MATH Graduate Student Conference Papershttps://soar.wichita.edu/handle/10057/5382021-06-12T00:00:44Z2021-06-12T00:00:44ZOn the inverse gravimetry problem with minimal dataTiti, Aseelhttps://soar.wichita.edu/handle/10057/199652021-05-04T22:48:45Z2021-04-02T00:00:00ZOn the inverse gravimetry problem with minimal data
Titi, Aseel
The inverse problem in gravimetry is to find a domain D inside the reference domain Ω from measurements of gravitational force outside Ω. We first considered the two-dimensional case where we found that about five parameters of the unknown D can be stably determined given data noise in practical situations. An ellipse is uniquely determined by five parameters. We proved uniqueness and stability of recovering an ellipse for the inverse problem from minimal amount of data which are the gravitational force at three boundary points. In the proofs we derived and used simple systems of linear and nonlinear algebraic equations for natural parameters of an ellipse. To illustrate the technique we used these equations in numerical examples with various location of measurements points on the boundary of Ω. We also considered the problem in three dimensions where we proved uniqueness for an ellipsoid in some particular cases.
Presented to the 17th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held online, Wichita State University, April 2, 2021.; Research completed in the Department of Mathematics, Statistics and Physics, Fairmount College of Liberal Arts and Sciences
2021-04-02T00:00:00ZAttenuation simulations and hardware design for the nuSol Space-based Neutrino ProbeFolkerts, Jonathanhttps://soar.wichita.edu/handle/10057/199312021-05-04T22:48:29Z2021-04-02T00:00:00ZAttenuation simulations and hardware design for the nuSol Space-based Neutrino Probe
Folkerts, Jonathan
INTRODUCTION: The nuSol project aims to design, build, and launch a small payload which will perform several near-solar approaches in order to demonstrate the viability of a space-based neutrino detector and perform scientific measurements. Under the previous NASA Innovative Advanced Concepts (NIAC) grant work was performed to simulate basic measures of performance of the probe. Under the NIAC phase II grant, we are tasked to refine simulation and to begin measurements using prototype detectors. PURPOSE: To determine the viability of the neutrino probe, we have been performing tests in the lab at our test stand, and I have been creating monte-carlo simulations of a simplified flight path to find best case limits for evaluating the viability of the space-flight. The lab tests are to characterize the performance of the detector before and after the target doping. METHODS: To simulate performance, I have created a C++ code which applies the results of more detailed simulations to find the approximate neutrino counting rate during a simple elliptical flight near Venus and Mercury as well as the physical flight paths found by simulation from another member of the project. The hardware uses liquid scintillator from the NOvA experiment in a cylindrical container on our test stand to characterize the detector's performance in cosmic ray backgrounds and in radioactive decay signals that mimic our expected signals. RESULTS: The simulated performance is promising and gives us confidence that we can meet the standards of a technology demonstration mission. Hardware development has been stalled by COVID-related delays, but we hope to be taking the post-doping measurements within two weeks of writing. CONCLUSION: Work on the nuSol probe progresses well. The results are promising, and this contribution to the larger project to build a neutrino detector in space is on schedule for the next phases of the project.
Presented to the 17th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held online, Wichita State University, April 2, 2021.; Research completed in the Department of Mathematics, Statistics, and Physics, Fairmount College of Liberal Arts and Sciences
2021-04-02T00:00:00ZOn inverse gravimetry problemTiti, Aseelhttps://soar.wichita.edu/handle/10057/176232020-06-11T08:26:46Z2020-05-01T00:00:00ZOn inverse gravimetry problem
Titi, Aseel
The inverse problem in gravimetry is to find a domain D inside the unit disk Ω from boundary measurements of exterior gravitational force. We found that about five parameters of the unknown D can be stably determined given practical noise. These five parameters uniquely determine an ellipse. We proved uniqueness and stability of recovering that ellipse for the inverse problem from minimal amount of data. To illustrate the technique we considered different numerical examples based on the location of the optimal points on Ω. In the proofs we used a system of nonlinear equations. We considered the problem in the plane as a model for the three-dimensional problem due to simplicity. One of the interesting applications of this research is the problem of water scarcity. One can recover water lakes of known density under the ground from exterior measurements.
Presented to the 16th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held online, Wichita State University, May 1, 2020.; Research completed in the Department of Mathematics, Statistics, and Physics, Fairmount College of Liberal Arts and Sciences
2020-05-01T00:00:00ZAdvanced forecasting model on land market value based on USA real estate marketWang, Leihttps://soar.wichita.edu/handle/10057/162352019-07-25T07:03:51Z2019-04-26T00:00:00ZAdvanced forecasting model on land market value based on USA real estate market
Wang, Lei
This research presents a time series estimation and prediction methods with the use of classic and advanced forecasting tools. Our discussion about different time series models is supported by giving the experimental forecast results, performed on several macroeconomic variables. Also, the main section deal with the experience of using such data in econometric analysis. Besides, the implementation of SAS and R software improve the parameter estimation and forecasting accuracy. The objective in providing crucial statistical techniques is to enable government and investors to make informed decisions regarding real estate. Most importantly, we obtain how to add value to business and apply skills set real estate in a real world environment. Eventually, the summary of various existing forecasting models can provide information to develop an appropriate forecasting model which describes the inherent feature of the series.
Presented to the 15th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held at the Rhatigan Student Center, Wichita State University, April 26, 2019.; Research completed in the Department of Mathematics, Statistics and Physics, Fairmount College of Liberal Arts and Sciences
2019-04-26T00:00:00Z