Projective Cross-Ratio on Hypercomplex Numbers

The paper presents a new cross-ratio of hypercomplex numbers based on projective geometry. We discuss the essential properties of the projective cross-ratio, notably its invariance under Mobius transformations. Applications to the geometry of conic sections and Mobius-invariant metrics on the upper half-plane are also given

Kaluza-Klein Masses and Couplings: Radiative Corrections to Tree-Level Relations

The most direct experimental signature of a compactified extra dimension is the appearance of towers of Kaluza-Klein particles obeying specific mass and coupling relations. However, such masses and couplings are subject to radiative corrections. In this paper, using techniques developed in previous work, we investigate the extent to which such radiative corrections deform the expected tree-level relations between Kaluza-Klein masses and couplings. As toy models for our analysis, we investigate a flat five-dimensional scalar \lambda\phi^4 model and a flat five-dimensional Yukawa model involving both scalars and fermions. In each case, we identify the conditions under which the tree-level relations are stable to one-loop order, and the situations in which radiative corrections modify the algebraic forms of these relations. Such corrections to Kaluza-Klein spectra therefore have the potential to distort the apparent geometry of a large extra dimension.Comment: 34 pages, LaTeX, 12 figure

Differences in Mental Health and Ethnic-Racial Identity between White Gender Variant Students and Gender Variant Students of Color

Differences in Mental Health and Ethnic-Racial Identity between White Gender Variant Students and Gender Variant Students of Color Xuxa Sky Lark, Depts. of International Social Justice and French, Arlenis Santana, Dept. of Psychology Graduate Student, & Chloe Walker, Dept. of Psychology Graduate Student, with Dr. Diamond Y. Bravo, Dept. of Psychology, University of California, Riverside, and Dr. Chelsea Derlan Williams, Dr. Amy Adkins, and Dr. Danielle M. Dick, Dept. of Psychology Gender variant college students (i.e., transgender, genderqueer, and questioning) experience increased risk for mental health disparities, discrimination, bullying, family disownment, homelessness, and hate crimes, to name a few (Eisenberg, 2017). Further disparities arise when the intersections of gender and race are both considered; however, few studies have tested ethnic-racial identity (ERI) development among gender variant individuals (Kattari, 2016), which is predominantly tested in cisgender populations (e.g., Aoyagi et al, 2017; Umaña-Taylor et al., 2014). This is a notable gap given that ERI is a normative aspect of adolescence and emerging adulthood that is associated with positive development (Umaña-Taylor et al., 2014). Understanding ERI and mental health among diverse gender variant individuals is important to be able to create effective interventions and resources across ethnic-racial backgrounds that considers individuals’ unique lived experiences (Mossakowski, 2003). To address these gaps, the current study, grounded in the minority stress framework (Meyer, 2003) and ERI frameworks (Umaña-Taylor et al., 2014), tested differences in mental health (i.e., anxiety and depression) and ERI (i.e., exploration, resolution, and affirmation) between White gender variant students and gender variant students of color. The sample in the current study was from a larger university-wide study (i.e., Spit for Science; Dick et al., 2014), and consisted of 112 ethnically diverse gender variant students who identified as a White student (n = 72) or identified as a student of color (n = 40) in college. Students ranged in age from 18-24 years old (M = 20.15, SD = 1.61), and were 4.6% transgender women, 11.11% transgender men, 30.16% questioning, and 53.97% genderqueer. The Symptom Checklist 90-R (SCL-90-R; Derogatis & Cleary, 1977) was used to measure levels of depression and anxiety, and the Ethnic Identity Scale-Brief (EIS-B; Douglass & Umaña-Taylor, 2015) was used to assess ERI exploration, resolution, and affirmation. First, descriptive statistics were conducted to examine correlations among variables (Table 1). Next, hypotheses were tested with five t-tests that tested mean differences in mental health and ERI between gender variant White students and students of color. Findings indicated gender variant students of color (compared to White gender variant students) had significantly higher ERI exploration (t (107) = -6.49, p = .00), ERI affirmation (t (106) = -2.23, p = .03), and ERI resolution (t (106) = -5.61, p = .00). Although gender variant students of color had higher mean levels of anxiety and depression than White gender variant students, this difference was not significant (p \u3e .05). Discussion will center on how ERI may be a protective factor for gender identity-based risk factors among gender variant students of color, which will be a fruitful area for continued investigation and intervention efforts.https://scholarscompass.vcu.edu/uresposters/1318/thumbnail.jp