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In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the convergence rate and some convergence conditions including the case that the coefficient matrix is rank deficient. By varying three parameters in the new method and convergence theorems, the new method recovers an array of well-known algorithms and their convergence results. Meanwhile, with the use of Gaussian sampling, we can obtain the Gaussian global randomized Kaczmarz (GaussGRK) method which shows some advantages in solving the matrix equation AXB = C. Finally, numerical experiments are given to illustrate the effectiveness of recovered methods., Comment: arXiv admin note: text overlap with arXiv:1506.03296, arXiv:1612.06013, arXiv:2204.13920 by other authors

In this paper, several Kaczmarz-type numerical methods for solving the matrix equation $AX=B$ and $XA=C$ are proposed, where the coefficient matrix $A$ may be full rank or rank deficient. These methods are iterative methods without matrix multiplication. Theoretically, the convergence of these methods is proved. The numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrices., Comment: arXiv admin note: text overlap with arXiv:2305.16684

Fast and reliable localization of high-energy transients is crucial for characterizing the burst properties and guiding the follow-up observations. Localization based on the relative counts of different detectors has been widely used for all-sky gamma-ray monitors. There are two major methods for this counts distribution localization: $\chi^{2}$ minimization method and the Bayesian method. Here we propose a modified Bayesian method that could take advantage of both the accuracy of the Bayesian method and the simplicity of the $\chi^{2}$ method. With comprehensive simulations, we find that our Bayesian method with Poisson likelihood is generally more applicable for various bursts than $\chi^{2}$ method, especially for weak bursts. We further proposed a location-spectrum iteration approach based on the Bayesian inference, which could alleviate the problems caused by the spectral difference between the burst and location templates. Our method is very suitable for scenarios with limited computation resources or time-sensitive applications, such as in-flight localization software, and low-latency localization for rapid follow-up observations.

Recently, the gapless Dirac/Weyl nodal semimetals with linear dispersion and topologically protected modes degeneracy are rapidly growing frontiers of topological physics. Especially, type-I, type-II, and critical type-III nodal semimetals are discovered according to the tilt angles of the Dirac/Weyl cones. Here, by introducing hyperbolic metamaterials into one-dimensional photonic crystals, we design the "hyper-crystal" and study the photonic four-fold degenerate Dirac nodal line semimetals (DNLSs) with two types of perpendicularly polarized waves. Moreover, the flexibly controlled photonic DNLSs using the phase compensation effect of hyperbolic dispersion are studied. Our results not only demonstrate a new platform to realize the various photonic DNLSs, where the optical polarization plays the role of electron spin in electronic DNLSs, but also may pave a novel way to explore the abundant Dirac/Weyl physics in the simple classical wave systems., Comment: 31 pages, 14 figures

Since April 28, 2020, Insight-HXMT has implemented a dedicated observation on the magnetar SGR J1935+2154. Thanks to the wide energy band (1-250 keV) and high sensitivity of Insight-HXMT, we obtained 75 bursts from SGR J1935+2154 during a month-long activity episode after the emission of FRB 200428. Here, we report the detailed time-integrated spectral analysis of these bursts and the statistical distribution of the spectral parameters. We find that for 15%(11/75) of SGR J1935+2154 bursts, the CPL model is preferred, and most of them occurred in the latter part of this active epoch. In the cumulative fluence distribution, we find that the fluence of bursts in our sample is about an order of magnitude weaker than that of Fermi/GBM, but follows the same power law distribution. Finally, we find a burst with similar peak energy to the time-integrated spectrum of the X-ray burst associated with FRB 200428 (FRB 200428-Associated Burst), but the low energy index is harder., Comment: 35 pages, 20 figures, accepted for publication in ApJS

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 ApJS

The growth model of black hole is still a controversial topic. In the stationary metric, all in-falling matter must be accumulated outside the event horizon of the black hole, as clocked by a distant external observer. In the time-dependent metric, all in-falling matter can fall into the event horizon of the final black hole within very short time. We test these two growth models by joining LIGO and Insight-HXMT observations. We find the stationary model is inconsistent with LIGO and Insight-HXMT observations., Comment: 6 pages