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The Arecibo Observatory (AO) is a multidisciplinary research and education facility that is recognized worldwide as a leading facility in astronomy, planetary, and atmospheric and space sciences. AO's cornerstone research instrument was the 305-m William E. Gordon telescope. On December 1, 2020, the 305-m telescope collapsed and was irreparably damaged. In the three weeks following the collapse, AO's scientific and engineering staff and the AO users community initiated extensive discussions on the future of the observatory. The community is in overwhelming agreement that there is a need to build an enhanced, next-generation radar-radio telescope at the AO site. From these discussions, we established the set of science requirements the new facility should enable. These requirements can be summarized briefly as: 5 MW of continuous wave transmitter power at 2 - 6 GHz, 10 MW of peak transmitter power at 430 MHz (also at 220MHz under consideration), zenith angle coverage 0 to 48 deg, frequency coverage 0.2 to 30 GHz and increased Field-of-View. These requirements determine the unique specifications of the proposed new instrument. The telescope design concept we suggest consists of a compact array of fixed dishes on a tiltable, plate-like structure with a collecting area equivalent to a 300m dish. This concept, referred to as the Next Generation Arecibo Telescope (NGAT), meets all of the desired specifications and provides significant new science capabilities to all three research groups at AO. This whitepaper presents a sample of the wide variety of the science that can be achieved with the NGAT, the details of the telescope design concept and the need for the new telescope to be located at the AO site. We also discuss other AO science activities that interlock with the NGAT in the white paper., Comment: 82 pages (executive summary 10 pages), 21 figures, Arecibo observatory white paper (Updated with the complete author list and minor edits)

We describe the arrival time measurements and timing modeling of the periodic radio flares and optical brightness variations of the M9 ultracool dwarf, TVLM 513-46546. We confirm the stability of the observed period and determine its best-fit value to be 7054.468(+/-)0.007 s over the last 7 years, based on both the new and archival radio observations and the archival optical data. The period, when measured separately for the radio flare and the optical periodicities, is the same to within (+/-)0.02 s. We show that the radio flares are out of phase with respect to the optical brightness maxima by 0.41(+/-)0.02 of the period. Our analysis also reveals that, on shorter timescales, the period varies with the amplitude of (+/-)1-2 s about its long-term average and that these variations are correlated between the radio and the optical wavelengths. These results provide further evidence that TVLM 513-46546 is equipped with a stable, approximately dipolar magnetic field which powers the activity of the star observed over a wide wavelength range, and that the active area has been maintaining its identity and positional stability over no less than 7 years. A stepwise decline of the apparent radio flaring period of TVLM 513-46546 deduced from timing observations with the Arecibo radio telescope in late 2012 and early 2013 suggests that this effect may be the manifestation of differential rotation of the star., Comment: Accepted for publication in ApJ; 11 pages, 4 figures, 1 table

Scenarios are developed for runs at a Linear Collider, in the case that there is a rich program of new physics., Comment: 12 pages, 10 tables, Latex; Snowmass 2001 plenary report