# News

## Math Undergraduate Receives NSF Research Fellowship

Math undergraduate Tony Allen awarded NSF Summer Fellowship. Please congratulate him. Great work Tony!

## Fatma Mohamed Defense

On Some Parabolic Type Problems from Thin Film Theory and Chemical Reaction-Diffusion Networks

Abstract: In the first part of this dissertation we study the evolution of a thin film of fluid modeled by the lubrication approximation for thin viscous films. We prove existence of (dissipative) strong solutions for the Cauchy problem when the sub-diffusive exponent ranges between 3/8 and 2; then we show that these solutions tend to zero at rates matching the decay of the source-type self-similar solutions with zero contact angle. We introduce the weaker concept of dissipative mild solutions and we show that in this case the surface-tension energy dissipation is the mechanism responsible for the $H^1$--norm decay to zero of the thickness of the film at an explicit rate. Relaxed problems, with second-order nonlinear terms of porous media type are also successfully treated by the same means.

In the second part we are concerned with the convergence of a certain space-discretization scheme (the so-called method of lines) for mass-action reaction-diffusion systems. First, we start with a toy model, namely AB and prove convergence of the method of lines for this linear case (weak convergence in L^2 is enough in this case). Then we show that solutions of the chemical reaction-diffusion system associated to A+BC in one spatial dimension can be approximated in L^2 on any finite time interval by solutions of a space discretized ODE system which models the corresponding chemical reaction system replicated in the discretization subdomains where the concentrations are assumed spatially constant. Same-species reactions through the virtual boundaries of adjacent subdomains lead to diffusion in the vanishing limit. We show convergence of our numerical scheme by way of a consistency estimate, with features generalizable to reaction networks other than the one considered here, and to multiple space dimensions.

Date: 4/20/2017

Time: 12:30PM-2:30PM

Place: 315 Armstrong Hall

All are welcome.

## Mushtaq Abd Al-Rahem Defense

A Multidimensional Technique for Measuring Consensus Within Groups via Conditional Probability

Abstract: A recent increase in the use of the term “consensus” in various fields has led researchers to develop various ways to measure the consensus within and across groups depending on the areas. Numerous studies use the mean or the variance alone as a measure of consensus, or lack of consensus. Most of the time, high variance is viewed as more disagreement in a group. Using the variance as a measure of disagreement is meaningful in an exact comparison cases (same group, same mean). However, it could be meaningless when it is used to compare groups that have different sizes, or if the mean is different. In this thesis, we establish the fact that the range of the variance is a function of the mean, we present a new index of disagreement and measure of consensus that depend on both, the mean and the variance, by utilizing the conditional distribution of the variance for a given mean. Initially, this new index is developed for comparison of data collected using a Likert scale of size five. This new measure is compared with the results of two other known measures, to show that in some cases they agree, but in other cases the new measure provides additional information. Next, to facilitate generalization, a new algorithmic method to determine the index using a geometric approach is presented. The geometric approach makes it easier to compute the measure of consensus and provides the foundational ideas for generalizing the measure to Likert scales for any n. Finally, a multidimensional computational technique was developed to provided the final step of generalization to Likert scales of any n.

Date: 4/10/2017

Time: 3:00PM-5:00PM

Place: 313 Armstrong Hall

All are welcome.

## Pantea Receives Award

The Eberly College of Arts and Sciences has named two recipients of the 2016-17 Outstanding Researcher Award: Christina Duncan and Casian Pantea.

Congratulate Professor Pantea the next time you see him!

## Junior Math Competition

This competition will be open to all students grades 7-12. The questions will be at AMC difficulty level.

More information can be obtained from the following links.

Please direct questions/comments:

Casian Pantea: cpantea@math.wvu.edu

Charis Tsikkou: tsikkou@math.wvu.edu

Megan Henry: mhott1@mix.wvu.edu

## Janet Anderson Defense

A Study of arc strong connectivity of digraphs

Abstract: This dissertation studies the extremal, structural and minimax properties related to digraph arc strong connectivity. Motivated by the former researches by Mader and Matula, we defined the digraph arc strength of a digraph $D$ to be the maximum arc strong connectivity of subdigraphs of $D$, and investigate extremal conditions for a strict digraph that is saturated with respect to the condition that it digraph arc strength is bounded by a positive integer $k$. Extremal size of such digraphs are obtained and structural characterization of the extremal digraphs are also obtained. In addition, a minimax duality theorem to determine the digraph arc strength of a digraph is found. Similar minimax results on related desity functions of digraphs are also obtained.

Date: 4/7/2017

Time: 3:30PM-5:00PM

Place: 315 Armstrong Hall

All are welcome.

## Celebrating Einstein

When Black Holes Collide! Gravitational Waves and Other Tales from the Horizon

As part of the month-long Celebrating Einstein event here at WVU, Dr. Zach Etienne from Department of Mathematics will be giving a public lecture this Friday on black holes and gravitational waves. A planetarium show on the top floor of White Hall will follow immediately after his lecture. His talk is accessible to general audience and even kids may enjoy the talk and the show.

Abstract:What happens if you fall into a black hole? Einstein's theory of gravity provides us a means to answer questions that, like this one, fuzz the boundary between science fiction and science fact. But the equations behind this theory are extremely complex, and solving them to advance our scientific understanding--particularly now that gravitational waves have been discovered--usually requires the use of supercomputers. In a nutshell, this is my field of expertise. I will review my career path and present results from some of my latest supercomputer simulations, which have given us both deeper insights into the gravitational waves we have already observed, as well as important predictions for those we are likely to observe in the near future.

Immediately after the lecture, at 8:30PM, there will be a planetarium show on the top floor of White Hall.

For more information on the Celebrating Einstein event, check out these links:

Date: 4/07/2017

Time: 7:30PM

Place: White Hall Room G09

All are welcome.

## 4th Annual Integration Bee

This will be an integration contest open to all WVU students.

All integrals can be solved by techniques of Math 156.

More information can be obtained from the following links.

Website

Flyer

Please direct questions/comments:

Charis Tsikkou: tsikkou@math.wvu.edu

Casian Pantea: cpantea@math.wvu.edu

## Mr. Xiangming Wu Dissertation Prospectus

A Comparative Study of Three Versions of Calculus I

Date: 1/20/2017

Time: 11:00AM-1:00PM

Place: 320 Armstrong Hall

All are welcome.

## Mr. Salah Hamad Dissertation Prospectus

Compactification and Asymptotics for Banach and Hilbert Spaces and applications.

Date: 12/14/2016

Time: 3:30PM-5:30PM

Place: 315 Armstrong Hall

All are welcome.

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