Session Index
Click a session title to jump to the abstracts.
Faculty Session 1
1:00pm--2:00pm, G-246
Speakers: Yevgeniy Galperin, Lin Tan, Eugene Boman
Faculty Session 2
1:00pm--2:00pm, G-245
Speakers: Myung Song, Michael Yatauro
Faculty Session 3
1:00pm--2:00pm, G-247
Speakers: Eric Takyi, Dr. Sanju Vaidya, Tania Hazra
Faculty Session 4
1:00pm--2:00pm, G-248
Speakers: Soumyadip Acharyya, Robert Freeman
Faculty Session 1, G-246
1:00pm, Yevgeniy Galperin (East Stroudsburg University of PA)
Digital Image Processing in College Mathematics
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We provide meaningful context for reviewing key topics of the college mathematics curriculum by studying a variety of methods for digital image processing. In the process, we help students gain confidence in using concepts and techniques of applied mathematics, improve student awareness of recent developments in mathematical sciences, and help students prepare for graduate studies.
Close Abstract1:20pm, Lin Tan (West Chester University)
Why Let "ε > 0" ?
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Most of the definitions, hence proofs, in analysis with "for any/each/every ε > 0, ..." together with absolute value sign. Why? We trace it back to Euclid and Eudoxus, identifying its root in the Ancient Greek proof of the proportionality of the corresponding sides of similar triangles.
Close Abstract1:40pm, Eugene Boman (Penn State, Harrisburg campus)
Putting the Differential Back Into Calculus
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After many years of discussing and puzzling over our student's struggles in first year Calculus, Bob Rogers (SUNY, Fredonia) and I decided to reorganize our Calculus syllabi to allow for a more intuitive development, one that reflects the way that Calculus developed historically. The result has taken the form of a OER Calculus textbook. In our text we explicitly and assertively reintroduce the differentials of Leibniz as a computational device, we use historical and real-world problems to motivate the concepts, and we place the theoretical underpinnings at the end of the course.
In this talk I will describe some aspects of our text and discuss why we made the choices we did. In particular, we will discuss some of the more radical features of our text. For example, we place the theory of limits at the end of the course rather the beginning, as is standard in most texts.
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Faculty Session 2, G-245
1:00pm, Myung Song (Kutztown University of Pennsylvania)
Using Integer Programming Software to solve large multi-demand multidimensional knapsack problems
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An important generalization of the classic 0-1 knapsack problem is the multi-demand multidimensional knapsack problem (MDMKP). In addition to being theoretically difficult to solve (it is NP-hard), it can be in practice difficult to solve because of its conflicting knapsack and demand constraints. Since there are significant large-scale applications of the MDMKP, approximate solution approaches are commonly used to solve these problems. However, using 810 MDMKPs discussed in the literature by Lu and Vasko (2019), along with 810 MDMKPs defined in 2005 by Cappanera and Trubi-an, this article demonstrates which types of large MDMKPs can be solved efficiently by operations research practitioners on a standard personal computer within 0.1% of optimum using general purpose integer programming software (CPLEX version 12.9). Statistical analyses are used to determine which problem parameters significantly impact solution time. Finally, based on these 1620 MDMKP instances, classification trees are generated to recommend when CPLEX should and should not be used to solve MDMKPs. These results can be used to guide practitioners in solving MDMKPs that arise in business and industry.
Close Abstract1:20pm, Michael Yatauro (Penn State - Brandywine)
A Tribute to Douglas Ira Bauer
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Douglas Bauer was Professor of Mathematics at Stevens Institute of Technology and a prolific researcher in the field of Graph Theory for nearly four decades. Doug was diagnosed with Multiple Sclerosis in 1986, and he remained highly active in the face of this adversity. I had the good fortune of having Doug as my thesis advisor and a collaborator. He was a mentor and an inspiration, and the impact he had on my life stays with me to this day. His research topics included the study of hamiltonicity, cycle structure, graph parameters (most notably toughness and binding number), and degree sequence theorems. In this talk, I will present some of the most impactful results published by Doug and his coauthors (which he affectionately referred to as the “usual suspects”).
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Faculty Session 3, G-247
1:00pm, Eric Takyi (Ursinus College)
The (De)Stabilizing effect of juvenile prey cannibalism in a stage-structured model
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Cannibalism, or intraspecific predation, is the act of an organism consuming another organism of the same species. In predator-prey relationships, there is experimental evidence to support the existence of cannibalism among juvenile prey. In this work, we propose a stage-structured predator-prey system where cannibalism occurs only in the juvenile prey population. We show that cannibalism has both a stabilizing and destabilizing effect depending on the choice of parameters. We perform numerical experiments to further support our theoretical findings. We discuss the ecological implications of our results.
Close Abstract1:20pm, Dr. Sanju Vaidya (Mercy College)
Bounds for Neighborhood Degree Based Indices of Graphs
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In the last forty years, scientists have developed mathematical models for analyzing structures and properties of various chemical compounds. Graph Theory plays a vital role in developing several models such as Quantitative Structure-Property Relationships (QSPR) models. In molecular graphs of chemical compounds vertices correspond to atoms and edges correspond to the bonds between them. In 1947 Harry Wiener introduced a topological index related to molecular branching. He correlated the indices with the boiling points of certain chemical compounds. This inspired mathematicians and chemists to develop more topological indices for molecular graphs. Now there are more than100 topological indices for graphs. The main research question is how to compute bounds of various topological indices for graphs. In 2019, Modal S., De N., and Pal A. introduced Neighborhood Degree based indices and proved their significance for prediction of physicochemical properties. In this presentation, we will establish formulas and bounds for Neighborhood Degree based indices of graphs and we will describe graphs which attain the bounds. Moreover, we will establish a lower bound for the spectral radius of any graph.
Close Abstract1:40pm, Tania Hazra (Misericordia University)
Can we estimate the solvation free energy of a protein using a reference state replacing the vacuum state?
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The electrostatic analysis is essential for studying various important biological processes at the atomistic level, which involve charged objects such as proteins, DNAs and RNAs, immersed in an aquatic environment with mobile ions. The Poisson Boltzmann Equation (PBE), an implicit solvent model, has been widely used to simulate electrostatic interactions between the solute macromolecular and the surrounding solvent molecules. The PBE is commonly used to calculate the electrostatic free energy or polar solvation energy, which is defined as the polar energy released when a solute is dissolved in a solvent. The solvation free energy (FE) is calculated in two steps: first, a macromolecule is placed in water (state) and the electrostatic potential is calculated. The same procedure is followed in the vacuum state. The difference between these two electrostatic potentials is a crucial part of the electrostatic FE. Now the question is: can we write this solvation FE in the water-vacuum state in terms of any other reference state replacing the vacuum? This study explores a multiple regression model with some special cases.
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Faculty Session 4, G-248
1:00pm, Soumyadip Acharyya (University of South Carolina Sumter)
A Generalization of m-topology and U-topology on rings of measurable functions
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Let $(X, \mathcal{A})$ stand for a nonempty set $X$ equipped with a $\sigma$-algebra $\mathcal{A}$ over $X$. Let $\mathcal{M}(X, \mathcal{A})$ be the set of all real-valued $\mathcal{A}$-measurable functions on $X$, which forms a commutative lattice ordered ring with unity if the relevant operations are defined pointwise. The $m$-topology and $U$-topology on $\mathcal{M}(X, \mathcal{A})$ are studied extensively in literature. This work generalizes these two topologies to the so-called $m_{\mu_{I}}$ and $U_{\mu_{I}}$ topology, respectively, where $\mu$ is a measure on ($X,\mathcal{A}$) and $I$ is an ideal in the ring $\mathcal{M}(X,\mathcal{A})$. This talk will discuss (a) the components of $0$ in $m_{\mu_{I}}$ and $U_{\mu_{I}}$ topology, and (b) the completeness of the pseudonormed linear space $L_{I}^{\infty} \left(\mu\right)$.
Close Abstract1:20pm, Robert Freeman (PennSt Berks)
On the parabolic $\texttt{p}(x)$-Laplace Equation in Carnot groups
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In this talk, we discuss some results on the parabolic $\texttt{p}(x)$-Laplace Equation in Carnot groups. We will introduce the notion of the parabolic $\texttt{p}(x)$-Laplace Equation in Carnot groups and the notions of weak and viscosity solutions to it. We then discuss some results, including the uniqueness of viscosity solutions, taking $t \rightarrow \infty$, and, if time, a discussion on the equivalence of weak and viscosity solutions.
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