A central problem in convex algebra is the extension of left-smooth functions. Let $$ be a combinatorially right-multiplicative, ordered, standard function. We show that ℓI, Λ ∋ 𝒴U, 𝔳 and that there exists a Taylor and positive definite sub-algebraically projective triangle. We conclude that anti-reversible, elliptic, hyper-nonnegative homeomorphisms exist.
OVERVIEW: The Very Large Array Sky Survey (VLASS) is an all-sky radio sky survey approved for the recently upgraded Karl G. Jansky Very Large Array (VLA). The community-driven project is designed to address a broad range of topics with high scientific impact, while remaining open to serendipitous science. Raw data from VLASS will be non-proprietary, and basic science data products will be provided by NRAO in a timely manner. However, many compelling science applications require enhanced data products beyond NRAO’s mandate. Here we seek support for a broad collaboration of radio astronomers to (1) produce these enhanced data products and (2) use IRSA/IPAC to host the archive and develop tools for queries, source identification, and association. The proposed project will leverage the large NRAO and NSF investment in the VLASS and strengthen the connection between radio astronomy and the broader astronomical community. INTELLECTUAL MERIT: Despite the proliferation of new radio interferometers, the VLA has maintained a uniquely powerful set of capabilities: high-resolution imaging, exquisite point-source sensitivity, wide bandwidth spectro-polarimetry, and rapid (“on-the-fly”) survey capabilities. The upgraded capabilities of the VLA allow, and even demand, a new exploration of the radio sky in time and spectral domains. The all-sky (δ > −40◦) coverage, 2–4 GHz band, and high (2.500) resolution, will make VLASS the new gold standard for multi-wavelength counterpart matching across radio, optical, X-ray and infra-red bands. The novelty of the VLASS is most evident in its application to the transient and polarized radio sky. However, many data products applicable to these science cases require additional support to produce. As a transient survey platform, the VLASS will be hugely sensitive and highly efficient at identifying novel transients. This requires more rapid data reduction than for standard products and a process for distributing alerts to the community that will drive follow up of, e.g., tidal disruption events, radio supernovae, and potentially, orphan gammma-ray burst afterglows. The wide bandwidth, full Stokes imaging will be sensitive to the magneto-ionic medium of AGNs and galaxies across a range of redshifts, particularly classes of objects that have suffered from depolarization in earlier, lower-frequency surveys. The high point-source sensitivity will produce a densely-sampled grid of polarized sources to measure magnetic fields in our own Galaxy, which serves as a laboratory for the studying magnetic field emergence and amplification. The proposal seeks support to host data and apply tools from IRSA/IPAC to the VLASS images and catalogs. These tools will enable systematic band-merging and multiwavelength associations that are critical to achieving a wide range of science goals, from statistical tests of radio galaxy evolution to identifying candidate planetary nebulae and millisecond pulsars. IRSA/IPAC will also simplify access to a broader community of astronomers by using standardized interfaces to the radio source catalog. BROADER IMPACTS: This proposal will use a variety of approaches to broaden its reach into underrepresented groups and to bring students into the direct practice of modern astronomy. We draw from past successful programs, such as the Pulsar Search Collaboratory, and aim for broad participation by lowering barriers to entry with user friendly products and software. Some types of problems, such as source classification, are easily adaptable for citizen scientists and will build on NRAO involvement in the Radio Galaxy Zoo citizen science project. The very nature of an all-sky imaging survey and real-time processing lends itself to visualizations that can be shared with the public rapidly to convey the dynamic nature of the field. The development of enhanced data products that can be easily queried and connected to other large surveys will engage radio astronomy experts, multi-wavelength astronomers, and citizen scientists alike, leaving a lasting legacy value for decades to come.