Movable antenna (MA)-enabled near-field (NF) communications offer significant potential for 6G, yet existing designs often neglect the practical constraints of hybrid beamforming (HBF) for extremely large-scale MIMO (XL-MIMO). Conversely, MA-aided HBF frequently overlooks the rich NF degrees of freedom (DoFs). This paper proposes a movable subarray (MSA)-aided HBF architecture for NF multiuser systems, which strikes a strategic balance between hardware practicality and spatial flexibility. By coupling MSA movement with HBF, the proposed design simultaneously exploits NF distance-dependent and MSA position-dependent DoFs, enabling highly precise beamfocusing and superior interference mitigation. To alleviate the computational burden, a hybrid planar-spherical wave model is introduced for efficient channel approximation. Furthermore, an alternating optimization (AO) algorithm is developed by integrating fractional programming, the alternating direction method of multipliers (ADMM), and projected gradient ascent. Simulation results validate substantial sum-rate gains over fixedposition antenna (FPA) benchmarks.

A standard intensional account of probabilistic computation represents a randomized program as a deterministic computation that consumes an explicit random tape. This yields a two-layer perspective: an intensional layer that makes reuse of randomness and correlation visible, and an extensional layer obtained by interpreting tapes under a chosen probability measure. We develop an evidence-tracked tape semantics using the monadic-core-to-evidenced-frame pipeline (and its induced realizability tripos), obtaining a higher-order logic in which entailments are witnessed by uniform evidence transformers. Quantitative statements are recovered by interpretation: once a tape measure is fixed, probabilities and expectations arise by extracting numerical summaries from tape-indexed predicates, and entailments yield sound inequalities, with an almost-sure quotient supporting probability-one reasoning. We also study intensional principles that are lost at the level of laws, including proof-relevant transport along realizable tape-rewiring maps and a canonical splitting discipline for stream tapes enforcing independent draws. Finally, we relate tape-based reasoning to an extensional law semantics via pushforward, isolating a probability-one must abstraction as a sound summary of tape-based proofs.

The low-energy $Ξ$-deuteron scattering is investigated through the solution of Faddeev equations, employing three sets of the currently available parametrization of the $Ξ$-nucleon interactions. One of these is the chiral NLO interaction parametrized by the Jülich group, and the other two are based on the calculations by the HAL-QCD method. The $s$-wave phase shifts in the $J=3/2$ and $J=1/2$ states are presented. Three-body wave functions in coordinate space are constructed from the Faddeev amplitudes in momentum space. These functions are used in the calculation of $Ξd$ momentum correlation functions. The effects of the deuteron breakup are significant in the $J=3/2$ channel. The differences in the magnitude of the calculated correlation function show the quantitative difference of the $ΞN$ interactions in the spin-isospin channels. The prospective experimental data on the $Ξd$ momentum correlation function could contribute to a better description of the $ΞN$ interactions.

Magnetars are a subclass of neutron stars with ultra-strong surface magnetic fields. Some magnetars exhibit persistent hard X-ray emission, characterized by power-law tails with photon indices around 1--1.5, extending from ${\sim}$10 keV to several hundred keV. The leading explanation for this hard X-ray component is resonant Compton scattering, in which the thermal seed photons are upscattered by relativistic electron-positron pairs flowing along magnetic field lines in the magnetosphere. In this work, we adopt the pair outflow framework of the magnetar magnetosphere and calculate the resonant Compton scattering opacity, as well as the spectrum and polarization of the upscattered emission. We find that resonant cooling can substantially modify the magnetospheric plasma density and impose strong optical depth constraints on the hard X-ray emission regions. Under the viewing geometry inferred from IXPE, an equatorial twist near the stellar surface provides a viable configuration for the NuSTAR hard X-ray spectrum of 4U 0142+61, while a polar-twist geometry is disfavored. Joint spectral, timing, and polarimetric modeling will be essential for distinguishing between the magnetospheric scattering geometries and understanding the physical properties of the pair plasma.

Multilingual Information Retrieval is increasingly important in real-world search settings, where users issue queries over mixed-language corpora. Existing evaluations mainly reward language-agnostic semantic relevance, treating relevant passages equally regardless of language. Yet retrieval utility also depends on the language of the retrieved passages: users may prefer results they can read and verify in the query language, and query--passage language mismatch can complicate downstream grounding and answer verification in Retrieval-Augmented Generation systems. To evaluate this language-aware dimension, we introduce MLAIRE, a Multilingual Language-Aware Information Retrieval Evaluation protocol that disentangles cross-lingual semantic retrieval from query-language preference. MLAIRE constructs controlled pools with parallel passages across languages, enabling measurement of semantic retrieval accuracy and query-language preference when equivalent translations are available. We propose language-aware metrics, including Language Preference Rate (LPR) and Lang-nDCG, together with a 4-way decomposition separating semantic and query-language preference failures. Evaluating 31 dense, sparse, and late-interaction retrievers, we show that standard metrics obscure distinct behaviors: semantically strong retrievers may return correct content in a non-query language, while retrievers with stronger query-language preference may retrieve less semantically relevant passages.

This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspection. In other words, no computation is required for decoupling the variables of multivariate rational functions. The key tool for this development is the Loewner Framework for multivariate functions. Applications of this result involve approximating multivariate non-rational functions by low-complexity multivariate rational and polynomial functions.

Commercial FPGAs, such as AMD Versal devices, increasingly incorporate AI engines that exploit low-precision packed-SIMD fused multiply-accumulate (FMA) to achieve proportional throughput gains. However, trans-precision FMA (e.g., multiplying two FP16 numbers and adding their result to an FP32 accumulator), which preserves numerical stability by accumulating in higher precision, remains bottlenecked by the highest-precision, lowest-throughput operation. Dot-product accumulation (DPA) (e.g., performing a dot-product on two 4-element FP8 vectors and adding its result to an FP32 accumulator) can fully utilize the input/output bandwidth and computational resources. Existing flexible open-source FPUs, such as FPnew, do not support DPA and implement SIMD FMA on low-precision formats by replicating independent FMA lanes, which increases area, underutilizes shared arithmetic resources, and complicates the integration of DPA operations. This paper presents TransDot, a reconfigurable FPU that unifies multi-precision SIMD FMA and trans-precision DPA within a shared, reconfigurable datapath. TransDot extends the baseline design with 2-term FP16, 4-term FP8, and 8-term FP4 dot-product accumulation into FP32 using reconfigurable subcomponents. Evaluation shows that TransDot delivers 2$\times$ FP16, 4$\times$ FP8, and 8$\times$ FP4 throughput via DPA with FP32 accumulation, and 1.46$\times$ area efficiency in FP16 DPA and 2.92$\times$ area efficiency in FP8 DPA, at the cost of 37.3% larger area on average and an additional pipeline stage in dot-product mode compared to the FPnew baseline. These results demonstrate that TransDot's area-efficient design enables scalable deployment in next-generation AMD Versal AI engines.

The proliferation of deepfake audio challenges voice-based authentication systems; passive forensic detectors are sensitive to evolving generative models and to real-world channel distortions. We propose Asymmetric Phase Coding (APC), a training-free cryptographic signing layer for audio, designed as a compact and auditable provenance primitive that can stand alone or be stacked with learned watermarks. APC combines Ed25519 digital signatures (EdDSA, FIPS 186-5; 64-byte signatures) with Reed-Solomon error correction, pseudo-random STFT phase-bin selection, and a redundant quantization-index-modulation (QIM) code on log-magnitude differences of adjacent bin pairs, yielding a compact, non-repudiable, blind-extractable watermark. We evaluate APC on 1,000 LibriSpeech test-clean clips (10 s each, 44.1 kHz) under eight attack configurations -- identity, 10% end-cropping, 20% end-cropping, 8 kHz low-pass, 16 kHz round-trip resampling, FLAC re-encoding, MP3 at 128 kbps, and OGG-Vorbis at 128 kbps -- and achieve cryptographic verification rates between 97.5% and 98.3% on every condition at mean PESQ=3.02 and tens-of-milliseconds CPU latency. We explicitly compare APC against recent neural baselines (AudioSeal, WavMark, SilentCipher), detail the threat model (forgery resistance vs. erasure), characterize the dataset, define all metrics, quantify an adaptive white-box erasure attack, and release code, keys, and metadata for reproducibility.

Current research applying N-level Stackelberg Game to multi-agent systems often uses the default decision order of agents provided by the environment. However, this raises the question: does the order of agents necessarily affect the final equilibrium point of the game? To address this, we formally analyze the N-level Stackelberg Game, where changing the order in which agents make decisions typically leads to an overdetermined system. As a result, the equilibrium point shifts unless special structural conditions are satisfied. Based on this analysis, we propose the Hierarchical Priority Adjustment (HPA) method, which adjusts and selects the agents' decision order. At the upper level, an upper policy dynamically selects the optimal decision order of agents based on the current game state. At the lower level, agents execute strategies in the Spatio-Temporal Sequential Markov Game (STMG) according to the selected order. To coordinate learning across time scales, we employ a slow-fast update scheme with shared intrinsic rewards derived from the advantage function of the upper policy. Experimental results on high-precision control tasks, including multi-agent MuJoCo, show that HPA outperforms benchmark algorithms and robustly adapts to changing environments. These results highlight the crucial role of optimizing the agents' decision order in N-level Stackelberg Game.

Large language model (LLM) applications are increasingly executed as heterogeneous multi-stage workflows rather than isolated inference calls. In these workflow directed acyclic graphs (DAGs), scheduling decisions affect not only the currently ready stage, but also the execution state inherited by downstream stages, including model residency, parent-output locality, prefix reuse, and future device reachability. Existing serving and DAG-scheduling policies mainly optimize immediate queue state, placement cost, or reuse signals in isolation, which can fragment useful state and increase end-to-end latency. We present FATE, a future-state-aware scheduler for heterogeneous LLM workflows. FATE combines a CP-SAT-backed frontier planner, horizon-aware candidate scoring, bounded multi-device shard execution, and state-conditional cost estimation. Rather than solving a monolithic full-DAG problem, FATE repeatedly plans over the current ready frontier and scores assignments by both immediate cost and the downstream state they induce. Across real-DAG and controlled prefix-reuse benchmarks, FATE outperforms practical heuristics, classical DAG scheduling, and proxy adaptations of recent workflow-serving policies. On the real-DAG benchmark, it achieves normalized makespan and normalized P95 latency of 0.675 and 0.677, reducing them by 32.5% and 32.3% over RoundRobin and by 8.9% and 8.8% over the strongest non-FATE baseline. Mechanism analysis and ablations show that these gains arise from jointly preserving multiple dimensions of future execution state rather than prefix reuse alone. These results indicate that future-state preservation should be treated as a first-class scheduling objective for heterogeneous LLM workflow serving.

We extend the restricted phase space formalism for spherically symmetric black hole solutions of Einstein-Maxwell theory to the quasi-local regime, with the static observers located at a finite radial distance. The first law and Euler relation for the RN and RN-AdS black holes are proved to hold, but only with the inclusion of an extra pair of thermodynamic variables, i.e. the pressure and the area of the codimension-2 hypersurface on which the observers reside. For the RN black holes, the quasi-local behavior is analyzed in detail. It turns out that the RN black holes in the quasi-local description behaves significantly different from itself in the asymptotic description, but is extremely similar to the RN-AdS black holes in the asymptotic description, e.g. allowing for isocharge temperature-entropy phase transitions and lack of isovoltage temperature-entropy phase transitions. In the neutral limit, the Hawking-Page-like transitions appear in the quasi-local description which is absent in the asymptotic description.

Galaxy clusters contain a hot, diffuse, and weakly magnetized plasma known as the intracluster medium (ICM). In this environment, how thermal conduction influences plasma dynamics and the conditions under which it operates efficiently remain open questions in cluster physics. Systems in which active galactic nuclei (AGN) jets interact with cold fronts produced by cluster mergers provide a unique setting to examine the interplay between conduction, jet dynamics, and ordered magnetic fields. To interpret the detailed structures revealed by recent observations, it is therefore important, as a first theoretical step, to quantify how thermal conduction modifies AGN jet morphology and the surrounding magnetic-field configuration. We perform two-dimensional magnetohydrodynamic (MHD) simulations of an AGN jet in an ICM environment, incorporating anisotropic thermal conduction with varying efficiency. The simulations show that thermal conduction transports heat from the jet head backward along magnetic field lines into the inner cocoon. This process increases the inner cocoon pressure, enhancing jet collimation by a factor of $\sim 4$ compared to models without conduction. This stronger collimation stretches the magnetic fields along the cold-front surface, resulting in a maximum field strength up to a factor of $\sim 1.5$ larger. Jet collimation increases as the conduction efficiency increases, which is interpreted as a conductive collimation mechanism. These results suggest that anisotropic thermal conduction can operate effectively on jet scales in galaxy clusters, and that accounting for conduction may be important when interpreting jet morphology and magnetic field structure in merging cluster environments.

We present topological characterization of classical stochastic processes described by discrete-time Markov chains on lattices. We point out that point-gap topology of stochastic matrices entails two distinct physical consequences that hinge on the choice of the reference point. The point-gap topology around a generic reference point is related to the direction of transport, and nontrivial topology around the origin of the complex spectrum of a stochastic matrix implies non-Markovianity caused by, e.g., feedback control. On the basis of this characterization, we identify the topological origin of directed transport in a classic experiment of Maxwell's demon [S. Toyabe et al., Nat. Phys. 6, 988 (2010)] and find the topological nature of feedback control beyond thermodynamic interpretation. We demonstrate that a topologically enforced non-Markovian classical stochastic process can be simulated by a Markovian quantum master equation, indicating a topological form of quantum advantage.

Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) provides unconditional security against detector vulnerabilities, but its practical deployment is severely hindered by asymmetric channel turbulence. Fluctuations in optical fibers induce arbitrary polarization drift, degrading Hong-Ou-Mandel interference and forcing extensive calibration downtime. In this work, we propose a hardware-free polarization stabilization technique utilizing a Correlated Twirling protocol based on a unitary 2-design. By applying a synchronized, public twirling supermap, Alice and Bob mathematically transform deterministic, asymmetric geometric rotations into an isotropic Pauli depolarizing channel. Executed entirely as a virtual post-processing step during classical sifting, this protocol mathematically suppresses intrinsic channel noise by a factor of 2/3. We demonstrate through exact quantum state simulations that this induced symmetry neutralizes catastrophic axis-dependent failures, extending the Y-bias tolerance from 0.68 to 0.84 radians. Furthermore, the protocol passively extends the absolute angular misalignment tolerance for the 11% security threshold from $38.7^\circ$ to $47.9^\circ$, sustaining secure key distillation over extended fiber distances in highly turbulent regimes where standard architectures fail. Inherently compatible with decoy-state weak coherent pulses, this algorithmic approach provides a highly scalable, resource-efficient framework for robust long-distance quantum networks.

We consider an ontology, in which contextual nonlocal hidden variables are stored as pre-existing possibilities in a repository outside space-time; and in which the context can be chosen ``freely'' (measurement independence) by each agent, both in spacelike and timelike configurations. We show that, in Bell-type experiments involving several agents, for this ontology to be consistent, the context must include not only the measurements that can be performed, but also the time ordering of the choices of different agents.

The fundamental quantity governing the mechanical and thermodynamic properties of a crystalline solid is its electronic charge density. Yet, its direct use for the rapid prediction of materials properties remains challenging due to its high dimensionality. Here, we present a physics-informed deep learning framework that directly predicts mechanical and thermodynamic properties from the three-dimensional electronic charge density derived from density functional theory (DFT). The proposed approach first utilizes a three-dimensional convolutional autoencoder for unsupervised dimensionality reduction, compressing a high-resolution charge-density grid (128 x 128 x 128) into a compact latent representation (16 x 16 x 16 x 16) while preserving physically meaningful features, as confirmed by negligible reconstruction errors across diverse crystal systems. The compressed latent-space representation of charge density is then used by two different regression models for property prediction: Light Gradient Boosting Machine (LightGBM) and Attention-based 3D Convolutional Neural Networks (Att CNN), and their performance is compared. Combining composition-based descriptors (Material Agnostic Platform for Informatics and Exploration or MAGPIE) with electronic charge density data further improves the model accuracy. Using a dataset of about 6059 inorganic compounds spanning multiple crystal symmetries, the models achieve strong predictive performance for bulk modulus K (R2 = 0.94), Young's modulus E (R2 = 0.88), shear modulus G (R2 = 0.87), formation energy Eform (R2 = 0.96), and Debye temperature Θ (R2 = 0.89). This work establishes electronic charge density as a transferable, physics-grounded descriptor for materials property prediction, requiring ~ 1/25 the computational resources of full-fledged DFT calculations.

Very recently, two new notions of para-linear mappings and weak associative orthonormal bases were introduced in octonionic functional analysis, which have been proved to be powerful in formulating the basic theory, such as the Riesz representation theorem and the Parseval theorem. In this article, we continue exploring more properties of these two concepts and initiate the study of octonionic para-linear isometric operators. Surprisingly, it is proven that the condition of the para-linear operator on a Hilbert octonionic bimodule being an isometric isomorphism is equivalent to it mapping any associative orthonormal basis to a weak associative orthonormal basis, which implies also that an octonionic matrix is an isometry if and only if the system of its row vectors is a weak associative orthonormal basis. Furthermore, we introduce the concept of para-linear partial isometric operators and establish the aforementioned analogue in this new setting. Based on these facts, we can provide naturally a new viewpoint of James questions by modifying the definition of octonionic Stiefel space.

Wind-speed processes exhibit substantial temporal variability and spatial dependence, yet volatility dynamics across monitoring networks remain relatively unexplored. This study investigates the spatiotemporal behaviour of wind-speed volatility using daily observations from 141 stations in Northern Italy over 2016--2021, with measurements at 10 m and 100 m enabling the analysis of spatial and vertical dependence. We adopt a parsimonious spatiotemporal volatility framework based on GARCH-type dynamics, in which conditional variance depends on past local shocks and spatially aggregated information from neighbouring stations. The approach combines a spatial mean specification with structured volatility models using distance-based and directionally informed weight matrices. Results show that properly modelling spatial dependence in the mean is essential for well-behaved residuals and reliable inference. Forecast performance is strongly driven by the mean specification: flexible structures perform better when residual spatial dependence remains, while parsimonious distance-based models yield robust out-of-sample forecasts once spatial interactions are captured. Persistence increases with height, and a multivariate extension reveals cross-height dependence.

We investigate static and spherically symmetric traversable wormhole solutions in the framework of $f(Q)$ gravity by considering a power-law model of the form $f(Q)=γ(-Q)^m$. By adopting an anisotropic matter distribution and imposing an equation of state relating the radial pressure and energy density, we obtain an analytic shape function that satisfies the geometric requirements for a traversable wormhole. The model parameter is constrained to $0<m<1/2$, corresponding to a quintessence-like regime with $-1<ω<-1/3$. The energy conditions are analyzed in detail, showing that violations of the null and weak energy conditions are unavoidable but remain localized near the wormhole throat. The anisotropy parameter is positive throughout the spacetime, indicating that repulsive anisotropic stresses play a key role in sustaining the wormhole. The equilibrium configuration is examined using the generalized Tolman-Oppenheimer-Volkoff (TOV) equation for both zero and logarithmic redshift functions, where a consistent force balance is achieved with anisotropic effects providing the dominant outward support. Dynamical stability is studied through scalar perturbations, leading to a Schrödinger-like wave equation with a single-peak effective potential. The quasinormal modes are computed using the sixth-order WKB method with Padé approximation. The resulting frequencies possess negative imaginary parts, indicating stable damping of perturbations. Time-domain simulations further confirm the stability of the solutions and show good agreement with the WKB results, with small deviations in the damping rates. Thus, these results establish that $f(Q)$ gravity admits traversable wormhole solutions that are geometrically consistent and dynamically stable, with $f(Q)$ gravity effects effectively regulating the required matter content.

Associative memory retrieves complete patterns from partial or corrupted inputs and constitutes a primitive form of generative inference. Classical Hopfield networks (CHN) provide a canonical framework for associative memory but suffer from limited memory capacity. Recently, modern Hopfield networks (MHN) were introduced to achieve higher capacity by using explicit pattern-wise storage and neurons with the softmax activation function, which makes the MHN vulnerable to noise and the hardware implementation complicated due to its network size varying with the number of stored patterns. Here, we introduce a hardware-aware Hopfield network (HHN), in which the intrinsic nonlinear current-voltage characteristics of a charge-trap memristor are leveraged to engineer the energy landscape of the HN, increasing the memory capacity. Using a 25 x 25 nonlinear memristor array, we demonstrate reliable reconstruction of corrupted patterns with memory capacity far exceeding the classical limit (K ~ 0.14N, where N is the number of neurons). The HHN preserves Hopfield-type energy-minimization dynamics and remains robust to synaptic conductance noise. Large-scale simulations on high-dimensional image data reveal an empirical memory capacity scaling of K ~ 0.3 x N^1.2 under a fixed synaptic budget. These results establish HHN as a scalable hardware-native architecture for low-power associative memory and generative inference.

We propose a feed-forward perturbation-based method that uses the noisy received signal to compensate for nonlinear distortion, which outperforms the conventional decision-based method and avoids decision feedback. Additionally, combining it with the EEPN-free carrier phase recovery shows additional gain due to a fully symmetrical propagation-backpropagation structure.

This paper presents a high-precision gravitational redshift test using the China Space Station (CSS) Laser Time Transfer (CLT) system. We develop a comprehensive observation equation based on a c^{-3} order relativistic model for space-ground clock comparison. While the CSS optical clock system is currently in the orbital debugging phase, our simulation using actual CSS orbit data achieves a gravitational redshift verification precision of (1.8 \pm 47)*10^{-7} -- approximately one order of magnitude improvement over previous experiments. Our work represents the first application of laser-based time transfer for gravitational redshift verification at such precision, and the first use of the CSS CLT link for testing this fundamental aspect of General Relativity. Unlike microwave-based methods, our laser approach avoids ionospheric effects and first-order Doppler shifts. Residual analysis identifies tropospheric delay variations and atmospheric turbulence as the primary remaining uncertainty contributors. The achieved precision enables gravitational potential difference measurements with 0.1 m^2/s^2 precision -- offering new capabilities for both fundamental physics investigations and geodetic applications including intercontinental height transfer. This work establishes a new benchmark for high-precision tests of relativistic physics and demonstrates the transformative potential of space-based optical time transfer.

Spiking Neural Networks (SNNs) have gained increasing attention due to their potential for low-power computation on neuromorphic hardware. A widely adopted training strategy for SNNs is direct coding, which enable backpropagation on neuron implementations using continuous-valued surrogate activations. However, recent studies have shown that direct-coded SNNs remain substantially less energy-efficient than their event-based counterparts, limiting their practical deployment in energy sensitive scenarios. Still, to promote the reusability of pretrained SNN database on direct code, this motivates an important yet underexplored question: How can a SNN pretrained with direct code be effectively converted into an event-based representation? In this research, we present the first systematic investigation into this transfer problem, analyze the key challenges that arise when transitioning from direct-coded to event-based computation and propose a set of methods to enable energy-efficient transfer while preserving model performance.

We theoretically demonstrate hybrid-order topology in a two-dimensional nonsymmorphic antiferromagnet. Utilizing a generic antiferromagnetic Dirac model with a symmetry-allowed, momentum-dependent spin-density-wave (SDW) mass, we show that a single bulk insulating phase exhibits distinct topological boundary manifestations governed solely by the termination geometry. For screw-compatible edges, nonsymmorphic screw symmetry protects gapless first-order edge states. In contrast, for a $45^\circ$ diamond-shaped termination, the screw symmetry is broken at the boundary, resulting in gapped edges. However, the finite geometry still preserves magnetic mirror symmetries $\mathcal{M}_x\mathcal{T}$ and $\mathcal{M}_y\mathcal{T}$, which enforce an alternating pattern of edge masses, thereby binding zero-dimensional corner states. This second-order phase is characterized by a quantized quadrupole moment, with corner states pinned to zero energy by the chiral symmetry. We further demonstrate that explicit lattice perturbations can selectively gap the first-order edge modes while robustly preserving the corner states. Our work establishes a symmetry-based route to a termination-controlled duality between first- and second-order topology in magnetic nonsymmorphic systems.

Conventional reference targets for Synthetic Aperture Radar (SAR) calibration, such as corner reflectors and standard transponders, are often inherently large and suffer from limited viewing angles. This paper presents a novel frequency-translating transponder architecture that circumvents these limitations, enabling a truly compact, single-antenna design capable of omnidirectional operation. While the operational bandwidth is consequently narrowed, restricting its use primarily to azimuth-direction calibrations, the design excels at providing highly accurate pulse-to-pulse phase measurements across the synthetic aperture. The transponder was prototyped and experimentally validated with a drone-mounted SAR. The results demonstrate the transponder's significant potential for applications requiring omnidirectional reference targets, such as Circular SAR (CSAR) and bistatic SAR.

We establish a criterion for the validity of the classical (non-semiclassical) Weyl law for Schrödinger operators $ H=Δ+V $ on complete Riemannian manifolds. In contrast to existing results, our approach does not rely on standard geometric assumptions such as bounded geometry, nor on analytic assumptions such as the doubling condition on the potential. Instead, we identify a geometric-analytic invariant that encodes the precise balance between the geometry of the manifold, the growth of $V$, and the oscillation scale of $V$. This intrinsic quantity, denoted $c_δ(λ)$ admits effective quantitative estimates. We prove that the Weyl asymptotic holds provided $\lim_{λ\to\infty} c_δ(λ)=0 .$ The sharpness of this criterion is demonstrated through explicit examples showing that the Weyl law can fail when the criterion is violated.

This paper presents results on the unboundedness and minimal speed of traveling wave solutions for a one-dimensional spatial reaction-diffusion equation with an asymptotically linear reaction term and a saturation parameter. By applying a Poincaré-type compactification, we reveal the full dynamics (including infinity) of the two-dimensional system of ordinary differential equations satisfied by traveling wave solutions. This yields essential information characterizing traveling wave solutions: the classification of trajectories in the phase plane, the positivity and unboundedness of front-type and sign-changing profiles, and the explicit form of the minimal speed. This paper examines a special equation with an asymptotically linear reaction term. While, our results differ from those of conventional linear determinacy. We claim that the minimal speed is derived from information at infinity within the traveling wave system.

As a fundamental process in atomic physics, charge exchange relies on quantum state-resolved data that is crucial for various fields such as astrophysics and plasma physics. However, there remains a g in the research on multi-electron target systems. This study aims to investigate the dynamic mechanisms of single/double electron capture in collisions between Ar2+ ions and Ar atoms or N2 molecules at an energy of 40 keV, thereby supplementing high-precision experimental data in this field. The experiment is conducted on the electron beam ion source (EBIS) platform at the Institute of Modern Physics, Chinese Academy of Sciences, using the cold target recoil ion momentum spectroscopy (COLTRIMS) technique. An ion beam containing ground-state Ar2+ (3s^2 3p^(4 3) P) and metastable Ar2+ (3s^2 3p^(4 1) D,(_^1)S) is used as the projectile, colliding with a supersonic Ar/ N2 mixed gas target. Three-dimensional momentum of recoil ions is reconstructed through coincidence measurements of recoil ions and scattered ions, and the Q-value and scattering angle distribution are calculated. Theoretical comparisons are performed using the molecular Coulombic over barrier model (MCBM).

The inertia of a graph $G$ is $\operatorname{In}(G)=(n^+(G),n^0(G),n^-(G))$, where $n^+(G),\, n^0(G),\, n^-(G)$ are the numbers of positive, zero and negative eigenvalues of the adjacency matrix of $G$, respectively, counted with multiplicities. Akbari, Elphick, Kumar, Pragada and Tang [Discrete Math. 349 (2026) 114953] conjectured that every graph $G$ satisfies \[ 2n^+(G)\le n^-(G)(n^-(G)+1). \] In this note, we construct a family of reduced graphs $\{W_{k}:\,k\ge5\}$ with \[ \operatorname{In}(W_k) = \left(\binom{k}{2}+1,\ 0,\ k-1\right), \] each of which violates the conjectured inequality. We also observe that deleting the vertex $a_1$ from $W_5$ gives a reduced graph with inertia $(10,0,4)$, answering a question raised in the same paper. The family also refutes a weaker inequality proposed there.

We investigate bound and periodic timelike geodesics and their associated gravitational-wave (GW) signatures in the spacetime of a regular black hole arising in asymptotically safe gravity (ASG). The geometry incorporates quantum corrections via a running gravitational coupling, encoded in a dimensional scaling parameter $ξ$, that modifies the near-horizon structure while preserving asymptotic flatness. We derive the effective potential for massive test particles and determine the conditions for stable circular and bound motion as functions of $ξ$, including the shift in the innermost stable circular orbit (ISCO). The three topological integers $(z,w,v)$, which represent the number of zooms, whirls, and vertices per radial cycle, are used to categorize the test particles' periodic orbits using Levin's zoom -- whirl taxonomy. Moreover, we employ the rational frequency ratio $q = \frac{ω_ϕ}{ω_r} - 1$ to find closed orbits, where $ω_ϕ$ and $ω_r$ stand for the azimuthal and radial frequencies, respectively. We examine how the orbital frequency spectrum is altered, whirl behaviour is enhanced, and deviations from the Schwarzschild limit are produced by the quantum parameter $ξ$. The GW forms for extreme mass-ratio inspirals (EMRIs) are calculated within the quadrupole approximation. We find that as $ξ$ increases, the signals that are released exhibit detectable amplitude modulations and phase shifts. The corresponding typical strain spectra fall within the anticipated sensitivity limits of space-based detectors such as LISA, Taiji, and TianQin, as they peak in the millihertz frequency band. Peak strain increases monotonically with $ξ$, indicating that observational restrictions on quantum-gravity-induced deviations from classical general relativity in the strong-field domain can be obtained from precise measurements of zoom -- whirl dynamics in EMRIs.