MATH Theses and Dissertations
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Item Real zeros of rational polynomials and iteration: Leonardo to Raphson(Wichita State University, 1962-08) Fugate, Justus H.Item Cancellation in direct products of loops(Wichita State University, 1962-06) Crown, Gary D.In the examination of the structure of certain classes of Abelian groups, the question arises, “Given a class of Abelian groups satisfying a certain structure theorem A, then is theorem A really applicable, or is theorem A so complicated and restricted that it is absolutely useless?" Kaplansky [1] proposed a list of three test problems for which he stated that, if theorem A can produce satisfactory results to these three test problems, then this might be a test of the usefulness of this class of Abelian groups. However, Walker [l], proved that test problem III, of Kaplansky, was true for all Abelian groups, and thus it cannot serve as a test for the usefulness of a certain theorem which applies only to a certain class of Abelian groups. It is the purpose of this thesis to generalize some of the main results of Walker's thesis, which lead up to the solution of Kaplansky's test problem III, to the more general case of a loop.Item Applications of conformal mapping to engineering problems(Wichita State University, 1962-06) Boothe, O.K.The purpose of this paper will be to illustrate the application of conformal mapping to the solution of some potential problems in engineering situations.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.