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We construct the definition of Brownian motion on the N-legged spider graph with infinite legs and Kirchhoff’s gluing conditions at the origin and calculate the transition probability of this process. In addition, we study several important Markov moments, for instance the first exit time τL from the spider with the length L of all legs. The calculations give not only the moments of τL but also the distribution density for τL (all results of this section are new ones). For the spectral theory on the spider like quantum graphs, we start by constructing the spectral analysis on the finite interval of a three-legged spider graph and then pass it to infinity. Spectral analysis is performed for three different types of potentials. The fast-decreasing potentials, the fast-increasing potentials, mixed potentials, and its spectral theory. The details contain, the absolute continuous spectrum of multiplicity 3 and its construction using the reflection-transmission coefficients on each leg for the fast-decreasing potential, Bohr’s asymptotic formula for N(λ) (the negative eigenvalues), instability of the discrete spectrum for the mixed potential on each leg of the spider graph. Furthermore, we have done symplectic analysis, and its representation on the spider quantum graph.
This study examines the decision-making logics of 220 small and micro-entrepreneurial businesses throughout the United States and presents a model for a better understanding of the impact of decision-making approaches on relative profitability through the lens of effectuation theory in the small business and entrepreneurial context. The study fills existing gaps in literature by accounting for the moderating influences of the decision-maker’s emotions (affect) as well as accounting for entrepreneurial orientation. The study finds that effectuation is positively related to small business relative profitability. Entrepreneurial orientation as well as positive and negative owner / manager affect are shown to moderate the relationship between either decision-making logic and firm relative profitability.
Affect has long been a central topic in marketing, particularly within branding. Despite the extensive research on affect, however, a significant lack of attention has been paid to the concept of wonder. This is surprising given that Adam Smith (1869), the father of modern capitalism, considered wonder to be the most important emotion, and Descartes (1649), known as the father of all passions, described wonder as the “first of all emotions.” The absence of understanding regarding the construct of wonder in marketing represents a significant gap in the literature. This research aims to address this gap by exploring the construct of brand wonder. By better understanding brand wonder, marketers may gain insights into how and why consumers connect with their brands and products. This study employs Hunt's indigenous theory development and inductive realist methodology to develop an initial theoretical framework, as this methodology is ideal for relatively new research areas. This theoretical foundation will likely accelerate future academic research on wonder and branding and facilitate the development of more effective branding strategies. This dissertation will also include an empirical analysis using a textual analytics methodology to support the theoretical framework. Finally, the dissertation concludes with directions for future research.
Supply chain disruptions have been a major concern in businesses and society. Our goal is to study these disruptions and analyze ways to mitigate their effects. To do so, we propose an agent-based model simulation. In our model, we consider the following: a supply chain that is generic in the structure; however, we will focus on three types of supply chains, customer-focused, low-cost, and dual-purpose supply chains. Disruptions will include repeatable small-scale events and non-repeatable large events. The managerial decisions considered include excess capacity, the amount of safety stock at each echelon of the supply chain, and the geographical dispersion of partners. To measure the resiliency in our simulation, we will compute the service levels, the time needed to return to normal operations, and the profit.
The growing complexity of high-performance computing (HPC) systems has led to the development of parallel programming models, such as OpenMP and OpenACC, to make it easier to utilize modern HPC architectures. These models provide a higher-level interface for specifying parallelism patterns and reducing programming effort, but performance optimization and customization are left to the compilers. Despite the availability of state-of-the-art OpenMP compilers, including LLVM, GCC, and ROSE, there remains a need for a compiler that is easily usable and extendable by researchers and students who are not in the field of compiler development, supports multiple parallel programming models, and has comparable performance to mainstream compilers.
The REX compiler has been proposed as a solution to these challenges. It is built upon the ROSE compiler and uses a unified parallel intermediate representation (UPIR), targeting the LLVM OpenMP runtime for optimal performance. REX provides essential OpenMP 5.0/5.1 constructs and preliminary support for OpenACC 3.2. Its source-to-source transformation capabilities offer flexibility and ease of use with minimal overhead. It can be installed as a Docker image or used through a cloud service. The REX compiler's performance has been evaluated using an enhanced version of the parallel benchmark, Rodinia, which compares GPU offloading performance across different parallel programming models and compilers. In conclusion, the REX compiler provides a unique solution for parallel programming research and education, balancing performance, portability, flexibility, and usability.
This dissertation examines whether there are unintended consequences that emerge from status interventions in task groups in relation to cohesion and solidarity. Past theorists have argued that inconsistent status structures produce weaker levels of cohesion and solidarity in
comparison to consistent status structures. To contextualize the issue of group processes as they relate to public policy, I first introduce the complexity framework for public policy and then outline the history of group processes and the concept of solidarity. Despite centuries noting the complexity of group processes and their implications, policymakers remain myopically focused on either individual responsibility or social structure as the root of social inequality. After providing a theoretical overview, I then proceed to discuss the procedure of the study more in-depth. Data come from an online experiment involving mixed-sex dyads interacting in one of three conditions. Participants individually completed an ambiguous problem-solving task and then worked together over Zoom audio to form a group decision. In the three conditions, participants were either given no performance feedback before the problem-solving task or were informed the male or the female participant performed better on a pre-test related to the task. The conversations were recorded and analyzed using measures related to paraverbal synchronization and accommodation. In terms of self-reported cohesion, there appeared to be a difference, albeit a weak one, in only the inconsistent-status condition, with female participants reporting higher levels of cohesion in comparison to males. However, in terms of solidarity, there was no significant difference between the conditions. Although inconsistent status structures were associated with weaker perceptions of cohesion, it did not appear to impact solidarity like theorists have suggested. Status structures do not appear to impact group solidarity. The nature of group membership in conjunction with status consistency/inconsistency may produce the significant differences in solidarity that theorists have suggested. To date, there has been little empirical examination of how status consistency affects cohesion and solidarity. Relatedly, the current study advances the research on vocal accommodation by analyzing status and solidarity simultaneously. The implications of the findings on status interventions for public policy, in particular the nature of feasibility strategies, are discussed in detail at the end.
Latinx students already constitute the largest minority group of students graduating from the United States secondary school systems and projections show the Latinx population continuing to increase between now and 2036 (WICHE, 2020). Both in the United States overall, and within the Appalachian Region, the increase in the Latinx population and continued projected increase in population, warranted a closer examination as to how these individuals engaged with higher education and ultimately the impact their participation in higher education can have on the economy. Research exists on the deficits of Latinx students and reasons which impact their lack of persistence at the four-year college level, but little literature exists focusing on the assets of these individuals, and little if any literature exists on Latinx students from the Appalachian Region. This phenomenological study explored the lived experiences of 6 Latinx students from the Appalachian Region who utilized a two-year institution in the Appalachian Region and then transferred to an urban four-year institution. The participants had to have persisted at the institution for at least two semesters and be in good academic standing. The research study examined the lived experiences of the participants through the theoretical framework of Yosso’s (2005) community cultural wealth model, examining the various assets these students utilized to help them transition from the two-year institution and persist at the four-year institution. The purpose of this study was to provide a foundation for understanding factors that are important to Latinx students from the Appalachia Region in successfully persisting at a four-year institution after transferring from a two-year institution. The research was guided by a primary research question (RQ) and three sub questions (SQ); RQ: What are the lived experiences of first-generation Appalachian Region Latinx students who successfully transfer from a two-year institution to a four-year institution? SQ 1: How does a student’s community cultural wealth impact their transition experience? SQ 2: What are the roles of significant individuals, such as mentors, advisors, teachers, and counselors, in students' lives on their educational journeys? SQ 3: What other factors do these students identify as critical in their successful transition experience? Primary data collection was captured through two semi-structured interviews with each participant. These interviews were analyzed, revealing eight themes and sixteen sub-themes, all which demonstrate the participant’s ability to successfully navigate and persist in higher education. The findings of this study provide possible suggestions and examples of how institutions can better support Latinx students from the Appalachian Region.
Facilitating productive mathematical discussions is considered a core practice of mathematics education. The complexity of this teaching practice presents the need for pedagogical tools to provide structure for preservice teachers (PST) developing their practice, yet little is known about how PSTs use these tools. This multiple case study sought to understand what pedagogical tools PSTs use to plan and enact mathematical discussions with elementary students and how they use these tools to support their practice. In particular, this study focused on capturing the experiences of three elementary PSTs as they transitioned from university-based methods course instructions into early clinical teaching experiences in elementary classrooms. These experiences were captured through multiple one-on-one interviews, observations of teaching in clinical classroom settings, and analysis of artifacts of teaching and learning. This study has implications for mathematics teacher education, practice-based teacher education, and the refinement of tools to support teachers’ practice facilitating mathematical discussions with students.
