Transforms for minimal surfaces in the 5-sphere.

We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how to associate to such a surface a corresponding ruled minimal Lagrangian submanifold of complex projective 3-space, which gives the converse of a construction considered in a previous paper, and illustrate this explicitly in the case of bipolar minimal surfaces

Explorations in price (un)fairness.

Consumers may use multiple reference points-including cost of goods, past prices, and competitive prices-to judge price fairness. Across a series of studies we show that consumers are inclined to overestimate profits, often to an extreme extent. We further demonstrate that prices are perceived to be unfair because consumers fail to take into account vendor costs, underestimate the effects of inflation, and attribute competitive price differences to profits. Potential corrective interventions by marketers-such as cueing costs, providing historical price information, and explaining price differences-were insufficient to eliminate unfairness perceptions. In addition, prices for goods were found to be stickier than prices for services and therefore were especially susceptible to these systematic perceptions of unfairness.Prices; Studies; Costs; Effects;

The Structure & Dynamics of Massive Early-type Galaxies: On Homology, Isothermality and Isotropy inside one Effective Radius

Based on 58 SLACS strong-lens early-type galaxies with direct total-mass and stellar-velocity dispersion measurements, we find that inside one effective radius massive elliptical galaxies with M_eff >= 3x10^10 M_sun are well-approximated by a power-law ellipsoid with an average logaritmic density slope of = -dlog(rho_tot)/dlog(r)=2.085^{+0.025}_{-0.018} (random error on mean) for isotropic orbits with beta_r=0, +-0.1 (syst.) and sigma_gamma' <= 0.20^{+0.04}_{-0.02} intrinsic scatter (all errors indicate the 68 percent CL). We find no correlation of gamma'_LD with galaxy mass (M_eff), rescaled radius (i.e. R_einst/R_eff) or redshift, despite intrinsic differences in density-slope between galaxies. Based on scaling relations, the average logarithmic density slope can be derived in an alternative manner, fully independent from dynamics, yielding =1.959 +- 0.077. Agreement between the two values is reached for =0.45 +- 0.25, consistent with mild radial anisotropy. This agreement supports the robustness of our results, despite the increase in mass-to-light ratio with total galaxy mass: M_eff ~ L_{V,eff}^(1.363+-0.056). We conclude that massive early-type galaxies are structurally close-to homologous with close-to isothermal total density profiles (<=10 percent intrinsic scatter) and have at most some mild radial anisotropy. Our results provide new observational limits on galaxy formation and evolution scenarios, covering four Gyr look-back time.Comment: Accepted for publication by ApJL; 4 pages, 2 figure

The Sloan Lens ACS Survey. IX. Colors, Lensing and Stellar Masses of Early-type Galaxies

We present the current photometric dataset for the Sloan Lens ACS (SLACS) Survey, including HST photometry from ACS, WFPC2, and NICMOS. These data have enabled the confirmation of an additional 15 grade `A' (certain) lens systems, bringing the number of SLACS grade `A' lenses to 85; including 13 grade `B' (likely) systems, SLACS has identified nearly 100 lenses and lens candidates. Approximately 80% of the grade `A' systems have elliptical morphologies while ~10% show spiral structure; the remaining lenses have lenticular morphologies. Spectroscopic redshifts for the lens and source are available for every system, making SLACS the largest homogeneous dataset of galaxy-scale lenses to date. We have developed a novel Bayesian stellar population analysis code to determine robust stellar masses with accurate error estimates. We apply this code to deep, high-resolution HST imaging and determine stellar masses with typical statistical errors of 0.1 dex; we find that these stellar masses are unbiased compared to estimates obtained using SDSS photometry, provided that informative priors are used. The stellar masses range from 10^10.5 to 10^11.8 M$_\odot$ and the typical stellar mass fraction within the Einstein radius is 0.4, assuming a Chabrier IMF. The ensemble properties of the SLACS lens galaxies, e.g. stellar masses and projected ellipticities, appear to be indistinguishable from other SDSS galaxies with similar stellar velocity dispersions. This further supports that SLACS lenses are representative of the overall population of massive early-type galaxies with M* >~ 10^11 M$_\odot$, and are therefore an ideal dataset to investigate the kpc-scale distribution of luminous and dark matter in galaxies out to z ~ 0.5.Comment: 20 pages, 18 figures, 5 tables, published in Ap

Non-Traditional Middle School Programs in the Rochester Area

The purpose of this study was to develop the characteristics of the non-traditional middle school programs in the Rochester area. Three programs were investigated, then compared to the literature for similarities. The programs were also compared to each other for similarities and differences. Student, parent, teacher, and administrator surveys were conducted at all three programs. A considerable amount of data was collected. Students were asked: why were they in the program, what and how did they learn, their favorite way of learning and what would they like to learn more about. Parents were asked: why is your child in the program; what skills should students learn in school and how are students graded. Teacher were asked: how they became involved in the program, how do they assess students and what did their curriculum consists of. Administrators were interviewed and gave the history and an overview of their program. All surveys asked each person\u27s feelings about their school\u27s program. Two of the three schools fit both models and improvements called for in the literature. The third school is also making many of the improvements called for in the literature. All of the programs investigated have strengths, and are models of an improved traditional educational system

Abstracts from Spring 2019 Research and Creative Activities Day Presentations

This is a summary of abstracts from the poster and oral presentations made by undergraduate students during Research and Creative Activities Day at West Chester University in April of 2019. The abstracts describe research and creative activities that the students conducted in collaboration with their faculty mentors who are listed with the abstracts. For more information about the study or the creative activity, please contact the mentor directly using the contact email address. Student Authors Included: Emily Rodden, Alissa Grady, Joyce Pour-Azar, Lauren Stricker, MacKenzie Holm, Samantha Bobst, Joelle Buenaventura, Julianne Duko, Angel Jacabella, Taylor Stuart, Liam Pierson, Kathleen Shultz, Amanda Johnston, Justin Gibson, Taylor Potts-Gordon, Sofia Vanderhyde, Ryan Manzo, Natha Helfrick, Olivia King, Rebecca Burr, Mary Ann Blumenthal, Zachary Weaver, Keriann Mosley, Alyssa Allen, Dominique McQuade, Amelia Oberholtzer, Jacquelyn Redmond, Terrence Riley, Kelly O’Donnell, Megan Ray, James Palmer, Tiffany Kennedy, Samantha Walsh, Kateri Sload, Colin Mancini, Erin Walsh, Ali Donohue, Ashley Nielsen, Adam Vanluvanee, Rebecca Spackman, Jenna Cummings, Garrett Compton, James Devor, Emily Feldman, Brady Barley, and Cassidy Tennit

B2 and G2 Toda systems on compact surfaces: a variational approach

We consider the B2 and G2 Toda systems on compact surfaces. We attack the problem using variational techniques. We get existence and multiplicity of solutions under a topological assumption on the surface and some generic conditions on the parameters. We also extend some of the results to the case of general systems.Comment: 28 pages, accepted on Journal of Mathematical Physic