Mathematical Modeling And Analysis Of The Zika Virus Epidemic With Human Mobility And Parameter Estimation For Localities In Puerto Rico,
2020
Inter American University of Puerto Rico - Bayamon
Mathematical Modeling And Analysis Of The Zika Virus Epidemic With Human Mobility And Parameter Estimation For Localities In Puerto Rico, Carmen Caiseda
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Prime Supporters In College Students' Support Networks,
2020
VCU
Prime Supporters In College Students' Support Networks, David Chan, Hollee Mcginnis, Michael Broda, Haya Hamid, Jeremy Winslow, Quindel Jones, Joy Ma
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Application Of Tda Mapper To Water Data And Bird Data,
2020
University of Wisconsin - La Crosse
Application Of Tda Mapper To Water Data And Bird Data, Wako Bungula
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modelling Of Temperature Effects On The Afd Neuron Of Caenorhabditis Elegans,
2020
Illinois State University
Mathematical Modelling Of Temperature Effects On The Afd Neuron Of Caenorhabditis Elegans, Zachary Mobille, Rosangela Follmann, Epaminondas Rosa
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Ethnomathematics: Art, Culture, And Social Justice,
2020
University of Delaware
Ethnomathematics: Art, Culture, And Social Justice, John R. Jungck
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Community-Based Curriculum: A Novel Approach In Collaborative Teaching,
2020
Illinois State University
Community-Based Curriculum: A Novel Approach In Collaborative Teaching, Christopher Hay-Jahans
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Algebraic And Combinatorial Approaches For Counting Cycles Arising In Population Biology,
2020
University of Central Florida
Algebraic And Combinatorial Approaches For Counting Cycles Arising In Population Biology, Brian Chau
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Testing The Effect Of Acetaminophen Overdose On The Liver And The Role Of Biomarkers To Predict Death Or Survival,
2020
University of Wisconsin-Whitewater
Testing The Effect Of Acetaminophen Overdose On The Liver And The Role Of Biomarkers To Predict Death Or Survival, Christine Brasic
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects,
2020
University of New Mexico
From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov
Mathematics & Statistics ETDs
In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present …
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation,
2020
Doctoral Student, Applied Mathematics
Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova
Mathematics & Statistics ETDs
The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …
On The Construction And Mathematical Analysis Of The Wavelet Transform And Its Matricial Properties,
2020
Universidad Mayor de San Simón
On The Construction And Mathematical Analysis Of The Wavelet Transform And Its Matricial Properties, Diego Sejas Viscarra
Rose-Hulman Undergraduate Mathematics Journal
We study the properties of computational methods for the Wavelet Transform and its Inverse from the point of view of Linear Algebra. We present a characterization of such methods as matrix products, proving in particular that each iteration corresponds to the multiplication of an adequate unitary matrix. From that point we prove that some important properties of the Continuous Wavelet Transform, such as linearity, distributivity over matrix multiplication, isometry, etc., are inherited by these discrete methods.
This work is divided into four sections. The first section corresponds to the classical theoretical foundation of harmonic analysis with wavelets; it is used …
Dna Self-Assembly Design For Gear Graphs,
2020
Converse College
Dna Self-Assembly Design For Gear Graphs, Chiara Mattamira
Rose-Hulman Undergraduate Mathematics Journal
Application of graph theory to the well-known complementary properties of DNA strands has resulted in new insights about more efficient ways to form DNA nanostructures, which have been discovered as useful tools for drug delivery, biomolecular computing, and biosensors. The key concept underlying DNA nanotechnology is the formation of complete DNA complexes out of a given collection of branched junction molecules. These molecules can be modeled in the abstract as portions of graphs made up of vertices and half-edges, where complete edges are representations of double-stranded DNA pieces that have joined together. For efficiency, one aim is to minimize the …
Generalised Fibonacci Sequences Under Modular Arithmetic,
2020
Concordia University of Edmonton
Generalised Fibonacci Sequences Under Modular Arithmetic, Connor Riddlesden
Rose-Hulman Undergraduate Mathematics Journal
In this paper, we find patterns and count the number of distinct generalised Fibonacci sequences under modular arithmetic. We will start with the repetition of the normal Fibonacci sequence modulo an integer, m, where m is greater than or equal to two and make connections to its dependency on the prime factorisation of m. We will then extend the complexity of the problem into generalised Fibonacci sequences with different starting values. Finally we will present some interesting observations that are still open problems.
The Name Tag Problem,
2020
Boise State University
The Name Tag Problem, Christian Carley
Rose-Hulman Undergraduate Mathematics Journal
The Name Tag Problem is a thought experiment that, when formalized, serves as an introduction to the concept of an orthomorphism of $\Zn$. Orthomorphisms are a type of group permutation and their graphs are used to construct mutually orthogonal Latin squares, affine planes and other objects. This paper walks through the formalization of the Name Tag Problem and its linear solutions, which center around modular arithmetic. The characterization of which linear mappings give rise to these solutions developed in this paper can be used to calculate the exact number of linear orthomorphisms for any additive group Z/nZ, which is demonstrated …
Configuration Spaces For The Working Undergraduate,
2020
Reed College
Configuration Spaces For The Working Undergraduate, Lucas Williams
Rose-Hulman Undergraduate Mathematics Journal
Configuration spaces form a rich class of topological objects which are not usually presented to an undergraduate audience. Our aim is to present configuration spaces in a manner accessible to the advanced undergraduate. We begin with a slight introduction to the topic before giving necessary background on algebraic topology. We then discuss configuration spaces of the euclidean plane and the braid groups they give rise to. Lastly, we discuss configuration spaces of graphs and the various techniques which have been developed to pursue their study.
On The Equitable Total (𝑘+1)-Coloring Of 𝑘-Regular Graphs,
2020
Youngstown State University
On The Equitable Total (𝑘+1)-Coloring Of 𝑘-Regular Graphs, Bryson Stemock
Rose-Hulman Undergraduate Mathematics Journal
A graph is considered to be totally colored when one color is assigned to each vertex and to each edge so that no adjacent or incident vertices or edges bear the same color. The \textit{total chromatic number} of a graph is the least number of colors required to totally color a graph. This paper focuses on $k$-regular graphs, whose symmetry and regularity allow for a closer look at general total coloring strategies. Such graphs include the previously defined M\"obius ladder, which has a total chromatic number of 5, as well as the newly defined bird's nest, which is shown to …
Colorings And Sudoku Puzzles,
2020
Murray State University
Colorings And Sudoku Puzzles, Katelyn D. May
Rose-Hulman Undergraduate Mathematics Journal
Map colorings refer to assigning colors to different regions of a map. In particular, a typical application is to assign colors so that no two adjacent regions are the same color. Map colorings are easily converted to graph coloring problems: regions correspond to vertices and edges between two vertices exist for adjacent regions. We extend these notions to Shidoku, 4x4 Sudoku puzzles, and standard 9x9 Sudoku puzzles by demanding unique entries in rows, columns, and regions. Motivated by our study of ring and field theory, we expand upon the standard division algorithm to study Gr\"obner bases in multivariate polynomial rings. …
Investigating First Returns: The Effect Of Multicolored Vectors,
2020
Howard University
Investigating First Returns: The Effect Of Multicolored Vectors, Shakuan Frankson, Myka Terry
Rose-Hulman Undergraduate Mathematics Journal
By definition, a first return is the immediate moment that a path, using vectors in the Cartesian plane, touches the x-axis after leaving it previously from a given point; the initial point is often the origin. In this case, using certain diagonal and horizontal vectors while restricting the movements to the first quadrant will cause almost every first return to end at the point (2n,0), where 2n counts the equal number of up and down steps in a path. The exception will be explained further in the sections below. Using the first returns of Catalan, Schröder, and Motzkin numbers, which …
New Theorems For The Digraphs Of Commutative Rings,
2020
Indiana Wesleyan University
New Theorems For The Digraphs Of Commutative Rings, Morgan Bounds
Rose-Hulman Undergraduate Mathematics Journal
The digraphs of commutative rings under modular arithmetic reveal intriguing cycle patterns, many of which have yet to be explained. To help illuminate these patterns, we establish a set of new theorems. Rings with relatively prime moduli a and b are used to predict cycles in the digraph of the ring with modulus ab. Rings that use Pythagorean primes as their modulus are shown to always have a cycle in common. Rings with perfect square moduli have cycles that relate to their square root.
On The Enumeration Of Shapes,
2020
Georgia Institute of Technology
On The Enumeration Of Shapes, May Cai, Nicholas Liao
Rose-Hulman Undergraduate Mathematics Journal
We define a shape as a union of finitely many line segments. Given an arrangement of lines on a plane, we count the number of shapes in the arrangement by examining the symmetries of the arrangement and applying Burnside's lemma. We further establish a generating function for the number of distinct line segments on a line with k distinguished points. We list all affine line arrangements of four and five line segments, together with the corresponding number of shapes on them.
