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Extending the Radius of Convergence of the Drinfeld Module Logarithm
Get PDFDrinfeld modules are, in essence, a way to create a function field analogue to complex multiplication. With these modules, we can define a logarithm function analogous to the natural logarithm by virtue of a power series. Similarly to how we extend the radius of convergence of the natural logarithm with complex numbers, we can also extend the radius of convergence for these Drinfeld module logarithms. While there are proofs for extending the radius of convergence of the Carlitz module, the simplest form of Drinfeld module, there is no proof for a generalized Drinfeld. In this paper, a method of extending the Carlitz logarithm’s radius of convergence using Newton polygons will be examined. Afterwards, a way to apply this proof to a general Drinfeld logarithm function will be walked through
Does the Three Point Shot Affect Winning Percentage
Get PDFThe three-point shot, introduced in the late 1970s, is a shot that occurs typically 24 feet away from the basket at the professional level. Strategically the game of basketball was originally based on two-point field goals. Recently, there has been a noticeable trend in the popularity of the three-point shot amongst professional teams. Nowadays, three point shot attempts account for more than a third of average NBA shot selection. Statistical analysis is becoming integral to athletics. Statistics has become a critical component to the development of not only on court basketball strategies, but also team structure as well. There are multiple studies that use linear and logistic regression models to form a prediction algorithm for the outcome of games. Many have statistically characterized the increase in three-point shooting on a year-toyear basis. Especially after the 2012 – 2013 season, three shooting began to become the more favorable shot for teams. The purpose of this research is to analyze this statistical jump and determine if three-point shooting is statistically significant to winning probability before and after the jump. By progressing from linear to logistic regression, the three-shot point shot was found to be statistically insignificant to winning probability. However, the model was accurate predicting the winning probability for seasons before and after the statistical jump year
Insufficient Effort Responding
Get PDFThe quality of self-report data has long been a concern, with increasing attention to the issue of insufficient effort responding (IER). Researchers have made considerable progress in developing techniques for handling IER (Meade & Craig, 2012; Huang, Bowling, Liu, & Li, 2014). This dissertation examines the use of IER best practices in survey research within the management literature through a series of essays. The results of the first study indicate that there is a lack of methodological transparency regarding how IER is addressed in the management literature. Simply stated, few authors report addressing IER in their manuscripts; thus, no conclusions could be drawn regarding management researchers use of IER best practices. Based on the findings of Study 1, the aim of Study 2 was to investigate this lack of reporting through a job performance lens. The essay explored several potential reasons for low methodological transparency regarding IER practices, including (1) insufficient KSAs (i.e., understanding or awareness of IER best practices), thus IER was not addressed nor reported, and (2) a lack of extrinsic motivation to report how IER was addressed in studies (i.e., reviewer requirements and page limitations). The results of Study 2 indicate that though management researchers do not report utilizing IER technique, IER is being addressed in various ways by management researchers.
The most common techniques management researchers use to address IER are employing infrequency technique items to detect IER and deleting respondents flagged by the detection method from samples. Taken as a whole, these findings suggest there is room for improvement regarding how IER is addressed in management research using self-report survey data. Subsequently, Study 3 introduces a technique for examining and addressing the effects of IER on data quality that does not require researchers to delete respondent data, which may inadvertently bias samples or eliminate otherwise “good” data. Specifically, the final essay demonstrates how to create an IER method factor that can be used to examine the effects of IER detected in a sample and control for the effects of IER if it appears to bias research conclusions
Glucose as a Mediator of the Relationship Between Sleep and Cognitive Performance
Get PDFABSTRACT The Centers for Disease Control and Prevention (Y. Liu et al., 2016) reports that 34.8% of adults living in the United States of America are getting less than their recommended amount of sleep per night. Additionally, the National Sleep Foundation (2014) reports that 35% of adults have poor sleep quality. Sleep problems appear most prevalent in young adults (Hershner, 2015). Rates of type 2 diabetes mellitus are also on the rise in this specific population (Kaufman, 2002). Interestingly, research has consistently found that both sleep quantity and quality are associated with glucose levels (Ip & Mokhlesi, 2007; Padilha et al., 2011; Taub & Redeker, 2008). Further, both sleep quantity and quality, as well as glucose, can have a significant effect on cognitive performance (Alhola & Polo-Kantola, 2007; Zilliox et al., 2016). The purpose of the present study was to investigate the mediating effect of glucose on the relationship between sleep and cognitive performance. Sleep included sleep quantity and quality. Cognitive performance included both sustained attention and visuospatial working memory. It was predicted that sleep would be positively related to cognitive performance, and negatively related to glucose levels. It was also predicted that glucose levels, even in a prediabetic range, would be negatively related to cognitive performance, and that this would mediate the relationship between sleep and cognitive performance. To test these hypotheses, data were collected from 82 young adults. Participants answered demographic questionnaires, and surveys assessing their sleep quantity and quality. They then had their glucose levels assessed via finger-stick glucose monitoring. Following this, they completed computerized tasks measuring sustained attention and visuospatial working memory. A hierarchical multiple regression analysis was conducted to test the proposed hypotheses. After cleaning, 81 cases were found to be viable for analysis. Results obtained were in partial support of hypotheses. Poor sleep quality, as measured by the Adult Sleep-Wake Scale (ADSWS; Fortunato et al., 2008), was found to be associated with decreased visuospatial working memory (β = -.02, p = .039). No other hypotheses were supported, though some trending results were found. It is believed had a larger and/or more diverse sample been used, more significant results would have been found. Implications exist not only for students, but for all young adults. They are likely to be of interest to young adults, as well as those working with young adults. This includes mental health professionals, various medical personnel, teachers, and school administrators
Understanding Principal Influence: A Descriptive-Embedded Case Study of the Attributes of Path-Goal Style of Leadership and Its Influence on Principal\u27s Decision-Making in Response to School Performance Scores
No full textThe purpose of this study was to investigate how Path-Goal leadership styles impact the decision-making process of school principals in response to school performance scores. Using purposive sampling, the researcher selected participants from public high schools in the Northwest Southern region for inclusion in a descriptiveembedded case study, specifically focusing on principals and their instructional leaders. The data collection process encompassed various sources, such as field observations, state-released test data, and semi-structured one-on-one interviews with principals and instructional leaders. The theoretical framework underpinning this study was the Path-Goal theory of leadership, which posits four distinct leadership styles: Directive, Supportive, Participative, and Achievement-Oriented. The study revealed that while principals consistently exhibited a specific Path-Goal leadership style, they demonstrated flexibility in employing all four styles as needed. Furthermore, the alignment between a principal’s self-perception of their leadership style, their actual style, and the perceptions of their instructional leaders was consistently observed in practice. This research study underscores the importance of a leader’s influence on followers. It emphasizes the need for leaders to cultivate adaptability in their leadership styles while making decisions that enhance school performance scores effectively
Financial Decision-Making among Community College Leaders
No full textThe purpose of this qualitative study was to learn about financial decision-making practices of community college chancellors. This study employed an instrumental case study with three embedded cases guided by organizational decision-making theory and distributive leadership perspective. Participants were community college chancellors within the same college system. Primary data for this study included questionnaire responses, semi-structured interviews, and document analysis using constant comparative method. Chancellors deemed budget shortfalls, programs, and self-generated revenue as major decisions. Chancellors in the study used financial reports to make decisions about programs, to design organizational structure and practice, and to construct college budgets—all of which can positively or negatively impact stakeholders, especially students. The findings substantiated the need for conversations and shared best practices for organizational structures, integrated financial and programmatic planning, and budgeting within the community college setting to ensure sustainability given reduced state funding
The Impact of Leaf Litter Diversity on the Colonization of Aquatic Insects
Get PDFEphemeral pools provide habitat to a wide diversity of aquatic insects which colonize pools to establish new populations in higher quality habitats. These pools rely on nutrient inputs from the surrounding terrestrial landscape, predominantly through leaf litter. Using mesocosms, we tested for the effect of leaf litter diversity (richness and functional diversity) on the colonization of aquatic insects. Leaf litter influences characteristics of a pool (tannins, water color, and nutrients) which may make them more or less desirable to potential colonizers. I added unique mixtures of leaf litter with different numbers of species (0, 3, 5, 7, and 9) and calculated functional diversity for each. I also examined which characteristics make different mesocosms more attractive to potential colonizers. Colonizers preferred mesocosms with leaves rather than ones without. Leaf litter functional diversity was a better predictor of colonizer abundance than leaf species richness. I found that colonizer communities were largely influenced by N:P ratios, conductivity, water color, and tannins. By understanding the relationship between leaf litter diversity and colonizing aquatic insects, we can understand the community dynamics of ephemeral pools
Development and Validation of an Instrument to Evaluate Social Media Engagement with Millennial Alumni
No full textHigher education leaders may need assistance creating engaging social media content for alumni. Research questions for the current study included: What values, attitudes, and behavior variables are associated with engaging millennials? What motivations and gratification variables are associated with engaging millennials on social media? How would university leaders use the instrument to assess engagement with millennial alumni via social media through an understanding of millennial values, attitudes, behaviors, motivations, and gratifications variables? Both generation and uses and gratification theories provided the frameworks for developing the instrument. The study used the modified Delphi method to create the instrument. Building the instrument criteria required a literature review of millennials\u27 characteristics and social media uses and gratifications. A panel of experts in university communication, social media, program directors, and alumni outreach evaluated the criteria. Lawshe’s Content Validity Ratio determined consensus for the instruments criteria. The results have practical application for program, department, college, and campus-wide leaders planning alumni engagement using social media. The instrument helps create, edit, and evaluate social media engagement with millennial alumni
Digital Implementation of an Incremental Quantity Directional Protective Relay Element and Its Applications Using an Automated Testing Procedure
Get PDFThis thesis presents the design and analysis of a digital model of an incremental-quantity-based directional protective relay element using the electromagnetic transient program (EMTP). The digital model is based on a similar protective element present in commercially available time-domain-based relays and provides directional fault detection using incremental quantities. Such models are not readily available in transient study programs.
The element’s operating principles are discussed in detail, and the digital design process is outlined. The digital model is designed in a simplified test system, and upon validation using a real-world time-domain-based relay, its performance is analyzed using the model of a real power transmission network. An automation script is developed to perform more robust testing. The development of the automation script is also discussed in detail within this thesis.
The digital model is intended to predict the performance of the same element in commercially available time-domain relays. Model performance was compared with a commercially available relay and the results were found to be similar
Nutrition-Related Factors Impacting the Bone Health of Female Sports and Performance Collegiate Athletes
Get PDFLow bone mineral density is commonly found in female athletes and has been related to the energy adequacy and nutrient density of the athlete’s diet. Insufficient dietary energy intake and/or excessive energy expenditure can lead to low energy availability in female athletes, which has been shown to disrupt endocrine, metabolic, and physiological functions. Psychological distress in competitive athletes may affect dietary choices and patterns. To meet their personal or performance standards/goals, an athlete may go to extremes to achieve those standards/goals, including altering their dietary intake.
This study aimed to evaluate the nutrition-related factors affecting the bone health of collegiate female sports and performance athletes. Specifically, this study explored the associations between diet quality, bone health, low energy availability symptoms, and mental health risks. It was a cross-sectional study that obtained data from female athletes attending NCAA Division I programs in the state of Louisiana, with a subset group of female athletes attending Louisiana Tech University providing additional physical data (BMD measurements & InBody 770). The online questionnaire obtained data to examine diet quality (REAP-S), mental health as measured by the APSQ and BTPS-SF, low energy availability symptoms (LEAF), and bone fracture history. The participant sample included Louisiana Tech University female athletes (n = 44) and non-Louisiana Tech athletes (n = 52), for a total of 96 participants.
Approximately half (54.2%) were White and non-Hispanic and 31.3% were classified as freshmen. The majority (69%) of the female athletes were less than 10 years of age when they began participating in their chosen collegiate sport. Of the 17.1% of the athletes who reported vaping, 73.7% vaped occasionally; two (2.1%) participants stated that they smoked. From the APSQ, 43.5% of the female athletes experienced “very high distress” during their season, while 30.6% of the female athlete tested experienced “high distress”. Correlations from the total sample are: the subscales of the BTPS-SF significantly correlated r (79) = .551, p \u3c .281 with each other, and the 3 subscales of the APSQ positively correlated with the total score of the APSQ, the correlation between the LEAF and the BTPS-SF subscale, Rigid Perfectionism, was significant and positive, r (81) = .305, p \u3c .006, the LEAF questionnaire negatively correlated with the total score of the APSQ and the subscale, Self-Regulation, r (81) = .443, p \u3c .001, the subscale of the APSQ, Self-Regulation, had a positive correlation with the subscale of the BTPS-SF, Rigid Perfectionism, r (82) = .270, p \u3c .014, we found that both subscales correlated with the LEAF, and the total score of the APSQ and its subscales Self-Regulation and Performance has a significant positive correlation with the BTPS-SF subscale, Self-Critical Perfectionism, r (81) = .397, p \u3c .001. The Louisiana Tech University female athletes had the physical measurements. Correlations were run for the sample with physical measurements and the following was found: The correlation between the APSQ and LEAF was significant and positive, r (42) = .245, p \u3c .028, the category of the BTPS-SF, “rigid perfection,” was significant and positive to the SI, T, and Z scores, r (42) = .424, p \u3c.005, Rigid perfectionism also had a significant positive correlation with the LEAF, r (42) = .305, p \u3c 0.06, and there was a positive correlation between the total score of the APSQ and the “self-critical” category of the BTPS-SF, r (42) = .397, p \u3c 0.01. An independent samples t-test was run to compare the diet quality and distress levels in those athletes with a bone fracture history to those without within the subset of Louisiana Tech female athletes (N = 42.. There was a difference between the fracture (M = 28.79, SD = 8.06) and non-fracture (M = 22.71, SD = 8.48) group for the APSQ, the athletes with a history of no fractures (M = 31.61, SD = 4.13) had a higher diet quality (M = 28.43, SD = 3.98) compared to the female athletes with a history of fractures and female athletes with a history of bone fractures (M = 4.18, SD = .59) had a higher average of rigid perfection (M = 3.57, SD = .96)than those with no history of bone fractures.
In summary, we found that mental health status risk was related to diet quality, low energy availability, and bone injury health frequency amongst female collegiate athletes. The more likely a female athlete is to strive to be perfect and is a harsh critic of herself, the higher the distress level of that individual. Nutritional professionals and athletic departments working with female athletes on their campus should consider all aspects of the athlete when treating them, such as mental health, diet quality, symptoms of low energy availability, and history of bone fractures