**Rose-Hulman Mathematical Sciences Technical Report Series**is a preprint and informal technical report publication series for faculty and undergraduate student research in the Mathematics Department at Rose-Hulman. Student authored publications have a faculty adviser who is typically a senior thesis/project adviser or adviser for a summer research project such as the Rose-Hulman NSF-REU program. A student's undergraduate institution at the time of the research is recorded in the author information.

This series is not peer reviewed. The authors (with guidance from mentors) are responsible for the correctness of results and exposition of the papers.

#### Submissions from 2022

Analysis of a Quantum Attack on the Blum-Micali Pseudorandom Number Generator, Tingfei Feng

Structure of Number Theoretic Graphs, Lee Trent

The Primitive Root Problem: a Problem in BQP, Shixin Wu

#### Submissions from 2021

Probability Distributions for Elliptic Curves in the CGL Hash Function, Dhruv Bhatia, Kara Fagerstrom, and Max Watson

Computer Program Simulation of a Quantum Turing Machine with Circuit Model, Shixin Wu

#### Submissions from 2020

Topological and H^q Equivalence of Cyclic n-gonal Actions on Riemann Surfaces - Part II, Sean A. Broughton

Modeling Braids with Space-Varying and Time-Varying Stranded Cellular Automata, Brian Chan

The Game of Life on the Hyperbolic Plane, Yuncong Gu

#### Submissions from 2019

Forward Selection via Distance Correlation, Ty Adams

Effects of Framing in Exams on Student Performance, Mariana Lane and Eric Reyes

Repeat Length Of Patterns On Weaving Products, Zhuochen Liu

Periodicity and Invertibility of Lattice Gas Cellular Automata, Jiawen Wang

#### Submissions from 2018

Branching matrices for the automorphism group lattice of a Riemann surface, Sean A. Broughton

Stranded Cellular Automaton and Weaving Products, Hao Yang

#### Submissions from 2017

Algorithmic Factorization of Polynomials over Number Fields, Christian Schulz

#### Submissions from 2016

Topological and Hq Equivalence of Prime Cyclic p-gonal Actions on Riemann Surfaces (Corrected), Sean A. Broughton

Counting fixed points and two-cycles of the singular map x ↦ x^(x^n), Joshua Holden, Pamela A. Richardson, and Margaret M. Robinson

Mathematical Modeling of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)

Counting Solutions to Discrete Non-Algebraic Equations Modulo Prime Powers, Abigail Mann

Variance of Clusterings on Graphs, Thomas Vlado Mulc

Statistical Analysis of Binary Functional Graphs of the Discrete Logarithm, Mitchell Orzech

Inverse Laplace Transform and Post Inversion Formula, Qinmao Zhang

#### Submissions from 2015

Quasi-platonic PSL2(q)-actions on closed Riemann surfaces, Sean A. Broughton

Spontaneous synchrony on graphs and the emergence of order from disorder, Dylan Linville and Daniel Trugillo Martins Fontes

Study of Extinction Time, Yilin Wang

#### Submissions from 2014

Calculation of the Killing Form of a Simple Lie Group, Sean A. Broughton

Continuous Dependence of Solutions of Equations on Parameters, Sean A. Broughton

Analytical Solution of the Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton and Jeffery J. Leader

Statistics for fixed points of the self-power map, Joshua Holden and Matthew Friedrichsen

Deconstructing the Welch Equation using p-adic Methods, Abigail Mann and Adelyn Yeoh

#### Submissions from 2013

A Numerical Analysis of PSM with Applications to DDEs, Dustin Lehmkuhl

#### Submissions from 2012

Thermal Detection of Inaccessible Corrosion, Matthew Charnley and Andrew Rzeznik

Robust Analysis of Metabolic Pathways, Emily Gruber, Amy Ko, Michael MacGillvray, and Miranda Sawyer

Fundamentals of Protein Structure Alignment, Allen Holder, Mark Brandt, and Yosi Shibberu

Determining Properties of Metal by Analyzing Changes in Impedance, Chase Mathison and Laura Booton

#### Submissions from 2011

Nondestructive Electrothermal Detection of Corrosion, Brittany Ambeau, Harris Enniss, and Stefan Schnake

Structure and Randomness of the Discrete Lambert Map, JingJing Chen and Mark Lotts

Algebraic Solutions to Overdefined Systems with Applications to Cryptanalysis, Eric Crockett

The Elliptic Curve Discrete Logarithm and Functional Graphs, Christopher J. Evans

Cloaking Against Thermal Imaging, Maple So

The Square Discrete Exponentiation Map, A Wood

#### Submissions from 2010

Discrete Logarithms on Elliptic Curves, Aaron Blumenfeld

Bilinear Programming and Protein Structure Alignment, J. Cain, D. Kamenetsky, and N. Lavine

Structure and Statistics of the Self-Power Map, Matthew Friedrichsen, Brian Larson, and Emily McDowell

Computational Biology, Harvey Greenberg and Allen Holder

G-lattices for an Unrooted Perfect Phylogeny, Monica Grigg

Parametric LP Analysis, Allen Holder

A Spectral Approach to Protein Structure Alignment, Yosi Shibberu and Allen Holder

Intrinsic Contact Geometry of Protein Dynamics, Yosi Shibberu, Allen Holder, and David Cooper

Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, and Kyla Lutz

#### Submissions from 2009

Anti-Cloaking: The Mathematics of Disguise, Theresa C. Anderson and Brooke E. Phillips

Flattening a Cone, Sean A. Broughton

Operations Research Methods for Optimization in Radiation Oncology, M Ehrgott and Allen Holder

The Digraph of the Square Mapping on Elliptic Curves, Katrina Glaeser

Electrical Impedance Imaging of Corrosion on a Partially Accessible 2-Dimensional Region, Court Hoang and Katherine Osenbach

Statistical Investigation of Structure in the Discrete Logarithm, Andrew Hoffman

A Decomposition of the Pure Parsimony Problem, Allen Holder and Thomas M. Langley

Structural Properties of Power Digraphs Modulo n, Joseph Kramer-Miller

A clustering approach for optimizing beam angles in IMRT planning, Gino J. Lim, Allen Holder, and Josh Reese

Solving the p-Median Problem with Insights from Discrete Vector Quantization, Gino J. Lim, Allen Holder, and Josh Reese

Discrete Logarithm over Composite Moduli, Marcus L. Mace

#### Submissions from 2008

Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, R Acosta, W Brick, A Hanna, Allen Holder, D Lara, G McQuillen, D Nevin, P Uhlig, and B Salter

Determining the Shape of a Resistor Grid, Esther Chiew and Vincent Selhorst-Jones

Optimization in the Undergraduate Curriculum, Allen Holder

Electrothermal Imaging in One and Two Dimensions, Michael Janus and David Kibbling

A Statistical Look at Maps of the Discrete Logarithm, Nathan Lindle

Do the Coefficients of a Modular Form Really "Encode Arithmetic Data"?, Ken McMurdy and Hari Ravindran

#### Submissions from 2007

The Barycenter of the Numerical Range of a Matrix, Sean A. Broughton, Roger G. Lautzenheiser, and Thomas Werne

The Discrete Logarithm Problem and Ternary Functional Graphs, Max F. Brugger and Christina A. Frederick

Isomorphisms of Elliptic Curves over Extensions of Finite Fields, Mathew Niemerg

Utilizing Thermal Testing for Recovering, James Preciado and Thomas Werne

#### Submissions from 2006

Thermal Imaging to Recover a Defect in Three Dimensional Objects, Breanne Baker

Non-Destructive Recovery of Voids within a Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi

#### Submissions from 2005

On the Action of Weight-Preserving Sets, Matthew Badger

Foundations of Generalized Cwatsets, Jesse Beder

Time-Dependent Thermal Imaging of Circular Inclusions, Donald L. Brouwn and Mark Hubenthal

Mapping the Discrete Logarithm, Daniel R. Cloutier

Big Cwatsets and Hamming Code, Matthew Davis, Thomas M. Langley, and Norah Mazel

Thermal Imaging of Circular Inclusions within a Two-Dimensional Region, Shannon Talbott and Hilary Spring

#### Submissions from 2004

The Birational Isomorphism Types of Smooth Real Elliptic Curves, Sean A. Broughton

Reconstruction of an Unknown Boundary Portion From Cauchy Data in N-dimensions, Kurt M. Bryan and Lester Caudill

Non-Destructive Testing of Thermal Resistances for a Single Inclusion in a 2-Dimensional Domain, Nicholas Christian and Mathew A. Johnson

Reconstruction of Partially Conductive Cracks using Boundary Data, David McCune and Janine Haugh

Determining the Length of a One-Dimensional Bar, Natalya Yarlikina and Holly Walrath

#### Submissions from 2003

When Abelian Groups Split, Rachel M. Thomas and Robert C. Rhoades

#### Submissions from 2002

A Review of Selected Works on Crack Indentification, Kurt M. Bryan

Congruences of Restricted Partition Functions, Matthew Culek and Amanda Knecht

Characterizing a Defect in a One-Dimensional Bar, Cynthia Gangi and Sameer Shah

Tilings of Low-Genus Surfaces by Quadrilaterals, John Gregoire and Isabel Averil

Fixed Point and Two-cycles of the Discrete Logarithm, Joshua Holden

Pigeon-Holing Monodromy Groups, Niles G. Johnson

Hyperbolic Billiard Paths, Rebecca Lehman and Chad White

The order at 2 of the odd-partition function, Chris Mehelich

Reconstruction of Cracks with Unknown Transmission Condition from Boundary Data, F Ronald Ogborne III and Melissa E. Vellela

The Galois Correspondence for Branched Covering Spaces and its Relationship to Hecke Algebras, Matthew Ong

Fast Reconstruction of Cracks Using Boundary Measurements, Nicholas A. Trainor and Rachel M. Krieger

A Restricted Partition Function Modulo 3, Naomi Utgof

Applications of Graph Theory to Separability, Stephen Young

#### Submissions from 2001

Separability of Tilings, Nicholas Baeth, Jason Deblois, and Lisa Powell