The East Asia VLBI Network (EAVN) has recently enabled dual-polarization observations at $22$ and $43\,\mathrm{GHz}$. We present the first systematic verification of its polarimetric performance using EAVN observations of M87, 3C 279, 3C 273, and OJ 287, calibrated with the GPCAL pipeline and evaluated against near-contemporaneous VLBA images at comparable frequencies. Most stations show stable polarimetric leakages with amplitudes of $5$-$10\%$ over monthly timescales. While several VERA stations exhibit D-term phase variations between epochs, we attribute these to field-rotator (FR) offsets and demonstrate that phase stability is restored after applying the analytically derived FR corrections. The resulting linear-polarization morphologies and EVPAs broadly agree with the VLBA results within uncertainties; fractional polarization measured by the EAVN tends to be slightly higher near polarization peaks. Although exact one-to-one comparisons are limited by moderate frequency and epoch differences, the combined evidence indicates robust EAVN polarimetric calibration and imaging capabilities at $22$ and $43\,\mathrm{GHz}$. These results support the scientific capability of EAVN polarimetry and lay the groundwork for expanded, higher-fidelity polarimetric studies in East Asia.

Single-atom catalysts (SACs), composed of isolated metal atoms dispersed on solid supports, represent the ultimate expression of atomic efficiency in catalysis. Their remarkable activity and selectivity arise from local coordination environments and adjustable oxidation states, yet precise determination of these features remains an enduring challenge. Among modern characterization techniques, X-ray absorption near-edge structure (XANES) spectroscopy stands out for its sensitivity to both electronic and geometric structure, though its interpretation is often constrained by empirical comparison with bulk references. Here we introduce a density functional theory (DFT) based computational spectroscopy framework for the quantitative interpretation of Cu K-edge XANES spectra. We then employ this framework to reveal the oxidation state, coordination geometry, and hydration environment of Cu single atoms supported on cyanographene, demonstrating direct correspondence between spectral signatures and atomic-scale structure. This methodology establishes a robust and transferable route for connecting XANES features with the underlying electronic and structural characteristics of SACs, thereby advancing the rational design of atomically precise catalysts.

We investigate the hypercontractivity property of generalized Mehler semigroups on the $L^p$-scale with respect to invariant measures. This property is first obtained in the purely theoretical setting of skew operators and, subsequently, deduced for generalized Mehler semigroups arising from linear stochastic differential equations perturbed by Lévy noise. When the associated invariant measure $μ$ lacks a purely Gaussian structure, jump components may prevent the validity of Nelson's classical $L^p$-$L^q$ estimates. However, a summability-improving property can be obtained in the setting of mixed-norm spaces $\mathcal{X}_{p,q}(E;γ,π)$ related to the factorization of the invariant measure $μ= γ* π$ into a Gaussian part $γ$ and an infinitely divisible non-Gaussian part $π$. As in the classical Gaussian case, some modified logarithmic Sobolev inequalities with respect to invariant measures can be inferred.

Let $t\geq2$ and $k\geq1$ be integers. Let $H_{k}(z)$ with $\left\vert z\right\vert <1$ be the limit of a certain subsequence of the Stern polynomials introduced by Dilcher and Eriksen. We use Mahler's method to prove the algebraic independence of the values at nonzero algebraic points of the functions $H_{k}(z)$ and $H_{k}(z^{t^{k}})$.

Exploiting quantum effects for energy storage, quantum batteries (QBs) offer compelling advantages over conventional ones in terms of superior energy density, ultrafast charging, and high conversion efficiency. However, their realization is hampered by decoherence, which causes incomplete charging, rapid self-discharging, and reduced extractable work. Here, we propose a QB architecture based on a chiral magnonic platform. It comprises two yttrium iron garnet (YIG) spheres, one serving as the charger and the other as the QB, coupled to a waveguide. The unique chiral coupling between magnons and the guided electromagnetic fields breaks inversion symmetry, inducing both nonreciprocal energy flow and coherent interference between the charger and QB. Their synergy endows our QB with a 34-fold increase in energy capacity and a 55-fold boost in extractable work compared to its achiral counterpart in an experimentally accessible regime. Our scheme harnesses the decoherence from the electromagnetic fields and turns its destruction into an asset, which enables the robustness and wireless-like remote charging features of the QB. Our analysis reveals that these extraordinary capabilities stem from quantum coherence. By establishing chirality as a useful quantum resource, our work paves a viable path toward the realization of QBs.

This paper investigates the traces of functions belonging to the inhomogeneous Besov spaces B $ξ$ p,q , where $ξ$ is a product of capacities defined as powers of Gibbs measures. We first establish that the traces of functions in B $ξ$ p,q along affine hyperplanes belong to another inhomogeneous Besov space. Furthermore, we derive an upper bound for the singularity spectrum of the traces of all functions in B $ξ$ $\infty$,q . This bound is then refined for a prevalent set of functions in B $ξ$ $\infty$,q , for which we explicitly compute the singularity spectrum of their traces. Notably, our analysis reveals that the regularity properties of these affine traces are highly sensitive to the choice of the hyperplane along which the trace is taken.

In 1973, Bardeen, Cater, and Hawking published "The Four Laws of Black Hole Mechanics", establishing the mathematical framework that would later be understood as the thermodynamics of black holes. Central to the paper is equation (33), which writes the variation of the total energy-momentum integral in terms of physically meaningful quantities: angular momentum, particle number, and entropy. Equation (33) feeds into the differential mass formula, equation (34), which is the first law of black hole mechanics. This note identifies two compensating sign errors in the BCH paper. The first error, demonstrated by a derivation from equation (32), is that equations (33) and (34) should carry minus signs rather than plus signs on the last two integrals, those involving the redshifted chemical potential and the redshifted temperature. he second error is that the definitions of total particle number N and total entropy S given after equation (20) are missing minus signs that are required for these quantities to be positive. These two errors cancel, in that reversing the signs in the definitions of N and S to ensure positive quantities makes equations (33) and (34) correct. All conclusions of the BCH paper remain valid. This note is intended merely as a guide for readers who, in working through the derivation step by step, might otherwise be puzzled by the sign discrepancies. Numbered equations refer to the BCH paper; lettered equations are introduced in this note.

In traditional views, the build-up of accelerating energy during faults can cause the well-known first-swing angle instability in synchronous generators (SGs). Interestingly, this letter presents a new insight that the accumulation of decelerating energy due to the low voltage ride-through (LVRT) and recovery control of grid-following inverter-based resources (GFL-IBRs), might also result in transient angle instability in SGs. The transient energy accumulated during angle-decreasing swing transforms into the acceleration energy of the subsequent swing, hence such phenomena often manifest as multi-swing instability. Both theoretical analysis and simulation support these findings.

Mechanical vibration monitoring often requires high sampling rates and generates large data volumes, posing challenges for storage, transmission, and power efficiency. Compressive Sensing (CS) offers a promising approach to overcome these constraints by exploiting signal sparsity to enable sub-Nyquist acquisition and efficient reconstruction. This study presents a comprehensive comparative analysis of the key components of the CS framework: sparse basis, measurement matrix, and reconstruction algorithm for machinery vibration signals. In addition, a hardware-efficient measurement matrix, the Wang matrix, originally developed for image compression, is introduced and evaluated for the first time in this context. Experimental assessment using the HUMS2023 and the CETIM gearbox datasets demonstrates that this matrix achieves superior reconstruction quality, with higher SNR, compared to conventional Gaussian and Bernoulli matrices, especially at high compression ratios.

Diffractive neural networks (DNNs) are an emerging approach for the realization of photonic artificial intelligence, especially due to their suitability for machine-vision applications and high-dimensional photonic information processing at lower power consumption. However, incorporating optical nonlinear activation functions to make DNNs a feasible alternative to their electronic counterpart remains a challenge. Here, we investigate the inclusion of second-harmonic generation (SHG), as one of the simplest and most efficient types of optical nonlinearities, in DNNs. We numerically investigate the impact of SHG on the performance of classification tasks in an all-optical nonlinear DNNs. Specifically, we investigate and discuss the essential requirements for an effective arrangement of the SHG layer in single and multilayer DNNs. We find that the performance, in terms of classification accuracy and class contrast, is affected strongly by the positioning of the SHG layer. Finally, we discuss and outline the constraints for including SHG in an experimental realization. Taking these constraints into account, we estimate the power-related efficiency of the nonlinear DNN system. Overall, our results provide a path towards implementing nonlinear DNNs using the SHG process.

We study the well-known Ptolemy-Alhazen problem on reflection of light at the surface of a spherical mirror in the case when the source of light is very far from the mirror.

Spatiotemporal optical vortices (STOVs) carry transverse orbital angular momentum and offer new degrees of freedom for light-matter interactions. Yet conventional focusing of STOVs introduces spatiotemporal astigmatism: the beam diffracts while the pulse duration stays constant, causing the vortex to deform away from focus. Here we overcome this limitation by introducing spectral phase modulation into a temporal focusing configuration, where angular dispersion forces the pulse to compress only at the geometric focus so that the spatial and temporal dimensions focus and defocus together. Our approach generates stable STOVs with self-similar, distortion-free evolution over an extended focal region. Besides, the orbital angular momentum vector can be continuously steered from purely longitudinal to strongly tilted orientations by adjusting the spatial dispersion, objective focal length, or input beam size. More importantly, our method offers full compatibility with high NA focusing geometry, allowing high-intensity and high-resolution applications. We validate these properties through femtosecond laser ablation under high-NA conditions and interferometric spatiotemporal field reconstruction under low-NA conditions.

Recently, a fractional version of the Schwarzschild-Tangherlini black hole with a fractal horizon has been introduced. Motivated by the key role of the Schwarzschild solution in gravitational and astrophysical studies, some consequences of this fractional-fractal generalization of the Schwarzschild black hole have been investigated. In this line, the corresponding i) Shapiro and Sagnac time delays, ii) shadow, iii) orbital precession, and iv) gravitational lensing are studied and confronted with observational data. MCMC analysis also unveils i) the potential of this metric in dealing with the solar-system tests and ii) the necessity of studying fractional spacetimes and objects.

In this paper the random channels and their compositions in the space of quantum states are studied. For compositions of i.i.d. random unitary channels, the limit behaviour of probability distributions is described. The sufficient condition for convergence in probability is obtained. The generalized convergence in distribution w.r.t. weak operator topology is obtained. The analysis of transmission of pure and normal states to the set of singular states is done. The dynamics of quantum states is described in terms of the evolution of the values of quadratic forms of operators from the algebra that implements the representation of canonical commutation relations.

This paper studies the number of limit cycles, known as the Smale-Pugh problem, for the generalized Abel equation \begin{align*} \frac{dx}{dθ}=A(θ)x^p+B(θ)x^q, \end{align*} where $A$ and $B$ are are piecewise trigonometrical polynomials of degree $ m $ with two zones $0\leqθ<θ_1$ and $θ_1\leqθ\leq2π$. By means of the first and second order analysis using the Melnikov theory and applying the new Chebyshev criterion that established by \cite{HLZ2023}, we estimate the maximum number of positive and negative limit cycles that such equations can have, and reveal how this maximum number, denoted by $H_{θ_1}(m)$, is affected by the location of the separation line $θ=θ_1$. For the equation of classical Abel type, our result not only includes the estimates provided in the recent paper (Huang et al., SIAM J. Appl. Dyn. Syst., 2020), i.e., $H_{2π}(m)\geq 4m-2$ for $θ_1=2π$, but also shows that the equation in the discontinuous case can possess more than two times as many limit cycles as in the continuous case. More accurately, $H_π(m)\geq 8m+2$ and $H_{θ_1}(m)\geq 14m-6$ for $θ_1\in (0,π)\cup (π,2π)$.

The superconducting diode effect (SDE), characterized by nonreciprocal critical currents, has attracted growing attention due to its potential applications in quantum technologies and energy-efficient devices. In this work, we explore the microscopic mechanism of the SDE by simulating asymmetric multilayer heterostructures within time-dependent Ginzburg-Landau theory. We systematically vary the layer thickness, external magnetic field and stacking order in a trilayer structure composed of niobium, vanadium, and tantalum, which share a similar structure to that in the pioneering experimental work, to clarify the role of vortex dynamics. Our simulations reveal a pronounced SDE originating from the interplay of Lorentz forces and asymmetric vortex dynamics, which strongly depend on layer stacking order. Besides, by simply changing the stacking order of the constituent layers, the SDE can be entirely suppressed. These findings offer insights into the microscopic mechanisms of the SDE and provide a feasible approach for controlling and eliminating the SDE in practical superconducting devices.

We present an analytical and numerical study of the dynamics and stability of exciton-polariton condensates described by the open-dissipative Gross-Pitaevskii equation, incorporating both binary and short-range three-body interactions. Using an asymptotic description, we identify the parameter regime and derive equations for the instability amplitude, providing insights into vortex formation via the snake instability of dark solitons. We find that a repulsive three-body interaction, when combined with a binary interaction, supports stable vortex-antivortex pair formation. On the other hand, the reinforcement of attractive three-body interactions with binary interaction triggers the emergence of snake instability, leading to boundary-driven vortex disintegration. The time evolution of the instability under the influence of reservoir effects indicates that the boundary effects are more pronounced, to the extent of destabilizing the vortices with attractive three-body interactions compared to repulsive three-body interactions, thereby underscoring the stable nature of vortices in the repulsive domain.

Femtosecond-laser direct waveguide writing is progressively emerging as an alternative to conventional techniques to develop complex photonic devices, for applications ranging from classical and quantum information processing, to sensing and metrology. Laser written waveguides typically offer low modal birefringence, thus preserving coherence of polarization-encoded information. Integrated waveplates have been reported, as waveguides with tilted birefringence axis, but with limited flexibility in terms of achievable rotation angle, birefringence magnitude or control in the modal shape. Here we investigate the multi-scan approach to realize low-loss optical waveguides in fused silica substrate with controlled modal birefringence. We show that by tuning the horizontal and vertical shifts between subsequent scans we can independently change both the magnitude and the axis inclination of the birefringence, while keeping efficient mode coupling with standard fibers.

These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.

We develop a comprehensive theory for a general class of multi-parameter function spaces of Besov-Triebel-Lizorkin type, with a matrix weight. We prove the equivalence of different quasi-norms, the identification of function and sequence spaces via the $φ$-transform, the boundedness of almost diagonal operators and multi-parameter singular integrals under minimal assumptions, molecular and wavelet characterisations, and Sobolev-type embedding theorems. We identify matrix-weighted $L^p$ spaces, Sobolev spaces, and multi-parameter BMO spaces as examples of our general scale of spaces. Thus, our result on the boundedness of multi-parameter singular integrals on these spaces is seen as an extension, with a different method, of a recent theorem of Domelevo et al. [J. Math. Anal. Appl. 2024] on matrix-weighted $L^p$ spaces. For this theory, we develop several tools of independent interest. Many previous results were restricted to integrability exponents $p\in(1,\infty)$, while Besov-Triebel-Lizorkin spaces naturally involve the full range $p\in(0,\infty)$. We extend the definition of multi-parameter $A_p$ matrix weights to $p\in(0,1]$ and establish their basic properties, culminating in the $L^p$-boundedness of a matrix-weighted strong maximal operator (suitably rescaled when $p\in(0,1]$) for all $p\in(0,\infty)$. For $p\in(1,\infty)$, this is due to Vuorinen [Adv. Math. 2024] by convex-set-valued techniques of Bownik and Cruz-Uribe [arXiv 2022; Math. Ann. (to appear)]; the lack of convexity requires us to develop a new approach that works for all $p\in(0,\infty)$. We also need and prove a multi-parameter extension of Carleson-type embeddings from Frazier and Roudenko [Math. Ann. 2021] but attributed by them to F. Nazarov. We prove the necessity of the conditions of the new embedding using a nontrivial elaboration of Carleson's classical counterexample [Mittag-Leffler Rep. 1974].

The hidden altermagnetism has been theoretically proposed and then experimentally confirmed in metal $\mathrm{Cs_{1-δ}V_2Te_2O}$, which exhibits two nearly degenerate ground-state magnetic configurations (C-type and G-type) corresponding respectively to apparent and hidden altermagnetism. Here, we propose that in-plane uniaxial strain can be utilized to distinguish apparent and hidden altermagnetism. Under uniaxial strain, apparent altermagnetism exhibits an obvious net magnetic moment, whereas hidden altermagnetism maintains zero net magnetic moment. The magnetic moment induced by uniaxial strain here, namely the piezomagnetic effect, differs from that in semiconductors, where strain must be applied first followed by carrier doping to generate net magnetism. First-principles calculations verify our proposal, revealing that the magnetic moment induced by uniaxial strain in C-type antiferromagnetic $\mathrm{CsV_2Te_2O}$ is much larger than that in the previously studied altermagnetic semiconductors. Furthermore, we also investigate the electronic state transitions of semiconductors featuring a crystal structure analogous to $\mathrm{CsV_2Te_2O}$ under uniaxial strain, and verify our proposal in specific material via first-principles calculations. Our work provides an experimentally feasible strategy to distinguish apparent and hidden altermagnetism in material $\mathrm{Cs_{1-δ}V_2Te_2O}$, and extends the physical implication of the piezomagnetic effect, which can be directly verified in experimentally synthesizable $\mathrm{KV_2Se_2O}$ and $\mathrm{Rb_{1-δ}V_2Te_2O}$.

In this paper, we study the Graded Invariant Basis Number (grIBN) property for Leavitt path algebras of finite graphs. Using the talented monoid as our main tool, we establish a complete matrix-theoretic characterization of when a Leavitt path algebra of a finite graph fails to have gr-IBN. Consequently, we identify several classes of graphs whose Leavitt path algebras have gr-IBN, including graphs with sinks, Cayley graphs, and Hopf graphs associated with finite groups. We also investigate the preservation of gr-IBN under quotients by hereditary saturated subsets and under Cartesian products of graphs.

This study proposes a novel adaptive finite volume-particle method (AFVPM) for accurate and efficient free surface flow simulations. The proposed AFVPM synergistically combines the Eulerian finite volume method (FVM) on unstructured meshes with the Lagrangian smoothed particle hydrodynamics (SPH) approach. Specifically, the mesh-based FVM is employed in the bulk flow regions to leverage its computational efficiency and numerical accuracy, while a weakly compressible SPH formulation is applied in the vicinity of the interface to maintain robust free-surface tracking capabilities. A key innovation of this framework is a block-based dynamic and adaptive conversion strategy between Eulerian mesh regions and Lagrangian particle regions and a buffer region-based cell-particle algorithm is designed to ensure seamless data communication across the Eulerian mesh-Lagrangian particle interface. Furthermore, isothermal gas-kinetic scheme (GKS) incorporating gravitational effects is utilized to calculate the fluxes in the mesh regions. The performance and reliability of the proposed AFVPM are validated through a series of benchmark cases that involve complex free surface phenomena. Numerical results demonstrate that AFVPM achieves superior accuracy and efficiency compared to full SPH approaches.

We present a measurement-based quantum thermal machine that extracts work from the back-action of generalized quantum measurements whose working medium is a coupled two-level quantum system. Specifically, we derive universal optimization criteria for a three-stroke measurement-based engine cycle with coupled two-level system of Ising-like interaction as a working medium. Furthermore, we present two numerical algorithms to optimize the engine work extraction and enhance its performance. Our numerical results demonstrate: (i) efficiency peaks in the projective-measurement limit; (ii) symmetry breaking (detuning or weak coupling) enlarges the exploitable energy gap; and (iii) performance remains robust ($>50\%$ of optimum) under $\sim\!10^\circ$ feedback-pulse errors. The framework is platform-agnostic and directly implementable with current superconducting, trapped-ion, or NMR technologies, providing a concrete route to scalable, measurement-powered quantum thermal machines.

We investigate a hybrid photon blockade (HPB) scheme in a driven two-qubit cavity QED system arising from the combination of eigenenergy-level anharmonicity (ELA) and quantum destructive interference (QDI). By tuning the detuning of a single qubit and pumping field, we identify precise parametric regimes that fully integrate the advantages of high brightness in ELA-based conventional photon blockade and strong antibunching in QDI-based unconventional photon blockade. Interestingly, these regimes are accompanied by hyperradiance, indicating that inter-emitter correlations give rise to enhanced collective emission. The HPB mechanism exhibits parametric generality across varying coupling asymmetries and remains accessible via detuning control, offering a feasible route for generating high-quality single-photon source in diverse quantum platforms.

Non-uniform product (color) distribution in colorimetric paper-based sensors affects the accuracy and reliability of measurements. The underlying mechanisms responsible for this are still unclear. The coffee ring effect explains the ring-formation at the periphery. However, ring-like patterns can also be found at intermediate radial positions in these sensors. In this work, we study the influence of mass transport and reaction dynamics within porous/paper substrates on the spatial product distribution. We consider one reactant embedded in a porous substrate, which reacts with another delivered through a sessile droplet. The process is modeled in two stages. In Stage 1, droplet imbibition creates two distinct flow domains in the substrate with moving boundaries. Stage 2 commences after complete penetration. Species-substrate interactions are addressed by including a mobility factor. The developed model is used to analyze the effects of different parameters on the product distribution for two configurations, Reagent-Embedded (RE) and Analyte-Embedded (AE). Our work demonstrates ring-like patterns can form even without evaporation effects. With decreasing analyte-reagent concentration ratio, the profile shifts inward. Thicker, more porous substrates yield greater uniformity but reduce color intensity. Immobilization of embedded species enhances uniformity in RE configuration with mobile product, and in AE configuration with immobile product. The model is validated with lead and nitrite detection experiments for RE and AE configurations respectively. It successfully captures three spatial color variations observed experimentally. This study also explains the emergence of multiple rings in these systems. The insights gained are useful for optimizing sensor design and protocols for colorimetry

Phase change materials based on Ge-Sb-Te alloys are widely explored for their potential in both memory devices and thermoelectric applications. In this study, films of Ge2Sb2Te5 (GST) doped with varying concentrations of Pb were prepared and systematically investigated to trace the effect of Pb doping on crystallization-induced phase transformations and thermoelectric properties. Via X-ray diffraction and Raman spectroscopy, the impact of Pb doping on the crystallization behavior was revealed and examined. According to the specific electrical resistivity measurements, the Pb doping resulted in decreasing both the amorphous-to-cubic and cubic-to-hexagonal transition temperatures, thereby facilitating the formation of the hexagonal phase at a lower thermal regime. Furthermore, Seebeck coefficient and electrical resistivity data of hexagonal Pb-doped GST were used to calculate the power factor, PF. A PF maximum equal to 1.3 was found for 2.5 at. Pb-GST at 633 K, with the highest carrier mobility also observed for this composition. Controlled Pb doping effectively modulates both structural transitions and thermoelectric performance, highlighting the potential of Pb-GST for applications that combine phase-change memory and thermoelectric functionality, such as opto-thermoelectric devices and non-volatile thermoelectric sensors.

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real applications are highly restricted by their poor generalization performance. Inspired by the rigorous mathematical statements on the well-posedness of PDEs, we develop a novel extension of PINNs by incorporating the additional information on the continuous dependence of PDE solutions with respect to parameters and initial/boundary values (abbreviated as cd-PINN). Extensive numerical experiments demonstrate that, with limited labeled data, cd-PINN achieves 1-3 orders of magnitude lower in test MSE than DeepONet and FNO. Therefore, incorporating the continuous dependence of PDE solutions provides a simple way for qualifying PINNs for operator learning.

Competing charge and spin orders are central to uncovering the nature of unconventional superconductivity. Here we utilize synchrotron X-ray diffraction on a high-quality single crystal to reveal the charge order of La$_3$Ni$_2$O$_7$ at ambient pressure, which competes with the high-temperature superconducting phase under pressure. Enabled by the high synchrotron photon flux and a large dynamic range, we resolve faint reflections -- nearly four orders of magnitude weaker than the main Bragg reflections -- that were overlooked in prior diffraction studies. This observation evidences a broken glide-mirror symmetry, leading to a polar crystal structure, rather than the widely used centrosymmetric structure model. The polarity is induced by checkerboard charge order on nickel sites in combination with octahedral tilting, reminiscent of bilayer manganese oxides. Our results provide a foundation for understanding phase competition and the mechanism of pressure-induced superconductivity in bilayer nickelates.

We present a general procedure for constructing triangulated categories, linear over a field, with distinct enhancements. Some of our examples can be equipped with a (non-degenerate) t-structure, thereby showing that the existence of a t-structure does not imply uniqueness of enhancements, whether in the strong or weak sense (depending on the example).