# MATH Theses and Dissertations

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Item Magnetic field simulation studies in the muon spectrometer(Wichita State University, 2024-07) Shivakoti, Sushil; Muether, MathewThe Deep Underground Neutrino Experiment (DUNE) is focused on addressing important questions in neutrino physics such as matter-antimatter asymmetry and neutrino mass. The experiment utilizes advanced technologies to study muon neutrino disappearance ( ) and electron neutrino ( e) appearance events. An important challenge is distinguishing wrong-sign events, such as antineutrinos, in a neutrino beam. The magnetized TMS is crucial for differentiating muons and antimuons, which allows for accurate oscillation rate predictions.Our study examines the impact of magnetic fields on charge identification in the TMS. Our goal is to determine the optimal field strength for accurate charge determination. We have developed a signed distance metric for charge identification: S.D>0 (for muons) and S.D<0 (for antimuons). We discovered that higher magnetic fields increased the signed distance, which improved the particle’s charge identification. Additionally, as opposed to lower momentum and lower magnetic fields, particle recognition was better at the low momentum range and higher magnetic fields, and even better results were achieved at higher magnetic fields and higher momentum ranges by reducing overlap between the distributions. Plots of Fraction vs. True muon kinetic energy and Fraction vs. momentumTMSStart demonstrate improved charge particle identification with increased magnetic field values.Item Novel micro-resonator design for electron paramagnetic resonance spectroscopy for volume-limited sample(Wichita State University, 2024-07) Aregbesola, Ayodimeji Emmanuel; Ambal, KapildebElectron Paramagnetic Resonance (EPR) is a powerful tool for analyzing the detailed properties of electron spins in paramagnetic samples. The efficiency of an EPR spectrometer is largely determined by its resonator, which acts as the sensing element. The resonator’s ability to store, transmit, and receive microwave signals is characterized by its quality factor and fill factor. Optimization of the quality factor and fill factor is crucial for the detected signal by the resonator. In this study, I simulated a novel resonator using Femtet Murata Software, one of the commercially available and cost-effective finite element analysis tools. This software provides comprehensive details about absorption spectra, as well as electric and magnetic field plots of simulated geometries. Using this simulation tool, three different resonator structures were developed to be manufactured: First a resonator on a Quartz Wafer. This design achieved a quality factor (Q-factor) of 8949 and a sample volume of 0.0012 nL. Second a resonator on a PCB substrate. This design achieved a Q-factor of 3000 and also a sample volume of 0.0012 nL. Lastly a liquid sample resonator. This design was optimized to accommodate liquid samples, achieving a Q-factor of 1774 and a sample volume of 0.0006 nL. These results demonstrate the potential of each resonator design for various applications in EPR spectroscopy, with significant implications for the analysis of both solid and liquid samples.Item Locating three-term arithmetic progressions in a closed subset of the unit interval(Wichita State University, 2024-07) Bowman, Elton; Fraser, RobertThis thesis investigates a closed subset E of the unit interval [0, 1] supporting a probability measure with size and Fourier decay constraints. We show that if these constraints are met, then E must contain at least one three-term arithmetic progression.Item Improper integrals(Wichita State University, 1960-06) Jackson, Don V.; Hanna, J. Ray; Huneke, HaroldThis thesis has been limited to real variable theory, except for one example in Laplace transform theory and in the treatment of the Residue Theorem where complex variable theory is necessary to construct the tool which is used in evaluating improper integrals in real variable theory. Many statements and theorems would necessarily have to be altered if the discussion were expanded to include all complex values. Improper integrals, as treated herein, are Riemann-type integrals. In the Riemann theory of integration the functions are assumed to be bounded, and the intervals or regions of integration are assumed to be bounded. Integrals are improper because the intervals or regions of integration are unbounded or because the functions are unbounded. The study of improper integrals is, therefore, an extension of the Riemann Theory which is taken as basic.Item The Laplace transformation with amplification to the dynamic longitudinal stability and response of aircraft(Wichita State University, 1960-06) Gertsen, William M.; Huneke, HaroldThe selection of the Laplace Transformation as my thesis' topic resulted from my experience with dynamic systems, and past observations of the usefulness of this transformation when ·applied to simultaneous systems of linear ordinary differential equations. The aims of the thesis work ·were two-fold: (1) to determine and set forth the more important properties of the Laplace Transformation, particularly with regard to applications to systems of linear ordinary differential equations; (2) to make use of the transformation in obtaining an exact solution for the equations which describe the controls free longitudinal motion of aircraft in response to a disturbance.