On The Utility Of I = √-1, 2011 Cedarville University

#### On The Utility Of I = √-1, Adam J. Hammett

*Science and Mathematics Faculty Presentations*

No abstract provided.

An Experimental Nexos Laboratory Using Virtual Xinu, 2011 Renaissance Computing Institute

#### An Experimental Nexos Laboratory Using Virtual Xinu, Paul Ruth, Dennis Brylow

*Mathematics, Statistics and Computer Science Faculty Research and Publications*

The Nexos Project is a joint effort between Marquette University, the University of Buffalo, and the University of Mississippi to build curriculum materials and a supporting experimental laboratory for hands-on projects in computer systems courses. The approach focuses on inexpensive, flexible, commodity embedded hardware, freely available development and debugging tools, and a fresh implementation of a classic operating system, Embedded Xinu, that is ideal for student exploration. This paper describes an extension to the Nexos laboratory that includes a new target platform composed of Qemu virtual machines. Virtual Xinu addresses two challenges that limit the effectiveness of Nexos. First, potential ...

A High-Resolution Finite-Difference Method For Simulating Two-Fluid, Viscoelastic Gel Dynamics, 2011 Boise State University

#### A High-Resolution Finite-Difference Method For Simulating Two-Fluid, Viscoelastic Gel Dynamics, Grady Wright, Robert D. Guy, Jian Du, Aaron L. Fogelson

*Mathematics Faculty Publications and Presentations*

An important class of gels are those composed of a polymer network and fluid solvent. The mechanical and rheological properties of these two-fluid gels can change dramatically in response to temperature, stress, and chemical stimulus. Because of their adaptivity, these gels are important in many biological systems, e.g. gels make up the cytoplasm of cells and the mucus in the respiratory and digestive systems, and they are involved in the formation of blood clots. In this study we consider a mathematical model for gels that treats the network phase as a viscoelastic fluid with spatially and temporally varying material ...

2011 (Fall), 2011 University of Dayton

#### 2011 (Fall), University Of Dayton. Department Of Mathematics

*Colloquia*

Abstracts of the talks given at the 2011 Fall Colloquium.

Completeness Of Interacting Particles, 2011 Technological University Dublin

#### Completeness Of Interacting Particles, Pavel Abramski

*Doctoral*

This thesis concerns the completeness of scattering states of n _-interacting particles in one dimension. Only the repulsive case is treated, where thereare no bound states and the spectrum is entirely absolutely continuous, so the scattering Hilbert space is the whole of L2(Rn). The thesis consists of 4 chapters: The first chapter describes the model, the scattering states as given by the Bethe Ansatz, and the main completeness problem. The second chapter contains the proof of the completeness relation in the case of two particles: n = 2. This case had in fact already been treated by B. Smit (1997 ...

Infinitary Equivalence Of Zp- Modules With Nice Decomposition Bases, 2011 Universitat Duisburg-Essen, Germany

#### Infinitary Equivalence Of Zp- Modules With Nice Decomposition Bases, Rüdiger Göbel, Katrin Leistner, Peter Loth, Lutz Strüngmann

*Mathematics Faculty Publications*

Warfield modules are direct summands of simply presented **Z**_{p }- modules, or, alternatively, are **Z**_{p }- modules possessing a nice decomposition basis with simply presented cokernel. They have been classified up to isomorphism by theor Ilm-Kaplansky and Warfield invariants. Taking a model theoretic point of view and using infinitary languages we give here a complete theoretic characterization of a large class of** Z**_{p }- modules having a nice decomposition basis. As a corollary, we obtain the classical classification of countable Warfield modules. This generalizes results by Barwise and Eklof.

A Gambler's Ruin In Monte Carlo, 2011 Selected Works

#### A Gambler's Ruin In Monte Carlo, Alicia Johnson

*Alicia A. Johnson*

No abstract provided.

Squaring, Cubing, And Cube Rooting, 2011 Harvey Mudd College

#### Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin

*All HMC Faculty Publications and Research*

We present mentally efficient algorithms for mentally squaring and cubing 2-digit and 3-digit numbers and for finding cube roots of numbers with 2-digit or 3-digit answers.

Lessons Learned As A Novice Researcher: A Pilot Study In Mathematics Education, 2011 Western Michigan University

#### Lessons Learned As A Novice Researcher: A Pilot Study In Mathematics Education, Nicole L. Fonger

*The Hilltop Review*

The lessons we learn in life are often catalyzed by events or happenings that we experience and that subsequently change us in some way. Life as a graduate student is replete with diverse experiences that mold and shape one‘s outlook on teaching, learning, and disciplined inquiry. As a doctoral candidate, my role as a novice researcher is increasingly budding with growth and my responsibilities to design and conduct research have engendered some important lessons. Often confined to private or classroom conversations with graduate students and faculty members, the lessons I have learned as a novice researcher seem worth sharing ...

A Branching Process For Virus Survival, 2011 Syracuse University

#### A Branching Process For Virus Survival, J. Theodore Cox, Rinaldo B. Schinazi

*Mathematics - Faculty Scholarship*

Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best adapted genotype, leading to a population composed of low replicating mutants that is eventually doomed. We propose a new branching model that shows that this is not necessarily so. That is, a population composed of ever changing mutants may survive.

Toric Symmetry Of Cp3, 2011 Harvey Mudd College

#### Toric Symmetry Of Cp3, Dagan Karp, Dhruv Ranganathan, Paul Riggins '12, Ursula Whitcher

*All HMC Faculty Publications and Research*

We exhaustively analyze the toric symmetries of CP^3 and its toric blowups. Our motivation is to study toric symmetry as a computational technique in Gromov-Witten theory and Donaldson-Thomas theory. We identify all nontrivial toric symmetries. The induced nontrivial isomorphisms lift and provide new symmetries at the level of Gromov-Witten Theory and Donaldson-Thomas Theory. The polytopes of the toric varieties in question include the permutohedron, the cyclohedron, the associahedron, and in fact all graph associahedra, among others.

On The K-Theory And Homotopy Theory Of The Klein Bottle Group, 2011 Boise State University

#### On The K-Theory And Homotopy Theory Of The Klein Bottle Group, Jens Harlander, Andrew Misseldine

*Mathematics Faculty Publications and Presentations*

We construct infinitely many chain homotopically distinct algebraic 2-complexes for the Klein bottle group and give various topological applications. We compare our examples to other examples in the literature and address the question of geometric realizability.

Adjoint Functors, Projectivization, And Differentiation Algorithms For Representations Of Partially Ordered Sets, 2011 Syracuse University

#### Adjoint Functors, Projectivization, And Differentiation Algorithms For Representations Of Partially Ordered Sets, Mark Kleiner, Markus Reitenbach

*Mathematics - Faculty Scholarship*

Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial construction of the derived set and for the differentiation functor.

How To Study Mathematics, 2011 Illinois Wesleyan University

#### How To Study Mathematics, Lawrence N. Stout

*Lawrence N. Stout*

In high school mathematics much of your time was spent learning algorithms and manipulative techniques which you were expected to be able to apply in certain well-defined situations. This limitation of material and expectations for your performance has probably led you to develop study habits which were appropriate for high school mathematics but may be insufficient for college mathematics. This can be a source of much frustration for you and for your instructors. My object in writing this essay is to help ease this frustration by describing some study strategies which may help you channel your abilities and energies in ...

A High-Resolution Finite-Difference Method For Simulating Two-Fluid, Viscoelastic Gel Dynamics, 2011 Boise State University

#### A High-Resolution Finite-Difference Method For Simulating Two-Fluid, Viscoelastic Gel Dynamics, Grady Wright, Robert D. Guy, Jian Du, Aaron L. Fogelson

*Grady Wright*

An important class of gels are those composed of a polymer network and fluid solvent. The mechanical and rheological properties of these two-fluid gels can change dramatically in response to temperature, stress, and chemical stimulus. Because of their adaptivity, these gels are important in many biological systems, e.g. gels make up the cytoplasm of cells and the mucus in the respiratory and digestive systems, and they are involved in the formation of blood clots. In this study we consider a mathematical model for gels that treats the network phase as a viscoelastic fluid with spatially and temporally varying material ...

Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, 2011 Institute for Applied Mathematics, University of Hanover, D-30167 Hanover, Germany

#### Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev

*Articles*

The geodesic equations of a class of right invariant metrics on the semi-direct product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra are found.

Operation Comics: Making Math Fun, 2011 Western Kentucky University

#### Operation Comics: Making Math Fun, Bruce Kessler

*Bruce Kessler*

This talk gives a background on the Operation Comics series, which integrates mathematics into a comic book storyline, as an example of how creativity is not exclusive to the traditional arts, like music and dance, but is a vital part of math, science, and engineering.

Operation Comics: Making Math Fun, 2011 Western Kentucky University

#### Operation Comics: Making Math Fun, Bruce Kessler

*Mathematics Faculty Publications*

This talk gives a background on the Operation Comics series, which integrates mathematics into a comic book storyline, as an example of how creativity is not exclusive to the traditional arts, like music and dance, but is a vital part of math, science, and engineering.

A New Framework For Network Disruption, 2011 Harvey Mudd College

#### A New Framework For Network Disruption, Susan E. Martonosi, Doug Altner, Michael Ernst, Elizabeth Ferme, Kira Langsjoen, Danika Lindsay, Sean S. Plott '08, Andrew S. Ronan

*All HMC Faculty Publications and Research*

Traditional network disruption approaches focus on disconnecting or lengthening paths in the network. We present a new framework for network disruption that attempts to reroute flow through critical vertices via vertex deletion, under the assumption that this will render those vertices vulnerable to future attacks. We define the load on a critical vertex to be the number of paths in the network that must flow through the vertex. We present graph-theoretic and computational techniques to maximize this load, firstly by removing either a single vertex from the network, secondly by removing a subset of vertices.

Advances In Graph-Cut Optimization: Multi-Surface Models, Label Costs, And Hierarchical Costs, 2011 University of Western Ontario

#### Advances In Graph-Cut Optimization: Multi-Surface Models, Label Costs, And Hierarchical Costs, Andrew T. Delong

*Electronic Thesis and Dissertation Repository*

Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or *energy minimization*. This is particularly true of "low-level" inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to ...