#### Submissions from 2005

Ted Talk: Arthur Benjamin Does "Mathemagic", Arthur T. Benjamin

Q.954 and A.954, Quickie Problem and Solution, Arthur T. Benjamin and Michel Bataille

Recounting the Odds of an Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, and Florence Newberger

Counting on Determinants, Arthur T. Benjamin and Naiomi T. Cameron

Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, and Jennifer J. Quinn

Pythagorean Primes and Palindromic Continued Fractions, Arthur T. Benjamin and Doron Zeilberger

Lower Bounds for Simplicial Covers and Triangulations of Cubes, Adam Bliss '03 and Francis E. Su

The Closed Topological Vertex via the Cremona Transform, Jim Bryan and Dagan Karp

Upper Estimates for the Energy of Solutions of Nonhomogeneous Boundary Value Problems, Alfonso Castro and Mónica Clapp

Construction of a Radial Solution to a Superlinear Dirichlet Problem that Changes Sign Exactly Once, Alfonso Castro and Jorge Cossio

Determinants and Polynomial Root Structure, Lisette G. de Pillis

A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth, Lisette G. de Pillis, Ami E. Radunskaya, and Charles L. Wiseman

Using Ultrasonic Atomization to Produce an Aerosol of Micron-scale Particles, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, M. Schubmehl '02, N. Schommer '04, Andrew J. Bernoff, S. Dasnurkar, and T. Ditmire

Properties of One-Point Completions of a Noncompact Metrizable Space, Melvin Henriksen, Ludvík Janoš, and R. G. Woods

C(X) Can Sometimes Determine X Without X Being Realcompact, Melvin Henriksen and Biswajit Mitra

Two-Dimensional Self-Assembly in Diblock Copolymers, Anette E. Hosoi, Dmitriy Kogan '03, Caitlin E. Devereaux '02, Andrew J. Bernoff, and Shenda M. Baker

Looking Beyond the Curriculum in Jamaica, Jon T. Jacobsen and Michael E. Orrison Jr.

Kinetics and Nucleation for Driven Thin Film Flow, Rachel Levy and Michael Shearer

Evaluating the Viability of 100 Per Cent Container Inspection at America’s Ports, Susan E. Martonosi, David S. Ortiz, and Henry H. Willis

SRT Division Algorithms As Dynamical Systems, Mark McCann and Nicholas Pippenger

A Mathematical Model for Treatment-Resistant Mutations of HIV, Helen Moore and Weiqing Gu

The Average Amount of Information Lost in Multiplication, Nicholas Pippenger

The Boolean Functions Computed by Random Boolean Formulas OR How to Grow the Right Function, Nicholas Pippenger and Alex Brodsky

A Constructive Proof of Ky Fan's Generalization of Tucker's Lemma, Timothy Prescott '02 and Francis E. Su

#### Submissions from 2004

A (not so) Complex Solution to a² + b² = cⁿ, Arnold M. Adelberg, Arthur T. Benjamin, and David I. Rudel '99

Mathematical Magic, Arthur T. Benjamin

Putnam, Pizza & Problem Solving, Andrew J. Bernoff and Francis E. Su

Semilinear Equations with Discrete Spectrum, Alfonso Castro

An Existence Result for a Class of Sublinear Semipositone Systems, Alfonso Castro, C. Maya, and Ratnasingham Shivaji

An Experimental Study of Micron-scale Droplet Aerosols Produced via Ultrasonic Atomization, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, N. Schommer '04, M. Schubmehl '02, Andrew J. Bernoff, and B. Forrest '02

Examples of Cayley 4-Manifolds, Weiqing Gu and Christopher Pries '03

Cozero Complemented Spaces; When the Space of Minimal Prime Ideals of a C(X) is Compact, Melvin Henriksen and R. G. Woods

Random Walks with Badly Approximable Numbers, Doug Hensley and Francis Su

A Liouville-Gelfand Equation for k-Hessian Operators, Jon T. Jacobsen

Radial Solutions of Quasilinear Elliptic Differential Equations, Jon T. Jacobsen and Klaus Schmitt

Comparison of Two Dynamic Contact Line Models for Driven Thin Liquid Films, Rachel Levy and Michael Shearer

Terror is in the Air, Susan E. Martonosi and Arnold Barnett

Computing Isotypic Projections with the Lanczos Iteration, David K. Maslen, Michael E. Orrison Jr., and Daniel N. Rockmore

Rooted Trees and Iterated Wreath Products of Cyclic Groups, Rosa C. Orellana, Michael E. Orrison Jr., and Daniel N. Rockmore

Radon Transforms and the Finite General Linear Groups, Michael E. Orrison

Essential P-Spaces: A Generalization of Door Spaces, Emad Abu Osba and Melvin Henriksen

Combining Local and Von Neumann Regular Rings, Emad Abu Osba, Melvin Henriksen, and Osama Alkan

Entropy and Expected Acceptance Counts for Finite Automata, Nicholas Pippenger

Random Walks on the Torus with Several Generators, Timothy Prescott '02 and Francis E. Su

Magical Miscellany, Francis Su

Blowup and Dissipation in a Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, and Andrea L. Bertozzi

#### Submissions from 2003

A Combinatorial Approach to Hyperharmonic Numbers, Arthur T. Benjamin, David Gaebler '04, and Robert Gaebler '04

A Probabilistic View of Certain Weighted Fibonacci Sums, Arthur T. Benjamin, Judson D. Neer, Daniel T. Otero, and James A. Sellers

The Fibonacci Numbers -- Exposed More Discretely, Arthur T. Benjamin and Jennifer J. Quinn

A Generalization of a Theorem on Biseparating Maps, Karim Boulabiar, Gerard Buskes, and Melvin Henriksen

Asymptotic Behavior of the Potential and Existence of a Periodic Solution for a Second Order Differential Equation, Alfonso Castro and Chen Chang

The Effect of the Domain Topology on the Number of Minimal Nodal Solutions of an Elliptic Equation at Critical Growth in a Symmetric Domain, Alfonso Castro and Mónica Clapp

A Sign-Changing Solution for a Superlinear Dirichlet Problem, II, Alfonso Castro, Pavel Drabek, and John M. Neuberger

The Dynamics of an Optimally Controlled Tumor Model: A Case Study, Lisette G. de Pillis and Ami E. Radunskaya

A Mathematical Model of Immune Response to Tumor Invasion, Lisette de Pillis and Ami Radunskaya

Spaces X in Which All Prime z-Ideals of C(X) Are Minimal or Maximal, Melvin Henriksen, Jorge Martinez, and R. G. Woods

A Pointfree Study of Bases For Spaces Of Minimal Prime Ideals, Melvin Henriksen and Joanne Walters-Wayland

Solitary Waves in Layered Nonlinear Media, Randall J. Leveque and Darryl H. Yong

SRT Division Algortihms as Dynamical Systems, Mark McCann and Nicholas J. Pippenger

Rates of Convergence to Self-Similar Solutions of Burgers' Equation, Joel C. Miller '00 and Andrew J. Bernoff

The Inequalities of Quantum Information Theory, Nicholas Pippenger

The Shortest Disjunctive Normal Form of a Random Boolean Function, Nicholas Pippenger

Consensus-Halving via Theorems of Borsuk-Ulam and Tucker, Forrest W. Simmons and Francis E. Su

Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media, Darryl H. Yong and Randall J. Leveque

#### Submissions from 2002

Infinitely Many Nonradial Solutions to a Superlinear Dirichlet Problem, Hugo Aduén and Alfonso Castro

Analysis of the N-Card Version of the Game Le Her, Arthur T. Benjamin and Alan J. Goldman

Two Quick Combinatorial Proofs, Arthur T. Benjamin and Michael E. Orrison

A Stirling Encounter with Harmonic Numbers, Arthur T. Benjamin, Gregory O. Preston '01, and Jennifer J. Quinn

Linear Stability of Source-Type Similarity Solutions of the Thin Film Equation, Andrew J. Bernoff and Thomas P. Witelski

A Polytopal Generalization of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, and Francis E. Su

Cesaro Limits of Analytically Perturbed Stochastic Matrices, Jerzy Filar, Henry A. Krieger, and Zamir Sayed

On Choosing and Bounding Probability Metrics, Alison L. Gibbs and Francis E. Su

Bidding for Envy-Freeness: A Procedural Approach to n-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, and Francis E. Su

Old and New Unsolved Problems in Lattice-Ordered Rings that need not be f-Rings, Melvin Henriksen

A Minimal Regular Ring Extension of C(X), Melvin Henriksen, Robert M. Raphael, and R. G. Woods

The Liouville-Bratu-Gelfand Problem for Radial Operators, Jon T. Jacobsen and Klaus Schmitt

Four-Person Envy-Free Chore Division, Elisha Peterson '00 and Francis E. Su

Analysis of Carry Propagation in Addition: An Elementary Approach, Nicholas Pippenger

Enumeration of Matchings in the Incidence Graphs of Complete and Complete Bipartite Graphs, Nicholas Pippenger

Galois Theory for Minors of Finite Functions, Nicholas Pippenger

Quantum Signal Propagation in Depolarizing Channels, Nicholas Pippenger

Expected Acceptance Counts for Finite Automata with Almost Uniform Input, Nicholas J. Pippenger

Nonlinear Dynamics of Mode-locking Optical Fiber Ring Lasers, Kristin M. Spaulding, Darryl H. Yong, Arnold D. Kim, and J Nathan Kutz

Initial Boundary-Value Problems for a Pair of Conservation Laws, Darryl H. Yong and J Kevorkian

Solving Boundary-value Problems for Systems of Hyperbolic Conservation Laws with Rapidly Varying Coefficients, Darryl H. Yong and J Kevorkian

#### Submissions from 2001

An Extension of a Criterion for Unimodality, Jenny Alvarez, Miguel Amadis, George Boros, Dagan Karp, Victor H. Moll, and Leobardo Rosales

Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, and Anandhan Jayaraman

Optimal Token Allocations in Solitaire Knock 'M Down, Arthur Benjamin, Matthew T. Fluet, and Mark L. Huber

Mathematical Constance (A Poem Dedicated to Constance Reid), Arthur T. Benjamin

Math Major, Math Major, Arthur T. Benjamin

Proof With Words: 2 + 11 - 1 = 12, Arthur T. Benjamin

Composite Fermions and Integer Partitions, Arthur T. Benjamin, Jennifer J. Quinn, John J. Quinn, and Arkadiusz Wojs

A Local Inversion Principle of the Nash-Moser Type, Alfonso Castro and J. W. Neuberger

An Inverse Function Theorem via Continuous Newton’s Method, Alfonso Castro and J. W. Neuberger

Model Updating by Adding Known Masses, Philip D. Cha and Lisette G. de Pillis

The Long-Term Impact of University Budget Cuts: A Mathematical Model, Emmeline G. de Pillis and Lisette G. de Pillis

A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach, Lisette G. de Pillis and Ami E. Radunskaya

Volume-Preserving Great Circle Flows on the 3-Sphere, Herman Gluck and Weiqing Gu

Uniqueness of Volume-Minimizing Submanifolds Calibrated by the First Pontryagin Form, Daniel A. Grossman and Weiqing Gu

Oxtoby's Pseudocompleteness Revisited, Melvin Henriksen, Ralph Kopperman, Marlon Rayburn, and Aaron R. Todd