PHD, Kent State University, 2022, College of Arts and Sciences / Department of Physics

Compact stars (CSs) are the remnants of “dead” stars that were too small to form black holes; the category includes both white dwarfs (WDs) and neutron stars (NSs). To produce a full description of any magnetized compact star requires solving Einstein's equations in unison with Maxwell's equations. However, when putting these two sets of equations together, there is an additional degree of freedom that requires the inclusion of the equation of state (EOS) of the stellar matter in question. The most notable difference between CSs and other stars is that CSs consist of degenerate fermion matter. Fermionic matter exists in a degenerate state when the temperature is low compared to the Fermi energy. Such states arise due to the Pauli exclusion principle, which states that no two identical fermions (particles with half integer spin) in the same quantum system may inhabit the same quantum state. In the case of WDs, this degeneracy is caused solely by electrons; whereas, in NSs, the degeneracy is in several species of particles including neutrons and protons, but also more “exotic” baryons, such as Lambdas, Sigmas, and Cascades. In the grand canonical ensemble, the stellar EOS is typically expressed as the relation between the total energy density of a gas of particles and their pressure. It is calculated using thermodynamics with, in the NS case, an additional contribution from the strong nuclear force, which must be modeled. Due to computational difficulty, the EOS is often calculated in a simplified way, assuming that one aspect or another is not significant. As such, EOSs exist with temperature effects or with magnetic field effects, but not with both. For example, higher temperatures (without additional degrees of freedom) lead to higher pressures at the same energy density; the EOS is “stiffer.” Magnetic fields lead to a pressure anisotropy and Landau quantization, which gives rise to De Haas-Van Alphen oscillations in the EOS. This thesis breaks new ground by sim (open full item for complete abstract)

Doctor of Philosophy, The Ohio State University, 2022, Astronomy

Galaxy formation and evolution are driven by stars and star formation. Star formation is fundamental for shaping the universe as we see it today as part of the cosmic ecosystems encompassing galaxies, yet half of the physics that determines how much gas forms into stars – the stellar feedback (injection of energy and momentum to the surrounding material) half of the tug-of-war between gravity and stellar feedback – have only recently become a focus for observational astronomers. Theoretical explorations of stellar feedback have been extensive for the past four decades and our current understanding of star-forming galaxies comes primarily through extensive modeling and simulations with sub-grid physics prescriptions based on a handful of observations. In order to secure the basis for these sub-grid physics models and expand our understanding of star-formation and the effects of massive stars during all epochs of the universe, more observations of these processes are needed. Observations of star forming regions provide the foundation to anchor simulations and observations of analogues to high-redshift galaxies help determine the sources that reionized the universe and the role stars played in during the Epoch of Reionization. With multiwavelength observations of H ii regions in the Milky Way, I have probed the effects of stellar feedback in dynamics of H ii regions, providing the necessary basis for defining the sub-grid physics in simulations. With multiwavelength observations of nearby galaxies with properties similar to galaxies in the EoR (low mass: < 107 M⊙; low metallicity: < 0.15 Z⊙; and high star-formation rates: > 10−1.2 M⊙/yr), I have determined the properties of sources that produce the photoionization feedback we observe and which sources ionized the universe in the Reionization Era. With X-ray observations of a massive colliding wind binary I have explored the effects of stellar wind feedback on small spatial scales and found that wind prescriptions assum (open full item for complete abstract)

Doctor of Business Administration (D.B.A.), Franklin University, 2020, Business Administration

Attaining high Overall Medicare Star ratings (MSR) is essential to the success of managed care organizations (MCOs) in the United States. Leaders are integral to the organizational performance in MCOs. This quantitative study focused on identifying the impact of Leadership practice and Years of leaders' Medicare experience in helping leaders influence high Medicare Star Ratings in MCOs. The study focused on two (2) research questions. (RQ1) Is overall leadership practice useful in predicting a leader's ability to influence the attainment of high MSRs in MCOs? (RQ2): RQ2: Is Years of leader's Medicare experience useful in predicting a leader's ability to influence the attainment of high MSR in MCOs? The study had 35 high (4, 4.5, and 5-Stars) MSR leaders and 35 low (3.5-Stars or less) MSR leaders, consisting of a total of 70 participants. Data for this study was gathered using the Leadership Practice Inventory (LPI ®) tool. The participants included supervisors, managers, directors, and executives in the MCO they worked. Parametric independent T-Test was used to test the statistical significance of the mean difference between the two (2) leader groups. Logistic regression was used to predict leaders' ability to influence the attainment of high MSR with leadership practices and years of Medicare experience. The result indicated a statistically significant relationship between leadership practices and MSR. Also, the practice of the five (5) LPI® themes autonomously cannot significantly predict a leader's ability to contribute to influencing MSR. The findings also showed that leaders' Medicare experience is effective in influencing the attainment of high MSR in MCOs.

Master of Science (MS), Bowling Green State University, 2017, Physics

We present the results of a 6-year observing campaign conducted using the PROMPT-5 telescope to detect, identify and characterize long-period variable (LPV) stars in the metal-rich globular cluster NGC 6388. LPV stars are asymptotic giant branch stars that exist on a Mira-to-semi-regular-to-irregular continuum in terms of the regularity of their variable behavior. The long time-baseline was found to be fruitful in characterizing that aspect of LPV pulsation that cannot be captured in shorter campaigns. The ISIS image subtraction package is used for variability detection and the production of flux difference photometric data. We have also manually recovered known variable stars with use of their published celestial coordinates. Newly detected sources of variability were ranked on the basis of a variability index. An attempt was also made to quantitatively characterize the positions of LPV stars on the regularity spectrum with a newly defined regularity index, with partial success in the case of known variables. The known and new variables are discussed and characterized and their cluster membership determined with the use of a color-magnitude diagram and the variable's projected distance from the cluster center. Out of 72 variables studied, two of which were found to be duplicated in the literature, 56 are known variables that were detected or recovered. The LPVs detected number to 26 and 16 known and new, respectively. Almost all LPVs' periods are determined using the period-dispersion minimization method. A list of suspected variables, which require higher-resolution observations to confirm, amounts to an additional 22 stars. A period-luminosity relation is determined using the available literature data and our own data.

Doctor of Philosophy, University of Toledo, 2015, Physics

Galaxy mergers were common in the early universe. To better understand this critical step in galaxy evolution, we perform detailed studies of three nearby merging systems. Using images from the Hubble Space Telescope, we identify hundreds of star clusters in these systems, most of which formed as a result of a merger. By studying these clusters, we are able to constrain the properties of their host galaxies. These properties include: the timescale of the interaction, morphology of the merger's progenitor galaxies, and the conditions in which stars and clusters formed. We find clusters in all tidal tails of our galaxy sample, even tails that were previously reported to be clusterless. Ages of clusters are similar to ages of their host tidal tails as predicted from simulations. We also find a color gradient across some tails, indicative of a gradient in ages that suggest star formation takes place primarily in the center of the tails, where gas is likely densest. In addition, cluster ages allow us to probe the star formation histories in these systems by predicting past SFRs in various regions of the galaxies using a new method involving the cluster mass function. The mergers also present an interesting environment to study star clusters themselves. We find that the formation and evolution of star clusters in mergers fits the ``quasi-universal'' picture of clusters seen in many other galaxies.

Doctor of Philosophy (PhD), Ohio University, 2015, Computer Science (Engineering and Technology)

This dissertation considers certain graph-theoretic combinatorial problems which have direct application to the efficient computation of derivative matrices (“Jacobians”) which arise in many scientific computing applications. Specifically, we analyze algorithms for Star Bicoloring and establish several analytical results. We establish complexity-theoretic lower bounds on the approximability of algorithms for Star Bicoloring, showing that no such polynomial-time algorithm can achieve an approximation ratio of O(N ^(1/3)-e ) for any e > 0 unless P = NP. We establish the first algorithm (ASBC) for Star Bicoloring with a known approximation upper-bound, showing that ASBC is an O(N ^(2/3 )) polynomial-time approximation algorithm. Based on extension of these results we design a generic framework for greedy Star Bicoloring, and implement several specific methods for comparison. General analysis techniques are developed and applied to both algorithms from the literature (CDC, Hossain and Steihaug, 1998 [1]) as well as those developed as part of the framework. We provide numerous approximability results including the first approximation analysis for the CDC algorithm, showing that CDC is an O(N ^(3/4) ) approximation algorithm. Finally, we observe that all algorithms within this generic framework produce a restricted class of star bicolorings that we refer to as Distance-2 Independent Set Colorings (D2ISC). We establish the relationship between Star Bicoloring and D2ISC. In particular we show that these two notions are not equivalent, that D2ISC is NP-complete and that it cannot be approximated to within O(N ^(1/3 -e) ) for any e > 0 unless P = NP.

B.S. in Exercise Science, University of Toledo, 2009, Exercise Science

Dynamic balance is a key component of normal daily activities such as walking, running and climbing stairs. Since balance is such an important aspect of every day life, it is imperative to find programs useful for maintaining proper balance. One such suggestion that has been made in an effort to improve balance is the correlation between muscular strength training and enhanced balance. Training the core muscles especially has been hypothesized as an improvement program, but there is a lack of current scientific evidence to support this claim. Further investigation on the effect of a core stability program on balance is therefore needed in a effort to provide a balance maintenance program. Therefore, this study sets out to compare the effects of a core stability program on dynamic balance as measured with the Star Excursion Balance Test.Thirty participants (15 male, 15 female) with no known musculoskeletal injuries or neurologic deficits volunteered for the study. The participants were randomly divided into two groups, a control group and an exercise group. The control group performed an initial Star Excursion Balance Test followed by six weeks of no core strengthening exercises and a second Star Excursion Balance Test. The exercise group performed the first Star Excursion Balance Test followed by six weeks of a core stability program and a second Star Excursion test. The maximum excursion distances as normalized to leg length were recorded for each test. For a majority of the reach directions, maximum excursion distances improved for the exercise group when compared to the control group. This improvement in reach distance justifies the proposal of core strengthening improving dynamic postural control.

Doctor of Philosophy, The Ohio State University, 2005, Astronomy

The new requirements for accuracy and completeness in atomic data from astronomers demand more challenging calculations. Current problems require the relaxation of approximations and detailed studies of different effects like relativistic effects. We carry out relativistic atomic calculations using the Breit-Pauli R-matrix method to generate radiative and collisional data for ions of astrophysical interest. Electron impact excitation of He-like ions have been calculated including relativistic effects, radiation damping and other effects. The comparison with previous works shows differences of up to 30% in the effective collision strengths for the z-line. This line with 3 other transitions between the complexes n=1 and n=2 constitute an important tool for plasma diagnostics and such differences will have strong consequences in the analysis of X-Ray spectra of astronomical objects. We present the relativistic calculation of Kα resonances for oxygen ions that are responsible for X-Ray absorption features observed in the spectrum of AGNs. Resonance oscillator strengths have been computed and are in good agreement with the recent experimental and theoretical study of Kα photoionization of O II. These data should allow a more complete analysis of X-Ray spectra from AGNs and refine the general picture of such complex objects. We report the first large relativistic calculation of the photoionization cross section of Fe II. The detailed fine structure in the present work agrees well with the experimental results from Kjeldsen et al. (2002) and represents an improvement over the previous non-relativistic results. These data should be useful to the theoretical template of Fe II emissions crucial in the analysis of the UV/O/IR spectrum of AGNs. The new OP opacities are presented, outlining the importance of the inner-shell transitions at high temperature-high density regimes. This new set of data is used to determine constraints on the solar composition and to shed some light o (open full item for complete abstract)

Master of Music (MM), Bowling Green State University, 2009, Music Composition

We Are Not Alone is a programmatic work which lasts fourteen minutes. It is composed for flute/alto flute, oboe/English horn, Bb/bass clarinet, bassoon, horn, two C trumpets, two trombones, vibraphone, harp, two violins, viola, cello, soprano, and electronic sound effects. The first section explores technology and spacecraft, contrasting two distinct musical structures. The first is an aleatoric episode suggesting the interplay between small, maneuverable spacecraft and immense, daunting battleships. The second features a metered, theme-song-inspired adventure motive. These musical structures contrast in many ways, and comprise the core of the movement. The aleatoric episode has no clear tonality, while the adventure theme employs a deliberate tonal center. This sense of tonality diminishes as the section progresses. The second section focuses on the different roles in which alien life is portrayed in film, climaxing with a vocal song set in the fictional language of Klingon, a product of the Star Trek series. The soprano sings an original poem translated to Klingon with the assistance of Klingon-language expert Dr. d'Armond Spears and linguist Dr. Marc Okrand, creator of the official language. The diction of this highly guttural language requires the soprano to learn unique consonant and vowel production techniques. As such, it provides a significant technical challenge to the vocalist. To further enhance the other-worldly nature of the piece, the second section features extended instrumental techniques including key clicks and whispering through instruments. The electronic component serves primarily as a background texture, using various types of processing and synthesis to create sounds imitating space dust, engine noise, electronic bleeps, and alien chatter. These pre-recorded sounds are triggered live using Cycling ‘74's Max/MSP program, an object-oriented graphical software environment. We Are Not Alone is the culmination of thirty years of science fiction a (open full item for complete abstract)

Doctor of Philosophy in Clinical-Bioanalytical Chemistry, Cleveland State University, 2024, College of Arts and Sciences

Metabolomics is the study of small molecules (also termed as metabolites) in biological or botanical specimens using highly sophisticated analytical instruments, such as ultrahigh-performance liquid chromatography coupled with mass spectrometry (UHPLC-MS). The concept of computational chemistry is using software and algorithm-based analysis to pinpoint biomarkers by uncovering the molecular mechanisms that are helpful for treatment strategies. Integrating these two techniques (metabolomics and computational chemistry) enables a deeper understanding of the molecular mechanisms underlying diseases and therapeutic interventions, facilitating the identification of novel drug targets, biomarkers, and personalized treatment strategies. This integrative approach enhances our ability to unravel the complexity of biological networks and improve drug development and precision medicine. In the first half of the work, we developed a UHPLC-QTOF/MS-based untargeted metabolomics method to establish a biological model for allergic rhinitis by identifying, analyzing the regulation, and semiquantitative the key metabolites and exploring the impacted biological pathways. A computational chemistry approach was developed and applied to identify the potential therapeutic bioactive components of Astragalus radix, a traditional Chinese medicine, for allergic rhinitis treatment. In this, the protein targets were mined, and networks were constructed and analyzed to identify vital protein targets. Then, molecular docking simulations were conducted to identify the potential therapeutic components. Following this, the previously established metabolomics approach was used to investigate the therapeutic effects of the bioactive components on allergic rhinitis-induced human mast cells. In the second half of this work, we developed and validated a targeted metabolomic UHPLC-MS/MS analytical method for star anise samples. Building on our previous laboratory work, we quantified the three therapeuti (open full item for complete abstract)

Doctor of Philosophy, The Ohio State University, 2024, English

In 2008, Hollywood identified a (relatively) new storytelling strategy that I call the elegiac sequel. These kinds of films appear at least ten years after the prior entry in the franchise or series, and feature a returning cast member, usually a star who has maintained popularity in the time between films. I argue that these elegiac sequels allow filmmakers and audiences opportunities to revisit the past both within the storyworld and in the real world, using the gap between entries as a way of thinking through how the past has influenced the present. In the course of my dissertation, I write about the pre-history of the elegiac sequel starting with The Sin of Harold Diddlebock in 1947 and moving up through the start of the elegiac boom period in 2008 with the release of Indiana Jones and the Kingdom of the Crystal Skull. In this chapter I examine the industrial crises points at which these nostalgic films look to the past for answers about an uncertain present in Hollywood as it comes under threat from TV, cable, and streaming services, among others. The next chapter is an investigation of how elegiac sequel trailers (and, by extension, the films themselves) serve two audiences and create a heightened sense of emotional response from the core features of the elegiac sequel, namely their genre reinventions, story extensions, and the revivals of stars in beloved character roles. By studying the intensified form of the trailer, I highlight the pleasures audiences can derive from elegiac sequels in their full-length forms. Finally, my last chapter concerns the ways certain fans respond to elegiac sequels that modernize the ideas, themes, and casts with more diverse characters and actors being centered in roles that were primarily held by straight white cis men. I use the three Star Wars elegiac sequel films, The Force Awakens, The Last Jedi, and The Rise of Skywalker, to examine how some people who did not enjoy the first two films in the trilogy alongside con (open full item for complete abstract)

Doctor of Education , University of Dayton, 2024, Educational Administration

This research study sought to identify barriers that hinder a group of marginalized parents who live in (LIEM) low-income, economically marginalized communities overcome barriers that hinder them from being able to support their children's early literacy development. As well as how the intersectionality of societal factors contributes to the parents and families who cannot provide meaningful support to their young children's literacy development. These children, who attend an inner-city charter school in a Mid-West state with a 100% free and reduced lunch rate, are in urgent need of support from the school. Their parents, identified as members of a marginalized group, need immediate assistance to enhance their children's early literacy development by the time they enter the Fourth grade. It is crucial to provide support to the children and accurate information to their families regarding the low ranking their children receive of the STAR Early Literacy assessment data the students receive on these quarterly assessments administrated to these students. As a result of the individual interviews the researcher had with each of the six parent participants, another theme that emerged from these interviews was that the parents did not clearly understand what their children's STAR Early Literacy scores and classifications meant. The majority of the parents interviewed believed the teachers were doing a good job teaching their children to read. However, the majority of parents did not have a clear understanding of what their children's assessment score data meant. The fact that children of these parents all had STAR Early Literacy scores ranged from early to late literacy readers and probable readers by the time the children entered the Fourth grade. This information underscores the need for the teaching staff to give the parents of these children clear, direct information on their children's STAR data, as well as specific materials they can use to work with their childre (open full item for complete abstract)

Doctor of Philosophy, The Ohio State University, 2024, Physics

Stellar clusters form inside large clouds of gas, which collapse under gravity until the feedback from the newly formed stars begins to push the gas away, disrupting further star formation. In this dissertation we explore several of the feedback mechanisms responsible for stopping star formation. We will look in depth at two mechanisms in particular: Radiation pressure and cosmic ray diffusion. To analyze these pressures, we build simple models which we then expand. Radiation pressure's role depends greatly on the composition of the dust embedded in the gas the stars form from. The dust interacts with the photons from the star cluster, scattering and absorbing them, before re-radiating the photons in the infra-red. To build a more realistic model of radiation pressure, we use time dependent spectral data from simulations and realistic dust grain distributions and optical properties. The effects of cosmic ray diffusion are controlled by several parameters, such as the diffusion coefficient and the size scale of the shell of material the cosmic rays are acting on. We compare cosmic ray pressure to radiation pressure, and the pressure from hot ionized gas around the stellar cluster. We also apply our analysis of each of these pressures to observations. We do this to estimate the role of each pressure in observed regions, helping to explore the mechanisms which govern the star formation rates in star-forming regions of galaxies. Additionally, we analyze the dynamics of shells driven by radiation pressure, cosmic ray diffusion, and the pressure from hot ionized gas. From these simple dynamical models we draw conclusions about the roles of each of the pressures, and examine the parameter space where each dominates. We find that radiation pressure is highly important to the initial stages of feedback, dominating the other studied pressures for the youngest and most compact clusters. Radiation pressure can rapidly drive gas away from the central star cluster, (open full item for complete abstract)

Doctor of Philosophy, The Ohio State University, 2024, Physics

Directed flow ($v_1$) describes the collective sideward motion of produced particles and nuclear fragments in heavy-ion collisions.It carries information on the very early stage of the collision, especially at large pseudorapidity (in the fragmentation region), where it is believed to be generated during the nuclear passage time. Directed flow therefore probes the onset of bulk collective dynamics during thermalization, providing valuable experimental guidance to models of the pre-equilibrium stage. Model studies have indicated that directed flow is sensitive to the shear viscosity of the hot QCD matter. Furthermore, directed flow has demonstrated strong constraining power on the initial baryon stopping and can serve as a probe for the equation of state in heavy-ion collisions. Past measurements have indicated that the directed flow signal is most pronounced at the forward(backward) (pseudo)rapidity. Therefore, any sensitivity to the initial state, hydrodynamic evolution, or the equation of state may be more evident at large (pseudo)rapidities. In 2018, the Event Plane Detector (EPD, $2.1 <|\eta|< 5.1$) was installed in STAR and used for the Beam Energy Scan phase-II (BES-II) data taking. The combination of EPD and high-statistics BES-II data enables us to extend the $v_{1}$ measurement to the forward and backward $\eta$ regions. In this work, we present the measurement of $v_{1}$ over six units of $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}=$19.6 and 27 GeV using the STAR EPD. EPD is a pre-shower scintillator detector mainly designed for reconstructing the event plane angle. In order to use it as the particles of interest region rather than the reference, an entire new method was developed to ensure the accuracy of this analysis. The results of the analysis at $\sqrt{s_{NN}}=$19.6 GeV exhibit excellent consistency with the previous PHOBOS measurement, while elevating the precision of the overall measurement to a new level. The increased precision of the measureme (open full item for complete abstract)

MS, University of Cincinnati, 2023, Engineering and Applied Science: Computer Science

Clustering techniques are becoming a growing need in today's world where data is being accumulated on a large scale. Given a set of objects, clustering helps in dividing these objects into groups called clusters, where the objects in one cluster exhibit similarities while objects from different clusters are dissimilar. Clustering analysis is essential in data mining to find underlying patterns and information. Many complex systems in the real world are formed by multiple data type objects and interactions between them and such systems can be modeled as Heterogeneous Information Networks (HINs). A heterogeneous information network (HIN) is a network that consists of nodes of different object types and links representing relations between the nodes. Cluster analysis of heterogeneous information networks helps in revealing the underlying information between these complex systems. Most real-world applications that handle big data including social networks, medical information systems, online e-commerce systems, and most movie database systems (such as IMDB, Netflix, etc.,) can be structured into heterogeneous information networks. Therefore, effective clustering analysis of large-scale heterogeneous information networks poses an interesting challenge. In this research, we have developed an ‘approximate N-Clustering' model, which is based on the A* (pronounced as A-star) search algorithm, and Chernoff Upper Bound is used as the approximation limiting criterion (the heuristic function). Here ‘N' represents the number of databases/dimensions/object types. In our thesis, we have used a star distribution pattern (or star schema) for clustering on HINs. In a star network schema, there is one central object type and all other object types are connected to this central object type. The approximate n-clusters generated from our algorithm are the most informative occurrences (i.e., the probability of occurrence of any new n-cluster with higher priorities will (open full item for complete abstract)

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2023, Media and Communication

Understanding both gender and fandom as performative can help to identify and describe ways in which fans and fandom become gendered, influences of patriarchy on fandom, and how gendered hierarchies form. With an eye toward performativity, this dissertation explores gendering of fans and fandom through social and cultural forces, pressures within fandom, and influences from texts around which fandoms are built. Additionally, the dissertation examines the ways fandom spaces themselves become gendered and sometimes contested. Using theoretical frameworks of Judith Butler's theory of performativity, Laura Mulvey's theory of the male gaze, and Pierre Bourdieu's theory of cultural capital, this dissertation explores the Star Wars fandom as a gendered and contested space through the following research questions: RQ1: How is language used in Star Wars fan communities to uphold and perpetuate patriarchy and its associated phenomena of sexism and misogyny? RQ2: How is language used in Star Wars fan communities to resist patriarchy and its associated phenomena of sexism and misogyny? The dissertation employs critical discourse analysis (CDA) to study textual interactions of Star Wars fans at the Jedi Council Forums. It follows James Paul Gee's methodological approach to CDA, which highlights discourse in the interest of social justice, how sentence-level analysis can reveal writers' use of language, and Gee's seven building tasks for language use: Significance, practices, identities, relationships, politics, connections, and sign systems and knowledge. Because fandom is growing increasingly mainstream, this dissertation foregrounds women's stories and experiences to explain ways in which women audiences interact with and participate in media they consume and argues for future research in a political economy approach to understanding women audience members in creation of media and its subsequent marketing. It highlights an intersectional approach that considers how factors s (open full item for complete abstract)

Bachelor of Arts (BA), Ohio University, 2023, Art History

This thesis and body of work examines the experiences and collective histories of Appalachians and clay. It analyzes and responds to readings about the history of the material starting with the geological formation of clay, and moving through stories of the civilizations that have inhabited this region. Because of its history of glaciation, the Ohio Valley has an abundance of clay. For this reason, it is also one of the earliest places in the archeological record that we see pottery in North America. The use of clay in this region continued after Anglo-Americans settled on the land, with industrial uses of clay expanding and eventually leading to fine art potteries taking root in southern and central Ohio. In this body of work, I continue this collective experience in clay by engaging with my personal history in Appalachia and telling the story of how I have come to make sense of the world around me.

Doctor of Philosophy, The Ohio State University, 2023, Mathematics

As objects that appear throughout mathematics, integer-valued polynomials have been studied extensively. However, integer-valued rational functions are a much less studied generalization. We consider the set of integer-valued rational functions over an integral domain as a ring and study the ring-theoretic properties of such rings. We explore when rings of integer-valued rational functions are Bezout domains, Prufer domains, and globalized pseudovaluation domains. We completely classify when the ring of integer-valued rational functions over a valuation domain is a Prufer domain and when it is a Bezout domain. We extend the classification of when rings of integer-valued rational functions are Prufer domains. This includes a family of rings of integer-valued rational functions that are Prufer domains, as well as a family of integer-valued rational functions that are not Prufer domains. We determine that the classification of when rings of integer-valued rational functions are Prufer domains is not analogous to the interpolation domain classification of when rings of integer-valued polynomials are Prufer domains. We also show some conditions under which the ring of integer-valued rational functions is a globalized pseudovaluation domain. We also prove that even if a pseudovaluation domain has an associated valuation domain over which the ring of integer-valued rational functions is a Prufer domain, the ring of integer-valued rational functions over the pseudovaluation domain is not guaranteed to be a globalized pseudovaluation domain. Because rings of integer-valued rational functions are rings of functions, we can study their properties with respect to evaluation. These properties include the Skolem property and its generalizations, which are properties concerning when ideals are able to be distinguished using evaluation. We connect the Skolem property to the maximal spectrum of a ring of integer-valued rational functions. This is then generalized using st (open full item for complete abstract)

Master of Science, The Ohio State University, 2022, Mechanical Engineering

This thesis considers path planning with resource constraints and dynamic obstacles for an unmanned aerial vehicle (UAV), modeled as a Dubins agent. Incorporating dynamic obstacles and resource constraints into the path planning problem designs a model that is more realistic of what an agent will encounter during its missions. A resource constraint is a path dependent load variable, such as noise or probability of detection by radar, that accrues as the agent moves towards the goal position. The resource constraint represents the total cumulative noise disturbance created by the UAV along its trajectory during flight in or around an urban area. By prescribing a maximum allowable cumulative noise disturbance, the UAV can be constrained to follow appropriate noise regulations while navigating in an urban environment. Hazards such as storms, turbulence, and ice are important to consider during the path planning stage as dynamic obstacles because these hazards can damage or destroy the UAV if encountered. These weather hazard dynamics can be recorded and learned and occur in a time-scale that is within the duration of the flight of the UAV. Incorporating these obstacles into the path planner can allow the agent to forecast how the weather will change and have it react accordingly. Obstacles such as other aerial vehicles that are handled by detect-and-avoid methods will not be looked at in this thesis. Dynamic obstacles can pose a challenge as the computation time and storage needed increases the longer it takes to find the path. Ice data from the Aviation Weather Service was employed to create training data sets for learning dynamic weather (ice) phenomena. Dynamic Mode Decomposition (DMD) was used to learn and propagate the evolution of ice conditions at flight level. These obstacles were integrated into a Hybrid $A^\star$ path-planner with backtracking to handle resource constraints. It is shown through numerical simulations that the agent is able to navi (open full item for complete abstract)

Master of Science (MS), Bowling Green State University, 2022, Physics

Globular cluster M5 (NGC 5904), located in the constellation Serpens, was discovered over 300 years ago. Since then, several studies have sought to characterize and understand its origin and evolution. Of particular interest are the studies involving the cluster's variable star population. To date nearly two hundred variable stars have been identifed in the cluster. The majority of these are short period variable stars belonging to the category “RR Lyrae”. With advances in photometry and automated observation, recent studies have begun to investigate the cluster's population of long period variable stars (LPV's), but further study is needed to fully catalog and characterize them. Seven of the twenty known LPV's in M5 do have undetermined periods, and more are awaiting discovery. With the use of data acquired with the BGSU half-meter telescope and from the Panchromatic Robotic Optical Monitoring and Polarimetry Telescopes (PROMPT), period analysis was performed on M5's two II Cepheids, 20 known LPV's and one newly discovered LPV. The creation of a color-magnitude diagram (CMD) for M5 allows for testing the hypothesis that as a star evolves further along the red giant branch of the CMD, that the star's periodicity becomes more regular, and will show a larger amplitude of variability. The positions of the stars of interest, and the conclusions drawn from their light curves in our data was compiled and the variability type for each star was assessed. Suggestions for future observational work are provided with the aim of further improving upon the characterization of these LPV's