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Combinatorics of periodic orbits on quantum circulant graphs.
No full textQuantum graphs arose as models of mesoscopic structures such as aromatic molecules, photonic crystals, and microwave networks, where particles/waves move in straight lines along edges and scatter at vertices. A quantum graph can be defined either by a self-adjoint operator on a metric graph or by a set of unitary vertex scattering matrices. A periodic orbit on a graph is an equivalence class of closed paths, up to rotation, and a periodic orbit is primitive if it is not a repetition of a shorter orbit. Spectral properties of quantum graphs are frequently expressed as sums over the primitive periodic orbits of the graph via trace formulae. We find the number of primitive periodic orbits for 2-regular directed circulant graphs. A 2-regular circulant digraph is the Cayley graph of Zn with two generators. To count the primitive periodic orbits on these graphs, we analyze the lattice structure of possible lengths and generator counts for orbits, and evaluate the number of Lyndon words on an alphabet of two letters with fixed letter counts. A related formula which counts the primitive periodic orbits using the Möbius function and powers of the adjacency matrix is also presented.
The coefficients of the characteristic polynomial of a quantum graph can be expressed as a sum over the irreducible pseudo orbits, sets of periodic orbits with no repeated edges. We count the number of irreducible pseudo orbits on circulant digraphs with generators 1 and 2, by classifying the possible self-intersections and rearrangements, which allows us to evaluate the variance of the coefficients, which is the first non-trivial moment. We also present numerical calculations of the variance for circulant graphs of higher degree. When the number of generators is fixed, the variance converges to zero in the semi-classical limit, which is the limit of a sequence of graphs of increasing size. Alternatively, if the proportion of generators to the size of the graph is fixed, the variance converges to a nonzero constant in the semi-classical limit
Community cultural wealth in action : a single case study exploring academic experiences of refugee graduates from Colorado public high schools.
No full textAs refugee students enter the U.S. education system and begin high school, they encounter significant obstacles and schools struggle to address their unique needs. In the United States, the dropout rate among immigrant and refugee students exceeds 12%, significantly higher than the 5.2% observed among their non-immigrant and non-refugee peers. In Colorado, high school refugee students experience lower graduation rates than their non-refugee peers. The U.S. education system often merges the data of refugee and immigrant students, which obscures the specific challenges refugee students face. Several factors contribute to their academic struggles, which include stigmatization, inadequate teacher training for working with refugee students, ineffective implementation of culturally responsive pedagogies, lack of support for linguistic diversity, limited parental involvement in school systems, and economic hardship, as refugee families often resettle in lower-income communities. Consequently, refugee students experience higher dropout rates compared to their non-refugee counterparts.
To address these challenges, I conducted a qualitative single case study exploring how high school refugee students within a Colorado metroplex utilized community cultural wealth to navigate their academic experiences. This study examined the role of community cultural wealth in the educational journeys of refugee students. I collected data through individual semi-structured interviews, photo-elicitation interviews, and a focus group. Four East African high school refugee graduates from a Colorado metroplex participated in this study. Their experiences provided valuable insights into how they leveraged their aspirational capital, familial capital, linguistic capital, navigational capital, social capital, and resistant capital in high school. Their perspectives informed strategies that educators, policymakers, and community leaders can use to better support refugee students in American school systems.
The study’s findings included three themes. First, although high school refugee students prioritized graduation, they also recognized that English proficiency was essential for effective communication, meaningful connections, and achieving their goals. Second, high school refugee students described the critical role of parental involvement in their academics, including offering encouragement, instilling the value of education, and alleviating financial burdens. Third, in pursuit of their desire to graduate and to meet parental expectations, high school refugee students leveraged support from teachers and peers within the school environment and utilized community-based resources to foster their academic success
The algebraic structure of nonlinear skew quasi-cyclic codes.
No full textIn error-correcting codes, we are interested in designing strategies to detect and correct errors that arise from communication and storage problems.
In this work, we analyze a variety of Fq-linear evaluation codes over Fqm, where the evaluation is carried out in the classical sense. These codes exhibit properties similar to those of skew cyclic and skew quasi-cyclic codes, whose definition is based on the ring of skew polynomials: a non-commutative collection of polynomials with very different properties when compared with the usual ring of polynomials. This connection motivates the study of Fq-linear skew quasi-cyclic Fqm-codes, where q is a prime and m is a positive integer. We determine their module structure and propose a definition of the dual space that satisfies (C⊥)⊥ = C. Additionally, we identify generators, as Fq[X]/(Xn − 1)-submodules, of the trace dual spaces of Fq-linear cyclic and skew cyclic Fq2-codes of length n.
This dissertation compiles results from the articles [1] and [2], one of which is under review and the other to be submitted shortly for publication in academic journals
Organizational culture : a non-experimental examination of the competing values of higher education administrators, faculty, and online program management partnerships.
No full textWhile higher education is no stranger to distance education, the internal organizational change required to adapt and succeed in the competitive online space poses challenges (Klempin & Karp, 2018; Matkin, 2022; Syed et al., 2021). Recognizing that COVID-19 accelerated the significance of an online strategy, higher education remains inundated with rising tuition costs, technological advances, international influence, hyper-competition, and stakeholder demands (Gigliotti & Wear, 2021; Parsons & Shelton, 2019). While continuous academic innovation and ingenuity are essential, the organizational culture often hinders the success of institutional change projects (Cameron & Quinn, 2011; Hald et al., 2021; Schein, 2017). Despite many institutions’ collaborations with online program management (OPM) vendor companies, concerns regarding online student satisfaction, faculty experiences, and institutional growth remain prevalent.
In this study, I conducted a quantitative, non-experimental examination using the competing values framework (CVF; Quinn & Cameron, 1983; Quinn & Rohrbaugh, 1981). Using this framework, I performed a correlational test and an independent samples t-test. Participants were adults who held appointments as faculty members or administrators associated with the online graduate programs in their respective institutions. I collected data using the Organizational Culture Assessment Instrument (OCAI; Cameron & Quinn, 2011) to examine the perceived and preferred organizational cultures of academic leaders of online graduate programs whose institutions partnered with OPM companies to support their programs.
The results demonstrate that online graduate program administrators and faculty members partnering with OPMs primarily identified clan culture as their dominant current and preferred culture type. The current clan culture displays statistically significant negative relationships between the current market culture (p < .001) and the current hierarchy culture (p = .011) types. The current clan culture had a strong positive relationship with the preferred clan culture (p = .001) type, which aligned with the clan culture as the dominant culture for the participants. Independent sample t-tests indicated no statistically significant difference in the participants’ perceived and preferred culture types. Implications of this study impact administrators, faculty, and leaders of online program management companies
The Boudouard reaction for thermal energy storage and transport.
No full textThe Boudouard reaction is the reversible conversion of carbon monoxide (CO) to carbon dioxide (CO2) and carbon. The reaction equilibrium is highly exo/endothermic, so it is being investigated as a means of transporting thermal energy from clean sources like nuclear and solar thermal to points of use for industrial process heat (IPH). At the point of use, CO is converted to CO2 and C, releasing 171 kJ/mol of reaction. The products are then transported to the thermal source, where the reaction is reversed, and the same amount of energy is stored. The present work focuses on two areas: first, experimental characterization of the Boudouard reaction set is presented; second, an economic analysis of one potential configuration integrating the Boudouard reaction for thermal storage and transport with existing industry is offered. Based on experimental results, the activation energy (Ea) for the forward reaction is ca. 140 kJ/mol for CO partial pressure of 0.55 atm and ca. 225 kJ/mol for CO partial pressure of 0.95 atm. The peak reaction rate occurs near 923.1 °C. The levelized cost of heat transported, exclusive of primary thermal source and gas separation, is calculated to range from 0.115/kWhth for networks with approximately 100 miles of pipeline, varying based on storage capacity
Structuring microscale flows with centripetal, Marangoni, and inertial effects.
No full textMicroscale flows are present in a variety of natural and industrial scenarios, showcasing their importance across a spectrum of applications. They are widely used in industries like chemical and process engineering, lab-on-chip technology, biomedical, thermal management, and environmental monitoring. Thus, the ability to structure and manage these flows is crucial to ensure the performance and reliability of the systems that utilize them. This work investigates the application of centripetal, Marangoni, and inertial effects in structuring different microscale flows. First, flow patterns and mixing in low aspect ratio serpentine microchannels are examined with an emphasis on how Dean vortices driven by the channel geometry and flow conditions impact the mixing. By altering the aspect ratios and introducing bumps, this study uncovers the role of centripetal forces in generating complex flow dynamics that enhance or diminish mixing performance. Next, the emergence of Marangoni-induced climbing films upon drainage of surfactant-laden liquids inside capillary tubes is explored. The interplay of different effects including diffusion, advection, adsorption, and desorption, and their impacts on the formation of these films are investigated. The study reveals how surface tension gradients initiate film formation and sustain upward movement, shedding light on the relationship between surfactant concentration, flow properties, and film stability. The final part of this work examines the impact dynamics of viscous oil droplets on inclined, prewetted oil films of the same material but with varying viscosities. By changing the droplet viscosity and release height, the interplay between the inertial and viscous forces is highlighted in determining the air entrainment and wetting behavior. Furthermore, introduction of Carbon black to the droplets and its effects on the air film rupture and wetting mechanisms are also studied. The results obtained from this dissertation provide new insights into how these forces shape microscale flow phenomena, with broader implications for the development of advanced microfluidic systems, surface treatments, and fluid handling technologies. It contributes to the fundamental understanding of flow behavior in micro scales, where the balance of forces significantly influences the overall dynamics
Analysis and computations of the numerical solution of degenerate Kawarada equations without freezing nonlinear source terms.
No full textThis dissertation develops a numerical method for approximating solutions to parabolic partial differential equations, focusing on the Kawarada equation. This class of equations models physical phenomena exhibiting bounded solutions with unbounded temporal derivatives, including ignition processes in solid fuel combustion and rapid cellular movement in tumor growth. The Kawarada equation is characterized by finite-time singularity formation and stochastic degeneracy within its domain. Our numerical approach addresses two key challenges: accurate approximation of solution singularities and preservation of essential physical properties, such as monotonicity and positivity. Spatial discretization employs a non-uniform mesh for one-dimensional cases to enhance accuracy. In contrast, a uniform mesh is adopted for two-dimensional problems due to the computational complexity introduced by the cross-derivative term. We implement an adaptive step-size algorithm for theoretical analysis, though a fixed time step is utilized for most simulations to maintain computational efficiency.
This research focuses on analyzing one- and two-dimensional degenerate Kawarada equations. While the methodology could be extended to higher dimensions, such extensions would primarily involve the repetitive application of existing theorems and are therefore not considered here. Our analysis establishes unconditional stability without requiring linearization or freezing of the nonlinear source term. Key theoretical results include the preservation of solution monotonicity and positivity in the one-dimensional case. Proven convergence for the two-dimensional case. Simulations are presented to show second-order accuracy through the Milne device despite the absence of exact solutions for rigorous convergence analysis. Numerical simulations are run across both dimensional cases to validate the theoretical predictions. These findings provide significant insights into the analytical properties of Kawarada-type equations and the development of effective numerical methods for similar classes of differential equations
Assessing dietary behavior changes in African Americans using the Veggie Meter and 24-hour dietary recall.
No full textIncreasing fruit and vegetable (F&V) intake is key goal for populations at risk for type 2 diabetes mellitus (T2DM). Many researchers assess F&V intake through traditional dietary assessment such as 24-hour dietary recalls, which can be prone to response bias. This study involved the Veggie Meter®, a non-invasive method of assessing skin carotenoid scores, to provide an objective measure of dietary intake coupled with traditional dietary recalls. Following a 6-week culturally-tailored healthy-eating program with a 6-week follow-up, dietary intake of carotenoids lutein and zeaxanthin was marginally significant (p=0.054), while no significant changes were detected in other carotenoids or VM scores. However, intake of vitamin D (p=0.039), total vegetables (p=0.016), and total starchy vegetables (p=0.018) significantly increased. These findings suggest the potential for culturally tailored dietary interventions to improve vegetable intake in African American adults at risk for T2DM, although further research is needed to expand on these results
Understanding retention : a qualitative single case study examining first-generation college students’ perceptions of retention practices.
No full textFirst-generation college students make up a significant portion of undergraduate students in the United States. Over the last decade, the number of first-generation college students who have composed incoming freshman classes has steadily climbed. However, first-generation college students are far less likely to retain compared to their legacy peers, and current retention practices in higher education fail to address the declining rate of persistence amongst first-generation college students.
I conducted a qualitative single case study with first-year first-generation college students at a rural Christian liberal arts university in the Southeast United States to determine what academic and social experiences and external factors students perceived influenced retention. I used Tinto’s (1994) model of student departure as the theoretical framework to align the purpose and data collection protocols. Participants responded to an open-ended questionnaire, participated in a semi-structured interview, and took part in a focus group interview, which allowed me to engage with the lived experiences of my participants.
This study revealed four key findings that shaped the collegiate experience for these first-generation college students and influenced retention. Finding 1: First-year FGCSs at Central University describe faculty approachability and support within formal and informal academic systems as contributors to a supportive environment essential to their retention. Finding 2: First-year FGCSs describe spiritual formation events and campus activities (e.g., on-campus jobs and sports) and the sense of belonging and community experienced on campus as the most influential reasons for retention related to formal and informal social constructs. Finding 3: First-year FGCSs expressed their goals were academic success (e.g., achieving good grades and graduating from the institution) and preparation for the workforce. Finding 4: Commuter first-year FGCSs reported that external commitments—such as family responsibilities, off-campus jobs, and daily commutes—limited their ability to engage in on-campus activities. This study provides greater context and considerations to address the complex issue of first-generation college student retention
The impact of shift work and sleep on strategic reasoning and advice-taking behavior.
No full textThis study explores how varying shift schedules—and the sleep deprivation that often accompanies them—affect decision-making ability. Building on research that links sleep loss to diminished cognitive function, we aim to evaluate behavioral differences in reasoning and advice-taking across night, day, and rotating shift workers. Using both surveys and higher order reasoning tasks, such as the beauty contest, my study seeks to highlight how shift type influences strategic thinking and collaboration. By addressing this gap in research, my study highlights the importance of team dynamics and cognitive support in shift-based industries. My findings can help create positive workplace practices, promote better decision-making, and contribute to organizational efficiency