complete $\lambda$-fold $n$-vertex $h$-uniform hypergraph with an edge set containing $\lambda$ copies of every …

Optimal Claim Settlement Strategies Under Constraint Of Cap On Claim Loss, Hong Mao, Krzysztof Ostaszewski

Faculty Publications – Mathematics

In this paper, we examine the question of how to devise an optimal insurance claim settlement scheme under the constraint of a cap on the amount of the claim payment. We establish objective functions to maximize the net benefit due to exaggerated claims while at the same time maximizing the total expected wealth of the insured. Then, we establish a dual objective function to minimize the total expected loss, including the perspective of the insurer. Finally, we illustrate applications of our work and provide numerical analysis of it along with an example.

Classification Of Holomorphic Functions As Pólya Vector Fields Via Differential Geometry, Lucian-Miti Ionescu, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae

Faculty Publications – Mathematics

We review Pólya vector fields associated to holomorphic functions as an important pedagogical tool for making the complex integral understandable to the students, briefly mentioning its use in other dimensions. Techniques of differential geometry are then used to refine the study of holomorphic functions from a metric (Riemannian), affine differential or differential viewpoint. We prove that the only nontrivial holomorphic functions, whose Pólya vector field is torse-forming in the cannonical geometry of the plane, are the special Möbius transformations of the form f(z)=b(z+d)−1" role="presentation">𝑓(𝑧)=𝑏(𝑧+𝑑)−1. We define and characterize several types of affine connections, related to the parallelism of Pólya …