In this paper, we focus on two different kinds of multipartite correlation, $k$-nonseparability and $k$-partite entanglement, both of which can describe the essential characteristics of multipartite entanglement. We propose effective methods to detect $k$-nonseparability and $k$-partite entanglement in terms of quantum Fisher information. We illustrate the significance of our results and show that they identify some $k$-nonseparability and $k$-partite entanglement that cannot be identified by known criteria by several concrete examples.

We observed a newly-discovered Galactic black hole X-ray binary Swift J1727.8$-$1613 with the European Very Long Baseline Interferometry Network (EVN) at 5 GHz. The observation was conducted immediately following a radio quenching event detected by the Karl G. Jansky Very Large Array (VLA). The visibility amplitude evolution over time reveals a large-amplitude radio flare and is consistent with an ejection event. The data can be interpreted either as a stationary component (i.e., the radio core) and a moving blob, or as two blobs moving away from the core symmetrically in opposite directions. The initial angular separation speed of the two components was estimated to 30 mas d^{-1}. We respectively fitted a single circular Gaussian model component to each of 14 sliced visibility datasets. For the case of including only European baselines, during the final hour of the EVN observation, the fitted sizes exhibited linear expansion, indicating that the measured sizes were dominated by the angular separation of the two components. The 6-h EVN observation took place in a rising phase of an even larger 4-day-long radio flare, implying that the ejection events were quite frequent and therefore continuous radio monitoring is necessary to correctly estimate the power of the transient jet. Combined with X-ray monitoring data, the radio quenching and subsequent flares/ejections were likely driven by instabilities in the inner hot accretion disk.

Magnetic braking (MB) mechanism plays a vital role throughout the evolution of low-mass X-ray binaries (LMXBs). Considering the standard MB prescription, the initial orbital periods of LMXBs that can evolve into binary millisecond pulsar (MSP) with He white dwarfs (WDs) and short orbital periods ($2-9~\rm hours$) are within an extremely narrow interval, which was named the fine-tuning problem. Employing the detailed binary evolution model, we investigate the evolution of LMXBs in both the standard and convection and rotation boosted (CARB) MB laws. In the standard MB case, it is difficult for donor stars to form a He core and exhaust H envelope through mass transfer at short orbital periods, making them semidetached systems. The CARB MB mechanism can drive LMXBs evolve toward compact detached MSP-WD systems in wide initial orbital periods, over which binary MSPs with long orbital periods will be produced. We obtain the initial parameter space of binary MSPs with He WDs in the initial orbital period and donor-star mass plane, which can be applied to future statistics study by population synthesis simulations. We also discuss a new relation between orbital period and WD mass, formation of persistent ultra-compact X-ray binaries with relatively long orbital periods, and detectability of compact MSP-WD systems as low-frequency gravitational wave sources.

Metal-oxide surfaces act as both Brønsted acids and bases, which allows the exchange of protons with the electrolyte solution and generates either positive or negative proton charges depending on the environmental pH. These interfacial proton charges are then compensated by counter-ions from the electrolyte solution, which leads to the formation of the electric double layer (EDL). Because the EDL plays a crucial role in electrochemistry, geochemistry and colloid science, understanding the structure-property relationship of the EDL in metal-oxide systems from both experimental and theoretical approaches is necessary. This chapter focuses on the physical chemistry of the protonic double layer at the metal-oxide/electrolyte interface. In particular, determinations of the EDL capacitance and the double-layer potential from potentiometric titration experiments, electrochemical methods, surface-sensitive vibrational spectroscopy and X-ray photoelectron spectroscopy are summarized. This is followed by discussions from the atomistic modelling aspect of the EDL, with an emphasis on the density-functional theory-based molecular dynamics simulations. A conclusion and outlook for future works on this topic are also given.

Understanding the formation mechanisms of stellar-mass black holes in X-ray binaries (BHXBs) remains a fundamental challenge in astrophysics. The natal kick velocities imparted during black hole formation provide crucial constraints on these formation channels. In this work, we present a new-epoch very long baseline interferometry (VLBI) observation of the Galactic BHXB AT2019wey carried out in 2023. Combining with archival VLBI data from 2020, we successfully measure the proper motion of AT2019wey over a 3-year timescale, namely $0.78\pm0.12$~\masyr\ in right ascension and $-0.42\pm0.07$~\masyr\ in declination. Employing the measured proper motion, we estimate its peculiar velocity and the potential kick velocity (PKV), through Monte Carlo simulations incorporating uncertainties of its distance and radial velocity. The estimated PKV distributions and height above the Galactic plane suggest that AT2019wey's black hole likely formed through a supernova explosion rather than direct collapse.

The black hole (BH) spin could significantly change the density of dark matter (DM) in its vicinity, creating a mini-spike of the density of DM. The dynamical friction (DF) between DM and the companion star of a BH can provide an efficient loss of angular momentum, driving the BH-main sequence (MS) star binary to evolve toward a compact orbit system. We investigate the influence of the DF of DM on the detectability of intermediate-mass black hole (IMBH)-MS binaries as low-frequency gravitational wave (GW) sources. Taking into account the DF of DM, we employ the detailed binary evolution code MESA to model the evolution of a large number of IMBH-MS binaries. Our simulation shows that the DF of DM can drive those IMBH-MS binaries to evolve toward low-frequency GW sources for a low donor-star mass, a high spike index, or a short initial orbital period. When the spike index $\gamma=1.60$, those IMBH-MS binaries with donor-star masses of $1.0-3.4~ M_{\odot}$ and initial orbital periods of $0.65-16.82~ \rm days$ could potentially evolve into visible LISA sources within a distance of $10~\rm kpc$. The DF of DM can enlarge the initial parameter space and prolong the bifurcation periods. In the low-frequency GW source stage, the X-ray luminosities of those IMBH X-ray binaries are $\sim 10^{35}-10^{36}~\rm erg\,s^{-1}$, hence they are ideal multimessenger objects.

Blazars are active galactic nuclei (AGN) whose relativistic jets point nearly to the line of sight. Their compact radio structure can be imaged with very long baseline interferometry (VLBI) on parsec scales. Blazars at extremely high redshifts provide a unique insight into the AGN phenomena in the early Universe. We observed four radio sources at redshift $z>4$ with the European VLBI Network (EVN) at 1.7 and 5 GHz. These objects were previously classified as blazar candidates based on X-ray observations. One of them, J2134$-$0419 is firmly confirmed as a blazar with our VLBI observations, due to its relativistically beamed radio emission. Its radio jet extended to $\sim$10 milli-arcsec scale makes this source a promising target for follow-up VLBI observations to reveal any apparent proper motion. Another target, J0839+5112 shows a compact radio structure typical of quasars. There is evidence for flux density variability and its radio "core" has a flat spectrum. However, the EVN data suggest that its emission is not Doppler-boosted. The remaining two blazar candidates (J1420+1205 and J2220+0025) show radio properties totally unexpected from radio AGN with small-inclination jet. Their emission extends to arcsec scales and the Doppler factors of the central components are well below 1. Their structures resemble that of double-lobed radio AGN with large inclination to the line of sight. This is in contrast with the blazar-type modeling of their multi-band spectral energy distributions. Our work underlines the importance of high-resolution VLBI imaging in confirming the blazar nature of high-redshift radio sources.

Type-C quasi-periodic oscillations (QPOs) in black hole X-ray transients typically manifest in the low-hard and hard-intermediate states. This study presents a detailed spectral and temporal analysis of the black hole candidate Swift J1727.8-1613 using NICER observations from August and September 2023, with a focus on the first flare period. We detected Type-C QPOs whose centroid frequency increased from 0.33 Hz to 2.63 Hz. An additional increase in frequency was observed when the outburst entered a flare period. The time-averaged spectra, along with the rms and phase-lag spectra of the QPOs, were jointly fitted using the time-dependent Comptonization model vkompthdk to examine the geometry of the corona during this flare. Correlations between spectral and temporal properties suggest that the detected type-C QPOs are primarily modulated by Lense-Thirring precession. Leveraging simultaneous radio observations that indicate discrete jet ejections, we proposed a scenario to describe the co-evolution of the disk-corona-jet during a flare (~3 days). This scenario is partially supported for the first time by polarization data in the soft gamma-ray band from INTEGRAL/IBIS. A phenomenological analysis of the corona scenario was also conducted.

The double neutron star PSR J1846-0513 is discovered by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) in Commensal Radio Astronomy FAST Survey. The pulsar is revealed to be harbored in an eccentric orbit with $e=0.208$ and orbital period of 0.613 days. The total mass of the system is constrained to be $2.6287(35)\rm{M}_{\odot}$, with a mass upper limit of $1.3455{\rm~M}_{\odot}$ for the pulsar and a mass lower limit of $1.2845{\rm~M}_{\odot}$ for the companion star. To reproduce its evolution history, we perform a 1D model for the formation of PSR J1846-0513 whose progenitor is assumed to be neutron star - helium (He) star system via MESA code. Since the large eccentricity is widely believed to originate from an asymmetric supernova explosion, we also investigate the dynamical effects of the supernova explosion. Our simulated results show that the progenitor of PSR J1846-0513 could be a binary system consisting of a He star of $3.3-4.0{\rm~M}_\odot$ and a neutron star in a circular orbit with an initial period of $\sim0.5$ days.

Previous research has established a relationship between radial action and scale height in Galactic disks, unveiling a correlation between radial and vertical heating. This finding poses a challenge to our existing comprehension of heating theories and consequently encodes crucial insights into the formation and heating history of Galactic disks. In this study, we perform N-body simulations with the aim of verifying the existence of this correlation between radial action and scale height, thereby enhancing our comprehension of the heating history of Galactic disks. We find that the relationship between radial action and scale height in our simulations can be described by the same functional form observed in previous work. Furthermore, the relationships derived from our simulations align well with those of the Galactic thin disk. However, they do not coincide with the inner thick disk but exhibit a rough correspondence with the outer thick disk, suggesting the possibility that additional heating mechanisms may be required to explain the inner thick disk. We also find that the mean radial action and scale height undergo rapid increases during the initial stages of the simulation, yet remain relatively unchanged as the disk evolves further. By tracing example particles, we uncover a correlation between radial and vertical heating in our simulation: as a particle in the disk gains or loses radial action, its vertical motion tends to oscillate on a more or less extended orbit, accompanied by a tendency to migrate outward or inward, respectively. The massive, long-lasting particles in our simulation contribute to disk heating by solely enhancing the rate of increase in scale height with radial action, while maintaining the functional form that describes the relationship between these two variables.

We are concerned with the likelihood ratio tests in the $p_0$ model for testing degree heterogeneity in directed networks. It is an exponential family distribution on directed graphs with the out-degree sequence and the in-degree sequence as naturally sufficient statistics. For two growing dimensional null hypotheses: a specified null $H_{0}: \theta_{i}=\theta_{i}^{0}$ for $i=1,\ldots,r$ and a homogenous null $H_{0}: \theta_{1}=\cdots=\theta_{r}$, we reveal high dimensional Wilks' phenomena that the normalized log-likelihood ratio statistic, $[2\{\ell(\widehat{\bs\theta})-\ell(\widehat{\bs\theta}^{0})\}-r]/(2r)^{1/2}$, converges in distribution to a standard normal distribution as $r\rightarrow \infty$. Here,$\ell( \bs{\theta})$ is the log-likelihood function, $\widehat{\bs{\theta}}$ is the unrestricted maximum likelihood estimator (MLE) of $\bs\theta$, and $\widehat{\bs{\theta}}^0$ is the restricted MLE for $\bs\theta$ under the null $H_{0}$. For the homogenous null $H_0: \theta_1=\cdots=\theta_r$with a fixed$r$, we establish the Wilks-type theorem that $2\{\ell(\widehat{\bs{\theta}}) - \ell(\widehat{\bs{\theta}}^0)\}$ converges in distribution to a chi-square distribution with $r-1$ degrees of freedom as $n\rightarrow \infty$, not depending on the nuisance parameters. These results extend a recent work by \cite{yan2023likelihood} to directed graphs. Simulation studies and real data analyses illustrate the theoretical results.

In the bulge of M31, the Chandra observations discovered a possible black hole (BH) ultracompact X-ray binary (UCXB) Seq.1 with an orbital period of 7.7 minutes and a maximum X-ray luminosity $L_{\rm X}=1.09^{+0.02}_{-0.01}\times10^{38}~ \rm erg\,s^{-1}$in the$0.5-8$ keV band. The minimum orbital period of the BH UCXBs predicted by the standard magnetic braking (MB) model is longer than 8.3 minutes. In this work, we investigate whether the convection- and rotation-boosted (CARB) MB prescription can account for the formation of a BH UCXB like Seq.1. Our detailed stellar evolution models indicate that the CARB MB law can drive isolated BH-main sequence (MS) binaries to evolve toward BH UCXBs with an orbital period of $7.7~ \rm minutes$, in which a low-mass white dwarf transfers the material onto a BH in a short-term mass transfer episode, producing an X-ray luminosity of $10^{38}~\rm erg\,s^{-1}$. We also obtain an initial parameter space of BH-MS binaries as the progenitors of Seq.1 in the donor-star masses and orbital periods plane, which can be applied to future population synthesis simulations. If Seq.1 is indeed a BH UCXB, future spaceborne gravitational wave (GW) detectors can detect the low-frequency GW signals from this source, and a tidal disruption event will be expected after 0.12 Myr.

The magnetic braking (MB) plays an important role in driving the evolution of low-mass X-ray binaries (LMXBs). The modified MB prescription, convection and rotation boosted (CARB) model, is very successful in reproducing the detected mass-transfer rates of persistent neutron star (NS) LMXBs. In this work, we investigate whether the CARB MB prescription could account for the formation and evolution of some NS and black hole (BH) LMXBs with an observed orbital period derivative. Using the MESA code, we perform a detailed binary evolution model for six NS and three BH LMXBs. Our simulations find that the CARB MB prescription can successfully reproduce the observed donor-star masses, orbital periods, and period derivatives of four NS LMXBs and one BH LMXB. Our calculated effective temperatures are in good agreement with the detected spectral types of two NS LMXBs and one BH LMXB. However, the standard MB model is difficult to produce the observed period derivatives of those LMXBs experiencing a rapid orbital shrinkage or expansion.

Let $\mathscr{C}$ be an additive subcategory of left $\Lambda$-modules, we establish relations of the orthogonal classes of $\mathscr{C}$ and (co)res $\widetilde{\mathscr{C}}$ under separable equivalences. As applications, we obtain that the (one-sided) Gorenstein category and Wakamatsu tilting module are preserved under separable equivalences. Furthermore, we discuss when $G_{C}$-projective (injective) modules and Auslander (Bass) class with respect to $C$ are invariant under separable equivalences.

The extremely local electric field enhancement and light confinement is demonstrated in dielectric waveguide with corner and gap geometry. The numerical results reveal the local electric field enhancement in the vicinity of the apex of fan-shaped waveguide. Classical electromagnetic theory predicts that the field enhancement and confinement abilities increase with decreasing radius of rounded corner ($r$) and gap ($g$), and show singularity for infinitesimal $r$ and $g$. For practical parameters with $r=g=10\,\mathrm{nm}$, the mode area of opposing apex-to-apex fan-shaped waveguides can be as small as $4\times10^{-3}A_{0}$ ($A_{0}=\lambda^{2}/4$), far beyond the diffraction limit. This way of breaking diffraction limit with no loss outperforms plasmonic waveguides, where light confinement is realized at the cost of huge intrinsic loss in the metal. Furthermore, we propose a structure with dielectric bow-tie antenna on a silicon-on-insulator waveguide, whose field enhancement increases by one order. The lossless dielectric corner and gap structures offer an alternative method to enhance the light-matter interaction without metal nano-structure, and will find applications in quantum electrodynamics, sensors and nano-particle trapping.

It is believed that dual active galactic nuclei (dual AGN) will form during galaxies merge. Studying dual-AGN emission can provide valuable insights into galaxy merging and evolution. To investigate parsec-scale radio emission properties, we observed eight radio components of four selected dual-AGN systems using the Very Long Baseline Array (VLBA) at 5 GHz in multiple-phase-center mode. Among them, two compact radio components, labeled J0051+0020B and J2300-0005A, were detected clearly on parsec scales for the first time. However, the radio emission of the other six components was resolved out in the high-resolution images. We provided the values or upper limits of the brightness temperature and radio emission power, and analyzed the emission origins in detail for each target. Based on their physical properties reported in this work and in the literature, we suggest the radio emission in J0051+0020B and J2300-0005A originates primarily from compact jets, while the other six sources show more complex emission mechanisms. In addition, our VLBA observations suggest the systematic X-ray deficit in our dual-AGN sample is likely attributed to the tidally induced effect and possible viewing angle effect.

Let $\Lambda$ and $\Gamma$ be symmetrically separably equivalent Artin algebras. We prove that there exist symmetrical separable equivalences between certain endomorphism algebras of modules. As applications, we provide several methods to construct symmetrical separable equivalences from given ones and discuss when the rigidity dimension is an invariant under symmetrical separable equivalences. Moreover, we show that a symmetrical separable equivalence preserves the Frobenius-finite type, Auslander-type condition, the (strong) Nakayama conjecture, the Auslander-Gorenstein conjecture and so on.

Recently, it discovered two ultra-long period radio transients GLEAM-X J162759.5-523504.3 (J1627) and GPM J1839$-$10 (J1839) with spin periods longer than 1000 s. The origin of these two ultra-long period radio transients is intriguing in understanding the spin evolution of neutron stars (NSs). In this work, we diagnose whether the interaction between strong magnetized NSs and fallback disks can spin NSs down to the observed ultra-long period. Our simulations found that the magnetar+fallback disk model can account for the observed period, period derivative, and X-ray luminosity of J1627 in the quasi-spin-equilibrium stage. To evolve to the current state of J1627, the initial mass-accretion rate of the fallback disk and the magnetic field of the NS are in the range of $(1.1-30)\times10^{24}~\rm g\,s^{-1}$ and $(2-5)\times10^{14}~\rm G$, respectively. In an active lifetime of fallback disk, J1839 is impossible to achieve the observed upper limit of period derivative. Therefore, we propose that J1839 may be in the second ejector phase after the fallback disk becomes inactive. Those NSs with a magnetic field of $(2-6)\times10^{14}~\rm G$ and a fallback disk with an initial mass-accretion rate of $\sim10^{24}-10^{26}~\rm g\,s^{-1}$ are the possible progenitors of J1839.

Compared with quantum coherence, multilevel quantum coherence offers a hierarchical classification that enables a more refined characterization. In this paper, we investigate multilevel coherence and introduce two $\alpha$-affinity-based indicators to quantify it, which exhibit a range of desirable properties. We further define $\alpha$-affinity-based indicators of multipartite correlation and analyze their properties. Finally, we explore and establish the relationship between these multilevel coherence indicators and the multipartite correlation indicators, thereby clarifying the connection between multilevel coherence and multipartite correlation.