Physical Sciences and Mathematics Commons^™

An Infinite Dimensional Stochastic Analysis Approach To Local Volatility Dynamic Models, R Carmona, S Nadtochiy

Communications on Stochastic Analysis

No abstract provided.

Hedging Claims With Feedback Jumps In The Price Process, Kiseop Lee, Philip Protter

Communications on Stochastic Analysis

No abstract provided.

Abstract Wiener Space, Revisited, Daniel W Stroock

Communications on Stochastic Analysis

No abstract provided.

Large-Time Behavior Of Non-Symmetric Fokker-Planck Type Equations, Anton Arnold, Eric Carlen, Qiangchang Ju

Communications on Stochastic Analysis

No abstract provided.

The Shapley Value Of Phylogenetic Trees, Claus-Jochen Haake, Akemi Kashiwada '05, Francis E. Su

All HMC Faculty Publications and Research

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space …

Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen

All HMC Faculty Publications and Research

We consider traveling wave phenomena for a viscoelastic generalization of Burgers' equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth traveling waves, piecewise smooth waves, and piecewise constant (shock) solutions. Each solution type is possible for a given pair of asymptotic limits, and we characterize the dynamics in terms of the relaxation time and viscosity.

Quasigeometric Distributions And Extra Inning Baseball Games, Darren B. Glass, Philip J. Lowry

Math Faculty Publications

Each July, the eyes of baseball fans across the country turn to Major League Baseball’s All-Star Game, gathering the best and most popular players from baseball’s two leagues to play against each other in a single game. In most sports, the All-Star Game is an exhibition played purely for entertainment. Since 2003, the baseball All-Star Game has actually ‘counted’, because the winning league gets home field advantage in the World Series. Just one year before this rule went into effect, there was no winner in the All-Star Game, as both teams ran out of pitchers in the 11th inning and …

Two Classes Of Time-Inhomogeneous Markov Chains: Analysis Of The Periodic Case, Attahiru Sule Alfa, Barbara Haas Margolius

Mathematics and Statistics Faculty Publications

We consider the M/G/1 and GI/M/1 types of Markov chains for which their one step transitions depend on the times of the transitions. These types of Markov chains are encountered in several stochastic models, including queueing systems, dams, inventory systems, insurance risk models, etc. We show that for the cases when the time parameters are periodic the systems can be analyzed using some extensions of known results in the matrix-analytic methods literature. We have limited our examples to those relating to queueing systems to allow us a focus. An example application of the model to a real life problem is …

The Role Of Prediction In The Teaching And Learning Of Algebra, Lisa Kasmer

Dissertations

Research has shown that including prediction questions within reading and science instruction has been advantageous for students, yet minimal research existed regarding the use of such questions within mathematics instruction. In order to extend and build on our knowledge about the effects of prediction in mathematics instruction, this study explored the impact of this paradigm in the teaching and learning of algebra. Specifically, this study probed whether utilizing prediction questions provided students opportunities for engaging in mathematical thinking, retrieving prior knowledge, and discussing related mathematical ideas, could increase such students' conceptual understanding and mathematical reasoning in the content area of …

Analysis And Application Of Perfectly Matched Layer Absorbing Boundary Conditions For Computational Aeroacoustics, Sarah Anne Parrish

Mathematics & Statistics Theses & Dissertations

The Perfectly Matched Layer (PML) was originally proposed by Berenger as an absorbing boundary condition for Maxwell's equations in 1994 and is still used extensively in the field of electromagnetics. The idea was extended to Computational Aeroacoustics in 1996, when Hu applied the method to Euler's equations. Since that time much of the work done on PML in the field of acoustics has been specific to the case where mean flow is perpendicular to a boundary, with an emphasis on Cartesian coordinates. The goal of this work is to further extend the PML methodology in a two-fold manner: First, to …

Bioinspired Broadband Antireflection Coatings On Gasb, Wei-Lun Min, Amaury P. Betancourt, Peng Jiang, Bin Jiang

Mathematics and Statistics Faculty Publications and Presentations

We report an inexpensive yet scalable templating technique for fabricating moth-eye antireflection gratings on gallium antimonide substrates. Non-close-packed colloidal monolayers are utilized as etching masks to pattern subwavelength-structured nipple arrays on GaSb. The resulting gratings exhibit superior broadband antireflection properties and thermal stability than conventional multilayer dielectric coatings. The specular reflection of the templated nipple arrays match with the theoretical predictions using a rigorous coupled-wave analysis model. The effect of the nipple shape and size on the antireflection properties has also been investigated by the same model. These biomimetic coatings are of great technological importance in developing efficient thermophotovoltaic cells.

Volume 01, Jessica Fields, Stephanie Neeley, Derek W. Hambright, Mary E. Lehman, Andrew R. Grzankowski, Zachary Johnson, Boone M. Prentice, Ashley M. Swandby, Victoria Morgan, Katie Williamson, Kristine G. Bender, Katelyn N. Romaine, D. Nicole Swann, Jessica Fox, Mike Mcateer, Alex Grabiec, Laura Nodtvedt, Nick Costa, Rachel Wolfe, Zack Dalton

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Three Decades of Digging: Undergraduate Archeology at Longwood by Jessica Fields and Stephanie Neeley

Interactions of Allelopathy and Heat Stress in Plants by Derek W. Hambright and Mary E. Lehman

Inertial Electrostatic Confinement D-D Fusion Device: Construction and Simulation by Andrew R. Grzankowski

Shackled Nim by Zachary Johnson

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Boone M. Prentice

A Comparison of Image Analysis Methods in cDNA Microarrays by Ashley M. Swandby

Perceived Sexual Activity of Short and Long-Term Relationships by Victoria Morgan and Katie Williamson

Elderly …

An Impregnable Lightweight Device Discovery (Ildd) Model For The Pervasive Computing Environment Of Enterprise Applications, Munirul H. Haque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

The worldwide use of handheld devices (personal digital assistants, cell phones, etc.) with wireless connectivity will reach 2.6 billion units this year and 4 billion by 2010. More specifically, these handheld devices have become an integral part of industrial applications. These devices form pervasive ad hoc wireless networks that aide in industry applications. However, pervasive computing is susceptible and vulnerable to malicious active and passive snoopers. This is due to the unavoidable interdevice dependency, as well as a common shared medium, very transitory connectivity, and the absence of a fixed trust infrastructure. In order to ensure security and privacy in …

A Closer Look At The Crease Length Problem, Sean F. Ellermeyer

Faculty Articles

An optimization problem that appears as an exercise in most modern calculus textbooks is the crease length problem. Here, Ellermeyer provides a solution of the general crease length problem in which all possible foldings of a corner to the opposite edge are taken into account. One of his findings will be that the minimum crease length is never produced by a Case 2 fold and hence that the general crease length problem always yields a different minimum than the constrained problem that is treated in the textbooks. He discovers a criterion that determines which foldings must be performed in order …

Estimating Absolute Transcript Concentration For Microarrays Using Langmuir Adsorption Theory, Min Mo

Mathematics Dissertations

This paper estimates the Langmuir parameters for probe on microarray then improves estimation of absolute transcript concentration using Langmuir adsorption model. We use the spike-in probes found on commercial microarrays, along with Langmuir adsorption model to estimate Langmuir parameters for spike-in probes, then combine with an assumed log-linear model for those Langmuir parameters in terms of the spike-in probe sequence features, to estimate the assumed-invariant model coefficients. These estimated coefficients are then used, along with the probe sequence features of the target probes, to estimate the Langmuir parameters for each target probe. Finally, these estimated Langmuir parameters are combined with …

Motivation In Secondary Mathematics: How Lesson Structure Impacts Student Engagement, Vicki Beata

Leah A. Nillas

The purpose of this research is to see how students are engaged emotionally, behaviorally, and cognitively in different types of math lessons. Shernoff, Csikszentmihalyi, Schneider, and Shernoff (2003) found that students had a higher quality of experience (mood, esteem, intensity, and motivation) when they were involved in individual or group work. This study analyzed transcriptions, observations and student work from three pre-calculus lessons, a survey about students’ engagement in different types of lessons and an open-ended survey about the researcher’s teaching style. The results of the study were that students enjoy and are more engaged in lessons that require the …

Reading Rainbow: Assessing Effectiveness In Literacy Technology, Liz Russ, Erin Meehan

Leah A. Nillas

“Children’s Television Workshop and the University of Nebraska created a program, ‘Reading Rainbow’ to promote recreational reading in early readers” (Tarnauskas, 1995). Since its creation, this literacy technology has thrilled and delighted first and second grade audiences, but little to no research has been done on the effectiveness of this program. What is the outcome of the Reading Rainbow program on students’ literacy? This research study investigated the effect of the Reading Rainbow program on literacy of 21 diverse first grade students. Data was obtained through qualitative methods including observations and focus group interviews with students, as well as interviews …

On A = Mp Heronian Triangles And V = Ma Cones, John Hawkins, David Stone

John B. Hawkins

A determining all such triangles with area = m (perimeter). We also consider the analogous problem of finding cones with integer radius and height satisfying volume = m (total surface area). Recent activity and results on both problems have appeared recently in the School Science and Mathematics Problem Section and in the Mathematics Magazine, where our conjecture that the largest A = mP triangle is m2 +2, (4m2 +1)2,(16m4 +12m2) +1 was settled affirmatively.

A Wavelet-Based Method For Overcoming The Gibbs Phenomenon, Nataniel Greene

Publications and Research

The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities. Here we describe a numerical procedure for overcoming the Gibbs phenomenon called the inverse wavelet reconstruction method. The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series.

College Algebra Applications Using Ti-84 Apps, Lisa Yocco

Lisa S. Yocco

No abstract provided.

College Algebra Applications Using Ti-84 Apps, Lisa Yocco

Lisa S. Yocco

No abstract provided.

The Mixed Problem For Harmonic Functions In Polyhedra, Moises Venouziou, Gregory C. Verchota

Mathematics - All Scholarship

R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the boundary into Dirichlet and Neumann sets is used on (2) manifold boundaries that are not locally given as the graphs of functions. Examples are constructed to illustrate necessity and other implications of the geometric hypotheses.

Hua's Matrix Equality And Schur Complements, Chris Paige, George P. H. Styan, Bo-Ying Wang, Fuzhen Zhang

Mathematics Faculty Articles

The purpose of this paper is to revisit Hua's matrix equality (and inequality) through the Schur complement. We present Hua's original proof and two new proofs with some extensions of Hua's matrix equality and inequalities. The new proofs use a result concerning Shur complements and a generalization of Sylvester's law of inertia, each of which is useful in its own right.

Failure Of Metric Regularity For Major Classes Of Variational Systems, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to the study of metric regularity, which is a remarkable property of set-valued mappings playing an important role in many aspects of nonlinear analysis and its applications. We pay the main attention to metric regularity of the so- called parametric variational systems that contain, in particular, various classes of parameterized/perturbed variational and hemivariational inequalities, complementarity systems, sets of optimal solutions and corresponding Lagrange multipliers in problems of parametric optimization and equilibria, etc. Based on the advanced machinery of generalized differentiation1 we surprisingly reveal that metric regularity fails for certain major classes of parametric variational systems, which …

Beam Selection In Radiotherapy Design, M Ehrgott, Allen G. Holder, Josh Reese

Mathematics Faculty Research

The optimal design of a radiotherapy treatment depends on the collection of directions from which radiation is focused on the patient. These directions are manually selected by a physician and are typically based on the physician's previous experiences. Once the angles are chosen, there are numerous optimization models that decide a fluency pattern (exposure times) that best treats a patient. So, while optimization techniques are often used to decide the length of time a patient is exposed to a high-energy particle beam, the directions themselves are not optimized. The problem with optimally selecting directions is that the underlying mixed integer …

An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene

Publications and Research

Conditional and biconditional statements are a standard part of symbolic logic but they have only recently begun to be explored in probability for applications in artificial intelligence. Here we give a brief overview of the major theorems involved and illustrate them using two standard model problems from conditional probability.

Grid Vertex-Unfolding Orthogonal Polyhedra, Mirela Damian

Computer Science: Faculty Publications

No abstract provided.

Preconditioned Conjugate Gradient Algorithm, Elena Caraba

Honors Theses

No abstract provided.

Enrich Your Algebra Course With Apps And Ti Smart View On The Ti-84, Lisa Yocco

Lisa S. Yocco

No abstract provided.

Enrich Your Algebra Course With Apps And Ti Smart View On The Ti-84, Lisa Yocco

Lisa S. Yocco

No abstract provided.