Mathematics Commons^™

Stable Generalized Finite Element Method (Sgfem), I. Babuska, U. Banerjee

Mathematics - All Scholarship

The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions, which are also known as the enrichments, mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully used to solve a variety of problems with complicated features and microstructure. However, the stiffness matrix of GFEM is badly conditioned (much worse compared to the standard FEM) and there could be a severe loss of accuracy in the computed solution …

Game Theory And Von Neumann’S Minimax Theorem, Megan Hall

Honors Student Works

We encounter many situations of conflict on a day‐to‐day basis. When trying to find a solution, we consider all the possible consequences of our choices. Sometimes, the outcome of a situation depends on the decisions of others. This is where the discussion of game theory begins. Game theory seeks to construct a mathematical model for these decision making processes. The players in a game want to find the best outcome for themselves; is it possible to guarantee that a particular outcome, no matter what the other player does? Perhaps the most important result of game theory is the Minimax Theorem, …

2011 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2011 Spring Colloquium.

A Nonnegative Analysis Of Politics, Tim Chartier, Charles D. Wessell

Math Faculty Publications

The article investigates how linear algebra can recover mathematical information from the electronic messages using the Enron Email Sets in Pennsylvania. It states that a term-by-email matrix has been created to cluster algorithm, which allows one to mine through data and discover meaning. Moreover, nonnegative matrix factorization (NMF) enables one to interpret the resulting factorization in terms of the original problem.

Traveling Waves Of Selective Sweeps, Rick Durrett, John Mayberry

College of the Pacific Faculty Articles

The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps in an exponentially growing population. To better understand this process, Beerenwinkel et al. [PLoS Comput. Biol. 3 (2007) 2239- 2246] consider a Wright-Fisher model in which cells from an exponentially growing population accumulate advantageous mutations. Simulations show a traveling wave in which the time of the first k-fold mutant, Tk, is approximately linear in k and heuristics are used to obtain formulas for ETk. …

Results In Lattices, Ortholattices, And Graphs, Jianning Su

Doctoral Dissertations

This dissertation contains two parts: lattice theory and graph theory. In the lattice theory part, we have two main subjects. First, the class of all distributive lattices is one of the most familiar classes of lattices. We introduce "π-versions" of five familiar equivalent conditions for distributivity by applying the various conditions to 3-element antichains only. We prove that they are inequivalent concepts, and characterize them via exclusion systems. A lattice L satisfies D0π, if a ✶ (b ✶ c) ≤ (a ✶ b) ✶ c for all 3-element antichains { a, b, c}. We consider …

Quantitative Stability Of Linear Infinite Inequality Systems Under Block Perturbations With Applications To Convex Systems, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is loo(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn …

Section Abstracts: Astronomy, Mathematics And Physics With Materials Science

Virginia Journal of Science

Abstracts for the Astronomy, Mathematics, and Physics with Materials Science Section for the 89th Annual Meeting of the Virginia Academy of Science, May 25-27, 2011, University of Richmond, Richmond VA.

A New Summation Formula For Wp-Bailey Pairs, James Mclaughlin

Mathematics Faculty Publications

No abstract provided.

Characterization Of The Threshold For Nad(P)H:Quinone Oxidoreductase Activity In Intact Sulforaphane-Treated Pulmonary Arterial Endothelial Cells, Robert D. Bongard, Gary S. Krenz, Adam J. Gastonguay, Carol L. Williams, Brian J. Lindemer, Marilyn P. Merker

Mathematics, Statistics and Computer Science Faculty Research and Publications

Treatment of bovine pulmonary arterial endothelial cells in culture with the phase II enzyme inducer sulforaphane (5 μM, 24 h; sulf-treated) increased cell-lysate NAD(P)H:quinone oxidoreductase (NQO1) activity by 5.7 ± 0.6 (mean ± SEM)-fold, but intact-cell NQO1 activity by only 2.8 ± 0.1-fold compared to control cells. To evaluate the hypothesis that the threshold for sulforaphane-induced intact-cell NQO1 activity reflects a limitation in the capacity to supply NADPH at a sufficient rate to drive all the induced NQO1 to its maximum activity, total KOH-extractable pyridine nucleotides were measured in cells treated with duroquinone to stimulate maximal NQO1 activity. NQO1 activation …

The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm

Department of Mathematics: Dissertations, Theses, and Student Research

The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a linear, fractional initial value problem in Chapters 2 and 3. We then apply fixed point strategies of Krasnosel'skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4.

Adviser: Lynn Erbe and Allan Peterson

Rank One Perturbations Of Self-Adjoint Operators, Haoxuan Zheng

Honors Theses

No abstract provided.

A Three Dimensional Green's Function Solution Technique For The Transport Of Heavy Ions In Laboratory And Space, Candice Rockell Gerstner

Mathematics & Statistics Theses & Dissertations

In the future, astronauts will be sent into space for longer durations of time compared to previous missions. The increased risk of exposure to ionizing radiation, such as Galactic Cosmic Rays and Solar Particle Events, is of great concern. Consequently, steps must be taken to ensure astronaut safety by providing adequate shielding. The shielding and exposure of space travelers is controlled by the transport properties of the radiation through the spacecraft, its onboard systems and the bodies of the individuals themselves. Meeting the challenge of future space programs will therefore require accurate and efficient methods for performing radiation transport calculations …

Examination Timetabling With Mathematical Programming An Application In Turkish Air Force Academy, Emrah Koksalmis

Engineering Management & Systems Engineering Theses & Dissertations

The focus of this thesis is the educational timetabling problem, which is a very challenging problem to solve especially with a high number of the departments, branches, classes, and students. Due to the large scale of educational timetabling problems and preferences of the stakeholders, it is almost impossible to form a general model that solves all of the timetabling problems in the literature. This resulted in the need to develop and employ specific models for specific institutions.

The purpose of this study is to develop a mathematical programming model that solves the examination timetabling problem in Turkish Air Force Academy …

Epistemic Strategies For Solving Two-Dimensional Physics Problems, Mary Elyse Hing-Hickman

Physics Theses & Dissertations

An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process.

In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving two-dimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student's ability to apply the …

Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette

Department of Mathematics: Dissertations, Theses, and Student Research

In this work, I offer an alternative presentation theory for C*-algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegative-valued function which ensures existence of a C*-algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*-algebra and utilization of classical algebraic tools, such as Tietze transformations.

Uniqueness Conditions For Low-Rank Matrix Recovery, Yonina C. Eldar, Deanna Needell, Yaniv Plan

CMC Faculty Publications and Research

Low-rank matrix recovery addresses the problem of recovering an unknown low-rank matrix from few linear measurements. Nuclear-norm minimization is a tractible approach with a recent surge of strong theoretical backing. Analagous to the theory of compressed sensing, these results have required random measurements. For example, m >= Cnr Gaussian measurements are sufficient to recover any rank-r n x n matrix with high probability. In this paper we address the theoretical question of how many measurements are needed via any method whatsoever --- tractible or not. We show that for a family of random measurement ensembles, m >= 4nr - 4r^2 …

Wealth Inequality And Economic Performances., Sahana Roy Chowdhury Dr.

Doctoral Theses

Ever since the inception of Development Economics as a separate discipline inequality has been a major area of extensive study. Economists and researchers have deliberated both on the causes and the effects of inequality in a wide range of treatise, books and essays. So far, in this regard, two fundamental approaches came across viz., the Classical approach and the Credit Market Imperfection approach. The Classical approach was originated by Smith (1937) and was further interpreted and developed by Keynes (1920), Lewis (1954), Kaldor (1957), and Bourguignon (1981). According to this approach, savings rate is an increasing function of wealth and …

Age-Gaps In Sexual Partnerships: Seeing Beyond ‘Sugar Daddies’, Miles Q. Ott, Till Bärnighausen, Frank Tanser, Mark N. Lurie, Marie-Louise Newell

Statistical and Data Sciences: Faculty Publications

We examine for the first time age-mixing in sexual relationships in a population with very high HIV incidence and prevalence in rural South Africa. The highest levels of age assortativity (the pairing of like with like) were casual partnerships reported by men, the lowest levels were spousal relationships reported by women. Given the age–sex distribution of HIV prevalence in this population, interventions to decrease age-gaps in spousal relationships may be effective in reducing HIV incidence.

A “Peak” At The Algorithm Behind “Peaklet Analysis” Software, Bruce Kessler

Mathematics Faculty Publications

In response to a problem posed by faculty at the Applied Physics Institute at Western Kentucky University, the speaker has developed an algorithm for providing an automated analysis of spectrum data for the purpose of determining the elemental composition of the item generating the data. A full, non-provisional patent application has been filed on the idea, and a full marketing campaign has started to license software implementing the algorithm. This presentation will give a brief explanation of the mathematics in use in the algorithm, and will give some examples of the software in action.

Weak Type Inequalities For Maximal Operators Associated To Double Ergodic Sums, Paul Hagelstein, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

Given an approach region Γ ∈ Z₊² and a pair U, V of commuting nonperiodic measure preserving transformations on a probability space (Ω, Σ, μ), it is shown that either the associated multiparameter ergodic averages of any function in L¹(Ω) converge a.e. or that, given a positive increasing function ϕ on [0,∞) that is o(log x) as x → ∞, there exists a function g ∈ Lϕ(L)(Ω) whose associated multiparameter ergodic averages fail to converge a.e.

Relocatable Field Programmable Gate Array Bitstreams For Fault Tolerance, David P. Montminy, Rusty O. Baldwin, Paul D. Williams

AFIT Patents

A Field Programmable Gate Array (FPGA) circuit capable of operating through at least one fault. The FPGA circuit includes a configuration memory and an embedded microprocessor. The embedded microprocessor having access to the configuration memory, static modules, at least one relocatable module, and at least one spare module. The relocatable module being relocatable from a first target area to a second target area. The relocatable module being relocatable by manipulating a partial bitstream with the embedded microprocessor. The microprocessor calculating a plurality of bitstream changes, to relocate the at least one relocatable module using at least triple modular redundancy (TMR).

On The Existence Of Equilibrium Points, Boundedness, Oscillating Behavior And Positivity Of A Sveirs Epidemic Model Under Constant And Impulsive Vaccination, Manuel De La Sen, Ravi P. Agarwal, Asier Ibeas, Santiago Alonso-Quesada

Mathematics and System Engineering Faculty Publications

This paper discusses the disease-free and endemic equilibrium points of a SVEIRS propagation disease model which potentially involves a regular constant vaccination. The positivity of such a model is also discussed as well as the boundedness of the total and partial populations. The model takes also into consideration the natural population growing and the mortality associated to the disease as well as the lost of immunity of newborns. It is assumed that there are two finite delays affecting the susceptible, recovered, exposed, and infected population dynamics. Some extensions are given for the case when impulsive nonconstant vaccination is incorporated at, …

Much More Than Symbolics: The Early History Of Algebra And Its Significance For Introductory Algebra Education, Calvin Jongsma

Faculty Work Comprehensive List

No abstract provided.

Hybrid Proofs Of The Q-Binomial Theorem And Other Identities, Dennis Eichhorn, James Mclaughlin, Andrew V. Sills

Mathematics Faculty Publications

No abstract provided.

Three Channel Polarimetric Based Data Deconvolution, Kurtis G. Engelson

Theses and Dissertations

A three channel polarimetric deconvolution algorithm was developed to mitigate the degrading effects of atmospheric turbulence in astronomical imagery. Tests were executed using both simulation and laboratory data. The resulting efficacy of the three channel algorithm was compared to a recently developed two channel approach under identical conditions ensuring a fair comparison amongst both algorithms. Two types of simulations were performed. The first was a binary star simulation to compare resulting resolutions between the three and two channel algorithms. The second simulation measured how effective both algorithms could deconvolve a blurred satellite image. The simulation environment assumed the key parameters …

Comparison Of Development Test And Evaluation And Overall Program Estimate At Completion, William R. Rosado

Theses and Dissertations

Historically, cost growth regression models analyze aggregate, program-level information. Initiatives by the Office of Secretary of Defense, Cost Assessment and Program Evaluation (OSD CAPE) require direct, centralized reporting of the complete Work Breakdown Structure (WBS) Earned Value (EV) data. Centralized reporting allows access to unfiltered, unaltered, EV data for multiple programs. Using regression, we evaluate if WBS element Development Test and Evaluation (DT&E) EV data is related to program estimate at completion (EAC). Identifying a relationship provides evidence validating pertinence and reliability of low level EV data. Additionally, a relationship between a specific WBS element and program EAC establishes a …

Voter Model Perturbations And Reaction Diffusion Equations, J. Theodore Cox, Richard Durrett, Edwin A. Perkins

Mathematics - All Scholarship

We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions d > 3. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic …

Wild Hypersurfaces, Andrew Crabbe, Graham J. Leuschke

Mathematics - All Scholarship

Complete hypersurfaces of dimension at least 2 and multiplicity at least 4 have wild Cohen-Macaulay type.

Quantitative Interpretation Of A Genetic Model Of Carcinogenesis Using Computer Simulations, Donghai Dai, Brandon Beck, Xiaofang Wang, Cory Howk, Yi Li

Mathematics and Statistics Faculty Publications

The genetic model of tumorigenesis by Vogelstein et al. (V theory) and the molecular definition of cancer hallmarks by Hanahan and Weinberg (W theory) represent two of the most comprehensive and systemic understandings of cancer. Here, we develop a mathematical model that quantitatively interprets these seminal cancer theories, starting from a set of equations describing the short life cycle of an individual cell in uterine epithelium during tissue regeneration. The process of malignant transformation of an individual cell is followed and the tissue (or tumor) is described as a composite of individual cells in order to quantitatively account for intra-tumor …