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Articles 1 - 30 of 36
Full-Text Articles in Physical Sciences and Mathematics
Infinitary Equivalence Of Zp- Modules With Nice Decomposition Bases, Rüdiger Göbel, Katrin Leistner, Peter Loth, Lutz Strüngmann
Infinitary Equivalence Of Zp- Modules With Nice Decomposition Bases, Rüdiger Göbel, Katrin Leistner, Peter Loth, Lutz Strüngmann
Mathematics Faculty Publications
Warfield modules are direct summands of simply presented Zp - modules, or, alternatively, are Zp - modules possessing a nice decomposition basis with simply presented cokernel. They have been classified up to isomorphism by theor Ilm-Kaplansky and Warfield invariants. Taking a model theoretic point of view and using infinitary languages we give here a complete theoretic characterization of a large class of Zp - modules having a nice decomposition basis. As a corollary, we obtain the classical classification of countable Warfield modules. This generalizes results by Barwise and Eklof.
Operation Comics: Making Math Fun, Bruce Kessler
Operation Comics: Making Math Fun, Bruce Kessler
Mathematics Faculty Publications
This talk gives a background on the Operation Comics series, which integrates mathematics into a comic book storyline, as an example of how creativity is not exclusive to the traditional arts, like music and dance, but is a vital part of math, science, and engineering.
A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh
A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh
Mathematics Faculty Publications
The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …
Characterizing Convergence Conditions For The Mα-Integral, Ian June L. Garces, Abraham P. Racca
Characterizing Convergence Conditions For The Mα-Integral, Ian June L. Garces, Abraham P. Racca
Mathematics Faculty Publications
Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.
Operation Comics: The Story Continues, Bruce Kessler, Tressa Tullis
Operation Comics: The Story Continues, Bruce Kessler, Tressa Tullis
Mathematics Faculty Publications
This talk was given, with Tressa Tullis as the main presenter and Bruce Kessler as a minor co-presenter, at the 2011 Bridges Conference in Coimbre, Portugal, on the current developments on our Operation Comics project with Cumberland Trace Elementary.
Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis
Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis
Mathematics Faculty Publications
During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …
Polynomial Generalizations Of Two-Variable Ramanujan Type Identities, James Mclaughlin, Andrew V. Sills
Polynomial Generalizations Of Two-Variable Ramanujan Type Identities, James Mclaughlin, Andrew V. Sills
Mathematics Faculty Publications
No abstract provided.
The Graph Distance Game, Wayne Goddard, Anne Sinko, Peter J. Slater, Honghai Xu
The Graph Distance Game, Wayne Goddard, Anne Sinko, Peter J. Slater, Honghai Xu
Mathematics Faculty Publications
In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this note, we examine the distance game for various graphs, and provide general bounds, exact results for special graphs, and an algorithm for trees. Computer calculations suggest interesting conjectures for grids.
“Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, Bruce Kessler
“Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, Bruce Kessler
Mathematics Faculty Publications
During Spring 2009, Dr. Kessler created and published a comic book series that embedded math content into the story for 4th-6th grade students. The comics were well received in the classrooms at Cumberland Trace Elementary. Dr. Kessler contends that this approach to teaching and learning can be used in any content area, and is useful for engaging students who might not be as interested otherwise. This session will explore ways of utilizing the skills of your students to construct learning comics in your classes, regardless of the funds, technology, and artistic experience at your disposal. The session will include a …
Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, Bruce Kessler, Alexander Barzilov, Phillip Womble
Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, Bruce Kessler, Alexander Barzilov, Phillip Womble
Mathematics Faculty Publications
Neutron-based methods of non-destructive inter- rogation of objects for the purpose of their characterization are well-established techniques, employed in the field of bulk material analysis, contraband detection, unexploded ordnance, etc. The characteristic gamma rays produced in nuclear reactions initiated by neutrons in the volume of the irradiated object (inelastic neutron scattering, thermal neutron capture, and activation) are used for the elemental identification. In many real-world applications, an automated spectral analysis is needed, and many algorithms are used for that purpose. The Applied Physics Institute at Western Kentucky University has recently started to employ a mathematical spectrum analysis technique based on …
Phase Retrieval For Characteristic Functions Of Convex Bodies And Reconstruction From Covariograms, Gabriele Bianchi, Richard J. Gardner, Markus Kiederlen
Phase Retrieval For Characteristic Functions Of Convex Bodies And Reconstruction From Covariograms, Gabriele Bianchi, Richard J. Gardner, Markus Kiederlen
Mathematics Faculty Publications
The Phase Retrieval Problem of Fourier analysis involves determining a function f on Rn from the modulus |f�| of its Fourier transform f�. This problem arises naturally and frequently in various areas of science, such as X-ray crystallography, electron microscopy, optics, astronomy, and remote sensing, in which only the magnitude of the Fourier transform can be measured and the phase is lost.
A New Summation Formula For Wp-Bailey Pairs, James Mclaughlin
A New Summation Formula For Wp-Bailey Pairs, James Mclaughlin
Mathematics Faculty Publications
No abstract provided.
A “Peak” At The Algorithm Behind “Peaklet Analysis” Software, Bruce Kessler
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.
Hybrid Proofs Of The Q-Binomial Theorem And Other Identities, Dennis Eichhorn, James Mclaughlin, Andrew V. Sills
Hybrid Proofs Of The Q-Binomial Theorem And Other Identities, Dennis Eichhorn, James Mclaughlin, Andrew V. Sills
Mathematics Faculty Publications
No abstract provided.
A Primer On Chaos And Fractals, Bruce Kessler
A Primer On Chaos And Fractals, Bruce Kessler
Mathematics Faculty Publications
This is a prelude to a performance of the play "Arcadia" exclusively for the science and math majors of Lipscomb University. One of the main characters of the story is a mathematical genius, and has realized the power and limitations of iterations in generating mathematical models and structures, although she is living in the early 1800's. This talk gives an introduction to the ideas of chaos theory, fractals, and randomness.
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.
The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle
The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle
Mathematics Faculty Publications
We will give a positive answer for the unimodality of the Hilbert functions in the smallest open case, that of Artinian level monomial algebras of type three in three variables.
Making Algebra More Accessible: How Steep Can It Be For Teachers?, Diana Cheng, Polina Sabinin
Making Algebra More Accessible: How Steep Can It Be For Teachers?, Diana Cheng, Polina Sabinin
Mathematics Faculty Publications
Teacher educators need to support middle grades teachers in developing mathematical knowledge for teaching algebraic concepts. In particular, teachers should become familiar with possible introductions and sequencing to the concept of slope, and common middle school students’ limited conceptions about measuring the steepness of an incline. Steepness can be expressed directly in terms of an angle or indirectly as a slope. Encouraging middle school students to find a measure of steepness using a ratio may help support students’ transition to multiplicative thinking. This mixed – methods study explores middle school students’ responses in solving a comparison problem involving the steepness …
Traveling Wave Solutions Of Burgers’ Equation For Power-Law Non- Newtonian Flows, Dongming Wei, Harry Borden
Traveling Wave Solutions Of Burgers’ Equation For Power-Law Non- Newtonian Flows, Dongming Wei, Harry Borden
Mathematics Faculty Publications
In this work we present some analytic and semi-analytic traveling wave solutions of a generalized Burgers' equation for unidirectional flow of power-law non-Newtonian fluids. The solutions include the corresponding well-known traveling wave solution of the Burgers' equation for Newtonian flows. We also derive estimates of shock thickness for the power-law flows.
Stability Of The Gauge Equivalent Classes In Inverse Stationary Transport In Refractive Media, Stephen R. Mcdowall, Plamen Stefanov, Alexandru Tamasan
Stability Of The Gauge Equivalent Classes In Inverse Stationary Transport In Refractive Media, Stephen R. Mcdowall, Plamen Stefanov, Alexandru Tamasan
Mathematics Faculty Publications
In the inverse stationary transport problem through anisotropic attenuating, scattering, and refractive media, the albedo operator stably determines the gauge equivalent class of the attenuation and scattering coefficients.
Modulation Spaces, Wiener Amalgam Spaces, And Brownian Motions, Árpád Bényi, Tadahiro Oh
Modulation Spaces, Wiener Amalgam Spaces, And Brownian Motions, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
We study the local-in-time regularity of the Brownian motion with respect to localized variants of modulation spaces Msp,q and Wiener amalgam spaces Wsp,q. We show that the periodic Brownian motion belongs locally in time to Msp,q(T) and Wsp,q(T) for (s−1)q
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.
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.
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, …
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.
Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, Marshal Ma, Scott Mcclintock
Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, Marshal Ma, Scott Mcclintock
Mathematics Faculty Publications
No abstract provided.
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.
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 …
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.