Real-Time Operating Systems (RTOSes) play a crucial role in safety-critical domains, where deterministic and predictable task execution is essential. Yet they are increasingly exposed to ionizing radiation, which can compromise system dependability. To assess FreeRTOS under such conditions, we introduce KRONOS, a software-based, non-intrusive post-propagation Fault Injection (FI) framework that injects transient and permanent faults into Operating System-visible kernel data structures without specialized hardware or debug interfaces. Using KRONOS, we conduct an extensive FI campaign on core FreeRTOS kernel components, including scheduler-related variables and Task Control Blocks (TCBs), characterizing the impact of kernel-level corruptions on functional correctness, timing behavior, and availability. The results show that corruption of pointer and key scheduler-related variables frequently leads to crashes, whereas many TCB fields have only a limited impact on system availability.

We are interested in the molecule reduction algorithm introduced by Deng and Hani. They use this algorithm to establish a rigidity theorem, which plays a central role in the kinetic-time derivation of the wave equation associated with the cubic Schrödinger equation. In the present article, we show that this algorithm is a graph traversal algorithm of Kruskal type, and we prove that it constructs a Kruskal spanning tree of the input molecule. This reveals the origin of the main tool for deriving kinetic equations which has also been used for the long time derivation of the Boltzmann equation.

Classical energy detection (ED) methods for cognitive radio (CR) have addressed noise uncertainty as deviations in noise power and signal uncertainty as variability in signal characteristics, which use probabilistic methods and assume fixed probability distributions for both. In practical scenarios, due to the uncertainty in probability models and the significant variation of primary signals encountered by receivers across different radio technologies, wireless environments exhibit not only distributional uncertainty but also substantial signal variety. In this paper, we develop a generalized formulation of energy detection based on nonlinear expectation theory, where both the signal and noise distributions are uncertain. We utilize the $G$-normal distribution to characterize channel noise. Moreover, to capture practical signal variety, the absolute values of transmitted signal random variables are assumed to lie within a bounded range $[\underlineσ_X,\overlineσ_X]$. The worst-case detection performance is then characterized by a double supremum, meaning over all admissible distributions and all possible signal realizations. We derive estimations for the minimum and the maximum detection error probabilities, and demonstrate the validity of the results through numerical simulations. The proposed model generalizes the classical theoretical analysis of energy detection and offers a potential theoretical foundation for robust detection and information-theoretic analysis under distributional uncertainty.

Symmetry-adapted variational quantum eigensolvers (VQE) based on the Unitary Coupled-Cluster ansatz (SymUCCSD) effectively reduce the parameter count for Abelian molecular point groups. For non-Abelian groups, they systematically fail, without a theoretical explanation. In this work, we prove that the Abelian-subgroup restriction induces a spurious splitting of multidimensional irreducible representations, prematurely discarding cross-component excitations. At the Lie-algebraic level, this filter confines the Dynamical Lie Algebra (DLA) to the Abelian subalgebra $\mathfrak{u}(1)^{d_λ}$, restricting the reachable state manifold to a measure-zero torus $\mathbb{T}^{d_λ}$. However, completing the algebra is insufficient on its own, due to a numerical obstruction. Molecular orbitals adapted solely to an Abelian subgroup produce cross-component integrals that vanish identically, creating a zero-gradient plateau along non-Abelian algebraic directions. A proof-of-principle experiment on NH$_3$/STO-3G ($C_{3v}$, 16 qubits) confirms both the predicted DLA confinement and the gradient plateau, with SymUCCSD converging to an error of $21.8$ mHa above the FCI energy despite full optimizer convergence. Our analysis provides an algebraic and geometric diagnosis of the observed numerical breakdown, establishing that recovering full equivariant dynamics requires both the inclusion of complete off-diagonal generators and the independent parametrization of cross-component excitations.

The counterintuitive Mpemba effect, wherein a hotter system cools faster, critically lacks a general macroscopic theory. Here, starting from linear irreversible thermodynamics, we formulate a generalized Newton's cooling law, $\mathrm{d}T/\mathrm{d}t = -[γ_0 + \mathcal{M}Q(t)](T-T_r)$, for a system at temperature $T$ relaxing in a thermal reservoir at $T_r$, where the bare relaxation rate $γ_0$ is modified by an initial-state memory term, $Q(t) \propto T(0)-T_r$. Arising from the interplay between heat flux and structural evolution, the coefficient $\mathcal{M}$ governs anomalous relaxation behaviors, where $\mathcal{M} > 0$ ($\mathcal{M} < 0$) induces the (inverse) Mpemba effect. This universal thermodynamic framework maps out phase diagram to provide general criteria for the Mpemba effect in complex systems, offering a macroscopic picture that bridges disparate microscopic approaches.

A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics. While real-time simulations have progressed toward resolving individual channels, existing approaches rely on knowledge of the asymptotic particle wavefunctions. This work introduces an experimentally inspired method to isolate scattering channels in Matrix Product State simulations based on the entanglement structure of the late-time wavefunction. Schmidt decompositions at spatial bipartitions of the post-scattering state identify elastic and inelastic contributions, enabling deterministic detection of outgoing particles of specific species. This method may be used in settings beyond scattering and is applied to detect heavy particles produced in a collision in the one-dimensional Ising field theory. Natural extensions to quantum simulations of other systems and higher-order processes are discussed.

Finite-player dynamic games with dispersed private information are difficult because actions both move payoffs and reshape what opponents learn, generating hierarchies of beliefs about beliefs. This paper provides a recursive representation for this problem. The noise state records agents' beliefs about the underlying shocks that generate histories, so higher-order beliefs are generated by composition rather than tracked as separate state variables. In the canonical continuous-time LQG benchmark, the representation becomes explicit: beliefs, value gradients, and policy rules are deterministic impulse-response functions, and equilibrium is a deterministic fixed point in those functions. Any fixed point in the noise-state linear class is a Nash equilibrium against arbitrary admissible \(L^2\) deviations. The first-order system contains an information wedge, the shadow price of changing opponents' posteriors. In a two-player benchmark, the wedge explains why pooling gains are mostly strategic, why optimal precision allocation can starve an inefficient player of information, and why signal precision changes policy rules themselves, so separation fails.

The Gauss-Bonnet (GB) scalarization for charged quantum Oppenheimer-Snyder (cqOS)-black holes is investigated in the Einstein-Gauss-Bonnet-scalar theory with the nonlinear electrodynamics (NED) term. Here, the scalar coupling function to GB term is given by $f(ϕ)=2λϕ^2$ with a coupling constant $λ$. Three parameters of mass ($M$), action parameter ($α$), and magnetic charge ($P$) are necessary to describe the cqOS-black hole, and it may become the qOS-black hole when $P=M$. The GB scalarization of cqOS-black holes comes into two cases GB$^\pm$, depending on the sign of GB term which triggers the different phenomena. For $α=0$ and $λ>0$, GB$^+$ scalarization is allowed, while for $α\not=0$ and $λ<0$, GB$^-$ scalarization appears for a narrow band of $3.5653\le α\le 4.6875$. After discussing the onset GB$^-$ scalarization, we construct scalarized cqOS-black holes which belong to the single branch. The scalar field decays much more rapidly compared to the GB$^+$ case. Stability analysis shows these scalarized black holes are linearly stable under scalar perturbations.

Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific state. This study introduces multi-tasking quantum annealing (MTQA), a method that enables the parallel processing of multiple optimization problems by embedding them into spatially distinct regions on quantum hardware. MTQA is evaluated using two NP-hard problems: the minimum vertex cover problem (MVCP) and the graph partitioning problem (GPP). This parallel approach optimizes quantum resource utilization by concurrently utilizing idle qubits. The findings demonstrate that MTQA achieves a solution quality comparable to single-problem quantum annealing and classical simulated annealing (SA), while notably reducing the time-to-solution (TTS) metrics. Eigenspectrum analysis further theoretically supports the hypothesis that parallel embedding preserves quantum coherence and does not increase computational complexity by efficiently utilizing available quantum hardware (e.g., qubits and couplers). MTQA enables efficient multitasking in quantum annealing, optimizing hardware utilization and improving throughput for concurrent tasks and demonstrating performance for problems up to 100 nodes in real-world applications.

Beyond solving the hierarchy problem, classically conformal (CC) theories naturally accommodate dark matter (DM). In this work, we explore the CC $SU(2)_X$ gauge theory with a triplet dark scalar, uncovering two distinct DM scenarios: weakly interacting massive particle (WIMP) and supercooled DM. The production mechanisms are strongly influenced by the CC model's unique first-order phase transition evolution history, which differs significantly from those in non-conformal models. We obtain the viable parameter space for each scenario and investigate the current constraints and future sensitivities at experiments, demonstrating that gravitational wave signals from the phase transition provide a common detection channel for both the WIMP and supercooled DM regimes.

We present a covariant field-theoretical framework for a rank-4 tensor gauge field theory describing fractonic string-like objects. We show that the most general quadratic, parity-preserving action naturally leads to a Maxwell-like sector, with tensorial analogues of electric and magnetic fields, Maxwell-like equations, a conserved energy-momentum tensor, and a Lorentz-like force. Remarkably, the theory gives rise to fracton-like string excitations purely from symmetry principles: constraints on the motion of these extended objects appear as Gauss-like laws, without being imposed by hand. One of these laws is new and corresponds to a generalised dipole conservation for closed strings, restricting their mobility and defining a novel class of fractonic string-like excitations. Finally, we uncover a connection to linearised area-metric gravity: in a suitable limit, the theory reduces to known covariant fracton models with rank-2 gauge fields, highlighting a deep link between fractonic matter and gravity-like structures. This provides a unified perspective on higher-rank gauge fields, extended excitations, and emergent gravitational features.

Quadratic quasinormal modes (QQNMs) and Christodoulou memory effect are key nonlinear phenomena in gravitational wave physics. QQNMs characterize the near zone nonlinear response of a perturbed black hole, whereas the memory effect is a nonlinear remnant imprinted at null infinity by outgoing radiation. This naturally raises the question of whether and in what sense the two can be bridged. We show that they are related through bridge coefficients which depend primarily on remnant black hole parameters during ringdown. Future space-based gravitational wave detectors can probe this relation. These results provide a new avenue for testing gravity and a fresh perspective on the nonlinear regime of general relativity.

We present a computational investigation of the parity-violating (PV) contributions to the vibrational transitions and nuclear magnetic resonance shieldings of helical osmocene. A number of promising transitions within the spectral window of currently available sub-Hz metrology-grade lasers are identified, exhibiting high intensities and parity violation shifts of up to 7 Hz. We discuss the prospects for the synthesis of this compound and for subsequent ultra-precise mid-IR spectroscopy towards the first detection of parity violation in a chiral molecule.

Pulsar halos provide a unique probe of cosmic-ray propagation in the vicinity of pulsars and have important implications for our understanding of particle diffusion in the interstellar medium. However, the number of firmly identified pulsar halos remains limited. One of the main challenges is the difficulty in unambiguously confirming halo candidates through precise morphological measurements with current $γ$-ray observations. In this work, we investigate the prospects for identifying pulsar halo candidates through morphological discrimination using simulations of two advanced $γ$-ray experiments: LHAASO-KM2A and the Cherenkov Telescope Array (CTA). Using mock observations with realistic instrumental responses, we assess the ability of each experiment to distinguish diffusion-based halo morphologies from alternative simplified spatial models. Our results show that both increased photon statistics and improved angular resolution significantly enhance the power of morphological discrimination. In particular, CTA benefits from its superior angular resolution, while LHAASO-KM2A gains sensitivity from its large effective area at the highest energies. These results indicate that future $γ$-ray observations have the potential to expand the sample of pulsar halos and provide further insights into cosmic-ray transport around pulsars.

A recently proposed generalized entropy by Luciano and Saridakis extends the standard Boltzmann-Gibbs and Bekenstein-Hawking framework through a microscopically motivated construction involving two independent entropic exponents. When applied within the gravity-thermodynamics correspondence, this entropy leads to a modified cosmological dynamics that can be interpreted as an effective dark energy sector of entropic origin, while recovering $Λ$CDM in appropriate limits. In this work, we perform the first observational confrontation of the resulting entropic cosmology at the background level. Focusing on the case $α_δ=0$, we constrain the model using Cosmic Chronometers, Pantheon$^+$ Type Ia supernovae calibrated with SH0ES, BAO measurements from DESI DR2 and compressed Planck 2018 CMB information. We find that the model yields a statistically robust fit to the combined data sets and can simultaneously satisfy Pantheon$^+$, SH0ES and CMB shift-parameter constraints, unlike $Λ$CDM. Although the entropic parameters remain close to their standard values, the $Λ$CDM limit is excluded at the $2σ$ level within the restricted parameter space considered. These results indicate that the Luciano-Saridakis entropic cosmology offers a viable extension of the standard model with the potential to alleviate the Hubble tension at the background level.

Context: Satellite dwarf galaxies provide key constraints on galaxy formation and evolution, since their abundance and spatial distribution reflect both the host properties and the large-scale environment. Aims: This study quantifies the dependence of satellite populations on the host stellar mass, morphology, and star formation activity across different environments, and traces their evolution with cosmic time within the $Λ$CDM framework. Methods: The Millennium-II simulation combined with the G11 semi-analytic model is used to construct consistent samples of host galaxies brighter than $M_{r}<-16$ and their satellites ($M_{\ast}\geq 3\times10^{5}\,M_{\odot}$, $M_{r}<-9$) within the virial radius. Satellite abundance and radial profiles are analysed in cluster, group, and void environments, and their evolution is traced from $z=2$ to $z=0$ across three host stellar mass bins. Results: Satellite abundance is correlated strongly with host stellar and bulge mass, whereas host morphology has little independent effect once stellar mass is accounted for. Dense environments suppress satellite populations relative to voids. Correlations between satellite abundance, specific star formation rate, and disk scale length become evident only in groups and clusters. At $z=0$, radial profiles show strong central concentrations in voids, flattened distributions in clusters, and intermediate trends in groups. Their redshift evolution reveals progressive flattening for low- and intermediate-mass hosts in dense environments, stability for massive hosts, and increasing central concentration in voids. The cosmic evolution of satellite abundance further highlights distinct pathways: gradual accumulation in voids, mass-dependent trends in groups, and strong late-time suppression in clusters.

The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling with adiabatic temporal modulation. This extension gives rise to unique topological features such as winding-number quantization, discontinuous phase-slip transitions, and hysteretic and non-reciprocal phase dynamics. We further extend the analysis to the quantum regime, where we find a counterintuitive result: the breakdown of winding-number quantization. This arises from the superposition of different winding-number states in a closed-space Thouless pump. Moreover, hysteretic dynamics, once eliminated in quantum adiabatic approximation, is recovered in non-adiabatic calculations, as the superposition of two Floquet states with different PT eigenvalues becomes the quantum counterpart of phase trajectory.

We present a radio-continuum survey of the LMC using the MeerKAT telescope, describe the full-Stokes products included in the first data release, and highlight some initial results. The observations are centred at 1.3 GHz with a bandwidth of 0.8 GHz. The imaging products comprise six fields of view, each encompassing $\sim$5$^\circ$ $\times$ 5$^\circ$ with the resulting images achieving a resolution of 8". The median broad-band Stokes~I image root-mean-square noise value is $\sim$11 $μ$Jy beam$^{-1}$. The survey enables a variety of astrophysical studies, which we showcase with the presentation of a few findings. Within the LMC we identify a new supernova remnant candidate; present planetary nebulae and Wolf-Rayet stars without previous radio detections; and show the MeerKAT view of the well-known star-forming region 30 Doradus. We also present some examples of interesting foreground and background sources in the field, including the AB~Dor multiple-star system, a radio ring galaxy, a possible Odd Radio Circle, and a remarkable bent-tail radio galaxy.

The NECTAR (Nuclear rEaCTions At storage Rings) experiment at the ESR heavy-ion storage ring at GSI/FAIR Darmstadt is dedicated to surrogate reaction studies of neutron-induced reactions on heavy nuclei in inverse kinematics. In this work, we report on the implementation and performance of a newly developed fission-fragment detection system integrated into the NECTAR experimental setup. The upgraded detector configuration enables, for the first time in a surrogate experiment, the simultaneous detection ofgamma-decay residues, multi-neutron-emission residues, and fission fragments. The full setup was used for the first time in an experiment where a stored beam of bare 238U92+ ions at 17.24 MeV/u interacted with a gas-jet deuterium target, populating excited 238U and 239U nuclei via the 238U(d,d') and 238U(d,p) reactions. We describe the geometry of the used fission fragment detectors, design constraints, and simulation-based efficiency determination. The target-like particle identification and beam-like residue spectra demonstrating the performance of the complete setup are also shown.

The deterministic preparation of quantum many-body ground states is essential for advanced quantum simulation, yet optimal algorithms often require prohibitive hardware resources. Here, we propose a highly efficient, non-variational protocol for ground state preparation using a Power-Cosine quantum signal processing (QSP) filter. By eschewing complex block-encoding techniques, our method directly utilizes coherent time-evolution operators controlled by a single ancillary qubit. The integration of mid-circuit measurement and reset (MCMR) drastically minimizes spatial overhead, translating iterative non-unitary filtering into deep temporal coherence. We analytically demonstrate that this approach achieves exponential suppression of excited states with a circuit depth scaling of $\mathcal{O}(Δ^{-2}\log(1/ε))$, where $Δ$ denotes the spectral gap, prioritizing implementational simplicity over optimal asymptotic complexity. Numerical simulations on the 1D Heisenberg XYZ model validate the theoretical soundness and shot-noise resilience of our method. Furthermore, an advantage analysis reveals that our protocol exponentially outperforms standard Trotterized Adiabatic State Preparation (TASP) at equivalent circuit depths. This single-ancilla framework provides a highly practical and deterministic pathway for many-body ground state preparation on Early Fault-Tolerant (EFT) quantum architectures.

We study the advection effect of the Galactic wind on the local cosmic ray spectra. The spectral hardening from a few hundred GV and softening from a few TV are reproduced by a velocity profile with a maximum velocity of $\sim 700~\mbox{km}~ \mbox{s}^{-1}$ without introducing a break in the power-law dependence of the diffusion coefficient. Additionally, we find that a hard CR spectrum below $\sim$ TV with an index of $\sim 2$ at an altitude $\sim 3$-$5$ kpc from the Galactic disk. This hard spectrum is favorable for the gamma-ray spectrum of the Fermi bubbles. With the obtained CR fluxes, we discuss the matter circulation in our Galaxy with the wind. While the wind has an essential role in maintaining the metal abundance in the disk, the production rate of Beryllium, which originates from CR spallation, is so low that the ratio Be/O in the halo should be larger than that in the disk gas.

This paper is devoted to the study of mappings with finite distortion, in particular, mappings satisfying the inverse Poletskii inequality. We study the problem of equicontinuity of families of such mappings in a given domain. We establish that a family of open discrete mappings with the inverse Poletskii inequality, omitting at least one point, is equicontinuous if the majorant responsible for the distortion of the modulus of families of paths under the mapping is integrable over almost all concentric spheres centered at the given point. Since analytic functions with finite multiplicity satisfy the inverse Poletskii inequality, this result generalizes the well-known Montel theorem on the normality of families.

Cross-correlation is an established tool to reduce the background in resistance noise measurements. However, the conventional method requires the amplifier, demodulator and digitizer channels to be duplicated, increasing the cost and complexity of the measurement circuit. We propose an alternating-current technique that allows cross-correlation with only a single channel by modulating the device under test with two carrier frequencies simultaneously. Using multiple software-based demodulators, we show that this method produces accurate amplitude measurements and noise spectra. The signal-to-noise-ratio is improved by 7 decibel for standard parameters. Longer measurement durations increase this improvement, which makes the new technique a true cross-correlation method.

Transformation optics uses coordinate mappings to emulate curved geometries and control electromagnetic fields. However, existing approaches primarily focus on geometric deformation while offering limited control over the global topology of the resulting optical space. Here we introduce a torus projection combined with a conformal mapping to construct a wormhole-like virtual optical geometry, providing a controllable route to manipulate virtual space topology within transformation optics. By tuning a single torus parameter, the virtual-space refractive index switches between isotropic and anisotropic forms, driving a transition from a disconnected horn-torus geometry to a connected ring-torus geometry in virtual space. In physical space, this virtual-space topology transition gives rise to switchable black-hole-like trapping, field redistribution, and geometry-controlled wave responses. Our results demonstrate how refractive-index anisotropy governs singularity structure and topology in transformation optics, while also suggesting practical functionalities including beam splitting, absorbing-like switching, and curvature-assisted focusing.

In this paper, we investigate the higher-group symmetry structure of a five-dimensional topological theory, which is described by a 3-crossed module. The model is obtained by a five-dimensional extension of topological axion electrodynamics in four dimensions. To study the symmetry structure, we couple background gauge fields to the symmetry currents via Stueckelberg couplings. We show that background gauge invariance requires modified gauge transformation laws, indicating the existence of a higher-group structure. Furthermore, we identify the underlying mathematical structure as a 3-crossed module by regarding the modified Stueckelberg couplings as curvatures of a higher-group gauge theory. We demonstrate that the gauge transformation laws derived from this algebraic structure are consistent with the analysis based on the gauge invariance. While our previous work introduced the concept of a 3-crossed module motivated by higher-group symmetries, this work provides concrete verification that this framework correctly captures the symmetry structure of physical theories.

The Lee-Yang phase transition theory applied in the anti-de Sitter (AdS) black hole has inspired the exploration of complex phase diagram and supercritical phenomena in black hole thermodynamics. In this study, we extend the approach to the four dimensional Born-Infeld AdS black hole. This system exhibits a rich phase structure, including reentrant phase transitions, due to the modulation of the Born-Infeld nonlinear parameter. Through the Lee-Yang zeros, we obtained the complex phase diagram of the Born-Infeld AdS black hole and derived the supercritical crossover line -- Widom line, which strictly originates from the first-order stable critical point. The results indicate that Born-Infeld nonlinear effects significantly alter the types and characteristics of phase transition in critical region, while do not disrupt the uniqueness of the Widom line in supercritical region. Our study uncovers a universal simplified feature of the thermodynamic behavior of nonlinear gravitational systems in supercritical region. It also deepens our understanding of the fundamental connection between critical phenomena and continuous phase transitions in the extended phase space of black holes.

Linear non-unitary dynamics arise in open quantum systems, non-Hermitian models, and numerical evolution problems, yet current quantum algorithms do not cleanly separate coherent and dissipative effects at the design level. We introduce Amplitude-Phase Separation (APS), a decomposition framework with two complementary forms: phase-driven APS isolates the unitary component and maps the remainder to a Hermitian problem, whereas amplitude-driven APS extracts the Hermitian component and treats the remaining interaction separately. For time-independent dynamics, the two routes capture complementary advantages within one framework: phase-driven APS yields additive rather than multiplicative tolerance dependence, while amplitude-driven APS yields square-root dissipative scaling in multiscale regimes. APS also provides a unified interpretation of representative methods, including LCHS (Linear Combination of Hamiltonian Simulation) and NDME (Non-Diagonal Density Matrix Encoding), and clarifies where coherent and dissipative bottlenecks enter non-unitary simulation. The benchmarks confirm the predicted crossover between phase-driven and amplitude-driven advantages in advection-diffusion and Bloch-relaxation models.

Context. The origin of the petrologic diversity observed in ordinary chondrites (OCs), the most common meteorites on Earth, remains debated. Competing models invoke either depth-dependent sampling of a single thermally stratified ("onion-shell") parent body or contributions from multiple distinct parent bodies. Aims. We aim to determine which of the two models is preferred for LL chondrites. These are unique among OCs in exhibiting a bimodal petrologic distribution, with most meteorites being LL3 or LL6. Methods. We compare the spectral and mineralogical properties of LL chondrites and corresponding LL-chondrite-like near-Earth objects (NEOs) with their possible sources in the main asteroid belt. We also model the thermal histories of the proposed parent bodies, based on revised estimates of parent-body sizes. Results. The spectral and mineralogical diversity of LL chondrites is consistent with contributions from the bright, S-type component of the Nysa family (NysaS) and the Flora family, with NysaS supplying mainly low-petrologic-type material and Flora higher-grade material. Unequilibrated, LL3 chondrites appear to originate exclusively from NysaS. Similarly, LL-chondrite-like NEOs form two distinct subpopulations consistent with origins in these same families. Conclusions. Our results favour multiple parent bodies for LL chondrites. The petrologic differences between the NysaS and Flora parent bodies can be explained by differences in their sizes, without requiring different formation times.

We present an explicit construction of the unitary irreducible representations of the two-dimensional Euclidean and Poincaré groups, together with their Spin double covers, by means of Mackey's theory of induced representations for semidirect products. In dimension D=2, the simplicity of the corresponding little groups allows a complete explicit treatment of momentum orbits, equivariant wavefunctions, and representation operators. For the Euclidean group, the matrix elements of the infinite-dimensional representations are expressed in terms of Bessel functions. For the Poincaré group, the richer Lorentzian orbit structure leads to matrix elements involving modified Bessel and Hankel functions and, in some cases, tempered distributions, requiring the use of Rigged Hilbert Spaces. This work illustrates the interplay among induced representations, harmonic analysis on Lie groups, Spin geometry, and special functions in a fully explicit relativistic setting.

Low-Earth-orbit (LEO) satellites and vehicle-to-everything (V2X) networks are driving integrated communication and navigation (ICAN) toward next-generation intelligent transportation. Affine frequency division multiplexing (AFDM) is a promising waveform for high-mobility LEO scenarios owing to its Doppler robustness, simple modulation, and low pilot overhead. However, applying existing high-accuracy AFDM fractional delay-Doppler estimators to LEO-ICAN entails substantial search or inference complexity, while the spectrum-wrapping-induced envelope structure in line-of-sight (LOS)-dominated channels remains underexploited. This paper analyzes and exploits the spectrum-wrapping-induced envelope structure of the fractional AFDM response, and proposes a low-complexity joint estimator that combines minimum-entropy fractional Doppler estimation with closed-form fractional delay estimation. Simulation results show that the proposed estimator approaches the root Cramér--Rao lower bound (RCRLB) and achieves root-mean-square error (RMSE) performance comparable to that of matched filtering (MF), matched filtering with generalized Fibonacci search (MF-GFS), and off-grid sparse Bayesian learning (OG-SBL), while requiring substantially lower computational complexity and runtime. This favorable accuracy-complexity profile highlights the potential of the proposed estimator for real-time ICAN processing in high-mobility LEO-assisted vehicular networks.