**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This series is not peer reviewed.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 2000

Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling, Kurt M. Bryan and Michael Vogelius

Lengths of Geodesics on Klein’s Quartic Curve, Ryan Derby-Talbot

Quest for Tilings on Riemann Surfaces of Genus Six and Seven, Robert Dirks and Maria Sloughter

Cwatset Isomorphism and its Consequences, Carolyn M. Girod, Matthew Lipinski, Joseph R. Mileti, and Jennifer R. Paulhus

Classification of Cwatsets Through Order 23, Ben Goodwin and Dennis Lin

#### Submissions from 1999

Tilings which Split a Mirror, Jim Belk

Constructing Kaleidscopic Tiling Polygons in the Hyperbolic Plane, Sean A. Broughton

Splitting Tiled Surfaces with Abelian Conformal Tiling Group, Sean A. Broughton

Divisible Tilings in the Hyperbolic Plane, Sean A. Broughton, Dawn M. Haney, Lori T. McKeough, and Brandy M. Smith

Elementary Inversion of the Laplace Transform, Kurt M. Bryan

Automorphic Subsets of the n-dimensional Cube are Translations of Cwatsets, Matthew Lepinski

#### Submissions from 1998

Stability and Reconstruction for an Inverse Problem for the Heat Equations, Kurt M. Bryan and Lester Caudill

A Messy, but Instructive, Case Study in Design of Experiments, Leroy A. Franklin, Belva J. Cooley, and Gary Elrod

Quadrilaterals Subdivided by Triangles in the Hyperbolic Plane, Dawn M. Haney and Lori T. McKeough

Maximally Disjoint Solutions of the Set Covering Problem, David J. Rader and Peter L. Hammer

Symmetry and Tiling Groups for Genus 4 and 5, C. Ryan Vinroot

#### Submissions from 1997

Generalized Conjugacy Classes, Pramod N. Achar

The Link between Scrambling Numbers and Derangements, Barry Balof, Eric Farmer, and Jamie Kawabata

Counting Ovals on a Symmetric Riemann Surface, Sean A. Broughton

Oval Intersections in Tilings on Surfaces, Dennis A. Schmidt

#### Submissions from 1996

A Stronger Triangle Inequality, Herb Bailey

Uniqueness for a Boundary Identification Problem in Thermal Imaging, Kurt M. Bryan and Lester F. Caudill

Effective Behavior of Clusters of Microscopic Cracks Inside a Homogeneous Conductor, Kurt M. Bryan and Michael Vogelius

CWATSETS: Weights, Cardinalities, and Generalizations, Richard Mohr

Divergence Diagrams: More than Cantor Dust Lies at the Edge of Feigenbaum Diagrams, John H. Rickert and Aaron Klebanoff

#### Submissions from 1995

Population Genetics: Estimation of Distributions through Systems of Non-Linear Differential Equations, Nacer E. Abrouk and Robert J. Lopez

Symmetries of Accola-MacLachlan and Kulkarni Surfaces, Sean A. Broughton, E Bujalance, A F. Costa, J M. Gamboa, and G Gromadzki

An Elementary Proof that Finite Groups Lack Unique Product Structures, Matthew Cushman

Rectangular Groups, Nick Fiala, Crystal Hanscom, Patrick Keenan, and Tung Tran

Conjugacy Classes of Triple Products in Finite Groups, Kevin Hutson and Emily Salvo

A Variable Time-Step Midpoint Scheme for Hamiltonian Systems, Yosi Shibberu

#### Submissions from 1994

Square Roots of Finite Groups, Kashi Abhyankar and Daniel Grossman

Finite Groups can be Arbitrarily Hamiltonian, Stephen Ahearn and Mark Huber

Counting Order Classes of Triple Products in Finite Groups, Scott Annin and Jennifer Ziebarth

An Inverse Problem in Thermal Language, Kurt M. Bryan and Lester Caudill

Square Roots of Finite Groups - II, Matthew Devos, David McAdams, and Rebecca Rapoport

Robot Space Coordinate Representation of Objects in Euclidean Space, Justin Gallagher

Distinct Products of Triples in Finite Groups, Curtis Z. Mitchell

#### Submissions from 1993

Approximation Methods for Singular Diffusions Arising in Genetics, Nacer E. Abrouk

Reconstruction of Multiple Cracks from Experimental, Electrostatic Boundary Measurements, Kurt M. Bryan, Valdis Liepa, and Michael Vogelius

When is the Number of p-Subgroups of a Group Satisfying a Property Congruent to 1 (mod p)?, Jason Fulman and Jeff Vanderkam

Hypergraph Representations and Orders of Cwatsets, Julie Kerr

Time-Discretization of Hamiltonian Dynamical Systems, Yosi Shibberu

Bounds on Squares of Two-Sets, Dan Slilaty and Jeff Vanderkam

Tracking Plasma Lactate Concentration in Vivo with a Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, and Shun P. Lim

#### Submissions from 1992

Counting Nilpotent Pairs in Finite Groups: Some Conjectures, H Dubose-Schmidt; Michael D. Galloy; and D,L, Wilson

Counting Nilpotent Pairs, Jason Fulman, Michael Galloy, and Jeffery Vanderkam

Vertex Coloring for Weighted Graphs with Application to Timetabling, Lynn Kiaer and Jay Yellen

Data on Four-Rewriteability in Finite Groups, Sharon A. Kineke

Some Facts About Cycels and Tidy Groups, Kevin O'Bryant, D. Patrick, Lawren Smithline, and Eric Wepsic

Some Upper Bounds for Commutativity and Cyclicity Measures in Finite Groups, David Patrick, Catherine Sugar, and Eric Wepsic

Simultaneous Rational Approximations and Related Diophantine Equations, John Rickert

Rewriteability, Commutators, and Fundamental n-Rewritings, Lawren Smithline

The 2/3 Bound for Rewritable n-tuples, Lawren Smithline and Catherine Sugar

Cubing Ordered 2-sets, Jeffery Vanderkam

Divisibility by |G| for Powers of Ordered k-sets, Jeffery Vanderkam

A4 Rewriteability, Eric Wepsic, Kevin O'Bryant, and Lawren Smithline

#### Submissions from 1991

Counting Centralizers in Finite Groups, Sarah Marie Belcastro and Gary J. Sherman

An Upper Bound for 3-Rewriteability in Finite Groups, Jordan Ellenberg

Integer Triangles with Rational Medians, Bart Goddard and Dale Mesner

Cyclicizers, Centralizers, and Normalizers, David Patrick and Eric Wepsic

Finite Abelian Groups in which the Probability of an Automorphism Fixing an Element is Large, Gary J. Sherman

Undergraduates, the Right Questions, and Cayley Produce Results, Gary J. Sherman

More Upper Bounds on the 3-Rewriteability of Non-3-Rewriteable Groups, Eric Wepsic

#### Submissions from 1990

Sets of Typical Subsamples, Joel Atkins and G.J Sherman

Dihedral Rewriteability, Cheryl P. Grood

Characterization of Joint Density by Conditional Densities, A.K. Gupta and T. Varga

Characterization of Matrix Variate Normal Distributions, A.K. Gupta and T. Varga

Fibonacci Sequences in Finite Groups, Steven W. Knox

A Numerical Approach to Rewriteability in Finite Groups, J.L. Leavitt, G.J. Sherman, and M.E. Walker

Rewriteable Sequencings of Groups, Jeanne Nielsen

Maximal Order Three-Rewriteable Subgroups of Symmetric Groups, John T. O'Bryan

How Hamiltonian Can a Finite Group Be?, G.J. Sherman, T.J. Tucker, and M.E. Walker

Some Facts About CWAT-Sets, Martin Wattenburg