Mathematics and Physics

The purpose of the present study was to examine the effect of breastfeeding on the relationship between executive functioning and math achievement for preschool-aged African American children. Although the effects of breastfeeding have been widely researched, the cognitive effects of breastfeeding on African American children has yet to be extensively researched. Thus, the following research will provide insights in identifying cognitive factors that promote development and reduce the achievement gap for African American children in mathematics. It was hypothesized that executive functioning will have a stronger association with math achievement among children who are breastfed. The sample for the study was part of a larger study conducted on nearly 200 four- and five-year-old African American children. The implications that will be discussed are in relation to the disparity of academic achievement among African American children. This study aims to inform future research about how breastfeeding affects the relationship between executive functioning and math achievement among African American children using statistical modeling to perform a moderated data analysis.

This research combines concepts from Abstract Algebra and Geometry. We start with a finite collection of hyperplanes in the Euclidean Space Rn. Arrangements of hyperplanes partition the plane into several sections.We call these sections faces. A binary operation is defined on the set of faces of the arrangement. This algebraic structure of faces with the binary operation forms a semigroup but not a group. We study other properties of this semigroup. As a special case we study hyperplane arrangements in R2 that come from invariant theory. Several examples will be given along with the presentation. 

X-ray binaries are a fascinating class of astrophysical objects. They tend to be highly variable over both short and long time scales, and can experience sudden flares and long intervals of quiescence. Several physical phenomena, including eclipses, can produce periodic behavior. It has even been hypothesized that some X-ray binaries are orbited by planets. If this is the case, dips in the observed X-ray emission may occur. Here we report on our study of archived Chandra data from several hundred X-ray sources in the galaxies M51, M101, and M104. We analyzed the data by searching for interesting time signatures in the light curves of the X-ray sources, most of which are X-ray binaries, and have found flares, dips, and periodic signatures. We present the results and consider their implications, including the prospects for planet detection and for the search of X-ray triples. This research was made possible by the SAO REU program and is funded in part by the National Science Foundation REU and Department of Defense ASSURE programs.