We investigate wetting phenomena between self-bound quantum fluids in a three-component Bose mixture of $^{23}$Na, $^{39}$K, and $^{41}$K atoms. Within a density-functional approach including mean-field interactions and Lee-Huang-Yang quantum-fluctuation corrections, we consider two binary quantum liquids, formed by components $(1,2)$ and $(2,3)$, and study the adsorption of the softer $(1,2)$ liquid on a stiffer $(2,3)$ substrate. By tuning the interspecies scattering length $a_{12}$, we show that the surface tension of the $(1,2)$ liquid can be strongly varied, driving a transition from partial wetting to complete wetting of the $(2,3)$ phase. The contact angle extracted from cylindrical-cap geometries decreases continuously with increasing $a_{12}$ and vanishes near a critical value $a_{12}^{c}= -42\,a_0$. In the complete-wetting regime, a finite amount of $(1,2)$ liquid wraps around a spherical $(2,3)$ droplet, producing a self-bound core-shell droplet without external confinement, whose component-1 density has a shell-like, hollow projection. We further show that such shell-shaped quantum droplets can sustain quantized vortical excitations. These results identify wetting as a route to engineering free-standing shell-shaped quantum liquids and suggest new possibilities for studying capillarity, topology, and superfluidity in multicomponent quantum droplets.

In 1979, Johnson and Wolfe proved that norm-attaining operators are dense in $L(C(K),C(S))$ when $K$ and $S$ are compact Hausdorff spaces in the real setting. The corresponding complex case has remained open since then, mainly because the real proof relies on order and sign-decomposition arguments that are no longer available for complex measures. In this paper, we settle the complex case. We prove that, for arbitrary compact Hausdorff spaces $K$ and $S$, the set of norm-attaining operators from the complex space $C(K)$ into the complex space $C(S)$ endowed with the supremum norm is dense in $L(C(K),C(S))$. The proof replaces the real order-theoretic mechanism by a measure-theoretic phase-correction argument, based on polar decompositions, unimodular approximation, and a semicontinuity principle for weighted total variation. This yields a complex defect-reduction procedure which recovers the Johnson-Wolfe density theorem in full generality for complex $C(K)$-spaces.

We demonstrate the possibility of engineering the topological band structure of a plasmonic Su-Schrieffer-Heeger (SSH) chain through the interaction with its electromagnetic environment. We find that the long-range interaction of the in-plane modes of the SSH chain with the surface plasmon polaritons of a planar substrate introduces a band hybridization connected to a change of the Zak phase. On the other hand, the short-range interaction with the substrate introduces a band touching, again with a change in the Zak phase. Surprisingly, this second mechanism enables the emergence of topologically protected edge modes for parameters which correspond to the topologically trivial phase for an isolated plasmonic SSH chain. We study these mechanisms by changing the chain-substrate distance and the dimerization parameter. Finally, we discuss the robustness against disorder and, as one example, the impact of the observed effects on the near-field radiative heat transfer along the chain. Our findings pave the way to the engineering of edge modes in plasmonic topological configurations via the coupling to a plasmonic environment.

In Grayson's combinatorial description of higher K-groups, the generators are bounded acyclic binary multi-complexes of arbitrary size. Generalising work by Kasprowski, Winges and the author, we show in this paper that multi-complexes of bounded size suffice and we provide the corresponding relations. Furthermore, we report on the progress in our attempt to algebraically prove the surjectivity of Quillen's dévissage isomorphism for K_1 and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach.

In this paper, we propose several constructions of Locally Recoverable Codes from elliptic surfaces. In particular, we are able to obtain codes with availability $t>2$, codes with hierarchical locality and, finally, codes which combine availability and hierarchical locality. Our constructions rely on the properties of the torsion groups of elliptic curves and on the fibered structure of elliptic surfaces. In particular, the geometry of the surface is used to introduce a multi-dimensional setting, allowing for more recovery sets, eventually nested one within another.

Chiroptical spectroscopy provides a non-invasive, label-free approach for resolving microscopic structural details via interactions with circularly polarized light. Despite the widespread application and complementary information provided for chiroptical materials characterization, the simultaneous acquisition of circular dichroism (CD) and circular differential scattering (CDS) spectra has remained challenging. In this work, we develop a dual-channel spectrometer that enables the acquisition of CD and CDS spectra from the same solution. To address the challenge of CDS baseline correction, we introduce a scattering spectral matching method. The performance of the instrument is validated using two representative model systems: a mixture of ammonium d-10 camphor sulfonate and polystyrene nanoparticles (PSNPs), and plasmonic gold helicoid nanoparticles, which exhibit both chiral absorption and scattering. For the former case, the CDS spectra show opposite signs to the CD spectra because the PSNPs are achiral scattering particles and the CDS spectra are affected by the chiral absorption. For the latter case, both CD and CDS spectra exhibit matched resonance wavelengths and stronger responses to the right-handed circularly polarized light, indicating that the chiral absorption and scattering arise from the same plasmonic resonance modes. To the best of our knowledge, this work represents the first experimental demonstration of the concurrent acquisition of ensemble-averaged CD and CDS spectra. The presented technique enables a direct and accurate comparison of CD and CDS spectra acquired under identical conditions.

Self-triggered radio detection of ultra-high-energy cosmic rays and neutrinos offers a scalable and cost-effective approach for next-generation astroparticle observatories, but remains challenging under realistic radio-frequency interference (RFI) conditions. In the classical air-shower radio band, the achievable sensitivity and trigger reliability are critically limited by the balance between external sky background noise and internal detector-unit noise, as well as by non-stationary anthropogenic interference. In this work, we present an end-to-end design and experimental characterization of a self-triggered radio detector unit explicitly optimized to operate in a galactic-noise-dominated regime. Rather than focusing on a single hardware component or trigger algorithm, we adopt a system-level methodology that coherently integrates sky-noise modeling, RF-chain noise budgeting, electromagnetic compatibility (EMC) mitigation, and measurement-driven validation. By using the galactic radio background as a quantitative reference, we assess the internal noise performance of the detector unit and demonstrate conditions under which extensive air shower (EAS) radio signals can be distinguished from anthropogenic interference at the system-response level. We further introduce an indirect noise-quantification method to estimate the low-noise amplifier contribution within the complete RF chain based on differential internal-noise measurements evaluated at the ADC level. The proposed detector unit is validated through laboratory and on-site measurements, demonstrating operation close to the galactic-noise limit in the core frequency band. These results provide a practical and transferable methodology for the design and deployment of large-scale self-triggered radio arrays such as GRAND.

We give almost sure convergence rate bounds of ratio consensus algorithms when the protocol can be reformulated to be linear updates of vector values on a possibly larger, augmented network. This is an improvement of the results of Gerencsér and Gerencsér from 2021 by allowing zero values on auxiliary nodes infinitely often which makes the technique applicable to a much larger family of algorithms.

Over-the-Air Computation (OAC) enables efficient data aggregation in large-scale distributed systems by exploiting the superposition property of wireless multiple-access channels. In contrast to most existing studies on OAC assuming exact channel state information, we consider non-coherent OAC (NC-OAC) where the channel phase is unknown at the transmitters. A three-step framework for NC-OAC with a mapping between source data and codewords is proposed: 1) Devices encode their data to non-negative codewords; 2) Devices transmit a sequence of symbols with amplitude proportional to their codewords, such that the receiver can estimate the codeword sum. Estimation of the codeword sum is studied under two scenarios of global channel amplitude knowledge: statistical or instantaneous; 3) The estimated codeword sum is decoded to the desired source data sum at the receiver. With the proposed framework, we first study prior work on NC-OAC and map these to the framework. Next, we define and compare the two most commonly (often implicitly) used mappings for NC-OAC: the Affine and the Augmented Affine mappings. Under the constraint of unbiased estimation, we show that with uniformly distributed data and standard channel assumptions, the Augmented Affine mapping exhibits an order of magnitude lower estimation variance than the Affine mapping with both statistical and instantaneous channel knowledge. This result is validated by extensive simulations. Finally, we propose and analyze a new mapping, which demonstrates superior performance over the previous two affine mappings.

Reconstructing a thermal model capable of efficiently simulating the behavior of a spacecraft from sparse and localized temperature measurements remains a challenging task. To address this, we introduce a physically-constrained calibration framework for Lumped Parameter Thermal Models (LPTMs), formulated as a trajectory-based inverse problem for graph dynamical systems. The model reconstructs thermal dynamics directly from temperature measurements and known inputs, without relying on a priori parameter values derived from material properties or geometric assumptions. Physical admissibility is enforced at the parameterization level: positivity of nodal coefficients and symmetry of conductive interactions are imposed by construction. This guarantees stable dynamics and restricts the identification problem to a physically meaningful parameter space, improving conditioning without the need of additional regularization. The identification problem is addressed through trajectory matching, ensuring stable rollout over extended time horizons. The methodology is validated on synthetic datasets generated from high-fidelity finite element simulations under progressively complex forcing conditions. The calibrated LPTMs accurately reproduce long-term temperature evolution and exhibit robustness to measurement noise. The proposed framework provides a systematic approach to the calibration of reduced-order thermal models by combining physical structure with data-driven identification. The numerical results show a favorable balance between accuracy and computational efficiency, making the models suitable for integration in spacecraft thermal Digital Twin applications.

Half precision (FP16) promises to double FFT throughput on GPUs, but the prevailing view is that its 10-bit mantissa makes it unsuitable for radar-grade signal processing. We show this framing is wrong on Apple Silicon: the binding constraint for FFT and Synthetic Aperture Radar (SAR) is not mantissa \emph{precision} but the 5-bit exponent's \emph{dynamic range}. We first measure that an FP16 FFT is mantissa-limited at 56--61~dB signal-to-quantization-noise ratio (SQNR) -- comfortably radar-usable -- yet a naïve FP16 SAR pipeline produces \emph{only} \texttt{NaN}, because the conjugate--FFT--conjugate inverse transform grows magnitudes by a factor of $N$, and the matched-filter product ($\sim\!5\times10^6$ at $N\!=\!4096$) overflows FP16's 65{,}504 ceiling. We resolve this with a fixed-shift \emph{block-floating-point} (BFP) schedule: a single $1/N$ scale applied before each inverse transform bounds every intermediate below 4096. A cascade follows: range-compression output becomes $O(1)$ instead of $O(N)$, which in turn keeps the downstream azimuth-FFT output FP16-loadable instead of overflowing at $O(N^2)$. The result is the first quality-preserving FP16 SAR pipeline: peak/integrated sidelobe ratios, target SNR, and resolution match the FP32 reference to within $0.1$~dB at $42$~dB end-to-end SQNR, while a radix-8 FP16 FFT reaches 306~GFLOPS -- $2.2\times$ over the 139~GFLOPS FP32 baseline -- on a fanless Apple~M1. Finally, we measure that FP8 (E4M3/E5M2) collapses to 14--20~dB SQNR, making FP16 \emph{today's} precision floor for FFT-based radar -- one that future precision-recovery methods may yet lower -- and showing that the lever for low precision here is range management, not mantissa bits.

Let $C_n=n2^n+1$ denote the $n$th Cullen number. There has been recent interest in finding all Cullen numbers having a given Diophantine property. We prove that, for a fixed integer $k$ and bounded integers $a_1,\ldots,a_k$, the greatest prime divisor of $C_n-a_1m_1!-\cdots-a_km_k!$ tends to infinity, in an effective way. We prove this for some more general families of ternary recurrence sequences as well. We also solve the Diophantine equation $$C_n = m_1! + m_2! + s,$$ where $s$ is a positive integer composed of primes $2,3,5,7$.

In this work we determine the finite-volume lattice QCD spectrum at the flavor symmetric $\mathrm{SU}(3)$ point in the meson-baryon singlet and octet irreducible representations. We construct the appropriate interpolation operators and perform the calculation on ensembles in quite large volume ($L=48$). We find three below-threshold energy levels, with the singlet having lower energy and the two octets being non-degenerate at one sigma, which for these large volumes ($M_π L\approx 14.5$) strongly suggests a bound state close to that energy at each of the irreducible representations. We confront this finite-volume spectrum with the prediction from UCHPT through the Lüscher method finding qualitative agreement. Finally we perform a re-fit of UCHPT free parameters to the available (experimental and lattice) data including the energy levels calculated in this work. This allows us to follow the pole trajectories to the physical point, identifying the $Λ(1405)$ as a lower octet, and $Λ(1380)$ as a singlet bound state in the $\mathrm{SU(3)}$ limit. Furthermore, $Λ(1670)$ is identified on a qualitative level as the heavier octet bound state and its relation to three-body final states is discussed.

This study investigates the influence of fiber spatial distribution on the transverse mechanical properties of unidirectionally reinforced continuous-fiber composites. A Swelling & Random Migration algorithm was employed to generate representative volume elements with controlled fiber arrangements, ranging from clustered to equilibrium configurations. Finite element homogenization with periodic boundary conditions was used to estimate effective elastic properties. To characterize fiber randomness and assess statistical equivalence with experimental microstructures, several descriptors are employed, including nearest neighbor distance, Ripley's K-function, pair distribution function, and local fiber volume fraction. Results reveal that, at constant fiber volume fraction, clustered fiber distributions yield significantly higher transverse stiffness but lower transverse tensile strength compared to the equilibrium distributions. For glass/epoxy composites, transverse stiffness varies by up to 20% depending on the degree of fiber clustering. A single scalar descriptor, the mean nearest neighbor distance, was shown to efficiently characterize sufficiently random fiber distributions: effective stiffness decreases, whereas transverse tensile strength increases linearly with mean nearest neighbor distance. The findings highlight the critical role of microstructural characteristics in tailoring composite performance and provide a robust framework for predictive modeling of fiber reinforced materials.

We consider a Brownian particle confined by an external potential and subject to stochastic resetting to the origin. Motivated by the repetitive nature of the dynamics, we describe the process as a thermodynamic cycle of thermal expansion and collapse, analyzed via a framework based on the Kullback-Leibler (KL) divergence between forward and reversed trajectory ensembles. While the entropy production generally depends on the full trajectory ensemble and cannot be reduced to thermodynamic state variables alone, we show that the harmonic potential constitute a special case, where the entropy production reduces exactly to a state-function-like expression determined solely by the distributions before and after resetting. Explicit analytical results are derived for periodic and Poissonian resetting. At low resetting rates $r$, the entropy production rate grows linearly with $r$ and is proportional to the symmetric KL divergence between the reset and equilibrium distributions. At very high rates, the resetting process becomes effectively perpetual and the entropy production vanishes. Langevin simulations for an anharmonic quartic potential display the same generic behavior, indicating that these features are not restricted to harmonic confinement. Our results establish a direct connection between stochastic resetting, thermodynamic cycles, and information-theoretic measures of irreversibility.

We prove a weak fundamental principle for $λ$-homogeneous solutions of homogeneous constant-coefficient systems on open pointed convex cones. Starting with the solution family $S_{\mathcal B}$ arising in the Ehrenpreis--Palamodov theory, we construct a corresponding family $S_{\mathcal B,λ}$ by replacing the exponential kernels $e^{\langle x,z\rangle}$ with homogeneous kernels $(-\langle x,z\rangle)^λ$. The key tool is a Mellin-type operator on Paley--Wiener spaces, which links the classical theory to the Euler-constrained setting. For $λ\in \mathbb{C}\setminus \mathbb{N}_0$ and under a visibility assumption, we show that the span of $S_{\mathcal B,λ}$ is dense in the space of $λ$-homogeneous solutions.

Dynamic circuits use real-time outcomes of mid-circuit measurements, processed by a classical controller, to adapt subsequent operations during circuit execution. This additional flexibility over static circuits comes at a price. Mid-circuit measurements are typically slower and noisier than unitary gates. Furthermore, classical feedforward requires exchanging information between the quantum processor (QPU) and the classical controller, introducing latency that erodes the practical performance of dynamic circuits. We propose a compile-time optimization framework that reduces the use of classical controls in dynamic circuits while preserving their semantics. At its core, the framework uses a static analysis that symbolically executes the circuit by propagating classical information alongside the quantum state. By combining this classical-quantum information with the Probabilistic Circuit Model extended with probabilistic controls that emulate classical feedforward, we obtain an intermediate probabilistic representation of the dynamic circuit. In this representation, mid-circuit measurements and classically controlled operations can be removed or rewritten as purely unitary operations and probabilistic components. Compared to existing compile-time optimizations that target only mid-circuit measurements, our method applies to a broader class of dynamic circuits expressible in modern quantum programming languages. We evaluated our framework on randomly generated dynamic circuits, achieving about 50% classical feedforward reduction and even higher reductions in favorable settings.

Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an alternative approach that avoids an explicit treatment of the continuum by formulating the problem in terms of discrete quantum states. Our discussion is based on the stabilization method, in which the system is confined to a finite region such that the continuum is replaced by a discrete energy spectrum. Resonances then appear as characteristic features in the energy levels under variation of the confining box size, providing an intuitive interpretation in terms of a two-level system while remaining closely connected to standard quantum mechanics curriculum. We review the method, derive selected results, and discuss practical strategies for extracting resonance parameters from stabilization diagrams. In addition to established fitting procedures, we introduce a novel approach based on the analysis of spatial localization of resonant states, which enables a robust identification of resonance properties. The approach is illustrated using both attractive and repulsive delta-shell potentials, which serve as simple and instructive model systems amenable to analytical treatment.

This paper gives a complete description of the solutions of the global positioning problem, emphasizing the under-determined case. We show that the solutions form a quadric, which may degenerate in various ways. Perhaps more surprisingly, the satellite positions also lie on a quadric, and these two quadrics exhibit a remarkable duality: They live on perpendicular affine spaces but share the same axis of symmetry. Moreover, the vertices of one quadric are the foci of the other and vice versa. The results of this paper are not only applicable to the global positioning problem, but to a wider class of problems known as pseudorange-multilateration. This includes a range of real-world localization problems where a signal is emitted at an unknown emission time, and received by sensors at known positions. In particular, the paper can be useful for solving an under-determined multilateration problem in the presence of additional constraints. We illustrate this with two examples: locating a cleaning robot on the ground and locating a raft on the ocean.

This article presents an overview of quasineutral limits in plasma models. Starting from the Vlasov-Poisson system, it explains the role of the Debye length, the emergence of a kinetic incompressibility constraint, and the stability issues caused by fast oscillations and singular electric fields. A central theme is that the geometry of the kinetic flow should be reflected in the way perturbations are measured. This leads to kinetic Wasserstein distances adapted to phase-space dynamics, which provide refined stability estimates for quasineutral limits. The article also discusses related models with thermalized electrons and the additional challenges of the electromagnetic Vlasov-Maxwell setting.

Modern naval surveillance demands multifunction radar systems capable of operating in cluttered and contested environments. This paper presents the experimental characterization of a compact, X-band Active Electronically Scanned Array (AESA) radar demonstrator. The system was evaluated in a realistic coastal field environment at Naval Support and Experimentation Centre (CSSN) and, specifically, its specialized institute, the G. Vallauri Institute, which has historical expertise in testing and evaluating the performance of operational sensors as well as those under development, using real maritime targets and an active noise jammer. The trials assessed three core functions: direction-of-arrival (DoA) estimation, adaptive jammer suppression using MVDR beamforming, and high-resolution Inverse Synthetic Aperture Radar (ISAR) imaging. The results confirm that the demonstrator successfully detects and localizes targets, effectively suppresses high-power interference, and generates clear ISAR images of non-cooperative vessels. These findings validate the multifunction performance of the AESA demonstrator, confirming its suitability for advanced naval surveillance applications.

Millimeter-wave Frequency Modulated Continuous Wave (FMCW) radar enables contactless cardiac monitoring, but heartbeat estimation becomes challenging when respiration and random body motion (RBM) distort the radar signal. In this paper, we propose a hybrid framework for 77 GHz FMCW radar that combines model-based signal processing with a Convolutional Neural Network (CNN)-Transformer network. The first block extracts chest displacement and constructs meaningful high-level motion features from raw radar data, while the second block reconstructs a photoplethysmography (PPG)-like signal from the extracted features. In this study, a synchronized PPG signal is used as the ground truth for heartbeat monitoring in supervised training. The method is evaluated following the IEEE AESS Radar Challenge Problem I protocol using the official datasets and figures of merit across three motion scenarios: stationary, deep breathing, and RBM. Results show that the proposed architecture reliably reconstructs the PPG signal in all scenarios, achieving high fidelity in controlled conditions and maintaining robust performance under motion. This enables reliable average heart rate (AHR) and heart rate variability (HRV) estimation even where benchmark methods fail, and leads to the highest total score among the compared approaches.

This paper presents a novel mathematical framework for phase unwrapping in three-dimensional interferometric ISAR (3D InISAR) imaging. The approach works on a scatterer-by-scatterer basis and does not rely on any spatial continuity assumptions, making it suitable for sparse point clouds. The formulation is derived from the Mixed-Integer Least Squares (MILS) theory, an optimal maximum-likelihood framework for joint estimation of integer and real unknowns in the presence of Gaussian noise. This provides a unified way to handle generic sensor geometries, multi-baseline, multi-frequency, or hybrid setups. The method also produces a natural a posteriori quality metric for each unwrapped phase, which can be used to build a statistical test to reject outliers. The algorithm is simple to implement and has a computational cost suitable for operational systems. This paper presents the theoretical foundations of the framework and a first validation study on a standard L-shaped dual-frequency setup using Monte Carlo simulations. Results show that the proposed framework enables reliable 3D reconstruction in challenging ambiguity conditions.

We study sums of locally dependent scores associated with general marked (i.e., labeled) Euclidean point processes. We introduce geometric mixing conditions on the underlying point process and a Lipschitz-"localization" condition on the scores, which jointly ensure a central limit theorem for the sums of the scores as well as expectation and variance asymptotics. Our localization condition is formulated using the bounded Lipschitz metric, providing a distributional criterion. This stands in contrast to the classical stabilization conditions in stochastic geometry, which are typically based on stopping-set constructions. To demonstrate the applicability of our general framework, we consider several stochastic processes indexed by spatial random graphs. These include spin systems, interacting diffusions, and interacting particle systems. In particular, spin systems highlight the importance of our localization condition. Additional applications include empirical random fields and geostatistical Boolean models.

Asynchronous iterative methods tolerate straggling processors by allowing workers to proceed with stale data, but at a cost: the iterates become inconsistent, potentially degrading convergence. We investigate whether convergence accelerators such as Anderson acceleration compensate for this degradation. We experimentally study three fixed-point iterations: the Jacobi method for sparse linear systems, value iteration for the Bellman equation, and the Hartree--Fock self-consistent field (SCF) iteration. The experiments are conducted using a high-performance execution framework Ray, which abstracts the complexity of distributed systems and enables code parallelization and fault injection with minimal changes. We establish two main results. First, straggler tolerance is universal: asynchronous execution provides wall-clock speedups of $2.9\times$ (Jacobi), $7.7\times$ (VI), and $16.9\times$ (SCF) over synchronous execution with a 100\,ms-delayed worker, independent of whether acceleration is used. Second, Anderson acceleration's effectiveness under asynchrony depends on where staleness enters the computation. We identify two staleness mechanisms: iterate-level corruption, where stale worker returns directly overwrite portions of the accelerated iterate (as in block Jacobi), and evaluation-level perturbation, where staleness acts as a bounded perturbation to the fixed-point map evaluation (as in VI and SCF). Anderson acceleration fails categorically under the first mechanism but retains its benefits under the second, consistent with the perturbation analysis of Toth et al.\ (2017). This distinction, rather than the contraction norm or smoothness of the map, is the primary determinant of whether acceleration survives asynchronous execution.

Dynamical control of Berry curvature remains an outstanding challenge in the engineering of topological phases. Here, we demonstrate control of magnon band structures via coherently driven phonons, based on \textit{ab initio} spin-lattice coupling and Floquet theory. We show that this control is symmetry selective: linearly polarized phonons leave the spectrum unchanged, whereas circular and elliptical phonons carrying finite phonon angular momentum (PAM) induce chiral interactions that open and tune gaps at Dirac points, generating and reversing topological magnon phases. The gap magnitude and Chern numbers are directly governed by the PAM, enabling handedness-selective topology control. Applied to monolayer CrI$_3$, and supported by symmetry analysis, our results establish driven lattice dynamics as a general route to engineering topological bosonic excitations and a versatile platform for Floquet control of magnetism.

We introduce the \emph{intersection orbital graph} $Γ(G_1, G_2; Ω)$ associated with two permutation groups $G_1, G_2 \leq \mathrm{Sym}(Ω)$ on a finite set $Ω$.

In a previous paper we introduced a version of associativity for a partial infinitary operation. We prove here that if $γ$ is an infinite ordinal and some associative infinitary operation is defined for all sequences indexed by ordinals $ \leq γ$, then such an operation can be uniquely expanded to apply to every sequence indexed by any ordinal of cardinality $ |γ|$. In particular, if some associative operation is defined for all finite sequences as well as for all $ ω$-indexed sequences, then the operation can be uniquely expanded to apply to every sequence indexed by a countable ordinal.

This paper presents a unified multi-asset, multi-group asset-flow model that integrates three foundational frameworks from the behavioral finance literature. The model captures the dynamics of financial markets where multiple assets are traded by multiple investor groups, each with distinct trend-following (momentum) and value-based (fundamental) strategies. Unlike classical efficient market models, our framework explicitly incorporates the finiteness of cash and shares, asymmetric cross-asset coupling in buying decisions, and endogenous wealth redistribution across groups. We derive the complete system of ordinary differential equations governing price, cash, share, and sentiment dynamics, and establish the fundamental properties of positivity and boundedness for all physically relevant variables. The equilibrium set is characterized as a manifold parameterized by cash distribution, with the fundamental equilibrium as a special point. Through linear stability analysis, we identify conditions under which the fundamental equilibrium loses stability via a supercritical Hopf bifurcation, giving rise to persistent limit cycles. The model is validated against three benchmark papers: the single-asset multi-group model of DeSantis, Swigon, and Caginalp (2012); the two-asset single-group model of Bulut, Merdan, and Swigon (2019); and the two-asset two-group Nigeria-Libya oil market model of Cavani (2026). Our numerical simulations reproduce all key theoretical predictions, including equilibrium manifolds, Hopf bifurcation thresholds, limit cycle periods, and asymmetric contagion patterns.

In a former paper we introduced partial infinitary noncommutative semigroups and showed, among other, that significant differences arise in comparison with the commutative case, previously studied in the literature. For example, in the commutative case we cannot have an infinitary identity $e$ together with two elements $a \not= e$, $b \not= e$ such that $ab= e$, just under the assumption that the countable product $abababa\dots$ is defined. Here we show that this is possible in the noncommutative case, actually, we can have an infinitary semigroup on a countable set with a complete identity and such that the operation is defined for every indexed linearly ordered set.