Mathematics Commons^™

Quantum Multiplexers, Parrondo Games, And Proper Quantization, Faisal Shah Khan

Dissertations and Theses

A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary accuracy, via a circuit consisting entirely of variations of the quantum multiplexer, and that certain one player games, the history dependent Parrondo games, can be quantized as games via a particular variation of the quantum multiplexer. However, to date all such quantizations have lacked a certain fundamental game theoretic property.

The main result in this dissertation is the development of quantizations of …

Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs.

The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent …

Quaternions, Octonions, And The Quantization Of Games, Aden Omar Ahmed

Dissertations and Theses

We present an effect on classical games that is obtained by replacing the notion of probability distribution with the notions of quantum superposition and measurement. Our particular focus will be on two and three player games where each player has precisely two pure strategic choices. Games in normal form are represented as "payoff" functions.

Game quantization requires the extension of these functions to much larger domains. The main result of this work is the co-ordinatization of these extended functions by either the quaternions or octonions in order to obtain computationally friendly versions of these functions. This computational capability is then …

Using Maxwells Z Model To Determine Lunar Mare Lava Thickness, Autumn Wille

Honors Capstones

Capstone submitted as a graduate requirement for the BSU Honors Program.

Development And Testing Of The Gait Assessment And Intervention Tool (G.A.I.T.): A Measure Of Coordinated Gait Components, J. J. Daly, J. Nethery, J. P. Mccabe, I. Brenner, J. Rogers, J. Gansen, K. Butler, R. Burdsall, K. Roenigk, John Holcomb

Mathematics and Statistics Faculty Publications

Recent neuroscience methods have provided the basis upon which to develop effective gait training methods for recovery of the coordinated components of gait after neural injury. We determined that there was not an existing observational measure that was, at once, adequately comprehensive, scored in an objectively-based manner, and capable of assessing incremental improvements in the coordinated components of gait. Therefore, the purpose of this work was to use content valid procedures in order to develop a relatively inexpensive, more comprehensive measure, scored with an objectively-based system, capable of incrementally scoring improvements in given items, and that was both reliable and …

Grünbaum Colorings Of Toroidal Triangulations, Michael O. Albertson, Hannah Alpert, Sarah-Marie Belcastro, Ruth Haas

Mathematics Sciences: Faculty Publications

We prove that if G is a triangulation of the torus and χ(G) 6 ≠ 5, then there is a 3-coloring of the edges of G so that the edges bounding every face are assigned three different colors.

A Snapshot Algorithm For Linear Feedback Flow Control Design, Benjamin T. Dickinson, Belinda A. Batten, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The control of fluid flows has many applications. For micro air vehicles, integrated flow control designs could enhance flight stability by mitigating the effect of destabilizing air flows in their low Reynolds number regimes. However, computing model based feedback control designs can be challenging due to high dimensional discretized flow models. In this work, we investigate the use of a snapshot algorithm proposed in Ref. 1 to approximate the feedback gain operator for a linear incompressible unsteady flow problem on a bounded domain. The main component of the algorithm is obtaining solution snapshots of certain linear flow problems. Numerical results …

Weak Sharp Minima On Riemannian Manifolds, Chong Li, Boris S. Mordukhovich, Jinhua Wang, Jen-Chih Yao

Mathematics Research Reports

This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, and global weak sharp minima for such problems and obtain their complete characterizations in the case of convex problems on finite-dimensional Riemannian manifolds and their Hadamard counterparts. A number of the results obtained in this paper are also new for the case of conventional problems in linear spaces. Our methods involve appropriate tools of variational analysis and generalized differentiation on Riemannian …

A Radial Basis Function Method For The Shallow Water Equations On A Sphere, Natasha Flyer, Grady Wright

Mathematics Faculty Publications and Presentations

The paper derives the first known numerical shallow water model on the sphere using radial basis function (RBF) spatial discretisation, a novel numerical methodology that does not require any grid or mesh. In order to perform a study with regard to its spatial and temporal errors, two nonlinear test cases with known analytical solutions are considered. The first is global steady-state flow with a compactly supported velocity field while the second is unsteady flow where features in the flow must be kept intact without dis- persion. This behavior is achieved by introducing forcing terms in the shallow water equations. Error …

Math/Compsci Newsletter, Spring 2009, Department Of Mathematics And Computer Science, Bridgewater State College

Department of Mathematics Newsletter

No abstract provided.

Fractional Calculus: Definitions And Applications, Joseph M. Kimeu

Masters Theses & Specialist Projects

No abstract provided.

Computational Simulation Of Strain Localization: From Theory To Implementation, Shouxin Wu

Doctoral Dissertations

Strain localization in the form of shear bands or slip surfaces has widely been observed in most engineering materials, such as metals, concrete, rocks, and soils. Concurrent with the appearance of localized deformation is the loss of overall load-carrying capacity of the material body. Because the deformation localization is an important precursor of material failure, computational modeling of the onset and growth of the localization is indispensable for the understanding of the complete mechanical response and post-peak behavior of materials and structures. Simulation results can also be used to judge the failure mechanisms of materials and structures so that the …

Counting On Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07

All HMC Faculty Publications and Research

Chebyshev polynomials have several elegant combinatorial interpretations. Specificially, the Chebyshev polynomials of the first kind are defined by T₀(x) = 1, T₁(x) = x, and T_n(x) = 2x T_n-1(x) - T_n-2(x). Chebyshev polynomials of the second kind U_n(x) are defined the same way, except U₁(x) = 2x. T_n and U_n are shown to count tilings of length n strips with squares and dominoes, where the tiles are given weights and sometimes color. Using these interpretations, many identities satisfied by Chebyshev polynomials can be given …

Capital Expansion And Organizational Growth: A Cost-Effective Analysis For Huntington Family Centers, Sean P. Burke

MPA Capstone Projects 2006 - 2015

Huntington Family Centers Inc., is a nonprofit social service agency located in the near-Westside of the City of Syracuse, N.Y. The agency currently employs 75 people and offers 25 programs, ranging in focus from preschool to services for senior citizens. It has developed a business plan with the goal of increasing program services by 35% over the next two years. However, as new programs are considered, it will be forced to rent space due to the lack of functional space at its primary are considered, it will be forced to rent space due to the lack of functional space at …

Finding Cost-Effective Methods For Language Access Services Administration At New York City Children's Services, Kerry Cook

MPA Capstone Projects 2006 - 2015

New York City Children's Services (CS) serves an increasing populations of persons with limited English language proficiency (LEP). Federal and local laws mandate that these persons are provided with meaningful language access services. This analysis attempts to find the most cost-effective strategy for CS' Division of Child Protection (DCP) to provide interpretation services to LEP persons involved in DCP cases of child abuse and neglect. The study first identifies alternative strategies for providing these services, and then qualifies the cost of the current methods and alternative methods. A framework of transaction cost economic theory guides the cost analysis process. Next, …

On The Distributions Of The Sup And Inf Of The Classical Risk Process With Exponential Claim, Jorge A León, José Villa

Communications on Stochastic Analysis

No abstract provided.

Optimal Consumption And Portfolio For An Insider In A Market With Jumps, Delphine David, Yeliz Yolcu Okur

Communications on Stochastic Analysis

No abstract provided.

Pac Commutators And The R-Transform, Aurel I Stan

Communications on Stochastic Analysis

No abstract provided.

A Stochastic Process Associated With The Weighted White Noise Differentiation, Issei Kitagawa

Communications on Stochastic Analysis

No abstract provided.

Stochastic Heat Equation With Infinite Dimensional Fractional Noise: L_{2}-Theory, Raluca Balan

Communications on Stochastic Analysis

No abstract provided.

Universal Malliavin Calculus In Fock And Lévy-Itô Spaces, David Applebaum

Communications on Stochastic Analysis

No abstract provided.

Volume 02, Joseph A. Mann, Kathryn J. Greenly, Scott E. Jenkins, Andrew E. Puckette, Daniel M. Honey, Jeffery P. Ravenhorst, Jamie Elizabeth Mesrobian, Thomas Scott, Jay Crowell, Sarah Spangenberg, Amy S. Eason, Kenny Wolfe, Liz Hale, Rachel Bouchard, Will Semonco, Carley York, Ryan Higgenbothom, Adrienne Heinbaugh, Melissa Dorton, Madeline Hunter, June Ashmore, Clark Barkley, Jay Haley

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Mike's Nite: New Jazz for an Old Instrument by Joseph A. Mann

Investigation of the use of Cucumis Sativus for Remediation Of Chromium from Contaminated Environmental Matrices: An Interdisciplinary Instrumental Analysis Project by Kathryn J. Greenly, Scott E. Jenkins, and Andrew E. Puckette

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Scott Jenkins

Building and Measuring Scalable Computing Systems by Daniel M. Honey and Jeffery P. Ravenhorst

Nomini Hall: A Case Study in the Use of Archival Resources as Guides for Excavation at An Archaeological Site by …

Convergence To Weighted Fractional Brownian Sheets, Johanna Garzón

Communications on Stochastic Analysis

No abstract provided.

An Interacting Fock Space Characterization Of Probability Measures, Luigi Accardi, Hui-Hsiung Kuo, Aurel I Stan

Communications on Stochastic Analysis

No abstract provided.

A Class Of Anticipating Linear Stochastic Differential Equations, Julius Esunge

Communications on Stochastic Analysis

No abstract provided.

Sample Properties Of Random Fields. I. Separability And Measurability, Jürgen Potthoff

Communications on Stochastic Analysis

No abstract provided.

2009 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2009 Spring Colloquium.

Numerical Simulations Of Snake Dissipative Solitons In Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, Harihar Khanal

Publications

Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation …

Some More Identities Of Rogers-Ramanujan Type, Douglas Bowman, James Mclaughlin, Andrew Sills

Mathematical Sciences: Faculty Publications

In this we paper we prove several new identities of the Rogers-Ramanujan-Slater type. These identities were found as the result of computer searches. The proofs involve a variety of techniques, including series-series identities, Bailey pairs, a theorem of Watson on basic hypergeometric series, generating functions and miscellaneous methods.

Math Island At Brewer Elementary School: A Learner-Centered Model For Education, Vikki K. Collins, H. Marguerite Yates

Georgia Educational Researcher

This paper examines a learner-centered model for the teaching of elementary mathematics established at an urban Georgia school that serves a highly mobile, diverse population of approximately 475 students. The school was on its state’s list of schools needing improvement because students continued to perform poorly on standardized tests. Math Island, a support center for students designed to facilitate the conceptual understanding of mathematics, was created, and professional development programs were implemented to assist teachers in developing their pedagogical and content expertise in the teaching of mathematics. The school made substantial progress after these initiatives were employed and was removed …