Poincare' inequalities for Sobolev spaces with matrix valued weights and applications to degenerate partial differential equations

For bounded domains Omega, we prove that the Lp-norm of a regular function with compact support is controlled by weighted Lp-norms of its gradient, where the weight belongs to a class of symmetric non-negative definite matrix valued functions. The class of weights is defined by regularity assumptions and structural conditions on the degeneracy set where the determinant vanishes. In particular, the weight A is assumed to have rank at least one when restricted to the normal bundle of the degeneracy set S This generalization of the classical Poincare' inequality is then applied to develop a robust theory of first order Lp-based Sobolev spaces with matrix valued weight A. The Poincare' inequality and these Sobolev spaces are then applied to produce various results on existence, uniqueness and qualitative properties of weak solutions to boundary value problems for degenerate elliptic, degenerate parabolic and degenerate hyperbolic PDEs of second order written in divergence form, where A is calibrated to the matrix of coefficients of the second order spatial derivatives. The notion of weak solution is variational in which the spatial states belong to the matrix weighted Sobolev spaces with p=2. For the degenerate elliptic PDEs, the Dirichlet problem is treated by the use of the Poincare' inequality and Lax-Milgram theorem, while the treatment of Cauchy-Dirichet problem for the degenerate evolution equations relies only on the Poincare' inequality and the parabolic and hyperbolic counterparts of the Lax-Milgram theorem

Multihospital Outbreak of a Middle East Respiratory Syndrome Coronavirus Deletion Variant, Jordan: A Molecular, Serologic, and Epidemiologic Investigation

Background An outbreak of Middle East respiratory syndrome coronavirus (MERS-CoV) in Jordan in 2015 involved a variant virus that acquired distinctive deletions in the accessory open reading frames. We conducted a molecular and seroepidemiologic investigation to describe the deletion variant’s transmission patterns and epidemiology. Methods We reviewed epidemiologic and medical chart data and analyzed viral genome sequences from respiratory specimens of MERS-CoV cases. In early 2016, sera and standardized interviews were obtained from MERS-CoV cases and their contacts. Sera were evaluated by nucleocapsid and spike protein enzyme immunoassays and microneutralization. Results Among 16 cases, 11 (69%) had health care exposure and 5 (31%) were relatives of a known case; 13 (81%) were symptomatic, and 7 (44%) died. Genome sequencing of MERS-CoV from 13 cases revealed 3 transmissible deletions associated with clinical illness during the outbreak. Deletion variant sequences were epidemiologically clustered and linked to a common transmission chain. Interviews and sera were collected from 2 surviving cases, 23 household contacts, and 278 health care contacts; 1 (50%) case, 2 (9%) household contacts, and 3 (1%) health care contacts tested seropositive. Conclusions The MERS-CoV deletion variants retained human-to-human transmissibility and caused clinical illness in infected persons despite accumulated mutations. Serology suggested limited transmission beyond that detected during the initial outbreak investigation

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society

Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run

Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available

Search for gravitational-wave transients associated with magnetar bursts in advanced LIGO and advanced Virgo data from the third observing run

Gravitational waves are expected to be produced from neutron star oscillations associated with magnetar giant f lares and short bursts. We present the results of a search for short-duration (milliseconds to seconds) and longduration (∼100 s) transient gravitational waves from 13 magnetar short bursts observed during Advanced LIGO, Advanced Virgo, and KAGRA’s third observation run. These 13 bursts come from two magnetars, SGR1935 +2154 and SwiftJ1818.0−1607. We also include three other electromagnetic burst events detected by FermiGBM which were identified as likely coming from one or more magnetars, but they have no association with a known magnetar. No magnetar giant flares were detected during the analysis period. We find no evidence of gravitational waves associated with any of these 16 bursts. We place upper limits on the rms of the integrated incident gravitational-wave strain that reach 3.6 × 10−²³ Hz at 100 Hz for the short-duration search and 1.1 ×10−²² Hz at 450 Hz for the long-duration search. For a ringdown signal at 1590 Hz targeted by the short-duration search the limit is set to 2.3 × 10−²² Hz. Using the estimated distance to each magnetar, we derive upper limits upper limits on the emitted gravitational-wave energy of 1.5 × 1044 erg (1.0 × 1044 erg) for SGR 1935+2154 and 9.4 × 10^43 erg (1.3 × 1044 erg) for Swift J1818.0−1607, for the short-duration (long-duration) search. Assuming isotropic emission of electromagnetic radiation of the burst fluences, we constrain the ratio of gravitational-wave energy to electromagnetic energy for bursts from SGR 1935+2154 with the available fluence information. The lowest of these ratios is 4.5 × 103

Open data from the third observing run of LIGO, Virgo, KAGRA, and GEO

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages

A joint Fermi-GBM and Swift-BAT analysis of gravitational-wave candidates from the third gravitational-wave observing run

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) searches for gamma-ray/X-ray counterparts to gravitational-wave (GW) candidate events identified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using Fermi-GBM onboard triggers and subthreshold gamma-ray burst (GRB) candidates found in the Fermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether there are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data around the GW times to determine whether a GRB counterpart is present. No counterparts are found. Using both the Fermi-GBM Targeted Search and the Swift-BAT search, we calculate flux upper limits and present joint upper limits on the gamma-ray luminosity of each GW. Given these limits, we constrain theoretical models for the emission of gamma rays from binary black hole mergers