Gravitational resonances on f(R)f(R)-brane

In this paper, we investigate various $f(R)$-brane models and compare their gravitational resonance structures with the corresponding general relativity (GR)-branes. {Starting from some known GR-brane solutions}, we derive thick $f(R)$-brane solutions such that the metric, scalar field, and scalar potential coincide with those of the corresponding GR-branes. {We find that for branes generated by a single or several canonical scalar fields, there is no obvious distinction between the GR-branes and corresponding $f(R)$-branes in terms of gravitational resonance structure.} Then we discuss the branes generated by K-fields. In this case, there could exist huge differences between GR-branes and $f(R)$-branes.Comment: 17 pages, 14 figures, published versio

Full linear perturbations and localization of gravity on f(R,T)f(R,T) brane

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. We try to get the analytic background solutions and discuss the full linear perturbations, especially the scalar perturbations. We compare how the brane world model is modified with that of general relativity coupled to a canonical scalar field. It is found that some more interesting background solutions are allowed, and only the scalar perturbation mode is modified. There is no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.Comment: v3: 8 pages, 2 figures, improved version with minor corrections, accepted by EPJ

One-off and Repeating Fast Radio Bursts: A Statistical Analysis

According to the number of detected bursts, fast radio bursts (FRBs) can be classified into two categories, i.e., one-off FRBs and repeating ones. We make a statistical comparison of these two categories based on the first FRB catalog of the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst Project. Using the Anderson-Darling, Kolmogrov-Smirnov, and Energy statistic tests, we find significant statistical differences ($p$-value $<$ 0.001) of the burst properties between the one-off FRBs and the repeating ones. More specifically, after controlling for distance, we find that the peak luminosities of one-off FRBs are, on average, higher than the repeating ones; the pulse temporal widths of repeating FRBs are, on average, longer than the one-off ones. The differences indicate that these two categories could have distinct physical origins. Moreover, we discuss the sub-populations of FRBs and provide statistical evidence to support the existence of sub-populations in one-off FRBs and in repeating ones.Comment: 10 pages, 6 figures, accepted for publication in Ap

Varstrometry Selected Radio-Loud Candidates of Dual and Off-Nucleus Quasars at Sub-kpc Scales

Dual super massive black holes at sub-kpc to kpc scales, the product of galaxy mergers, are progenitors of eventually coalescing binary SMBHs. If both or one of the dual SMBHs are accreting, they may appear as dual AGNs or off-nucleus AGNs. Studying such systems is essential to learn the dynamical evolution of binary SMBHs as well as the process of galaxy merging. Recently a novel astrometry-based method named varstrometry has been put forward to search for dual SMBHs at high redshift, as the unsynchronized flux variability of dual AGNs (or off-nucleus AGNs) will cause astrometric jitters detectable by Gaia without spatially resolving them. Based on Gaia varstrometry we select a rare sample of 5 radio loud quasars with clear Gaia astrometric jitters. With e-MERLIN observations we have revealed a single compact radio source for each of them. Remarkably all but one exhibit clear Gaia-radio offsets of ~ 9 -- 60 mas. The observed Gaia jitters appear consistent with the expected values. These detected Gaia-radio offsets suggest these candidate dual SMBHs may have projected separations as small as ~ 0.01 -- 0.1'' (~ 0.1 kpc, depending on the optical flux ratio of two SMBHs). Meanwhile, this work highlights the remarkably high efficiency of Gaia varstrometry selection of jittering sources.Comment: 6 pages, 5 figures, 1 table; accepted for publication in MNRAS Letter

Non-Rigid Registration via Global to Local Transformation

Non-rigid point set and image registration are key problems in plenty of computer vision and pattern recognition tasks. Typically, the non-rigid registration can be formulated as an optimization problem. However, registration accuracy is limited by local optimum. To solve this problem, we propose a method with global to local transformation for non-rigid point sets registration and it also can be used to infrared (IR) and visible (VIS) image registration. Firstly, an objective function based on Gaussian fields is designed to make a problem of non-rigid registration transform into an optimization problem. A global transformation model, which can describe the regular pattern of non-linear deformation between point sets, is then proposed to achieve coarse registration in global scale. Finally, with the results of coarse registration as initial value, a local transformation model is employed to implement fine registration by using local feature. Meanwhile, the optimal global and local transformation models estimated from edge points of IR and VIS image pairs are used to achieve non-rigid image registration. The qualitative and quantitative comparisons demonstrate that the proposed method has good performance under various types of distortions. Moreover, our method can also produce accurate results of IR and VIS image registration

Bis­(1H-benzimidazole-κN 3)bis(4-methyl­benzoato-κ 2 O,O′)cobalt(II)

In the title mononuclear complex, [Co(C8H7O2)2(C7H6N2)2], the CoII atom is coordinated by four carboxylate O atoms from two 4-methyl­benzoate ligands and two N atoms from two benzimidazole ligands in an octa­hedral coordination geometry. The molecules are assembled via inter­molecular N—H⋯O hydrogen-bonding inter­actions into a three-dimensional network