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Articles 181 - 210 of 323
Full-Text Articles in Mathematics
2011 (Spring), University Of Dayton. Department Of Mathematics
2011 (Spring), University Of Dayton. Department Of Mathematics
Colloquia
Abstracts of the talks given at the 2011 Spring Colloquium.
Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang
Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang
Mathematics Faculty Publications
In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global L2 a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.
Linear Systems Of Fractional Nabla Difference Equations, Ferhan M. Atici, Paul W. Eloe
Linear Systems Of Fractional Nabla Difference Equations, Ferhan M. Atici, Paul W. Eloe
Mathematics Faculty Publications
In this paper we shall consider a linear system of fractional nabla difference equations with constant coefficients. We shall construct the fundamental matrix for the homogeneous system and the causal Green’s function for the nonhomogeneous system. We employ transform methods and series methods, and we illustrate analogies with classical first-order differential or difference equations. We shall close the paper with an asymptotic result that follows from the analysis of a half-order nabla difference equation.
Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee
Research In Mathematics Educational Technology: Current Trends And Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, David K. Pugalee
Mathematics Faculty Publications
This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, …
Positive Solutions Of Nonlocal Boundary Value Problem For Higher Order Fractional Differential System, Mujeeb Ur Rehman, Rahmat Ali Khan, Paul W. Eloe
Positive Solutions Of Nonlocal Boundary Value Problem For Higher Order Fractional Differential System, Mujeeb Ur Rehman, Rahmat Ali Khan, Paul W. Eloe
Mathematics Faculty Publications
In this paper, we study existence and multiplicity results for a coupled system of nonlinear nonlocal boundary value problems for higher order fractional differential equations of the type (see PDF) where (see PDF) is Caputo fractional derivative. We employ the Guo-Krasnosel’skii fixed point theorem to establish existence and multiplicity results for positive solutions. We derive explicit intervals for the parameters _ and μ for which the system possess the positive solutions or multiple positive solutions. Examples are included to show the applicability of the main results.
Twelfth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics
Twelfth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics
Kenneth C. Schraut Memorial Lectures
No abstract provided.
Imaginary Numbers, Unsolvable Equations, And Newton's Method (Abstract), Jeffrey Diller
Imaginary Numbers, Unsolvable Equations, And Newton's Method (Abstract), Jeffrey Diller
Kenneth C. Schraut Memorial Lectures
You might have been led to believe that math is all about solving equations. Sadly, however, most equations can't actually be solved. The best one can do is to try to approximate their solutions.
2011 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics
2011 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics
Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials
No abstract provided.
Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman
Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman
Mathematics Faculty Publications
An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.
Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti
Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti
Mathematics Faculty Publications
This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.
Non-Normality Points Of Β X\X, William Fleissner, Lynne Yengulalp
Non-Normality Points Of Β X\X, William Fleissner, Lynne Yengulalp
Mathematics Faculty Publications
We seek conditions implying that (β X\X) \ {y} is not normal. Our main theorem: Assume GCH and all uniform ultrafilters are regular. If X is a locally compact metrizable space without isolated points, then (β X\X) \ {y} is not normal for all y ∈ β X\X. In preparing to prove this theorem, we generalize the notions “uniform”, “regular”, and “good” from set ultrafilters to z-ultrafilters. We discuss non-normality points of the product of a discrete space and the real line. We topologically embed a nonstandard real line into the remainder of this product space.
Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler
Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler
Mathematics Faculty Publications
We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.
Upper And Lower Solutions For Regime-Switching Diffusions With Applications In Financial Mathematics, Paul W. Eloe, R. H. Liu
Upper And Lower Solutions For Regime-Switching Diffusions With Applications In Financial Mathematics, Paul W. Eloe, R. H. Liu
Mathematics Faculty Publications
This paper develops a method of upper and lower solutions for a general system of second-order ordinary differential equations with two-point boundary conditions. Our motivation of study stems from a class of financial mathematics problems under regime-switching diffusion models. Two examples are double barrier option valuation and optimal selling rules in asset trading. We establish the existence of a unique C2 solution of the two-point boundary value problem. We construct monotone sequences of upper and lower solutions that are shown to converge to the unique solution of the boundary value problem. This construction provides a feasible numerical method to compute …
Optimal Intervals For Uniqueness Of Solutions For Nonlocal Boundary Value Problems, Paul W. Eloe, Johnny Henderson
Optimal Intervals For Uniqueness Of Solutions For Nonlocal Boundary Value Problems, Paul W. Eloe, Johnny Henderson
Mathematics Faculty Publications
For the nth order differential equation (see PDF for equation) we obtain optimal bounds on the length of intervals on which solutions are unique for certain nonlocal three point boundary value problems. These bounds are obtained through an application of the Pontryagin Maximum Principle from the theory of optimal control.
2011 Program And Abstracts, University Of Dayton. Department Of Mathematics
2011 Program And Abstracts, University Of Dayton. Department Of Mathematics
Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials
Program and abstracts of papers presented at the 2011 Undergraduate Mathematics Day held at the University of Dayton.
Perfect And Abundant Numbers - A Perfect And Abundant Source For Undergraduate Research Projects (Abstract), Judy Holdener
Perfect And Abundant Numbers - A Perfect And Abundant Source For Undergraduate Research Projects (Abstract), Judy Holdener
Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials
In June of 2009, the 47th perfect number was discovered by the Great Internet Mersenne Prime Search (GIMPS), a collaborative computing project involving volunteers from all over the world. Like all known perfect numbers before it, this number is even. Does an odd perfect number exist? Are there infinitely many perfect numbers?
2010 (Fall), University Of Dayton. Department Of Mathematics
2010 (Fall), University Of Dayton. Department Of Mathematics
Colloquia
Abstracts of the talks given at the 2010 Fall Colloquium.
Coarser Connected Metrizable Topologies, Lynne Yengulalp
Coarser Connected Metrizable Topologies, Lynne Yengulalp
Mathematics Faculty Publications
We show that every metric space, X, with w(⩾) c has a coarser connected metrizable topology.
2010 (Spring), University Of Dayton. Department Of Mathematics
2010 (Spring), University Of Dayton. Department Of Mathematics
Colloquia
Abstracts of the talks given at the 2010 Spring Colloquium.
Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, Naseer Ahmad Asif, Paul W. Eloe, Rahmat Ali Khan
Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, Naseer Ahmad Asif, Paul W. Eloe, Rahmat Ali Khan
Mathematics Faculty Publications
Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type (see PDF for details) are obtained. The nonlinearities (see PDF) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. … An example is provided to illustrate the results.
Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth
Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth
Mathematics Faculty Publications
We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.
The Marshall Differential Analyzer: A Visual Interpretation Of Mathematics, Bonita A. Lawrence, Richard P. Merritt, Devon A. Tivener
The Marshall Differential Analyzer: A Visual Interpretation Of Mathematics, Bonita A. Lawrence, Richard P. Merritt, Devon A. Tivener
Undergraduate Mathematics Day: Past Content
Mechanical integration is an idea dating back to the late 1800's discovered by James Thomson, brother of Lord Kelvin. This idea was then expanded to build a calculating machine, called a differential analyzer, by Vannevar Bush (M.I.T) in 1929. The Marshall University Differential Analyzer Team has followed in the footsteps of Dr. Bush and a gentleman named Dr. Arthur Porter, who was the first to build a differential analyzer in England when he was a student of Dr. Douglas Hartree. He built his machine of Meccano components, the British version of Erector Set. In the early days of Arthur Porter's …
2010 Vol. 4 Table Of Contents, University Of Dayton. Department Of Mathematics
2010 Vol. 4 Table Of Contents, University Of Dayton. Department Of Mathematics
Undergraduate Mathematics Day: Past Content
No abstract provided.
On The Construction Of Order Six Multilevel Hadamard Matrices, Keli Parker
On The Construction Of Order Six Multilevel Hadamard Matrices, Keli Parker
Undergraduate Mathematics Day: Past Content
The existence of multilevel Hadamard matrices (MHMs) of all orders as well as a construction for full-rate circulant MHMs of all orders n 6= 4 is known. We use computer search methods to look for previously unknown full-rate circulant MHMs of orders 5, 6, and 7 and find solutions that potentially do not follow from the known construction. We then give an alternate construction to explain some order six MHMs.
Uniqueness Of Solutions Implies Existence And Uniqueness Of Solutions Of Boundary Value Problems For Third Order Differential Equations, Veronica Respress
Uniqueness Of Solutions Implies Existence And Uniqueness Of Solutions Of Boundary Value Problems For Third Order Differential Equations, Veronica Respress
Undergraduate Mathematics Day: Past Content
In this paper we are concerned with uniqueness implies uniqueness and uniqueness implies existence questions for solutions of a class of boundary value problems for the third order ordinary differential equation (ODE). First we show uniqueness of solutions of a class of two-point problems implies the uniqueness of solutions of an associated class of three-point problems. Then we establish uniqueness of solutions of the class of two-point problems implies the existence of solutions of the class of two point problems and the associated class of three-point problems.
Just Sit Back And Let The Girth Model Make Money For You, Ellham Negahdary
Just Sit Back And Let The Girth Model Make Money For You, Ellham Negahdary
Undergraduate Mathematics Day: Past Content
The Girth Model will use the 10-period exponential moving average (EMA) and the 20-period EMA as their proxy for market trend. The Girth Model is a trend following model incorporating volatility, momentum and velocity. We will use girth as an early close indication to both long and short positions. Typically, early exit due to decreasing girth results in a more favorable profit position than that taken if the trader simply waited for an exit on the EMA cross to the downside.
Distance Functions And Attribute Weighting In A K-Nearest Neighbors Classifier, Alyssa C. Frazee, Matthew A. Hathcock, Samantha C. Bates Prins
Distance Functions And Attribute Weighting In A K-Nearest Neighbors Classifier, Alyssa C. Frazee, Matthew A. Hathcock, Samantha C. Bates Prins
Undergraduate Mathematics Day: Past Content
To assess environmental health of a stream, field, or other ecological object, characteristics of that object should be compared to a set of reference objects known to be healthy. Using streams as objects, we propose a k-nearest neighbors algorithm (Bates Prins and Smith, 2006) to find the appropriate set of reference streams to use as a comparison set for any given test stream. Previously, investigations of the k-nearest neighbors algorithm have utilized a variety of distance functions, the best of which has been the Interpolated Value Difference Metric (IVDM), proposed by Wilson and Martinez (1997). We propose two alternatives to …
Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn
Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn
Mathematics Faculty Publications
It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.
2010 Alumni Presenters, University Of Dayton. Department Of Mathematics
2010 Alumni Presenters, University Of Dayton. Department Of Mathematics
Biennial Alumni Seminar
No abstract provided.
Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik
Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik
Mathematics Faculty Publications
We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation, and like the …