Classification of Rational Lemniscates in the Complex Plane

Color poster with text and figures.Generalizing the work of Ebenfelt, Khavinson, and Shapiro, this study sought to find a means of classifying shapes in the complex plane by using "fingerprints" of shapes. These fingerprints are constructed to have useful properties, in that shapes will have the same fingerprint even when they are scaled in size or translated. Such a property is useful in applications such as computer imaging, where often images are zoomed or taken from a different angle, but would like to be able to identify the shapes within the image in a consistent manner.University of Wisconsin--Eau Claire Office of Research and Sponsored Programs

Personal and vicarious embarrassability: Common and unique personality correlates

Although distinct vicarious embarrassability (VE) and personal embarrassability (PE) dimensions have emerged in factor analytic research, few studies have compared theoretically relevant correlates to explore potential differences in underlying mechanisms. The current study sought to determine whether PE was best accounted for by a social evaluation model, and VE by emotional empathy. Four fifty three undergraduates completed embarrassability, emotional empathy, and social evaluation trait measures. Factor analysis with oblique rotation produced two correlated (r = .37) PE and VE factors. Multiple regression did not provide absolute support for two distinct underlying models, with fear of negative evaluation and emotional empathy significant predictors of both embarrassability factors. However, public self-consciousness and perceived social competence were predictive only of PE. These results suggest common mechanisms could underlie PE and VE, but that a negative perception and heightened awareness of one’s social image could confer a unique vulnerability to PE

A Study of Parent Involvement Regarding Children Living with Sickle Cell Disease and their Parent\u27s Perception of their Children\u27s 504/Individualized Education Plan

Sickle Cell Disease is an inherited blood disorder that affects approximately 100,000 individuals living in the United States. It is estimated 30,000 students are living with the disease. Issues such as a stroke, silent cerebral infarction, and cognitive impairment are some of the physical complications that affect learning opportunities of these individuals. There is a lack of awareness among educators despite the research indicting the high percentage of poor academic performance, high detainment, and limited career opportunities. Parents play a vital role in making sure their children have a chance to succeed academically despite living with a chronic disease. According to Joyce Epstein (2001), parents who are engaged in their children\u27s education will see the benefit of them being successful academically and socially. Parents are the bridge that connects the home school-learning environment with the classroom. It is imperative that parents make sure that schools are implementing their children\u27s 504 Plan and/or Individual Education Plan (IEP) so their children will have a competing chance to succeed academically. This study presented a qualitative analysis of purposeful selected parents implementing the 504 Plan and/or IEP\u27s with Children with Sickle Cell Disease. In an effort to understand the participants\u27 perception of their experience in the 504 Plan\u27s/IEP\u27s process, the study provided a critical analysis why parents believe their schools are not fully implementing the 504 Plan and/or IEP\u27s as required. The three primary sources of evidence for this study were semi-structured interviews, image-elicitation, and document analysis; these were analyzed through the development of individual responses for each participant, which resulted in a cross-case analysis narrative depicting the study\u27s findings

Student understanding of the Boltzmann factor

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions

Aspects of Mammalian Predation on Upland Nesting Waterfowl in Central North Dakota

The impact of mammalian predation on upland nesting waterfowl was studied in central- North Dakota during the summers of 1987 and 1988. Survival of artificial nests was examined in relation to nest density, vegetation cover, distance from roads, active predator dens, and other artificial nests in a plot. Survival of artificial nests was also compared between an area with predator control and one without predator control. Artificial waterfowl nests located in high density plots had a significantly lower probability of survival than nests located in low density plots. Although there were significant differences in vegetation height and density between years, the probability of survival of nests in dense vs. sparse vegetative cover was the same. There was also no relationship between nest survival and distance to roads, active predator dens, or other artificial waterfowl nests. The probability of survival of nests located in the predator control plot was significantly greater than nests located in the plot without predator control for the first experimental trial but not the second. Striped skunks (Mephitis mephitis) and red fox (Vulpes vulpes) were the 2 most important nest predators on artificial waterfowl nests. The majority of eggs depredated by both fox and skunk were missing (75% and 36%, respectively). Of the remaining 64% of remains found at destroyed nests attributed to skunks, crushed egg remains were the most common type found. Fox left only 25% of all depredated eggs at the nest, but again crushed eggs were prevalent. The majority of egg remains left by skunks were in or adjacent to the nest bowl, while most remains from foxes were found 0,5-2 m from the nest bowl. Although many researchers document nest predators from descriptions in the literature, conflicting reports for the same predator are often found. In this study, the type and location of egg remains attributable to fox and skunk overlapped approximately 30%. As nesting habitat decreases, waterfowl are forced to nest in smaller suitable areas at increased densities. The results of this study show that nests at higher densities had a significantly lower probability of survival than nests at lower densities, regardless of nesting cover, or distance to roads, active predator dens, or other artificial nests

Ethnicity, disadvantage and other variables in the analysis of Birmingham longitudinal school attainment datasets

Explaining and responding to inequalities in attainment are significant educational policy challenges in England as elsewhere. Data on four cohorts of Birmingham Local Education Authority (LEA) pupils, each approximately 13,000, were analysed by ethnicity, deprivation, gender and other relevant individual pupil variables. For the four successive cohorts of children, aged five in 1997–2001, analysis shows the attainment trajectory of each ethnic group from Baseline/Foundation Stage Profile (age 5) to GCSE (age 16). The relative constancy over time, the changes from one key stage to the next and the differences within broad ethnic categories argue against simplistic explanations. The ethnicity variable accounts for a relatively small amount of variance in pupil achievement, with the same ethnic subgroups recurrently low attainers. Considering explanatory perspectives on educational inequalities and ethnicity in the light of these data, we conclude that a structuralist perspective offers the best explanation recognising economic exploitation, dominance and oppression at the national and local levels. Notions of institutional racism and Critical Race Theory (CRT) are considered to be inadequate and counter-productive, in part shown by their inability to accommodate the range of attainment levels and educational experience of different ethnic groups. More tellingly, they lack causal explanations relevant to the United Kingdom and deflect attention from the need for sustained effort to reduce poverty and disadvantage as it affects children

Identifying Student Difficulties with Entropy, Heat Engines, and the Carnot Cycle

We report on several specific student difficulties regarding the Second Law of Thermodynamics in the context of heat engines within upper-division undergraduates thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the Second Law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students' struggles in reasoning about situations that are physically impossible and failures to differentiate between differential and net changes of state properties of a system. Results herein may be seen as the application of previously documented difficulties in the context of heat engines, but others are novel and emphasize the subtle and complex nature of cyclic processes and heat engines, which are central to the teaching and learning of thermodynamics and its applications. Moreover, the sophistication of these difficulties is indicative of the more advanced thinking required of students at the upper division, whose developing knowledge and understanding give rise to questions and struggles that are inaccessible to novices