A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations,
2012
HITEC University
A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman
Mathematics Faculty Publications
In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.
Existence And Uniqueness Conditions For A Class Of (K+4j)-Point N-Th Order Boundary Value Problems,
2012
University of Dayton
Existence And Uniqueness Conditions For A Class Of (K+4j)-Point N-Th Order Boundary Value Problems, Paul W. Eloe, Johnny Henderson, Rahmat Ali Khan
Mathematics Faculty Publications
No abstract provided.
A Leggett-Williams Type Theorem Applied To A Fourth Order Problem,
2012
Dakota State University
A Leggett-Williams Type Theorem Applied To A Fourth Order Problem, Richard Avery, Paul Eloe, Johnny Henderson
Mathematics Faculty Publications
We apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a fourth order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach spstce. Inequalities that extend the notion of concavity to fourth order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.
Bounded Solutions Of Almost Linear Volterra Equations,
2012
University of Dayton
Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul
Mathematics Faculty Publications
Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.
Creating Macroscopes With Technology And Analytics: New Possibilities In Our Lives – The Important Role Of Tomorrow’S Mathematics Professionals (Abstract),
2012
University of Dayton
Creating Macroscopes With Technology And Analytics: New Possibilities In Our Lives – The Important Role Of Tomorrow’S Mathematics Professionals (Abstract), Lilian S. Wu
Kenneth C. Schraut Memorial Lectures
Our world is increasingly computerized, interconnected, and instrumented with sensors. Massive amounts of data are being captured in computer systems about our natural environment and man-made engineered structures, processes, and systems. But it is necessary to make sense out of all this data. With new computer methods computers can in effect become macroscopes, enabling us to see the world portrayed by our data.
Thirteenth Kenneth C. Schraut Memorial Lecture (Poster),
2012
University of Dayton
Thirteenth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics
Kenneth C. Schraut Memorial Lectures
No abstract provided.
On Hall Magnetohydrodynamics: X-Type Neutral Point And Parker Problem,
2012
University of Central Florida
On Hall Magnetohydrodynamics: X-Type Neutral Point And Parker Problem, Kyle Reger
Electronic Theses and Dissertations
The framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is investigated. The phenomena of magnetic flux pile-up driving the merging of antiparallel magnetic fields at an ion stagnation-point flow in a thin current sheet, …
Improving Student Learning In Undergraduate Mathematics,
2012
University of Central Florida
Improving Student Learning In Undergraduate Mathematics, Gabrielle Rejniak
Electronic Theses and Dissertations
The goal of this study was to investigate ways of improving student learning, par- ticularly conceptual understanding, in undergraduate mathematics courses. This study focused on two areas: course design and animation. The methods of study were the following: Assessing the improvement of student conceptual understanding as a result of team project-based learning, individual inquiry-based learning and the modi ed empo- rium model; and Assessing the impact of animated videos on student learning with the emphasis on concepts. For the first part of our study (impact of course design on student conceptual understanding) we began by comparing the following three groups …
Instability In A Generalized Keller–Segel Model,
2012
University of Florida
Instability In A Generalized Keller–Segel Model, Patrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr
Mathematics and Statistics Faculty Publications and Presentations
We present a generalized Keller–Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although …
Mixed Finite Element Approximation Of The Vector Laplacian With Dirichlet Boundary Conditions,
2012
University of Minnesota - Twin Cities
Mixed Finite Element Approximation Of The Vector Laplacian With Dirichlet Boundary Conditions, Douglas N. Arnold, Richard S. Falk, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We consider the finite element solution of the vector Laplace equation on a domain in two dimensions. For various choices of boundary conditions, it is known that a mixed finite element method, in which the rotation of the solution is introduced as a second unknown, is advantageous, and appropriate choices of mixed finite element spaces lead to a stable, optimally convergent discretization. However, the theory that leads to these conclusions does not apply to the case of Dirichlet boundary conditions, in which both components of the solution vanish on the boundary. We show, by computational example, that indeed such mixed …
Wavenumber Explicit Analysis Of A Dpg Method For The Multidimensional Helmholtz Equation,
2012
University of Texas at Austin
Wavenumber Explicit Analysis Of A Dpg Method For The Multidimensional Helmholtz Equation, Leszek Demkowicz, Jay Gopalakrishnan, Ignacio Muga, Jeffrey Zitelli
Mathematics and Statistics Faculty Publications and Presentations
We study the properties of a novel discontinuous Petrov Galerkin (DPG) method for acoustic wave propagation. The method yields Hermitian positive definite matrices and has good pre-asymptotic stability properties. Numerically, we find that the method exhibits negligible phase errors (otherwise known as pollution errors) even in the lowest order case. Theoretically, we are able to prove error estimates that explicitly show the dependencies with respect to the wavenumber ω, the mesh size h, and the polynomial degree p. But the current state of the theory does not fully explain the remarkably good numerical phase errors. Theoretically, comparisons are made with …
A Class Of Discontinuous Petrov–Galerkin Methods. Part Iii: Adaptivity,
2012
University of Texas at Austin
A Class Of Discontinuous Petrov–Galerkin Methods. Part Iii: Adaptivity, Leszek Demkowicz, Jay Gopalakrishnan, Antti H. Niemi
Mathematics and Statistics Faculty Publications and Presentations
We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: for 1D and for 2D problems. The adaptive process is fully automatic and starts …
Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates),
2012
Durham University
Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates), Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector approximation estimates. Unlike in the first part of the paper, we now use conforming higher order finite elements, since the canonical choice of an appropriate norm to measure eigenvector approximation by discontinuous Galerkin methods is an open problem.
Supporting Implementation Of The Common Core State Standards For Mathematics: Recommendations For Professional Development,
2012
North Carolina State University
Supporting Implementation Of The Common Core State Standards For Mathematics: Recommendations For Professional Development, Paola Sztajn, Karen A. Marrongelle, Peg Smith, Bonnie L. Melton
Mathematics and Statistics Faculty Publications and Presentations
In 2010, the National Governor’s Association and the Council of Chief State School Officers published the Common Core State Standards for Mathematics (CCSSM) and to date, 44 states, the District of Columbia, and the U.S. Virgin Islands have adopted the document. These content and practice standards, which specify what students are expected to understand and be able to do in K-12 mathematics, represent a significant departure from what mathematics is currently taught in most classrooms and how it is taught. Developing teachers’ capacity to enact these new standards in ways that support the intended student learning outcomes will require considerable …
The Hammer-And-Nail Phenomenon In Mathematics Education,
2012
University of Texas at El Paso
The Hammer-And-Nail Phenomenon In Mathematics Education, Kien H. Lim
Departmental Papers (Math)
"For a person with a hammer, everything looks like a nail" is a proverb that can be used to highlight the phenomenon that students tend to rely on familiar ideas as opposed to taking time to think about and analyse a problem. Presented in this theoretical paper is the usefulness of the hammer-and-nail metaphor, other related theoretical constructs, pedagogical causes of student impulsive behaviours, and pedagogical suggestions for addressing them.
Nonresonance On The Boundary And Strong Solutions Of Elliptic Equations With Nonlinear Boundary Conditions,
2012
Swarthmore College
Nonresonance On The Boundary And Strong Solutions Of Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, M. N. Nkashama
Mathematics & Statistics Faculty Works
We deal with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions by imposing asymptotic nonresonance conditions of nonuniform type with respect to the Steklov spectrum on the boundary nonlinearity. Unlike some recent approaches in the literature for problems with nonlinear boundary conditions, we cast the problem in terms of nonlinear compact perturbations of the identity on appropriate trace spaces in order to prove the existence of strong solutions. The proofs are based on a priori estimates for possible solutions to a homotopy on suitable trace spaces and topological degree arguments.
Recurrence Relations, Fractals, And Chaos: Implications For Analyzing Gene Structure,
2012
Colby College
Recurrence Relations, Fractals, And Chaos: Implications For Analyzing Gene Structure, Sarah. M. Harmon
Honors Theses
The “chaos game” is a well-known algorithm by which one may construct a pictorial representation of an iterative process. The resulting sets are known as fractals and can be mathematically characterized by measures of dimension as well as by their associated recurrence relations. Using the chaos game algorithm, is it possible to derive meaningful structure out of our own genetic encoding, and that of other organisms? In this paper, I will present one method of applying the chaos game to biological data and subsequently will discuss both the mathematical and biological implications of the results.
Short-Term Plasticity At The Schaffer Collateral: A New Model With Implications For Hippocampal Processing,
2012
Portland State University
Short-Term Plasticity At The Schaffer Collateral: A New Model With Implications For Hippocampal Processing, Andrew Hamilton Toland
Dissertations and Theses
A new mathematical model of short-term synaptic plasticity (STP) at the Schaffer collateral is introduced. Like other models of STP, the new model relates short-term synaptic plasticity to an interaction between facilitative and depressive dynamic influences. Unlike previous models, the new model successfully simulates facilitative and depressive dynamics within the framework of the synaptic vesicle cycle. The novelty of the model lies in the description of a competitive interaction between calcium-sensitive proteins for binding sites on the vesicle release machinery. By attributing specific molecular causes to observable presynaptic effects, the new model of STP can predict the effects of specific …
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part I,
2012
Jacoby Consulting
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part I, Carol Jacoby, Katrin Leistner, Peter Loth, Lutz Strungmann
Mathematics Faculty Publications
We consider the class of abelian groups possessing partial decomposition bases in Lδ∞ω for δ an ordinal. This class contains the class of Warfield groups which are direct summands of simply presented groups or, alternatively, are abelian groups possessing a nice decomposition basis with simply presented cokernel. We prove a classification theorem using numerical invariants that are deduced from the classical Ulm-Kaplansky and Warfield invariants. This extends earlier work by Barwise-Eklof, Göbel and the authors.
Capability Of 2 Gait Measures For Detecting Response To Gait Training In Stroke Survivors: Gait Assessment And Intervention Tool And The Tinetti Gait Scale,
2012
Case Western Reserve University
Capability Of 2 Gait Measures For Detecting Response To Gait Training In Stroke Survivors: Gait Assessment And Intervention Tool And The Tinetti Gait Scale, Janice Zimbelman, Janis J. Daly, Kristen L. Roenigk, Kristi Butler, Richard Burdsall, John P. Holcomb Jr.
Mathematics and Statistics Faculty Publications
Zimbelman J, Daly JJ, Roenigk KL, Butler K, Burdsall R, Holcomb JP. Capability of 2 gait measures for detecting response to gait training in stroke survivors: Gait Assessment and Intervention Tool and the Tinetti Gait Scale. Objective:To characterize the performance of 2 observational gait measures, the Tinetti Gait Scale (TGS) and the Gait Assessment and Intervention Tool (G.A.I.T.), in identifying improvement in gait in response to gait training. Design: In secondary analysis from a larger study of multimodal gait training for stroke survivors, we measured gait at pre-, mid-, and posttreatment according to G.A.I.T. and TGS, assessing their capability to …
