The composite likelihood method reduces the computational cost of parameter estimation in time series by considering several subsets of observations instead of all observations at once. The asymptotic properties of this method are related to the Godambe information, an extension of the Fisher information that accounts for the dependence between subsets of observations. We aim to apply this method to linear Gaussian models, in particular fractional Brownian motion and fractional Gaussian noise. We derive theoretical expressions for their Fisher information and their Godambe information and deduce a subset selection design that sequentially maximizes the Godambe information. The size of the subsets then allows us to control the trade-off between estimation accuracy and computational cost. Through simulations, we compare this method with the method of moments and maximum likelihood estimation, and we apply it to real data, namely volatility series of a stock index and a wind speed time series.

We study Hartree-type nonlinear heat equations associated with fractional generalised anharmonic oscillators \(A_{k,l}\) in weighted modulation spaces. We first derive Strichartz-type estimates for the associated heat semigroup and then apply them to establish global well-posedness for small initial data. For \(s>\frac{d}{q'}\), the result is obtained via trilinear estimates exploiting the algebra property of the weighted modulation space, \(M^{p,q}_s\). We further establish refined trilinear estimates that bypass the algebra structure, thereby extending the global well-posedness theory to the wider range \(s\ge 0\).

$g$ mode resonances in eccentric binary neutron star systems are potential probes of internal stratification, superfluidity, composition gradients, and the equation of state. Although such weak dynamical tidal signatures are unlikely to be resolved with current detector sensitivities, third generation observations may make them accessible, in which case identifying the weak resonant phase shift would provide information beyond the bulk adiabatic tidal deformability. We build a four class dataset in an eccentric harmonic framework, containing point particle, adiabatic tide, resonant $g$ mode, and pure noise samples, and use Einstein Telescope (ET) and Cosmic Explorer (CE) detector data to test whether this weak resonant phase signature can be identified from noisy time domain strain. The ET, CE, and ET+CE deep learning models reach accuracies of $0.655$, $0.815$, and $0.897$, respectively. On the same simulated samples, the matched filtering method reaches lower accuracies of $0.514$, $0.677$, and $0.689$. This result arises from the fact that the resonant correction manifests as a weak phase morphology difference superimposed on the adiabatic tidal background, whereas matched filtering is sensitive only to the overall similarity. Hence, in the presence of weak phase differences, the neural classifier employed in deep learning is better able to learn these local phase and morphology features from the complete time domain strain segment. The results indicate that joint third generation observations improve the identifiability of weak internal mode phase information.

In this paper, we give a direct proof of determinantal formulas for connected $k$-point functions for hermitian matrix models. We also give a new proof of KP integrability for them. From the viewpoint of KP hierarchy, we further give a new proof of the explicit formula for the corresponding affine coordinates. Furthermore, duality for some hermitian matrix models is proved.

We prove rigidity in the equality case of the sharp bottom spectrum estimate under scalar curvature lower bound. Under the same topological assumptions as in our previous work, a closed manifold $(M,g)$ with $\mathrm{Sc}_g\geq -n(n-1)$ and $λ_1(\widetilde M,\widetilde g)=(n-1)^2/4$ must be hyperbolic. This gives rigidity results for closed hyperbolic manifolds and for closed manifolds admitting a metric of nonpositive sectional curvature.

We consider the problem of computing the dominant eigenvector of a symmetric matrix via the power iteration algorithm subject to constraints in the computation of matrix-vector pr ucts. In particular, we focus on scenarios where the entries of matrix-vector products with the input matrix are only partially observed. Such constraints frequently arise on cloud architectures implemented via the controller-worker model where the matrix-vector products are distributed across workers on remote servers. Instead of a prolonged delay incurred by waiting for the slowest workers to return their output to the controller, a phenomenon known as straggling, a set of pre-determined values can replace the values of the delayed workers and allow the power iteration to proceed to the next iteration. In this paper, we develop two algorithms whose expected approximation converges to the true dominant eigenvector. The first algorithm relies on a probabilistic switch between two different approaches to set the omitted entries: either set them to zero or to their previous recorded value. The second algorithm relies on averaging previously generated partial power iteration approximations obtained by ignoring a set of columns of the iteration matrix. several theoretical details are discussed while numerical experiments verify the effectiveness of the two proposed schemes and demonstrate their comparative performance advantage over current state-of-the-art.

In the present paper we are dealing with the following quasilinear elliptic problem: \begin{equation*} \begin{cases} -\mathrm{div}(ρ(x_N) |\nabla u|^{p-2}\nabla u) =a|u|^{s-2}u &\mbox{in }&\ \mathbb{R}^N_+, -|\nabla u|^{p-2}\frac{\partial u}{\partial x_N}=b|u|^{q-2}u&\mbox{on }&\ \mathbb{R}^{N-1}, \end{cases}\ \end{equation*} where $a,b\in \mathbb{R}$, $p,q,s\in(1,\infty)$ and $ρ$ is a continuous positive function on $[0,+\infty)$. We first prove new and sharp embedding results that we establish for the associted weighted energy spaces. In application, we establish existence and regularity of weak solutions to the above problem. We also prove for this problem the nonexistence of nontrivial weak solutions by a new Pohozaev-type identity we obtain. The new results about existence and nonexistence highlight the role of the weight $ρ$ on the solvability of the problem contrasting strongly with those when $ρ$ is constant.

AlScN wurtzite ferroelectrics are promising candidates for energy-efficient non-volatile memory. However, AlScN suffers from a high coercive field and reduced cycling endurance, and the limited tunability of its properties constrains further optimization. Co-doping AlScN with boron offers the promise of independently tailoring the chemical and structural properties, making AlScBN an attractive quaternary system. This material has already been explored for a few selected compositions, however, no systematic study of the full AlScBN compositional space exists. A combinatorial approach consisting of gradient deposition with HiPIMS at low temperatures of 250°C and automatic analysis of film properties allowed us to analyze a total of 850 unique samples within the AlScBN phase space. In addition to a full screening of the materials' chemical and structural properties, we fabricate and characterize combinatorial device libraries. XPS charge transfer analysis experimentally confirms that bond ionicity correlates with a reduction in the coercive field for AlScN and AlScBN systems, opposite trends are instead observed for AlBN. While the films maintain a high remanent polarization of 130-150 μC/cm2, Sc and B co-doping reduces the coercive field from 7 MV/cm to 3 MV/cm. Notably, B co-alloying lowers the amount of Sc needed to lower the coercive field, reducing reliance on this scarce element. In addition, we find that co-alloying with B, notably improves cycling endurance, which is related to a reduction in defect density. These results establish AlScBN as a scalable, CMOS-compatible ferroelectric, positioning it as an interesting alternative to AlScN.

We prove a Skorokhod decomposition for the Markov processes $X^a$ and $X$ associated to the gradient Dirichlet forms with respect to the measures $ρ^aμ^β$ and $ρμ^β$, respectively. Here, $μ^β$ is the law of the standard Brownian bridge $β$, while $ρ^a$ and $ρ$ denote densities which are given by $ρ^a(z) := \mathbf{1}_{[0,\infty)}(\bar{z}_a)$ and $ρ(z) := \int_0^1 \mathbf{1}_{[0,\infty)}(\bar{z}_x) \, dx$, respectively, for all $z\in L^2(0,1)$ which have a (unique) continuous representative $\bar{z}$ which vanishes at zero and one. To this end, we derive infinite-dimensional integration by parts formulas (IbPFs) w.r.t. $ρ^aμ^β$ and $ρμ^β$, which contain Hida distributions alongside the usual drift terms. We represent these Hida distributions by integration w.r.t. vector measures of bounded variation. The vector measures in question are constructed via an approximation argument, making use of a generalization of Prokhorov's theorem for vector measures. We further prove that, almost surely, the sample paths of $X^a$ and $X$ take values in the equivalence class of continuous functions vanishing at zero and one for all and $dt$-almost all times, respectively. The main motivation for studying $ρ^aμ^β$ and $ρμ^β$ lies in the fact that the distributional terms in their IbPFs are simplifications of the distributional term in the IbPF w.r.t. the law of the reflected Brownian bridge on the unit interval $μ^{|β|}$. Representing the latter by integration w.r.t. a vector measure of bounded variation is still an open problem.

The physics of active matter, wherein constituent particles consume energy to generate autonomous motion, has revolutionized non-equilibrium statistical mechanics. While a large body of work has successfully elucidated the behavior of dilute active systems, the dense regime -- characterized by ``active glasses and active solids'' -- presents profound challenges that defy conventional theoretical frameworks. Recent observations reveal two striking features in these dense systems: an apparent enhancement of Mermin-Wagner-Hohenberg (MWH) fluctuations leading to anomalous long-wavelength density fluctuations, and a remarkable correspondence between activity-induced annealing and annealing via oscillatory shear. In this perspective article, we propose a novel approach toward a deeper understanding of dense active matter: by developing active Hamiltonian models as equilibrium reference frameworks, we map out pathways toward non-equilibrium active systems. This strategy allows us to elucidate both the correspondence between driven and active systems and the enhanced MWH fluctuations, which likely arise from a strong coupling between spatially random active forces and long-wavelength density (phonon) modes. We outline a comprehensive roadmap employing complementary approaches, including the active Hamiltonian formalism, comparative studies of oscillatory shear in active and passive solids, and investigations of chiral active matter. Establishing this activity-oscillatory shear correspondence across diverse systems is essential to demonstrate its universality, reveal the underlying large-scale emergent physics, and place our hypothesis on a firmer theoretical ground.

High-voltage direct current (HDVC) transmission systems based on modular multilevel converters (MMCs) have become a key topology in modern power systems. The dynamics of MMCs exhibit strong multivariable coupling, constraints, and uncertainties, motivating the use of model predictive control (MPC) to enhance current regulation performance. However, MPC tuning is nontrivial and does not inherently guarantee stability or robustness, particularly in the presence of model uncertainties. This paper proposes a MPC tuning method that ensures robust performance under bounded model uncertainties. This method solves a convex linear optimization problem to compute the optimal weighting matrices Q, R, and P ensuring optimality and reproducibility. As a result, robustness is enhanced without increasing the online computation burden. The effectiveness of the method is validated through testing on a real-time digital simulator (RTDS) model of a point-to-point HVDC system. Results demonstrate improved performance compared to conventional LQR-based MPC tuning.

Molecular rare-earth-ion complexes offer unique opportunities for quantum technologies by combining the intrinsic coherence properties of rare-earth ions with chemically tunable molecular environments. A crucial capability is the realization of multi-qubit architectures with defined qubit couplings to enable two-qubit quantum gates. Here, we investigate the optical coherence properties and excitation-induced interactions of two Eu$^{3+}$-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu$^{3+}$ ions are positioned at a well-defined intramolecular distance of about 7 Angstrom. Using cryogenic ensemble spectroscopy, including spectral hole burning, free-induction decay, and photon echo measurements at temperatures down to 100 mK, we demonstrate long optical coherence times $T_{2,\text{o}}$ of up to 9 $μ$s. As a key step toward scalable multi-qubit architectures, a control-target sequence was implemented to probe conditional ion-ion interactions, revealing a stronger interaction-induced dephasing in the dinuclear complex. Finally, we show the integration of the dinuclear complex into a fiber-based optical microcavity, and observe an 380-fold emission enhancement of the $\mathrm{}^5\mathrm{D}_0\rightarrow\mathrm{}^7\mathrm{F}_0$ transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.

Examiner reports from six major UK exam boards published between 2017 and 2025 are analysed using a mixed-methods thematic analysis. Focusing on questions relating to gravity, the objective is to understand where students commonly drop marks. Findings reveal that the source of difficulty is dependent upon topic and question style. Mathematical errors account for the majority of lost marks in calculation-type questions, while a lack of conceptual understanding commonly results in lost marks on questions relating to fields, energy and gravitational potential. Pedagogical strategies for teaching gravity must emphasise algebraic skills for orbital mechanics topics while prioritising qualitative modelling and precise definitions for field theory.

We establish a complete structural classification for continuum-wise hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw$_F$-hyperbolic if, and only if, it is a pseudo-Anosov homeomorphism whose singularities consist exclusively of spines (1-prongs). Furthermore, we classify these systems up to topological conjugacy, showing that every such homeomorphism is conjugate to either an Anosov automorphism on the torus $\mathbb{T}^2$ or to its standard hyperelliptic quotient on the sphere $\mathbb{S}^2$. As a rigid consequence of this classification, we show that such dynamics are strictly obstructed on surfaces of genus greater than one, the Klein bottle, and the projective plane.

We investigate the critical regime $κ(R,T)=0$ in $κ(R,T)$ gravity. While most studies assume a non-vanishing effective gravitational coupling, the existence of critical hypersurfaces where $κ$ vanishes is a generic feature of many admissible coupling functions. We show that the apparent singularity of the non-conservation equation is an artifact of a rewritten form of the conservation law and that the fundamental equations remain regular at $κ=0$. We further analyze the structure of critical hypersurfaces, derive the associated compatibility condition $(\nabla^μκ)T_{μν}=0$, and discuss their interpretation as gravitational screening surfaces separating attractive and repulsive gravitational phases. The existence of critical coupling hypersurfaces also obstructs a global Einstein-frame description, distinguishing $κ(R,T)$ gravity from theories based solely on algebraic redefinitions of the energy-momentum tensor. Possible cosmological and astrophysical consequences are briefly explored.

The effect of using a graphene layer as a semitransparent contact layer is studied in solar cells based on AlInN on Si (100) substrates. The devices consist of AlxIn1-xN layers deposited on p-type Si (100) substrates incorporating a thin amorphous silicon (a-Si) buffer layer to improve the heterointerface quality. Three aluminum contents are studied, namely: x=0.22, 0.35 and 0.43. Subsequently, a monolayer graphene film was transferred onto the front surface of the devices using a simple and low-temperature transfer process, acting as a semitransparent conductive contact. The photovoltaic characteristics were then evaluated under illumination and dark conditions in devices with and without the graphene layer. The results show that the incorporation of graphene leads to a clear improvement in the short-circuit current density, fill factor, and overall power conversion efficiency for all studied compositions, while the open-circuit voltage remains largely unaffected. These findings demonstrate the potential of graphene as an effective transparent conductive contact for nitride-based solar cells.

The native processing of time-dependent signals from optical sensors by integrated photonic circuits can potentially bring significant advantages in terms of energy consumption, latency and processing power, as it allows skipping or reducing the use of fast digital electronics and directly exploiting optical degrees of freedom and parallelism. However, due to a short memory, optical operations usually struggle to directly process optical signals with relatively slow (<MHz) dynamics from optical sensors. In this work, we experimentally show that these limitations can be overcome by exploiting the self-pulsing dynamics in a microring resonator (MRR) network. In particular, we demonstrate that such dynamics can expand and retain information about perturbations sensed by a fiber sensor. This reduces the minimum sampling rate for the digitization of the sensor signal by at least one order of magnitude. The reduction is achieved by combining fiber sensing measurements at two different perturbation locations and frequencies with MRR network measurements at multiple output ports, input power levels and laser wavelengths. This work represents a first step in bridging time-dependent optical processing and optical sensing at sub-μs time scales.

The dynamics of nanoparticles within nanoscale liquid environments exhibit a range of complex phenomena driven by the interplay of processes at varying length scales. While these dynamics have profound technical implications, such as in nanoscale catalytic kinetics, ion-transport pathways in energy storage, and macromolecular crowding in biological systems, real-space imaging of dense, confined nanoparticle assemblies remains a significant challenge. Here, we present a liquid-phase transmission electron microscopy approach in which dense clouds of gold nanoparticles are formed within microfluidic channels, rendering the particle ensemble visible in bright-field electron imaging. This strategy enables direct imaging of different density-dependent particle ordering phenomena, including a local structuring of the colloidal liquid in nanoscale spaces, disordered dynamic clouds at high nanoparticle densities and the reversible formation of superlattice structures. Our results provide a unique window into the complex processes of colloidal self-organization at the nanoscale.

Fork-join parallelism, popularized by OpenMP, remains the dominant model for shared-memory parallel programming, but its implicit synchronization barriers can penalize algorithms with inhomogeneous workloads. Asynchronous many-task (AMT) runtimes sidestep these barriers by expressing work as a dependency graph of fine-grained tasks. Yet, the actual performance benefit over a carefully written fork-join baseline is rarely quantified. In this work, we introduce Cholesky-Bench and use it to revisit the tiled Cholesky decomposition, a canonical irregular kernel, comparing four parallelization variants of the right-looking algorithm across two runtimes: the OpenMP implementations shipped with GCC and LLVM, and the HPX AMT runtime. The variants span classical fork-join, a collapsed fork-join that exposes additional inner-loop parallelism, synchronous tasking, and asynchronous tasking with explicit data dependencies. We benchmark all eight combinations on a dual-socket 128-core AMD Zen 2 node across multiple tile sizes and problem sizes. Our results show that across all variants, HPX outperforms OpenMP at the optimal tile size by 15%-30%. Specifically, asynchronous HPX tasks are up to 26% faster than their OpenMP counterparts, and exhibit roughly 3.8x smaller task overhead. Furthermore, the collapsed fork-join variants close most of the gap to synchronous tasking. Removing redundant synchronization barriers yields an additional improvement of 7% (OpenMP) to 14% (HPX). A GCC-versus-LLVM comparison further reveals compiler-specific differences in fork-join scheduling and task-creation overheads.

We propose and analyze a polytopal discontinuous Galerkin method for the numerical approximation of a coupled non-Newtonian Stokes-Darcy system modeling the interaction between a non-Newtonian free-flow fluid and a non-Newtonian flow through a porous medium. Due to its geometric flexibility and arbitrary-order accuracy, the proposed discretization scheme is well-suited to configurations with complex geometries. We provide a complete a-priori analysis that considers shear-dependent and velocity-dependent non-Newtonian viscosity models for the free-flow and porous media regions, respectively. The well-posedness, stability, and error bounds of the method are established in the framework of generalized inf-sup theory. Error estimates are confirmed by numerical results.

This paper investigates dynamic Resource Unit (RU) allocation strategies for Wi-Fi~6 (IEEE 802.11ax) networks integrated with Time-Sensitive Networking (TSN), targeting the limitations of static RU scheduling under dynamic traffic conditions. We propose a dynamic RU allocation algorithm that maps TSN traffic classes to Wi-Fi~6 Quality of Service (QoS) mechanisms, including Enhanced Distributed Channel Access (EDCA) and aligns TSN control with Ethernet-based TSN domains. The proposed solution is evaluated using the ns-3 DetNetWiFi framework developed by fortiss, focusing on time-sensitive traffic. Simulation results demonstrate improved network efficiency with reductions in latency, jitter, and packet loss compared to static RU allocation schemes. These findings highlight the potential of dynamic RU allocation to support deterministic communication requirements in Wi-Fi~6-based TSN deployments and to enhance the reliability of hybrid industrial networks.

The article deals with the problem of testing conditional axial symmetry within a~multivariate linear heteroscedastic regression framework. A new test based on integrated rank scores is introduced and its asymptotic distribution is derived. The proposed method extends a similar procedure developed for multivariate data to the regression setting. The test may also be employed to assess specific hypotheses concerning distributional properties of the error term. Its performance and application is illustrated in a small simulation study and with real economic data. The article also contains a few theoretical results regarding axial symmetry that may be of independent interest.

In this paper, we study $S$-prime elements and $S$-primary elements within the framework of multiplicative lattices. Furthermore, we define and explore weakly $S$-prime elements and weakly $S$-primary elements, which generalize weakly prime elements and weakly primary elements in multiplicative lattices respectively. We show that the weakly $S$-prime ideals (weakly $S$-primary ideals) of a commutative ring $R$ with $1$ correspond precisely to the weakly $S_L$-prime elements (weakly $S$-primary elements) of the ideal lattice $Id(R)$ of $R$, where $S_L = \{(s) \mid s \in S\}$.

We study the effects of dimension-four and dimension-six nonminimal Higgs couplings to the Ricci scalar $R$ in the $R^2$-Higgs inflation model in light of the recent ACT and SPT observations. We show that the dimension-six operators $|Φ|^2 R^2$ and $|Φ|^4 R$ can accommodate the enhanced scalar spectral index $n_s$ preferred by the combined CMB+BAO analyses. Using a doubly covariant formalism, we find that the same region of parameter space that explains the observed value of $n_s$ can also induce rapid preheating through the production of the Goldstone modes. If thermalization proceeds efficiently through this preheating mechanism, it may help match the inflationary scale with the CMB reference scale.

Halide double perovskites (A$_2$BB'X$_6$) are a long-known class of materials that has recently been rediscovered for diverse applications, including photovoltaics, photocatalysis, and radiation detection. Their doubled unit cell provides immense chemical tunability, allowing the incorporation of magnetic ions and enabling access to a wide range of electronic-structure features, including different band-edge characters, alignments, and symmetries. Magnetic elements may further introduce spin degrees of freedom and magnetic behaviour, thereby broadening the functional landscape of these compounds. Here, we present the first comprehensive database of spin-polarised electronic-structure data for all halide double perovskites predicted to be stable by the recently introduced $τ$ tolerance factor by Bartel et al. The dataset focuses on the Cs$_2$BB'X$_6$ family, with X = I, Br, Cl, and F, and includes density of states (DOS) for $>$2,500 compounds, calculated using hybrid-functional density functional theory. Among these, 719 compounds exhibit band gaps in the visible range and 118 display half-metallic character. In addition, we provide chemical-bonding analysis using \textsc{lobster}, which provides insights into orbital interactions across the dataset. To facilitate exploration, we further offer UMAP-based visualisations and an interactive app for systematic investigation of chemical composition, electronic structure, and magnetic properties.

We build a three-dimensional (3D) red supergiant (RSG) stellar model for common envelope evolution (CEE) simulations by transporting a 1D stellar model to a 3D numerical grid, mimicking core nuclear power by depositing energy to an inner shell, and mimicking stellar emission by cooling grid cells with densities below the photospheric density. We do not relax the model; rather, we let it perform its natural pulsation. We find that when we mimic photospheric emission by cooling low-density grid cells, the oscillations slowly decay on a time scale much longer than in the absence of photospheric cooling. When we mimic both nuclear energy production, by depositing the stellar luminosity in an inner shell above the inert core of the stellar model, and the photospheric cooling, the oscillations do not decay and their amplitude slowly increases with time. The main pulsational period is about 1 year, comparable to the stellar dynamical time, suggesting a fundamental radial pulsation mode. The non-spherical structure of the stellar model and rapid low-amplitude temporal variations in the average stellar radius testify to the presence of non-radial oscillation modes on top of the fundamental radial mode. We also obtain vigorous convection, as RSG stars have. We conclude that the best way of preparing a giant star to simulate CEE and grazing-envelope evolution is to deposit energy with the stellar luminosity in an inner shell, and to cool the outer low-density numerical shell. There is no need to relax the model.

Given $n \in \mathbb{N}$, an Ahlors--David $n$-regular set $S \subset \mathbb{R}^{n+1}$, and a weight $γ$ satisfying the local Muckenhoupt $A_{1}$-condition, we present a complete intrinsic description of the trace-space $W_{1}^{1}(\mathbb{R}^{n+1},γ)|_{S}$ of the weighted first-order Sobolev space $W_{1}^{1}(\mathbb{R}^{n+1},γ)$ to $S$. Furthermore, we construct a new family of nonlinear bounded extension operators acting from $W_{1}^{1}(\mathbb{R}^{n+1},γ)|_{S}$ to $W_{1}^{1}(\mathbb{R}^{n+1},γ)$. Finally, we find conditions on $γ$ that sufficient for the existence of a bounded linear extension operator from $W_{1}^{1}(\mathbb{R}^{n+1},γ)|_{S}$ to $W_{1}^{1}(\mathbb{R}^{n+1},γ)$.

The propagation of very-high-energy (VHE; $E_γ \geq 100$ GeV) gamma rays from extragalactic sources is affected by interactions with photons of the extragalactic background light (EBL), resulting in pair production that attenuates the intrinsic gamma-ray flux. This interaction renders the Universe increasingly opaque to VHE photons at high energies and redshifts. New physics scenarios involving axion-like particles (ALPs) could modify this expected optical depth. In particular, ALPs with masses $m_a \sim 10$ eV can decay into two photons over cosmological timescales, thereby contributing to the diffuse EBL. If such ALPs constitute a significant fraction of the dark matter density, their decay would enhance the EBL intensity and consequently increase the gamma-ray optical depth. In this study, we investigate this scenario using a large sample of gamma-ray spectra observed with the High Energy Stereoscopic System (H.E.S.S.) and the Fermi Large Area Telescope. We model the contribution of decaying ALPs to the EBL and assess their impact on the spectra of blazars across redshifts. By comparing these observations with standard EBL models, we place constraints on the properties of heavy ALPs, specifically their mass and photon coupling, and evaluate their viability as a dark matter candidate capable of modifying the gamma-ray transparency of the Universe. From the combined analysis, and under the assumption that ALPs constitute the entire dark matter density, we derive 95% confidence exclusion limits on the photon-ALP coupling down to $g_{aγ} \sim 7 \times 10^{-12}$ GeV$^{-1}$ for masses $m_a\sim 15$ eV. These constraints are competitive with existing astrophysical bounds and provide complementary sensitivity to other techniques, closing a previously unconstrained region of parameter space in the $m_a \sim 2.5$-$20$ eV range.

With the aim to study the spectral properties of some X-ray sources from recently observed {\it Chandra} data, 9 galaxies which have been observed by {\it Chandra} ACIS-S during the year 2018 to 2022 have been considered for the present work. 27 sources with net source counts $ \ge$ 100 have been considered. The spectra of all the sources were fitted using two empirical models -- an absorbed powerlaw and an absorbed disk blackbody. From their estimated bolometric luminosities, the 27 X-ray sources are categorized as 6 X-ray binaries (XRBs) and 21 Ultraluminous X-ray sources (ULXs). All the six XRBs are found to be in the spectrally hard state ($Γ\sim$ 1.52-2.29) which indeed may be due to thermal comptonization. Only one ULX, CXOUJ032251.2-370950 (X-5), was found to be spectrally soft while the remaining 20 ULXs were spectrally hard. The spectral parameters of X-5 with an inner disk temperature (kT$_{in}$) $\sim $ 0.5 keV and an estimated bolometric luminosity, L$_X \sim$ 3.26 $\times$ 10$^{39}$ erg s$^{-1} $ requires a black hole of mass, M$_{BH} \sim$ 137.86$^{+66.62}_{-47.41}$ M$_\odot $ accreting at $ \sim$ 0.19 times its Eddington limit. 8 ULXs, X-4, X-8, X-9, X-10, X-11, X-12, X-20 and X-21, were found to be in the Extremely luminous X-ray sources (ELXs) regime with even their lower limit of luminosity $>$ 10$^{40}$ erg s$^{-1}$. Softening/Hardening of spectra with or without changes in the luminosity were also observed in some ULXs/ELXs. In the hard ELX, X-8, spectral softening with almost consistent luminosity was observed. While in the ULXs X-20 and X-25 spectral softening with increasing luminosity was observed. However spectral hardening with increase in luminosity were observed in the ULXs X-21 and X-26.

We establish the Kazhdan isomorphism for the $n$-fold metaplectic cover of the reductive group $\mathrm{SL}_2$ over two sufficiently close non-archimedean local fields $F$ and $F'$, both of which have residue characteristic coprime to $n$ and contain all distinct $n$th roots of unity.