Fifth Annual UMKC Math & Stat Research Day

 

Date: Friday, April 19, 2019
Time: 10:00am-3:00pm
Location: Miller Nichols Learning Center, Room 352

Deadline for Abstract Submission: April 10, 2019

The Math & Stats Research Day provides a platform for students and faculty to publicly present their research and scholarly activities in mathematics, statistics, and their applications in various fields.

In a broad context, we are interested in research projects that employ some mathematical or statistical methods.

There is no registration fee. This is a public event, open to all students and researchers.

The Math & Stats Research Day welcomes the submission of abstracts for original contribution to the field in the following scientific tracks:

1. Mathematical and statistical modeling

2. Numerical and statistical methods for data analysis

3. Mathematical methods in science and engineering

A great opportunity to present your scholarly work and to network with applied mathematicians and statisticians at UMKC.

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Schedule 

      • Friday, April 19, 2019
        9:30 am 9:50 am Registration
        9:50 am 10:00 am Welcome and Opening Remarks
        10:00 am 10:20 am Jeffrey T. Harris and Layla AM Shafei
        10:25 am 10:45 am Sarah Cole, Mohan Gajendran and Ronald Morris
        10:50 am 11:10 am Coffee Break
        11:20 am 11:40 pm Hope Pleasance Mertz and Arman Nokhosteen
        11:45 am 12:05 pm C. E. Hauptmann and K. R. Kuhlmann
        12:05 pm 1:00 pm Lunch – Hosted on site by the UMKC Math & Stat Department
        1:00 pm 1:20 pm Hussain JB Alantari and Mehmet Uylukcu
        1:25 pm 1:45 pm Babak Poorebrahim Gilkalaye
        1:50 pm 2:10 pm Vanessa R. Collins
        2:15 pm 2:35 pm Avary Kolasinski
        2:40 pm 3:00 pm Tahani Omer

Titles and Abstracts

Modeling and Simulation of Diffraction Through a Circular Aperture

Jeffrey Thomas Harris jthq67@mail.umkc.edu Layla Ali M Shafei las3b6@mail.umkc.edu

Department of Physics and Astronomy, University of Missouri-Kansas City

Electromagnetic plane waves incident on an aperture will always exhibit diffraction to some degree. The resultant diffraction pattern qualities depend on the properties of both the electromagnetic wave and the aperture. Such properties include wavelength, distance from aperture to plane of observation, ratio of wavelength to aperture scale, shape of aperture, and angle of incidence. In this project we have derived diffracting monochromatic plane wave solutions to the Helmholtz partial differential equation by the method of Green’s functions. The solutions are then used to find an intensity distribution on an observation plane as a function of the aforementioned properties of the diffracting wave-aperture system. The intensity distribution was them simulated using Mathematica so as to illustrate how changes in these properties are manifested in the diffraction patterning. Attempts were then made to reproduce these results by passing a plane wave 351nm excimer laser beam through a circular aperture.

  

Using Sturm-Liouville Theory to Analyze Steady State Schrodinger Wave Equation

Sarah Cole1 colesa@umkc.edu Mohan Gajendran2 mgz53@mail.umkc.edu Ronald Morris1 rmmv82@mail.umkc.edu

1Department of Mathematics and Statistics, University of Missouri-Kansas City,

2Department of Civil and Mechanical Engineering, University of Missouri-Kansas City

 

Quantum mechanics is concerned with finding a particle’s wave function, which is found by solving the Schrodinger equation. The focus here is on the steady state or time-independent wave equation where velocity is independent of time. There are many specific applications of the time-independent Schrodinger wave equation in quantum mechanics, but the focus here was the Harmonic Oscillator problem with a mass attached to a spring of constant force. We took an analytical and numerical approach to the study of the harmonic oscillation problem. Since this is a special case of a Sturm-Liouville problem, we were able to apply some approaches in SL theory to study this problem from an analytic perspective. The goals of the project were to solve the equation using separation of variables and then go through a series of steps using SL theory to show that the solutions (eigenpairs) take on discrete values only. In our numerical approach, we are confirming results in the paper “Numerical Determination of the Eigenenergies of the Schrodinger Equation in One Dimension” by Hugdal, HG and Berg, P. In the paper, the authors applied finite difference method to the harmonic oscillation problem. Using our own code and knowledge, we modeled the equation using finite difference method to confirm the results of the paper. We also took the paper a step further and used Runge-Kutta 4, and Runge-Kutta 8 to see how well the numerical results approximated the actual and the results given by finite difference method.

 

Approximate solutions of a projectile equation using perturbation theory

Hope Pleasance Mertz1 phmyhz@mail.umkc.edu Arman Nokhosteen2 any2r@mail.umkc.edu

1Department of Mathematics and Statistics, University of Missouri-Kansas City,

2Department of Civil and Mechanical Engineering, University of Missouri-Kansas City

In this study, the projectile motion of an object considered to be a concentrated mass has been studied using regular perturbation theory. The approximate solution has been obtained by using various numbers of approximation terms. By non-dimensionalizing the projectile motion equation, analytical solutions based on the number of utilized approximation terms were obtained and subsequently plotted to map out the trajectory of the projectile mass. By adding terms to the equation of motion that consider both the effect of changing gravitational attraction and wind resistance (modelled by using a constant value, K) on the object, the authors were able to show the accuracy of the utilized perturbation method for obtaining an object’s trajectory, described by a fairly complex equation of motion. For validation of the results, a separate solution was achieved by solving the equation of motion numerically using the built in, fifth-order, Runge-Kutta solver in MATLAB. The results show that as the terms used for approximation increase, so does the accuracy of the approximate solution. Furthermore, it is also shown that after a certain number of terms have been used, the accuracy of the results does not continue to increase; therefore, it is possible to truncate the approximate solution for simplicity. In this study, it is shown that by using second order approximation terms, an acceptable level of accuracy can be achieved, and therefore, the approximate solution of the perturbation method is in good agreement with the fully numerical solution obtained from the Runge-Kutta based solver.

 

 Connecting Sturm-Liouville Theory and The Principle of Stationary Action Through Free-Particle Dynamics

E. Hauptmann1 cehzr3@mail.umkc.edu R. Kuhlmann2 krkw44@mail.umkc.edu

1Department of Physics and Astronomy, University of Missouri-Kansas City

2Department of Mathematics and Statistics, University of Missouri-Kansas City

The principle of stationary action is one of the most important and fundamental concepts in physics. It states that a given physical system will evolve in a way such that the action of the system remains stationary. By applying this principle, one can obtain the equations of motion of a given system. This project recasts the process of finding the equations of motion into a Sturm-Liouville problem. In doing so, restrictions must be applied to the types of systems that can be analyzed using Sturm-Liouville theory. These restrictions, and how they come about, will be shown through applying Sturm-Liouville theory to a free-particle system; a point particle with no forces acting upon it.

 

A mathematical model to study the effects of partial remediation of groundwater contaminant source

Hussain Jabr B Alantari1 hacgm@mail.umkc.edu Mehmet Uylukcu2 mu6zc@mail.umkc.edu

1Department of Mathematics and Statistics, University of Missouri-Kansas City

2 Curriculum & Instruction EDSP, University of Missouri-Kansas City

Globally, groundwater resources have become a threat from growing demands, wasteful use, and contamination increasingly. To encounter this dilemma, proper planning and management practices are needed. To manage groundwater resource, key management is to be to model the movement of fluids and contaminants in the subsurface. The objectives of this project are to understand how the contamination moves in the groundwater by using a mathematical model and to know the concentration and mass rate of change of the contamination in the groundwater over time and distance. In the purpose of preparing such a model, we proposed a real-world model. This model is particularly useful to describe sources as the contaminant release due to the failure in underground tanks or pipelines. In this study, analytical models for predicting groundwater contamination is isotropic, and homogeneous porous formation is derived. The impact of dispersion and diffusion coefficients is included in the numerical solution of the advection-dispersion equation (ADE) subjected to transient (time-dependent) boundary conditions at the origin. Numerical solution is obtained by using Matlab. Numerical results are obtained to compare between two different chemical substances.

 

Applications of principal component analysis in multichannel image processing

Babak Poorebrahim Gilkalaye bpktk@mail.umkc.edu

Department of Electrical & Computer Engineering, University of Missouri-Kansas City

Principle component analysis is widely used to reduce the dimension of the data set, as working with lower dimension data set is more efficient in terms of both time and size. Time complexity of many tools in data science is polynomial or even exponential so avoiding higher dimension data set is crucial. In this project we plan to reduce an image size by using SVD replacing some less important singular values with zeros. We treat an image as a 3d matrix and apply SVD separately on each channel and then all reduced channels are combined again and reconstruct the compressed image. The image size could be reduced up to 50% in this method while the legibility and clearness still are preserved.

 

Cooperative Values and its Effect on Employee Satisfaction within the Multilevel Structure of Organizations

Vanessa R. Collins Vrcz76@mail.umkc.edu

School of Business, University of Missouri-Kansas City

Businesses cannot possibly operate efficiently on a one-way closed system management style. Several online shopping experiences ask for feedback from customers after they have been shopping on the website. In the same way, other businesses and government seek to gain valuable consumer opinions by conducting surveys. The National Partnership for Reinventing Government employee survey was conducted in the early nineties to gather information about employee satisfaction within their government entity employers. The survey was administered to measure the success of government employers through a business model that researches employer-employee relations. The dataset consists of survey responses from 21,257 government employees in the various fields of the United States’ national government. The survey is composed of 32 questions inquiring about employees’ opinion of their working group, office, and its operations.

Within this secondary data analysis, I use the SPSS statistical analysis tool to test my hypotheses statistically with a chi-square test for independence between the responses of two different questions from the government employee survey. In each scenario, I use two of the survey questions as the variables to the hypothesis. I’m seeking to answer the question: What types of employer involvement increase employee satisfaction? Another question that could be answered here is: Is there any consistency between the number of agree responses to one question and the number of agree responses to another question? So, the survey questions were taken as variables and compared against each other to determine whether there is a relationship between questionnaire responses.

 

Error Analysis of Inline ZFP Compression for Multigrid Methods

Avary Kolasinski, avaryk@ku.edu

Mathematics Department, University of Kansas

ZFP is a state-of-the-art lossy compression algorithm that can easily be used inline during numerical simulations due to the inherent locality of the algorithm. Using ZFP fixed-rate mode, which compresses a block to a fixed number of bits, ZFP can be implemented as a new data structure similar to a double precision array. Multigrid methods update the current iterate by approximating the error on coarse grids. Depending on the application, e.g. using multigrid as a preconditioner, the solution using ZFP compressed arrays can significantly reduce the storage cost while maintaining the required accuracy. The information that is lost during ZFP compression may represent the traditional errors however, any additional error caused by ZFP could contaminate the solution. It is important to understand if the error from ZFP compression overwhelms other sources of error. The goal of this talk is to analyze the stability of using ZFP in multigrid methods.  We use previous error bounds to establish a bound for the error for fixed-rate ZFP when used in multigrid methods. Furthermore, we analyze the relative error for an adaptive rate multigrid algorithm.

 

 Illustrating Regression Tree Using Boston Housing Data

Tahani Omer tao34c@mail.umkc.edu

Department of Mathematics and Statistics, University of Missouri-Kansas City

Regression tree is a commonly used method in data mining. Similar to regression analysis, the goal is creating a model to predict the value of a response from several predictors. In this work, we describe how to generate a regression tree using the decision tree method. This includes how to first build a large tree, how to prune it to find the best sub tree, and how to identify the cost complexity parameter via the cross-validation approach. Then, Regression is employed for the Boston housing data set. I find that the tree indicates the higher percent of lower status of the population, corresponds to less expensive houses.

 

Applied Mathematics Group