An algebraic integer is a complex number that is a root of a monic polynomial with integer coefficients. It is well-known that there is not always a single algebraic integer that can generate the ring of algebraic integers contained in a field extension of the rational numbers. The index of an algebraic integer is a natural number that measures how far a ring of integers is from having such a "primitive element." We investigate these indices in cubic fields and determine which natural numbers occur as indices in given families.

Located inside the Large Magellanic Cloud, fierce explosions called supernovae have thrown out massive amounts of gas in every direction. A portion of this gas is aimed toward the Milky Way and is on a crash course with our galaxy. We are observing this gas with the Wisconsin H-Alpha Mapper, which provides a window into how the gas is distributed. These observations show two periods of supernovae explosions that created two distinct gas winds. One of these winds is currently active while the other was produced roughly 300 Million years old. Studying these gas clouds will provide information on how massive these winds are and the rate at which they are produced. The ejected gas is headed toward the Milky Way could supply our galaxy with additional gas to form stars in the future.

Graphene oxide (GO) inherits high transparency, substantial conductivity, high tensile strength from its parent materials graphene. Apart from these properties, it emits fluorescence which makes it a potential material to use in optoelectronics and bio-sensing applications. In this work, we have utilized systematic ozone treatment to alter the optical band gap of single-layered graphene oxide in aqueous suspensions. Due to controlled ozonation, additional functionalization takes place in GO graphitic sheet which changes GO electronic structure. This is confirmed by the increase in vibrational transitions of a number of oxygen-containing functional groups with treatment and the appearance of the prominent carboxylic group feature at c.a. 1700 1/cm. Albeit, timed ozone induction introduces only slight change in color and absorption spectra of GO samples, the emission spectra show a gradual increase in intensity with a significant blue shift up to 100 nm from deep red to green. This large blue shift suggests an increase in optical band gap with additional functionalization introduced by ozone treatment. We utilize a semi-empirical theoretical approach to describe the effects of functionalization-induced changes. This model attributes the origins of fluorescence emission to the quantum confined sp² carbon islands in GO encircled by the functional groups. As we decrease the graphitic carbon cluster size on the GO sheet, the optical bandgap calculated via HyperChem molecular modeling increases, which supports the experimentally observed blue shifts in emission. This theoretical result is further supported by the TEM measurement of ozone-treated samples, which shows a decreasing trend of average ordered graphitic carbon cluster size on GO sheets with treatment time. Theoretical modeling, as well as the experimental results, indicate that the optical bandgap and emission intensity of GO are alterable with controlled ozone treatment, which allows tailoring the optical properties of GO for specific applications in optoelectronics and bio-sensing.

The Open Cluster Chemical Abundances and Mapping (OCCAM) survey is a systematic survey of Galactic open clusters using data primarily from the SDSS-III/APOGEE-1 survey. However, neutron capture elements are limited in the IR region covered by APOGEE. In an effort to fully study detailed Galactic chemical evolution, we are conducting a high resolution (R~60,000) spectroscopic abundance analysis of neutron capture elements for OCCAM clusters in the optical regime to complement the APOGEE results. As part of this effort, we present Ba II, La II, Ce II and Eu II results for a few open clusters without previous abundance measurements using data obtained at McDonald Observatory with the 2.1 m Otto Struve telescope and Sandiford Echelle Spectrograph.

The goal of this study was to conduct a survey of 913 M-dwarf stars from the Lepine and Shara Proper Motion(LSPM) catalog within 33 parsecs. This research was conducted to improve upon the statistics of nearby multiple M-dwarf star systems. Identifying and confirming multiple systems at both wide and small separations will expand understanding of M-dwarf formation by comparing these results to existing star formation models. Data for these targets was collected with the Robo-AO camera on the Palomar 60in telescope. Separation and position angles were determined and compared for two epochs of the images containing multiple stars, one taken in 2012 and the other taken in 2014, to look for changes in these values. Stars with little change in position with respect to one another suggest they are common proper motion pairs. The Washington Double Star(WDS) catalog and other resources were used to further determine binarity. There were 50 multiple star system candidates found with a multiplicity fraction of 28.6±3.0 and a companion star fraction of 34.7±2.1.