On the dynamics of a class of nonclassical parabolic equations

AbstractWe consider the first initial and boundary value problem of nonclassical parabolic equations ut−μΔut−Δu+g(u)=f(x) on a bounded domain Ω, where μ∈[0,1]. First, we establish some uniform decay estimates for the solutions of the problem which are independent of the parameter μ. Then we prove the continuity of solutions as μ→0. Finally we show that the problem has a unique global attractor Aμ in V2=H2(Ω)∩H01(Ω) in the topology of H2(Ω); moreover, Aμ→A0 in the sense of Hausdorff semidistance in H01(Ω) as μ goes to 0

Burst phase distribution of SGR J1935+2154 based on Insight-HXMT

On April 27, 2020, the soft gamma ray repeater SGR J1935+2154 entered its intense outburst episode again. Insight-HXMT carried out about one month observation of the source. A total number of 75 bursts were detected during this activity episode by Insight-HXMT, and persistent emission data were also accumulated. We report on the spin period search result and the phase distribution of burst start times and burst photon arrival times of the Insight-HXMT high energy detectors and Fermi Gamma-ray Burst Monitor (GBM). We find that the distribution of burst start times is uniform within its spin phase for both Insight-HXMT and Fermi-GBM observations, whereas the phase distribution of burst photons is related to the type of a burst's energy spectrum. The bursts with the same spectrum have different distribution characteristics in the initial and decay episodes for the activity of magnetar SGR J1935+2154.Comment: 12 pages, 9 figure

Constraining the X-ray - Infrared spectral index of second-timescale flares from SGR1935+2154 with Palomar Gattini-IR

The Galactic magnetar SGR1935+2154 has been reported to produce the first known example of a bright millisecond duration radio burst (FRB 200428) similar to the cosmological population of fast radio bursts (FRBs), bolstering the association of FRBs to active magnetars. The detection of a coincident bright X-ray burst has revealed the first observed multi-wavelength counterpart of a FRB. However, the search for similar emission at optical wavelengths has been hampered by the high inferred extinction on the line of sight. Here, we present results from the first search for second-timescale emission from the source at near-infrared wavelengths using the Palomar Gattini-IR observing system in J-band, made possible by a recently implemented detector read-out mode that allowed for short exposure times of 0.84 s with 99.9% observing efficiency. With a total observing time of 12 hours (47728 images) on source, we place median $3\,\sigma$ limits on the second-timescale emission of $< 20$ mJy (13.1 AB mag). We present non-detection limits from epochs of four simultaneous X-ray bursts detected by the Insight-{\it HXMT} and {\it NuSTAR} telescopes during our observing campaign. The limits translate to an extinction corrected fluence limit of $< 125$ Jy ms for an estimated extinction of $A_J = 2.0$ mag. These limits provide the most stringent constraints to date on the fluence of flares at frequencies of $\sim 10^{14}$ Hz, and constrain the ratio of the near-infrared (NIR) fluence to that of coincident X-ray bursts to $R_{\rm NIR} < 2.5 \times 10^{-2}$. Our observations were sensitive enough to easily detect a near-infrared counterpart of FRB 200428 if the NIR emission falls on the same power law as that observed across its radio to X-ray spectrum. The non-detection of NIR emission around the coincident X-ray bursts constrains the fluence index of the brightest burst to be steeper than $0.35$.Comment: 10 pages, 4 figures, submitted to ApJL. Comments welcom

Comparison of curative effect between OBS assisted by 3D printing and PFNA in the treatment of AO/OTA type 31-A3 femoral intertrochanteric fractures in elderly patients

ObjectiveTo compare and analyze the Ortho-Bridge System (OBS) clinical efficacy assisted by 3D printing and proximal femoral nail anti-rotation (PFNA) of AO/OTA type 31-A3 femoral intertrochanteric fractures in elderly patients.MethodsA retrospective analysis of 25 elderly patients diagnosed with AO/OTA type 31-A3 femoral intertrochanteric fracture was conducted from January 2020 to August 2022 at Yan’an Hospital, affiliated to Kunming Medical University. The patients were divided into 10 patients in the OBS group and 15 in the PFNA group according to different surgical methods. The OBS group reconstructed the bone models and designed the guide plate by computer before the operation, imported the data of the guide plate and bone models into a stereolithography apparatus (SLA) 3D printer, and printed them using photosensitive resin, thus obtaining the physical object, then simulating the operation and finally applying the guide plate to assist OBS to complete the operation; the PFNA group was treated by proximal femoral nail anti-rotation. The operation time, the intraoperative blood loss, Harris hip score (HHS), Oxford Hip Score (OHS), and complications were compared between the two groups.ResultsThe operation time and the intraoperative blood loss in the PFNA group were less than that in the OBS group, and there was a significant difference between the two groups (P &lt; 0.05). The HHS during the 6th month using OBS was statistically higher than PFNA (P &lt; 0.05), however, there were no significant differences in OHS during the 6th month between the OBS group and PFNA group (P &gt; 0.05). The HHS and OHS during the 12th month in the OBS group were statistically better than in the PFNA group (P &lt; 0.05).ConclusionThe OBS assisted by 3D printing and PFNA are effective measures for treating intertrochanteric fractures. Prior to making any decisions regarding internal fixation, it is crucial to evaluate the distinct circumstances of each patient thoroughly

Insight-HXMT dedicated 33-day observation of SGR J1935+2154 I. Burst Catalog

Magnetars are neutron stars with extreme magnetic field and sometimes manifest as soft gamma-ray repeaters (SGRs). SGR J1935+2154 is one of the most prolific bursters and the first confirmed source of fast radio burst (i.e. FRB 200428). Encouraged by the discovery of the first X-ray counterpart of FRB, Insight-Hard X-ray Modulation Telescope (Insight-HXMT) implemented a dedicated 33-day long ToO observation of SGR J1935+2154 since April 28, 2020. With the HE, ME, and LE telescopes, Insight-HXMT provides a thorough monitoring of burst activity evolution of SGR J1935+2154, in a very broad energy range (1-250 keV) with high temporal resolution and high sensitivity, resulting in a unique valuable data set for detailed studies of SGR J1935+2154. In this work, we conduct a comprehensive analysis of this observation including detailed burst search, identification and temporal analyses. After carefully removing false triggers, we find a total of 75 bursts from SGR J1935+2154, out of which 70 are single-pulsed. The maximum burst rate is about 56 bursts/day. Both the burst duration and the waiting time between two successive bursts follow log-normal distributions, consistent with previous studies. We also find that bursts with longer duration (some are multi-pulsed) tend to occur during the period with relatively high burst rate. There is no correlation between the waiting time and the fluence or duration of either the former or latter burst. It also seems that there is no correlation between burst duration and hardness ratio, in contrast to some previous reports. In addition, we do not find any X-ray burst associated with any reported radio bursts except for FRB 200428.Comment: 31 pages, 10 figures, accepted for publication in ApJ

Insight-HXMT observations of Swift J0243.6+6124 during its 2017-2018 outburst

The recently discovered neutron star transient Swift J0243.6+6124 has been monitored by {\it the Hard X-ray Modulation Telescope} ({\it Insight-\rm HXMT). Based on the obtained data, we investigate the broadband spectrum of the source throughout the outburst. We estimate the broadband flux of the source and search for possible cyclotron line in the broadband spectrum. No evidence of line-like features is, however, found up to $\rm 150~keV$. In the absence of any cyclotron line in its energy spectrum, we estimate the magnetic field of the source based on the observed spin evolution of the neutron star by applying two accretion torque models. In both cases, we get consistent results with $B\rm \sim 10^{13}~G$, $D\rm \sim 6~kpc$ and peak luminosity of $\rm >10^{39}~erg~s^{-1}$ which makes the source the first Galactic ultraluminous X-ray source hosting a neutron star.Comment: publishe