Weighted sieves are used to detect numbers with at most S prime factors with $S \in \mathbb{N}$ as small as possible. When one studies problems with two variables in somewhat symmetric roles (such as Chen primes, that is primes p such that $p+2$ has at most two prime factors), one can utilise the switching principle. Here we discuss how different sieve weights work in such a situation, concentrating in particular on detecting a prime along with a product of at most three primes.

As applications, we improve on the works of Yang and Harman concerning Diophantine approximation with a prime and an almost prime, and prove that, in general, one can find a pair $(p, P_3)$ when both the original and the switched problem have level of distribution at least $0.267$.

The high redshift ‘little red dots’ (LRDs) detected with the James Webb Space Telescope are considered to be the cores of emerging galaxies that host active galactic nuclei (AGN). For the first time, we compare LRDs with local compact stellar systems and an array of galaxy-morphology-dependent stellar mass-black hole mass scaling relations in the $M_\mathrm{ bh}$–$M_{\star}$ diagrams. When considering the 2023–2024 masses for LRDs, they are not equivalent to nuclear star clusters (NSCs), with the latter having higher $M_\mathrm{ bh}/M_{\star}$ ratios. However, the least massive LRDs exhibit similar $M_\mathrm{ bh}$ and $M_\mathrm{ \star,gal}$ values as ultracompact dwarf (UCD) galaxies, believed to be the cores of stripped/threshed galaxies. We show that the LRDs span the $M_\mathrm{ bh}$–$M_\mathrm{ \star,gal}$ diagram from UCD galaxies to primaeval lenticular galaxies. In contrast, local spiral galaxies and the subset of major-merger-built early-type galaxies define $M_\mathrm{ bh}$–$M_{\star,gal}$ relations that are offset to higher stellar masses. Based on the emerging 2025 masses for LRDs, they may yet have similarities with NSCs, UCD galaxies, and green peas. Irrespective of this developing situation, we additionally observe that low-redshift galaxies with AGN align with the quasi-quadratic or steeper black hole scaling relations defined by local disc galaxies with directly measured black hole masses. This highlights the benefits of considering a galaxy’s morphology – which reflects its accretion and merger history – to understand the coevolution of galaxies and their black holes. Future studies of spatially resolved galaxies with secure masses at intermediate-to-high redshift hold the promise of detecting the emergence and evolution of the galaxy-morphology-dependent $M_\mathrm{ bh}$–$M_{\star}$ relations.

We examine the optical counterparts of the 1 829 neutral hydrogen (H i) detections in three pilot fields in the Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY) using data from the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys DR10. We find that 17% (315) of the detections are optically low surface brightness galaxies (LSBGs; mean g-band surface brightness within 1 $ R_e$ of $\gt 23$ mag arcsec$^{-2}$) and 3% (55) are optically ‘dark’. We find that the gas-rich WALLABY LSBGs have low star formation efficiencies, and have stellar masses spanning five orders of magnitude, which highlights the diversity of properties across our sample. 75% of the LSBGs and all of the dark H i sources had not been catalogued prior to WALLABY. We examine the optically dark sample of the WALLABY pilot survey to verify the fidelity of the catalogue and investigate the implications for the full survey for identifying dark H i sources. We assess the H i detections without optical counterparts and identify 38 which pass further reliability tests. Of these, we find that 13 show signatures of tidal interactions. The remaining 25 detections have no obvious tidal origin, so are candidates for isolated galaxies with high H i masses, but low stellar masses and star-formation rates. Deeper H i and optical follow-up observations are required to verify the true nature of these dark sources.

Let $\pi$ be an irreducible cuspidal automorphic representation of ${\mathrm{GL}}_n(\mathbb{A}_{\mathbb{Q}})$ with associated L-function $L(s, \pi)$. We study the behaviour of the partial Euler product of $L(s, \pi)$ at the centre of the critical strip. Under the assumption of the Generalised Riemann Hypothesis for $L(s, \pi)$ in conjunction with the Ramanujan–Petersson conjecture as necessary, we establish an asymptotic, off a set of finite logarithmic measure, for the partial Euler product at the central point, which confirms a conjecture of Kurokawa (2012). As an application, we obtain results towards Chebyshev’s bias in the recently proposed framework of Aoki–Koyama (2023).

We present the Evolutionary Map of the Universe (EMU) survey conducted with the Australian Square Kilometre Array Pathfinder (ASKAP). EMU aims to deliver the touchstone radio atlas of the southern hemisphere. We introduce EMU and review its science drivers and key science goals, updated and tailored to the current ASKAP five-year survey plan. The development of the survey strategy and planned sky coverage is presented, along with the operational aspects of the survey and associated data analysis, together with a selection of diagnostics demonstrating the imaging quality and data characteristics. We give a general description of the value-added data pipeline and data products before concluding with a discussion of links to other surveys and projects and an outline of EMU’s legacy value.

The stars of the Milky Way carry the chemical history of our Galaxy in their atmospheres as they journey through its vast expanse. Like barcodes, we can extract the chemical fingerprints of stars from high-resolution spectroscopy. The fourth data release (DR4) of the Galactic Archaeology with HERMES (GALAH) Survey, based on a decade of observations, provides the chemical abundances of up to 32 elements for 917 588 stars that also have exquisite astrometric data from the Gaia satellite. For the first time, these elements include life-essential nitrogen to complement carbon, and oxygen as well as more measurements of rare-earth elements critical to modern-life electronics, offering unparalleled insights into the chemical composition of the Milky Way. For this release, we use neural networks to simultaneously fit stellar parameters and abundances across the whole wavelength range, leveraging synthetic grids computed with Spectroscopy Made Easy. These grids account for atomic line formation in non-local thermodynamic equilibrium for 14 elements. In a two-iteration process, we first fit stellar labels to all 1 085 520 spectra, then co-add repeated observations and refine these labels using astrometric data from Gaia and 2MASS photometry, improving the accuracy and precision of stellar parameters and abundances. Our validation thoroughly assesses the reliability of spectroscopic measurements and highlights key caveats. GALAH DR4 represents yet another milestone in Galactic archaeology, combining detailed chemical compositions from multiple nucleosynthetic channels with kinematic information and age estimates. The resulting dataset, covering nearly a million stars, opens new avenues for understanding not only the chemical and dynamical history of the Milky Way but also the broader questions of the origin of elements and the evolution of planets, stars, and galaxies.

Bow shocks generated by pulsars moving through weakly ionized interstellar medium (ISM) produce emission dominated by non-equilibrium atomic transitions. These bow shocks are primarily observed as H$\alpha$ nebulae. We developed a package, named Shu, that calculates non-LTE intensity maps in more than 150 spectral lines, taking into account geometrical properties of the pulsars’ motion and lines of sight. We argue here that atomic (C i, N i, O i) and ionic (S ii, N ii, O iii, Ne iv) transitions can be used as complementary and sensitive probes of ISM. We perform self-consistent 2D relativistic hydrodynamic calculations of the bow shock structure and generate non-LTE emissivity maps, combining global dynamics of relativistic flows, and detailed calculations of the non-equilibrium ionization states. We find that though typically $\text{H}_\alpha$ emission is dominant, spectral fluxes in [O iii], [S ii] and [N ii] may become comparable for relatively slowly moving pulsars. Overall, morphology of non-LTE emission, especially of the ionic species, is a sensitive probe of the density structures of the ISM.

The propagation and absorption of the slow waves in the plasma of the Joint European Torus (JET) tokamak have been investigated by ray tracing. The study aims to obtain a qualitative notion of the penetration into the plasma and absorption of the slow wave excited by the A2 ITER-like antenna. The slow waves are radiated by antennas in the ion cyclotron resonance frequency inverted minority heating or mode conversion heating regimes. It has been discovered that the rays propagate in the toroidal direction over a significant distance, up to 6 × 103 cm, from the antenna. Spreading in the peripheral plasma, mainly between the separatrix and the wall, they slowly shift in the poloidal direction and can reach the divertor region. The change in equilibrium of the JET tokamak has a strong influence on both the propagation and absorption of slow waves. Absorption of the slow waves is caused by ion–electron collisions and Landau damping. In the minority heating regimes, the slow waves are strongly damped in the cyclotron resonance of minority ions even at very low minority density.

Petabytes of archival high time resolution observations have been captured with the Murchison Widefield Array. The search for Fast Radio Bursts within these using established software has been limited by its inability to scale on supercomputing infrastructure, necessary to meet the associated computational and memory requirements. Hence, past searches used a coarse integration time, in the scale of seconds, or analysed an insufficient number of hours of observations. This paper introduces BLINK, a novel radio interferometry imaging software for low-frequency FRB searches to be run on modern supercomputers. It is implemented as a suite of software libraries executing all computations on GPU, supporting both AMD and NVIDIA hardware vendors. These libraries are designed to interface with each other and to define the BLINK imaging pipeline as a single executable program. Expensive I/O operations between imaging stages are not necessary because the stages now share the same memory space and data representation. BLINK is the first imaging pipeline implementation able to fully run on GPUs as a single process, further supporting AMD hardware and enabling Australian researchers to take advantage of Pawsey’s Setonix supercomputer. In the millisecond-scale time resolution imaging test case illustrated in this paper, representative of what is required for FRB searches, the BLINK imaging pipeline achieves a 3 687x speedup compared to a traditional MWA imaging pipeline employing WSClean.

Landau’s collisionless result for a weakly damped plasma wave is precisely recovered in a weakly collisional, steady state plasma by treating the physics of the narrow collisional boundary layer associated with the resonant electrons. To recover Landau’s results, the collision frequency must be large enough that islands are unable to form and/or the wave amplitude must be small enough to allow linearization. However, the Landau treatment fails once the collision frequency becomes too weak and/or the wave amplitude too large. Remarkably, Landau’s weakly damped plasma wave results require collisions and are shown to be inappropriate in the collisionless limit for a nonlinear, finite amplitude, steady state wave!