On Some Properties of Tribonacci Quaternions

In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them

The effect of disjoining pressure on the shape of condensing films in a fin-groove corner

Thin film condensation is commonly present in numerous natural and artificial processes. Phase-change driven passive heat spreaders such as heat pipes, which are widely used in electronics cooling, employ a continuous condensation process at the condenser region. When the wick structure of a heat pipe is composed of grooves, the top surfaces of the walls (fins) located between consecutive grooves function as the major source of condensation and the condensate flows along the fin top into the grooves. Modeling of this condensation problem is vital for the proper estimation of condensation heat transfer, which constitutes the basis for the overall performance of an heat pipe together with the evaporation process. In the current study, a solution methodology is developed to model the condensation and associated liquid flow in a fin-groove system. Conservation of mass and momentum equations, augmented Young-Laplace equation and Kucherov-Rikenglaz equation are solved simultaneously to calculate the film thickness profile. The model proposed enables the investigation of the effect of disjoining pressure on the film profile by keeping the fin-groove corner, where the film becomes thinnest, inside the solution domain. The results show that dispersion forces become effective for near isothermal systems with sharp fin-groove corners and the film profile experiences an abrupt change, a slope break, in the close proximity of the corner. The current study is the first computational confirmation of this behavior in the literature

Evaluation of mineral content in healthy permanent human enamel by Raman spectroscopy

An understanding of tooth enamel mineral content using a clinically viable method is essential since variations in mineralization may serve as an early precursor of a dental health issues, and may predict progression and architecture of decay in addition to assessing the success and effectiveness of the remineralization strategies. Twenty two human incisor teeth were obtained in compliance with the NIH guidelines and site specifically imaged with Raman microscope. The front portion of the teeth was divided into apical, medium and cervical regions and subsequently imaged with Raman microscope in these three locations. Measured mineralization levels have varied substantially depending on the regions. It was also observed that, the cervical enamel is the least mineralization as a populational average. Enamel mineralization is affected by a many factors such as are poor oral hygiene, alcohol consumption and high intake of dietary carbohydrates, however the net effect manifests as overall mineral content of the enamel. Thus an early identification of the individual with overall low mineral content of the enamel may be a valuable screening tool in determining a group with much higher than average caries risk, allowing intervention before development of caries. Clinically applicable non-invasive techniques that can quantify mineral content, such as Raman analysis, would help answer whether or not mineralization is associated with caries risk

A Spatial Inquiry into Childhood Lead Poisoning in Shelby County, Tennessee

Review of the recent literature suggests that integration of geographical information systems (GIS) into childhood lead exposure studies significantly enhances identifying lead hazards in the environment and determining at risk children. The purpose of this study is to find at-risk areas of childhood lead poisoning as well as determining risk factors in Shelby County, Tennessee. The two common deduplication methods: the first blood lead level (BLL) test result and the highest BLL test result were compared. Kappa statistic was used to investigate the effect of residential mobility on hot spots. Global and local spatial autocorrelations, Moran’s I and Getis and Ord’s Gi, were used to test the existence of global spatial autocorrelation as well as to find local pockets of high BLLs, and their trends. BLLs were grouped into four time periods during the 20 years between 1994 and 2013. Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) were used to model risk factors. Kappa agreement results indicated that residential mobility had an approximate effect of 10% agreement change for multiple-screened children. Spatial autocorrelation statistics indicate that there is a strong global spatial autocorrelation within the BLL dataset. Local statistics showed that local clusters of high BLLs are concentrated in the western part of the county in the first period: 1994-1998 and moved to a more disperse pattern towards the east and south. The global and local statistical models showed that there is a significant relationship between the percent of children with elevated blood lead levels (EBLLs) and the percent of screening, median construction year, old housing, median income, monthly rent, African American population, education attainment, public assistance, poverty, and median income. Population density and vacancy were not found to be associated with the percent of children with EBLLs

The universal values of community:a social dynamical view on culture

This dissertation examines the relationship between collectivist values and attitudes towards societal issues. According to this dissertation, cultural orientations serve an important role in regulating social interactions within communities and among community members. This group dynamics perspective has implications for how to conceptualise and operationalize collectivism and individualism. The dissertation develops a new measure of community collectivism on the basis of this perspective. The measure is able to differentiate between (sub)cultural groups, exactly as predicted. Accordingly, it can explain cross-cultural differences. More importantly, it is also related to attitudes and behaviors towards a wide variety of issues: sexism, political preferences, authoritarianism, and healthcare. Together, the results suggest that cultural values that stem from the dynamics of proximate communities are projected onto one's views for society as a whole and life in general

Investigating the changes in teachers\u27 pedagogical practices through the use of the Mathematics Reasoning Heuristic (MRH) approach

Our changing world needs many more mathematically literate individuals. Mathematical literacy can be defined, parallel to reading and writing literacy, as not only being able to understand the fundamental notions of mathematics, develop sophisticated mathematical models and evaluate someone else\u27s use of numbers and mathematical models but also being able to represent quantitative relations using algebraic reasoning and interpret and reflect on mathematical language patterns. In order to help students become mathematically literate, the National Council of Teachers of Mathematics (NCTM) has focused attention on students\u27 conceptual understanding of mathematics suggesting students need to be actively involved in the learning process using their experiences and prior knowledge. Along with this view on learning, understanding of teaching has also been revised in mathematics classrooms. Teachers now need to provide students with a challenging and supportive classroom environment in which they can build new knowledge by engaging in exploration of mathematical ideas by themselves. Since the publication of Curriculum and Evaluation Standards for School Mathematics in 1989, the National Council of Teachers of Mathematics (NCTM) has paid special attention on teacher change, problem solving, and, more recently, using writing in mathematics classrooms for helping students develop thorough mathematical understanding and to becoming more mathematically literate.;This change in the views of learning and teaching has placed students in the center of learning occurring in the classroom by altering students\u27 roles and requiring them to be actively involved in talking and writing in mathematics classrooms. The NCTM mandated that students at all levels should be able to use mathematical ideas in a variety of situations. For this purpose, students must have the opportunity to discuss their ideas publicly, to reflect on their thoughts and problem solving processes, and to communicate their ideas using various modes of representation (graphical, pictorial, oral, written, etc.). Writing in mathematics was emphasized in The Principles and Standards for School Mathematics (NCTM, 2000, p. 61), which said, Writing in mathematics can...help students consolidate their thinking... because it requires an active involvement of learners such that they use writing as a vehicle for learning and become the center of their own learning processes by engaging in reflection on mathematical experiences.;This study focused on examining the changes in pedagogical practices when three high school algebra teachers shift from their traditional teaching to more student-centered practices through the use of the Mathematics Reasoning Heuristic (MRH) approach. The study also looked at the performance differences on the Iowa Test of Educational Development (ITED) between the students in the control classes where the teachers engaged in their traditional instructional routines and the students in the treatment classes where the teachers used the MRH approach. The goal of the MRH approach is to help teachers improve their pedagogical practices to scaffold students\u27 understanding of mathematical concepts and their problem solving skills.;The major findings of this study are that teachers\u27 adoption of the required pedagogical practices varied as they attempted to move away from their traditional practices and that implementing a student-oriented approach such as the MRH approach which includes embedded writing-to-learn strategies does have an impact on student performance. The student performance on the standardized test was significantly enhanced for those students in the MRH classrooms compared to students who engaged in the more traditional approaches. The results from the analysis of the teachers\u27 pedagogical practices in their treatment and control classes indicate to us the importance of pedagogical skills to promote dialogical interaction during problem solving. In examining the results the researcher would suggest that there are two critical elements of the MRH approach. The first is the pedagogical approach needed and the second is the consistent use of the heuristic concept through the scaffolded writing component of the MRH approach