Real Simple Lie Algebras: Cartan Subalgebras, Cayley Transforms, and Classification

The differential geometry software package in Maple has the necessary tools and commands to automate the classification process for complex simple Lie algebras. The purpose of this thesis is to write the programs to complete the classification for real simple Lie algebras. This classification is difficult because the Cartan subalgebras are not all conjugate as they are in the complex case. For the process of the real classification, one must first identify a maximally noncompact Cartan subalgebra. The process of the Cayley transform is used to find this specific Cartan subalgebra. This Cartan subalgebra is used to find the simple roots for the given real simple Lie algebra. With this information, we can then create a Satake diagram. Then we match our given algebra\u27s Satake diagram to a Satake diagram of a known algebra. The programs explained in this thesis complete this process of classification

Evaluation of Plant- waxes to Estimate Forage Intake in Grazing Cattle

Although key to the efficiency of a cattle operation, feed intake is challenging to evaluate in a grazing setting. However, even within forage- based systems, plant- wax markers may be used to predict dietary choices and feed intake. Plant- waxes are a complex mixture of lipids found on the surface of plants. When sufficiently unique among plants, the composition of diets can be determined from the pattern of these compounds in the forages ingested. These markers were used to delineate the parts of the corn plant and, separately, 8 western rangeland grasses and legumes. Using plant waxes, the components of the corn plant were clearly distinguished. Th is technique therefore could be useful in a monoculture, such as a corn residue field, to determine the plant parts predominating in the diet. Delineating plants in a complex sward was more difficult, particularly among like species. Th e use of more markers may help to more explicitly distinguish plants within diverse pastures, such as western rangelands

Limits on Clouds and Hazes for the TRAPPIST-1 Planets

The TRAPPIST-1 planetary system is an excellent candidate for study of the evolution and habitability of M-dwarf planets. Transmission spectroscopy observations performed with the Hubble Space Telescope (HST) suggest the innermost five planets do not possess clear hydrogen atmospheres. Here we reassess these conclusions with recently updated mass constraints and expand the analysis to include limits on metallicity, cloud top pressure, and the strength of haze scattering. We connect recent laboratory results of particle size and production rate for exoplanet hazes to a one-dimensional atmospheric model for TRAPPIST-1 transmission spectra. Doing so, we obtain a physically-based estimate of haze scattering cross sections. We find haze scattering cross sections on the order of 1e-26 to 1e-19 cm squared are needed in hydrogen-rich atmospheres for TRAPPIST-1 d, e, and f to match the HST data. For TRAPPIST-1 g, we cannot rule out a clear hydrogen-rich atmosphere. We also modeled the effects an opaque cloud deck and substantial heavy element content have on the transmission spectra. We determine that hydrogen-rich atmospheres with high altitude clouds, at pressures of 12mbar and lower, are consistent with the HST observations for TRAPPIST-1 d and e. For TRAPPIST-1 f and g, we cannot rule out clear hydrogen-rich cases to high confidence. We demonstrate that metallicities of at least 60xsolar with tropospheric (0.1 bar) clouds agree with observations. Additionally, we provide estimates of the precision necessary for future observations to disentangle degeneracies in cloud top pressure and metallicity. Our results suggest secondary, volatile-rich atmospheres for the outer TRAPPIST-1 planets d, e, and f.Comment: 15 pages, 3 figures, 2 tables, accepted in the Astronomical Journa

Chapter 18- Case Study of the Statewide Faculty-to-Student Mentoring Program at Utah State University

The purpose of this article is to examine an undergraduate mentorship program through Utah State University (USU). The creation of the Faculty-to-Student Mentorship Program originated in an attempt to increase both retention and graduation rates throughout the statewide system. In the first year, a steering committee was formed, and the mentorship program was piloted on one statewide campus—Uintah Basin. During the next year, the program was expanded to all eight statewide campuses. The steering committee examined available literature regarding existing mentorship programs and identified three shortcomings: lack of theoretical framework, operational definition, and methodological rigor. This article discusses the program design for the mentorship program in addressing these shortcomings while providing a step-by-step approach to mentorship. This includes purpose, funding, recruitment, mentoring objectives, and description of measurement instruments. The article concludes with a discussion of lessons learned and recommendations for future mentoring programs

Using Assessments to Promote Growth Mindset in College Algebra

Scientific evidence highlights the positive impact of a growth mindset on student achievement. Students with a growth mindset view errors and obstacles as opportunities for growth and welcome challenges and the opportunity to learn from their mistakes. Much has been written about promoting growth mindset through lectures and attitudes, however, assessments can also be an important avenue for encouraging a growth mindset in students. In this paper, we describe how we used assessments to promote growth mindset in a college algebra class. In the sections that follow, we discuss the need for these assessments and the principles that underly their development. We then describe the three-part structure of the assessments we created, how they were implemented, how feedback and scoring was addressed, and student response to them. This is a novel approach to assessment that promotes growth mindset and lowered anxiety levels as was shown in the student survey responses. This reframed how we looked at summative assessments and allowed us to introduce formative assessment elements, like reworks and group feedback, into many aspects of the summative assessments. Later research will be used to show more definitive results for the change in mindset of students

Age-Related Microaggressions: A Follow-Up Descriptive Study

Age-related microaggressions are forms of ageist discrimination that occur during day-to-day interactions. The aim of this study was to identify common types of age-related microaggressions as well as to determine how negative affect influences emotional reactions to microaggressions. Using an online survey, participants (n = 200) were asked if they had experienced any of the 20 most common examples of age-related microaggressions reported in previous research (Gietzen et al, 2022). Follow up questions inquired about the frequency, emotional reactions, and behavioral responses to these microaggressions. Participants also rated their physical health and completed the Positive and Negative Affect Scale (PANAS; Watson et al., 1988). The results indicated that participants were familiar with these microaggressions 53% of the time. Participants also reported having negative reactions to 43% of these microaggression. The frequency of negative emotional responses to microaggressions was significantly correlated with scores on the negative affect subscale of the PANAS (r = .34, p \u3c .001) and with ratings of perceived physical health (r = -.32, p = .002). Finally, an analysis of the 20 survey items revealed that two items were “highly impactful” microaggressions, defined as microaggressions that older adults reported experiencing often and reported having a negative emotional reaction to at least one third of the time. The results of the study provide further insight into what age-related microaggressions look like, and how older adults experience these interactions

Delineating Complex Forage Mixtures Using Plant-Wax Markers

Plant waxes provide a marker profile of individual plants that, when sufficiently distinct, can be used to estimate the diet composition of grazing cattle. They also may provide a tool for reliably predicting feed intake. The traditional method (nonnegative least squares) to use these markers to predict diet composition has limitations. A newer statistical approach (Bayesian linear unmixing) deemed more efficient was tested with simulation. Samples from 8 forage species in Nebraska were analyzed for their plant- wax marker contents. Those concentrations were used to simulate 1000 diets for 4 mixtures containing 2, 3, 5 or 8 plants. The efficiency of the two methods to predict diet composition was compared. The newer approach outperformed the traditional one in all of the mixtures considered. However, predictions were considerably worse when the number of plants in the mixture was 5 or 8. When forage mixtures are complex, additional steps will be needed to predict diet composition, and thereby feed intake, in grazing cattle

Using APOGEE Wide Binaries to Test Chemical Tagging with Dwarf Stars

Stars of a common origin are thought to have similar, if not nearly identical, chemistry. Chemical tagging seeks to exploit this fact to identify Milky Way subpopulations through their unique chemical fingerprints. In this work, we compare the chemical abundances of dwarf stars in wide binaries to test the abundance consistency of stars of a common origin. Our sample of 31 wide binaries is identified from a catalog produced by cross-matching APOGEE stars with UCAC5 astrometry, and we confirm the fidelity of this sample with precision parallaxes from Gaia DR2. For as many as 14 separate elements, we compare the abundances between components of our wide binaries, finding they have very similar chemistry (typically within 0.1 dex). This level of consistency is more similar than can be expected from stars with different origins (which show typical abundance differences of 0.3-0.4 dex within our sample). For the best measured elements, Fe, Si, K, Ca, Mn, and Ni, these differences are reduced to 0.05-0.08 dex when selecting pairs of dwarf stars with similar temperatures. Our results suggest that APOGEE dwarf stars may currently be used for chemical tagging at the level of $\sim$0.1 dex or at the level of $\sim$0.05 dex when restricting for the best-measured elements in stars of similar temperatures. Larger wide binary catalogs may provide calibration sets, in complement to open cluster samples, for on-going spectroscopic surveys.Comment: 21 pages, 14 figures, accepted for publication in Ap

High temperature condensate clouds in super-hot Jupiter atmospheres

Deciphering the role of clouds is central to our understanding of exoplanet atmospheres, as they have a direct impact on the temperature and pressure structure, and observational properties of the planet. Super-hot Jupiters occupy a temperature regime similar to low mass M-dwarfs, where minimal cloud condensation is expected. However, observations of exoplanets such as WASP-12b (Teq ~ 2500 K) result in a transmission spectrum indicative of a cloudy atmosphere. We re-examine the temperature and pressure space occupied by these super-hot Jupiter atmospheres, to explore the role of the initial Al- and Ti-bearing condensates as the main source of cloud material. Due to the high temperatures a majority of the more common refractory material is not depleted into deeper layers and would remain in the vapor phase. The lack of depletion into deeper layers means that these materials with relatively low cloud masses can become significant absorbers in the upper atmosphere. We provide condensation curves for the initial Al- and Ti-bearing condensates that may be used to provide quantitative estimates of the effect of metallicity on cloud masses, as planets with metal-rich hosts potentially form more opaque clouds because more mass is available for condensation. Increased metallicity also pushes the point of condensation to hotter, deeper layers in the planetary atmosphere further increasing the density of the cloud. We suggest that planets around metal-rich hosts are more likely to have thick refractory clouds, and discuss the implication on the observed spectra of WASP-12b.Comment: Accepted for publication in MNRAS, 10 pages, 1 table, 5 figure