UNOmaha Problem of the Week (2021-2022 Edition)

The University of Omaha math department\u27s Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester\u27s end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes. Now there are three difficulty tiers to POW problems, roughly corresponding to easy/medium/hard difficulties, with each tier getting twelve problems per semester, and three problems (one of each tier) per week posted online and around campus. The tiers are named after the EPH classification of conic sections (which is connected to many other classifications in math), and in the present compilation they abide by the following color-coding: Cyan, Green, and Magenta. In practice, when creating the problem sets, we begin with a large enough pool of problem drafts and separate out the ones which are most obviously elliptic or hyperbolic, and then the remaining ones fall into parabolic. The tiers don\u27t necessarily reflect workload, though, only prerequisite mathematical background. Ideally, the solutions to elliptic problems, and any parts of solutions to parabolic and hyperbolic problems not covered in standard undergraduate courses, are meant to test participants\u27 creativity. Beware, though, many solutions also include additional commentary which varies wildly in the reader\u27s assumed mathematical maturity

Problem of the Week: A Student-Led Initiative to Bring Mathematics to a Broader Audience

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy engagement and praise from participants and observers

Understanding Super-Earths with MINERVA-Australis at USQ's Mount Kent Observatory

Super Earths, planets between 5-10 Earth masses, are the most common type of exoplanet known, yet are completely absent from our Solar system. As a result, their detailed properties, compositions, and formation mechanisms are poorly understood. NASA's Transiting Exoplanet Survey Satellite (TESS) will identify hundreds of Super-Earths orbiting bright stars, for the first time allowing in-depth characterisation of these planets. At the University of Southern Queensland, we are host to the MINERVA-Australis project, dedicated wholly to the follow-up characterisation and mass measurement of TESS planets. We give an update on the status of MINERVA-Australis and our expected performance.Comment: Accepted to appear in the peer-reviewed proceedings of the 17th Australian Space Research Conference, held at the University of Sydney, 13th-15th November, 201

Detection of Planetary and Stellar Companions to Neighboring Stars via a Combination of Radial Velocity and Direct Imaging Techniques

13 pages, 6 figures, 4 tables, accepted for publication in the Astronomical Journal (submitted 25 Feb 2019; accepted 28 April 2019). Machine readable tables and Posteriors from the RadVel fits are available here: http://stephenkane.net/rvfits.tarThe sensitivities of radial velocity (RV) surveys for exoplanet detection are extending to increasingly longer orbital periods, where companions with periods of several years are now being regularly discovered. Companions with orbital periods that exceed the duration of the survey manifest in the data as an incomplete orbit or linear trend, a feature that can either present as the sole detectable companion to the host star, or as an additional signal overlain on the signatures of previously discovered companion(s). A diagnostic that can confirm or constrain scenarios in which the trend is caused by an unseen stellar rather than planetary companion is the use of high-contrast imaging observations. Here, we present RV data from the Anglo-Australian Planet Search (AAPS) for 20 stars that show evidence of orbiting companions. Of these, six companions have resolved orbits, with three that lie in the planetary regime. Two of these (HD 92987b and HD 221420b) are new discoveries. Follow-up observations using the Differential Speckle Survey Instrument (DSSI) on the Gemini South telescope revealed that 5 of the 20 monitored companions are likely stellar in nature. We use the sensitivity of the AAPS and DSSI data to place constraints on the mass of the companions for the remaining systems. Our analysis shows that a planetary-mass companion provides the most likely self-consistent explanation of the data for many of the remaining systems.Peer reviewedFinal Accepted Versio

Astrocladistics of the Jovian Trojan swarms

The Jovian Trojans are two swarms of small objects that share Jupiter's orbit, clustered around the leading and trailing Lagrange points, L4 and L5. In this work, we investigate the Jovian Trojan population using the technique of astrocladistics, an adaptation of the 'tree of life' approach used in biology. We combine colour data from WISE, SDSS, Gaia DR2, and MOVIS surveys with knowledge of the physical and orbital characteristics of the Trojans, to generate a classification tree composed of clans with distinctive characteristics. We identify 48 clans, indicating groups of objects that possibly share a common origin. Amongst these are several that contain members of the known collisional families, though our work identifies subtleties in that classification that bear future investigation. Our clans are often broken into subclans, and most can be grouped into 10 superclans, reflecting the hierarchical nature of the population. Outcomes from this project include the identification of several high priority objects for additional observations and as well as providing context for the objects to be visited by the forthcoming Lucy mission. Our results demonstrate the ability of astrocladistics to classify multiple large and heterogeneous composite survey data sets into groupings useful for studies of the origins and evolution of our Solar system

Age at disability onset and self-reported health status

Background: The critical importance of improving the well-being of people with disabilities is highlighted in many national health plans. Self-reported health status is reduced both with age and among people with disabilities. Because both factors are related to health status and the influence of the age at disability onset on health status is unclear, we examined the relationship between disability onset and health status. Methods: The U.S. 1998–2000 Behavioral Risk Factor Surveillance system (BRFSS) provided data on 11,905 adults with disability. Bivariate logistic regression analysis modeled the relationship between age at disability onset (based on self-report of duration of disability) and fair/poor self-perceived health status, adjusting for confounding variables. Results: Key variables included demographics and other measures related to disability and general health status. Disability onset after 21 years of age showed significant association with greater prevalence of fair/poor health compared to early disability onset, even adjusting for current age and other demographic covariates. Compared with younger onset, the adjusted odds ratios (OR) were ages 22–44: OR 1.52, ages 45–64: OR 1.67, and age ≥65: OR 1.53. Conclusion: This cross-sectional study provides population-level, generalizable evidence of increased fair or poor health in people with later onset disability compared to those with disability onset prior to the age of 21 years. This finding suggests that examining the general health of people with and those without disabilities might mask differences associated with onset, potentially relating to differences in experience and self-perception. Future research relating to global health status and disability should consider incorporating age at disability onset. In addition, research should examine possible differences in the relationship between age at onset and self-reported health within specific impairment groups.This is the publisher’s final pdf. The published article is copyrighted by BioMed Central Ltd. and can be found at: http://www.biomedcentral.com/bmcpublichealth

The GALAH survey: using galactic archaeology to refine our knowledge of TESS target stars

An unprecedented number of exoplanets are being discovered by the Transiting Exoplanet Survey Satellite (TESS). Determining the orbital parameters of these exoplanets, and especially their mass and radius, will depend heavily upon the measured physical characteristics of their host stars. We have cross-matched spectroscopic, photometric, and astrometric data from GALAH Data Release 2, the TESS Input Catalog and Gaia Data Release 2, to create a curated, self-consistent catalogue of physical and chemical properties for 47 285 stars. Using these data, we have derived isochrone masses and radii that are precise to within 5 per cent. We have revised the parameters of three confirmed, and twelve candidate, TESS planetary systems. These results cast doubt on whether CTOI-20125677 is indeed a planetary system, since the revised planetary radii are now comparable to stellar sizes. Our GALAH-TESS catalogue contains abundances for up to 23 elements. We have specifically analysed the molar ratios for C/O, Mg/Si, Fe/Si, and Fe/Mg, to assist in determining the composition and structure of planets with Rp < 4R⊕. From these ratios, 36 per cent fall within 2$\sigma$ sigma of the Sun/Earth values, suggesting that these stars may host rocky exoplanets with geological compositions similar to planets found within our own Solar system

Transits of Known Planets Orbiting a Naked-Eye Star

© 2020 The American Astronomical Society. All rights reserved.Some of the most scientifically valuable transiting planets are those that were already known from radial velocity (RV) surveys. This is primarily because their orbits are well characterized and they preferentially orbit bright stars that are the targets of RV surveys. The Transiting Exoplanet Survey Satellite (TESS) provides an opportunity to survey most of the known exoplanet systems in a systematic fashion to detect possible transits of their planets. HD 136352 (Nu2 Lupi) is a naked-eye (V = 5.78) G-type main-sequence star that was discovered to host three planets with orbital periods of 11.6, 27.6, and 108.1 days via RV monitoring with the High Accuracy Radial velocity Planet Searcher (HARPS) spectrograph. We present the detection and characterization of transits for the two inner planets of the HD 136352 system, revealing radii of 1.482-0.056+0.058 R ⊕ and 2.608-0.077+0.078 R ⊕ for planets b and c, respectively. We combine new HARPS observations with RV data from the Keck/High Resolution Echelle Spectrometer and the Anglo-Australian Telescope, along with TESS photometry from Sector 12, to perform a complete analysis of the system parameters. The combined data analysis results in extracted bulk density values of ρb = 7.8-1.1+1.2 g cm-3 and ρc = 3.50-0.36+0.41 g cm-3 for planets b and c, respectively, thus placing them on either side of the radius valley. The combination of the multitransiting planet system, the bright host star, and the diversity of planetary interiors and atmospheres means this will likely become a cornerstone system for atmospheric and orbital characterization of small worlds.Peer reviewe