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The prime focus of this paper is the study of optimal duals of a given finite frame as well as optimal dual pairs, in the context of probability modelled erasures of frame coefficients. We characterize optimal dual frames (and dual pairs) which, among all dual frames (and dual pairs), minimize the maximum measure of the error operator obtained while considering all possible locations of probabilistic erasures of frame coefficients in the reconstruction with respect to each dual frame(dual pair). For a given weight number sequence associated with the probabilities, the measure of the probabilistic error operator is taken to be the weighted average of the operator norm and the spectral radius. Using this as an optimality measure, the existence and uniqueness of optimal dual frames (and optimal dual pairs) and their topological properties are studied. Also, their relations with probabilistic optimal dual frames as well as dual pairs in other contexts, such as those obtained using operator norm and spectral radius as the measure of the error operator, are analyzed.

The MIRI-MRS instrument onboard JWST allows for probing the molecular gas composition at mid-IR wavelengths at unprecedented resolution and sensitivity. It is important to study these features in low-mass embedded protostellar systems since the formation of planets is thought to start in this phase. We present JWST/MIRI-MRS data of 18 low-mass protostellar systems in the JOYS program, focusing on gas-phase molecular lines in spectra extracted from the central protostellar positions. Besides H2, the most commonly detected molecules are H2O, CO2, CO, and OH. Other molecules such as 13CO2, C2H2, 13CCH, HCN, C4H2, CH4, and SO2 are detected only toward at most three of the sources. The JOYS data also yield the surprising detection of SiO gas toward two sources (BHR71-IRS1, L1448-mm) and for the first time CS and NH3 at mid-IR wavelengths toward a low-mass protostar (B1-c). The temperatures derived for the majority of the molecules are 100-300 K, much lower than what is typically derived toward more evolved Class II sources (>500 K). Toward three sources (e.g., TMC1-W), hot (~1000 K) H2O is detected, indicative of the presence of hot molecular gas in the embedded disks, but such warm emission from other molecules is absent. The agreement in abundance ratios with respect to H2O between ice and gas point toward ice sublimation in a hot core for a few sources (e.g., B1-c) whereas their disagreement and velocity offsets hint at high-temperature (shocked) conditions toward other sources (e.g., L1448-mm, BHR71-IRS1). The typical temperatures of the gas-phase molecules of 100-300 K are consistent with both ice sublimation in hot cores as well as high-temperature gas phase chemistry. Molecular features originating from the inner embedded disks are not commonly detected, likely because they are too extincted even at mid-IR wavelengths by small not-settled dust grains in upper layers of the disk., Comment: 25 pages, 11 figures, accepted for publication in A&A

Active galactic nuclei (AGN) feedback and its impact on their host galaxies are critical to our understanding of galaxy evolution. Here, we present a combined analysis of new high resolution ultraviolet (UV) data from the Ultraviolet Imaging Telescope (UVIT) on AstroSat and archival optical spectroscopic data from VLT/MUSE, for the Seyfert galaxy, NGC 1365. Concentrating on the central 5 kpc region, the UVIT images in the far and near UV show bright star forming knots in the circumnuclear ring as well as a faint central source. After correcting for extinction, we found the star formation rate (SFR) surface density of the circumnuclear 2 kpc ring to be similar to other starbursts, despite the presence of an AGN outflow, as seen in [OIII] 5007 Angstrom. On the other hand, we found fainter UV and thus lower SFR in the direction south-east of the AGN relative to north-west in agreement with observations at other wavelengths from JWST and ALMA. The AGN outflow velocity is found to be lesser than the escape velocity, suggesting that the outflowing gas will rain back into the galaxy. The deep UV data has also revealed diffuse UV emission in the direction of the AGN outflow. By combining [OIII] and UV data, we found the diffuse emission to be of AGN origin., Comment: 12 Pages, 7 figures, Accepted for publication in ApJ

We use the James Webb Space Telescope (JWST) and its Mid-Infrared Instrument (MIRI) (5-28 um), to study the embedded HH 211 flow. We map a 0.95'x0.22' region, covering the full extent of the blue-shifted lobe, the central protostellar region, and a small portion of the red-shifted lobe. The jet driving source is not detected even at the longest mid-IR wavelengths. The overall morphology of the flow consists of a highly collimated jet, mostly molecular (H2, HD) with an inner atomic ([FeI], [FeII], [SI], [NiII]) structure. The jet shocks the ambient medium, producing several large bow-shocks, rich in forbidden atomic and molecular lines, and is driving an H2 molecular outflow, mostly traced by low-J, v=0 transitions. Moreover, 0-0 S(1) uncollimated emission is also detected down to 2"-3" (~650-1000 au) from the source, tracing a cold (T=200-400 K), less dense and poorly collimated molecular wind. The atomic jet ([FeII] at 26 um) is detected down to ~130 au from source, whereas the lack of H2 emission close to the source is likely due to the large visual extinction. Dust continuum-emission is detected at the terminal bow-shocks, and in the blue- and red-shifted jet, being likely dust lifted from the disk. The jet shows an onion-like structure, with layers of different size, velocity, temperature, and chemical composition. Moreover, moving from the inner jet to the outer bow-shocks, different physical, kinematic and excitation conditions for both molecular and atomic gas are observed. The jet mass-flux rate, momentum, and momentum flux of the warm H2 component are up to one order of magnitude higher than those inferred from the atomic jet component. Our findings indicate that the warm H2 component is the primary mover of the outflow, namely it is the most significant dynamical component of the jet, in contrast to jets from more evolved YSOs, where the atomic component is dominant., Comment: Paper accepted in A&A for publication

Weak R-duals, a generalization of R-duals, were recently introduced; for which duality relations were established. In this paper, we consider the problem of characterizing a given frame sequence to be a weak R-dual of a given frame. Further, we apply these characterization results to the Gabor frame setting and prove that the weak R-duality of the adjoint Gabor system leads to the R-duality of the same, thereby indicating an approach to answer the famous problem of the adjoint Gabor system being an R-dual of a given Gabor frame., Comment: 27 Pages

Blazars, the peculiar class of active galactic nuclei (AGN), are known to show flux variations across the accessible electromagnetic spectrum. Though they have been studied extensively for their flux variability characteristics across wavelengths, information on their ultraviolet (UV) flux variations on time scales of hours is very limited. Here, we present the first UV flux variability study on intraday time scales of a sample of 10 blazars comprising 2 flat spectrum radio quasars (FSRQs) and 8 BL Lacertae objects (BL Lacs). These objects, spanning a redshift (z) range of 0.034 <= z <= 1.003, were observed in the far-UV (FUV: 1300 - 1800 \text{\AA}) and near-UV (NUV: 2000 - 3000 \text{\AA}) wavebands using the ultraviolet imaging telescope on board AstroSat. UV flux variations on time scales of hours were detected in 9 sources out of the observed 10 blazars. The spectral variability analysis showed a bluer-when-brighter trend with no difference in the UV spectral variability behavior between the studied sample of FSRQs and BL Lacs. The observed UV flux and spectral variability in our sample of both FSRQs and BL Lacs revealed that the observed UV emission in them is dominated by jet synchrotron process., Comment: 23 pages, 5 figures, 6 tables; accepted for publication in The Astrophysical Journal

In this study, we demonstrate the efficacy of the Ultraviolet Imaging Telescope (UVIT) in identifying and characterizing white dwarfs (WDs) within the Milky Way Galaxy. Leveraging the UVIT point source catalogue towards SMC and crossmatching with Gaia DR3 data, we identified 43 single WDs (37 new detections), 13 new WD+main sequence (MS) candidates and 161 UV bright MS stars by analysing their Spectral Energy Distributions (SED). Using the WD evolutionary models, we determine the masses, effective temperatures, and cooling ages of these identified WDs. Masses of these WDs range from 0.2 to 1.3 M$_{\odot}$ and effective temperatures (T$_{eff}$) between 10000 K to 15000 K, with cooling ages spanning 0.1 to 2 Gyr. Notably, we detect hotter WDs compared to literature values, which is attributed to the sensitivity of UVIT. Furthermore, we report the detection of 20 new extremely low-mass (ELM) candidates from our analysis. Future spectroscopic studies of the ELM candidates will help us understand the formation scenarios of these exotic objects. Despite limitations in Gaia DR3 distance measurements for optically faint WDs, we provide a crude estimate of the WD space density within 1kpc as 1.3 $\times$ 10$^{-3}$ pc$^{-3}$, which is higher than previous estimates in the literature. Our results underscore the instrumental capabilities of UVIT and anticipate the forthcoming UV missions like INSIST for systematic WD discovery. Our methodology sets a precedent for future analyses in other UVIT fields to find more WDs and perform spectroscopic studies to verify their candidacy., Comment: Accepted for publication in Astronomy & Astrophysics

Alternative magnetic materials or ``altermagnets", characterized by their non-relativistic, momentum-dependent spin-split states, represent a cutting-edge advancement in the field of magnetism, offering promising avenues for spintronic applications. Among these materials, hexagonal MnTe has emerged as a standout material candidate for its substantial spin-splitting. In this study, employing first-principles electronic structure calculations and spin group symmetry analysis, we delve into the interplay of altermagnetism and pressure in two main phases of MnTe. Our relativistic calculations demonstrate the presence of tunable anomalous Hall effect (AHE) in hexagonal MnTe. In addition, our results underscore the pivotal role of pressure as a tuning parameter for the alternative magnetic traits in the system. Furthermore, we identify another phase of MnTe with orthorhombic structure, namely $\gamma$-MnTe, hosting altermagnetic characteristics. We study, in detail, its response in AHE and spin-spliting due to magnetization and pressure variations, respectively. Our study highlights the substantial impact of pressure on the properties of alternative magnetic materials, particularly emphasizing the pronounced tuning effect observed in the hexagonal and orthorhombic MnTe.

Videos are more informative than images because they capture the dynamics of the scene. By representing motion in videos, we can capture dynamic activities. In this work, we introduce GPT-4 generated motion descriptions that capture fine-grained motion descriptions of activities and apply them to three action datasets. We evaluated several video-text models on the task of retrieval of motion descriptions. We found that they fall far behind human expert performance on two action datasets, raising the question of whether video-text models understand motion in videos. To address it, we introduce a method of improving motion understanding in video-text models by utilizing motion descriptions. This method proves to be effective on two action datasets for the motion description retrieval task. The results draw attention to the need for quality captions involving fine-grained motion information in existing datasets and demonstrate the effectiveness of the proposed pipeline in understanding fine-grained motion during video-text retrieval., Comment: ACL Findings , 2024

Pressure changes travel at an infinite sound speed in an incompressible ideal fluid, opposite to what happens in a bubbly liquid, where the presence of bubbles adds compressibility such that the sound speed becomes finite. Here, the transmission of a pressure signal through a confined bubble array is studied numerically. An axisymmetric Boundary Integral (BI) code was used to simulate a horizontal array of spherical bubbles inside a cylindrical container. On one end of the container, a piston is able to move in either a sinusoidal or impulsive way to excite the bubbles, whereas the other end of the cylinder is fixed. A one-dimensional model, hereafter called the Multiple Bagnold Problem (MBP) model, was developed to predict the behavior of the 3D system. A good agreement between the model and the simulations was found for initial excitation times and qualitatively good agreement for later times. The MBP model was subsequently used to obtain an expression for the sound speed in monodisperse systems, which depends on the ratio between the driving and the natural bubble frequency. Two regimes were found, one where the pressure signal travels unattenuated and the other where attenuation is present. Subsequently we turn to more complex, bidisperse systems, where the influence of the presence of bubbles of two different sizes is explored. Analytical expressions to predict the eigenfrequencies were obtained for monodisperse and bidisperse alternating systems. For bidisperse stacked systems the eigenfrequencies were computed numerically giving a good agreement with the MBP simulations. Finally, we discuss the propagation of a pressure signal through a polydisperse system.

The presence of gas or vapour bubbles may strongly influence the forces that occur during the impact of a liquid mass onto a solid. Here, we study this effect numerically, in a well-controlled manner, by simulating the short-time interaction between an impacting droplet and a solid surface, mediated by the gas layer between droplet and solid just before collision, in the presence and absence of bubbles. A boundary integral method is used to simulate the falling droplet, the mediating air layer is modeled using lubrication theory, whereas uniform gas bubbles are added to the droplet that obey a polytropic equation of state. We show that the presence of gas bubbles inside the droplet can have a significant influence on the force exerted on the substrate, even before touchdown. This is due to the transmission of load from the solid, through the gas layer and finally into the bubbly droplet, buffering the impact. We simulate different bubble configurations, modifying their number, size, shape and initial position. It is found that larger bubbles, as well as those close to the impact zone, dampen the collision more as compared to small bubbles or the ones that are far from the droplet's surface. In addition, multiple small bubbles are shown to have a similar or even greater effect as a single large bubble.

In a recent study, Banerjee et al. (2021) produced an atlas of all major emission lines found in a large sample of 115 Galactic field Be stars using the 2-m Himalayan Chandra Telescope (HCT) facility located at Ladakh, India. This paper presents our further exploration of these stars to estimate the electron density in their discs. Our study using Balmer decrement values indicate that their discs are generally optically thick in nature with electron density (n_e) in their circumstellar envelopes (CEs) being in excess of 10^13 cm^-3 for around 65% of the stars. For another 19% stars, the average n_e in their discs probably range between 10^12 cm^-3 and 10^13 cm^-3. We noticed that the nature of the H{\alpha} and H\b{eta} line profiles might not influence the observed Balmer decrement values (i.e. D_34 and D_54) of the sample of stars. Interestingly, we also found that around 50% of the Be stars displaying D_34 greater than 2.7 are of earlier spectral types, i.e. within B0 -B3., Comment: 10 pages, 1 figure, accepted for publication in the Bulletin of Li\`ege Royal Society of Sciences as a Proceedings paper for the 3rd BINA Workshop held at ARIES, India during March 22-24 2023

Accretion and ejection sets the outcome of the star and planet formation process. The mid-infrared wavelength range offers key tracers of those processes that were difficult to detect and spatially resolve in protostars until now. We aim to characterize the interplay between accretion and ejection in the low-mass Class I protobinary system TMC1, comprising two young stellar objects: TMC1-W and TMC1-E with 85 au separation. With the {\it James Webb} Space Telescope (JWST) - Mid-Infrared Instrument (MIRI) observations in 5 - 28 $\mu$m range, we measure intensities of emission lines of H$_2$, atoms and ions, e.g., [Fe II] and [Ne II], and HI recombination lines. We detect H$_2$ outflow coming from TMC1-E, with no significant H$_2$ emission from TMC1-W. The H$_2$ emission from TMC1-E outflow appears narrow and extends to wider opening angles with decreasing E$_{up}$ from S(8) to S(1) rotational transitions, indicating a disk wind origin. The outflow from TMC1-E protostar shows spatially extended emission lines of [Ne II], [Ne III], [Ar II], and [Ar III], with their line ratios consistent with UV radiation as a source of ionization. With ALMA, we detect accretion streamer infalling from $>$ 1000 au scales onto the TMC1-E component. TMC1-W protostar powers a collimated jet, detected with [Fe II] and [Ni II] consistent with energetic flow. A much weaker ionized jet is observed from TMC1-E. TMC1-W is associated with strong emission from hydrogen recombination lines, tracing the accretion onto the young star. Observations of a binary Class I protostellar system show that the two processes are clearly intertwined, with accretion from the envelope onto the disk influencing a wide-angle wind ejected on disk scales, while accretion from the protostellar disk onto the protostar is associated with the source launching a collimated high-velocity jet within the innermost regions of the disk., Comment: 18 pages, 13 figures, accepted for publication in Astronomy and Astrophysics

The problem of random average sampling and reconstruction over multiply generated local quasi shift-invariant subspaces of mixed Lebesgue spaces in the setting of locally compact abelian groups is considered. The sampling inequalities as well as the reconstruction formulae are shown to hold with very high probability if the number of samples is taken to be sufficiently large., Comment: 29 pages

XTE J1946+274 is a Be/X-ray binary with a 15.8s spin period and 172 d orbital period. Using $\textit{RXTE/PCA}$ data of the 1998 outburst, a cyclotron line around 37 keV was reported. The presence of this line, its dependence on the pulse phase, and its variation with luminosity have been of some debate since. In this work, we present the reanalysis of two $\textit{AstroSat}$ observations: one made during the rising phase of the 2018 outburst and the other during the declining phase of the 2021 outburst. We also present a new analysis of the $\textit{Insight}$-HXMT observations of the source at the peak of the 2018 outburst. We find the source to be spinning up over the course of the outburst and spinning down between the two outbursts. We report the presence of a higher cyclotron line energy using the 2018 $\textit{AstroSat}$ observation ($\sim 45$ keV) and 2018 $\textit{Insight}$-HXMT observation ($\sim$ 50 keV) and a line at $\sim$ 40 keV during the declining phase of the 2021 outburst using data from $\textit{AstroSat}$. We also investigate the pulse phase dependence of the cyclotron line parameters and find that the line is significantly detected in all the phases of both $\textit{AstroSat}$ observations, along with showing variation with the pulse phase. This differs from the previous results reported using $\textit{BeppoSAX}$ and $\textit{NuSTAR}$. We explain this behaviour of the cyclotron line to be due to photon spawning and different accretion column radii at the two poles of this neutron star., Comment: Accepted for publication in MNRAS

With the exponential growth of digital data and the increasing complexity of legal documentation, there is a pressing need for efficient and intelligent tools to streamline the handling of legal documents.With the recent developments in the AI field, especially in chatbots, it cannot be ignored as a very compelling solution to this problem.An insight into the process of creating a Legal Documentation AI Chatbot with as many relevant features as possible within the given time frame is presented.The development of each component of the chatbot is presented in detail.Each component's workings and functionality has been discussed.Starting from the build of the Android app and the Langchain query processing code till the integration of both through a Flask backend and REST API methods., Comment: 5 pages, 5 figures

When objects are forced to flow through constrictions their transport can be frustrated temporarily or permanently due to the formation of arches in the region of the bottleneck. While such systems have been intensively studied in the case of solid particles in a gas phase being forced by gravitational forces, the case of solid particles suspended in a liquid phase, forced by the liquid itself, has received much less attention. In this case, the influence of the liquid flow on the transport efficiency is not well understood yet, leading to several apparently trivial, but yet unanswered questions, e.g., would an increase of the liquid flow improve the transport of particles or worsen it? Although some experimental data is already available, it lacks enough detail to give a complete answer to such a question. Numerical models would be needed to scrutinize the system deeper. In this paper, we study this system making use of an advanced discrete particle solver (MercuryDPM) and an approximated numerical model for the liquid drag and compare the results with experimental data., Comment: arXiv admin note: text overlap with arXiv:2205.04354

In this paper, we analyse the circumstances in which the adjoint Gabor system is an R-dual of a given Gabor frame in the context of separable uniform time-frequency lattices in locally compact abelian groups. In this regard, we also prove a necessary condition for a Gabor Bessel sequence in this setting to be complete.

When a drop of a volatile liquid is deposited on a uniformly heated wettable, thermally conducting substrate, one expects to see it spread into a thin film and evaporate. Contrary to this intuition, due to thermal Marangoni contraction the deposited drop contracts into a spherical-cap-shaped puddle, with a finite apparent contact angle. Strikingly, this contracted droplet, above a threshold temperature, well below the boiling point of the liquid, starts to spontaneously move on the substrate in an apparently erratic way. We describe and quantify this self-propulsion of the volatile drop. It arises due to spontaneous symmetry breaking of thermal-Marangoni convection, which is induced by the non-uniform evaporation of the droplet. Using infra-red imaging, we reveal the characteristic interfacial flow patterns associated with the Marangoni convection in the evaporating drop. A scaling relation describes the correlation between the moving velocity of the drop and the apparent contact angle, both of which increase with the substrate temperature.

The dissolution and subsequent mass transfer of carbon dioxide gas into liquid barriers plays a vital role in many environmental and industrial applications. In this work, we study the downward dissolution and propagation dynamics of CO2 into a vertical water barrier confined to a narrow vertical glass cylinder, using both experiments and direct numerical simulations. Initially, the dissolution of CO2 results in the formation of a CO2-rich water layer, which is denser in comparison to pure water, at the top gas-liquid interface. Continued dissolution of CO2 into the water barrier results in the layer becoming gravitationally unstable, leading to the onset of buoyancy driven convection and, consequently, the shedding of a buoyant plume. By adding sodium fluorescein, a pH-sensitive fluorophore, we directly visualise the dissolution and propagation of the CO2 across the liquid barrier. Tracking the CO2 front propagation in time results in the discovery of two distinct transport regimes, a purely diffusive regime and an enhanced diffusive regime. Using direct numerical simulations, we are able to successfully explain the propagation dynamics of these two transport regimes in this laterally strongly confined geometry, namely by disentangling the contributions of diffusion and convection to the propagation of the CO2 front., Comment: Submitted to Physical Review Fluids