Search Results (227)

This paper investigates the existence and uniqueness of local and global solutions to the incompressible three-dimensional Navier–Stokes equations within the framework of homogeneous Lei–Lin–Gevrey spaces ${\mathcal{X}}_{a,\gamma }^{\rho }({\mathbb{R}}^3)$, where $\rho \in [-1,0),a>0$, and $\gamma \in (0,1)$. These function spaces combine the critical scaling structure of the Lei–Lin spaces with the exponential regularity of Gevrey classes, thereby enabling a refined treatment of analytic regularity and frequency localization. The main results are obtained under the assumption of small initial data in the critical Lei–Lin space ${\mathcal{X}}^{\rho }({\mathbb{R}}^3)$, extending previous works and improving regularity thresholds. In particular, we establish that for suitable initial data, the Navier–Stokes system admits unique solutions globally in time. The influence of the Gevrey parameter $\gamma$ on the high-frequency behavior of solutions is also discussed. This work contributes to a deeper understanding of regularity and decay properties in critical and supercritical regimes. Full article

This paper investigates a new class of fractional integral operators, namely, the exponentially damped Riesz-type operators within the framework of variable exponent Lebesgue spaces $L^{\mathtt{p}(·)}$. To the best of our knowledge, the boundedness of such operators has not been addressed in any existing functional setting. We establish their boundedness under appropriate log-Hölder continuity and growth conditions on the exponent function $\mathtt{p}(·)$. To highlight the novelty and practical relevance of the proposed operator, we conduct a comparative analysis demonstrating its effectiveness in addressing convergence, regularity, and stability of solutions to partial differential equations. We also provide non-trivial examples that illustrate not only these properties but also show that, under this operator, a broader class of functions becomes locally integrable. The exponential decay factor notably broadens the domain of boundedness compared to classical Riesz and Bessel–Riesz potentials, making the operator more versatile and robust. Additionally, we generalize earlier results on Sobolev-type inequalities previously studied in constant exponent spaces by extending them to the variable exponent setting through our fractional operator, which reduces to the classical Riesz potential when the decay parameter $\mathsf{\lambda }=0$. Applications to elliptic PDEs are provided to illustrate the functional impact of our results. Furthermore, we develop several new structural properties tailored to variable exponent frameworks, reinforcing the strength and applicability of the proposed theory. Full article

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

The objective of this work is to investigate the global existence, general decay and blow-up results for a class of p-Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions. The global existence of solutions has been obtained by potential well theory and the general decay result of energy has been established, in which the exponential decay and polynomial decay are only special cases, by using the multiplier techniques combined with a nonlinear integral inequality given by Komornik. Finally, the blow-up of solutions is established with positive initial energy. To our knowledge, the global existence, general decay, and blow-up result of solutions to p-Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions has not been studied. Full article

The stability of a class of quaternion-valued switching neural networks (QVSNNs) with time-varying delays is investigated in this paper. Limited prior research exists on the stability analysis of quaternion-valued neural networks (QVNNs). This paper addresses the stability analysis of quaternion-valued neural networks (QVNNs). With the help of some symmetric matrices with excellent properties, the stability analysis method in this paper is undecomposed. The QVSNN discussed herein evolves with average dwell time. Based on the Lyapunov theoretical framework and Wirtinger-based inequality, QVSNNs under any switching law have global asymptotic stability (GAS) and global exponential stability (GES). The state decay estimation of the system is also given and proved. Finally, the effective and practical applicability of the proposed method is demonstrated by two comprehensive numerical calculations. Full article

The variance function (VF) is central to natural exponential family (NEF) theory. Prompted by an online query about whether, beyond the classical normal NEF, other real-line NEFs with bounded VFs exist, we establish three complementary sets of sufficient conditions that yield many such families. One set imposes a polynomial-growth bound on the NEF’s generating measure, ensuring rapid tail decay and a uniformly bounded VF. A second set relies on the Legendre duality, requiring a uniform positive lower bound on the second derivative of the generating function, which likewise ensures a bounded VF. The third set starts from the standard normal distribution and constructs an explicit sequence of NEFs whose Laplace transforms and VFs remain bounded. Collectively, these results reveal a remarkably broad class of NEFs whose Laplace transforms are not expressible in elementary form (apart from those stemming from the standard normal case), yet can be handled easily using modern symbolic and numerical software. Worked examples show that NEFs with bounded VFs are far more varied than previously recognized, offering practical alternatives to the normal and other classical models for real-data analysis across many fields. Full article

Industrial Control Systems (ICS) are increasingly targeted by sophisticated and evolving cyberattacks, while conventional static defense mechanisms and isolated intrusion detection models often lack the robustness required to cope with such dynamic threats. To overcome these limitations, we propose RHAD (Reinforced Heterogeneous Anomaly Detector), a resilient and adaptive anomaly detection framework specifically designed for ICS environments. RHAD combines a heterogeneous ensemble of detection models with a confidence-aware scheduling mechanism guided by reinforcement learning (RL), alongside a time-decaying sliding window voting strategy to enhance detection accuracy and temporal robustness. The proposed architecture establishes a modular collaborative framework that enables dynamic and fine-grained protection for industrial network traffic. At its core, the RL-based scheduler leverages the Proximal Policy Optimization (PPO) algorithm to dynamically assign model weights and orchestrate container-level executor replacement in real time, driven by network state observations and runtime performance feedback. We evaluate RHAD using two publicly available ICS datasets—SCADA and WDT—achieving 99.19% accuracy with an F1-score of 0.989 on SCADA, and 98.35% accuracy with an F1-score of 0.987 on WDT. These results significantly outperform state-of-the-art deep learning baselines, confirming RHAD’s robustness under class imbalance conditions. Thus, RHAD provides a promising foundation for resilient ICS security and shows strong potential for broader deployment in cyber-physical systems. Full article

Old-growth forests are rare in Europe, yet they play a critical role in biodiversity and carbon storage. This study examines the structural dynamics of the Janj old-growth forest in the Dinaric Alps using repeated field measurements from 2011 and 2021 at 39 systematically arranged 12 m radius plots. All trees (DBH ≥ 7.5 cm), regeneration (10 cm height to 7.5 cm DBH), and coarse woody debris (CWD) were assessed. Results revealed that total basal area declined by 3.5 m² ha⁻¹ over the decade, primarily driven by significant reductions in stem density for silver fir (p = 0.001) and Norway spruce (p = 0.001). In contrast, European beech maintained a stable basal area throughout the study period. Moreover, silver fir exhibited a significant increase in mean diameter (p = 0.032) and a pronounced rise in regeneration individuals (t = 3.257, p = 0.002). These findings underscore a gradual compositional shift towards European beech dominance, with conifers facing higher mortality in larger diameter classes. The substantial volume of CWD (463 m³ ha⁻¹) highlights advanced decay dynamics consistent with mature forest conditions. This study emphasizes the value of repeated measurements to capture subtle yet important successional changes in primeval forests, which is essential for conservation planning and sustainable forest management. Full article

The novel sub-stoichiometric copper oxide CuO_0.75 was prepared via the slow oxidation of Cu₂O. This compound retains the original crystallographic structure of tenorite CuO, despite the considerable presence of disordered oxygen vacancies. CuO_0.75 resembles the mixed valence oxide Cu²⁺/Cu¹⁺, while the unit cell contains one oxygen vacancy. Performance-wise, the electric resistivity and magnetic susceptibility data follow the Anderson–Mott localization theories. The exponential localization decay length was found to be α⁻¹ = 2.1 nm, in line with modern scaling research. Via cooling, magnetic double-exchange interaction, mediated by oxygen, results in Zener conductivity at T~122 K, which is followed by antiferromagnetic transition at T~51 K. The obtained results indicate that the CuO_0.75 compound can be perceived as a showcase material for the demonstration of a new class of high-performance magnetic materials. Full article

Metaconcrete (MC) is a class of engineered cementitious composites that integrates locally resonant inclusions to filter stress waves. While the dynamic benefits are well established, the effect of resonator content and geometry on static compressive resistance remains unclear. This study develops the first two-dimensional mesoscale finite-element model that explicitly represents steel cores, rubber coatings, and interfacial transition zones to predict the quasi-static behavior of MC. The model is validated against benchmark experiments, reproducing the 56% loss of compressive strength recorded for a 10.6% resonator volume fraction with an error of less than 1%. A parametric analysis covering resonator ratios from 1.5% to 31.8%, diameters from 16.8 mm to 37.4 mm, and coating thicknesses from 1.0 mm to 4.2 mm shows that (i) strength decays exponentially with volumetric content, approaching an asymptote at ≈20% of plain concrete strength; (ii) larger cores with thinner coatings minimize stiffness loss (<10%) while limiting strength reduction to 15–20%; and (iii) material properties of the resonator have a secondary influence (<6%). Two closed-form expressions for estimating MC strength and Young’s modulus (R² = 0.83 and 0.94, respectively) are proposed to assist with the preliminary design. The model and correlations lay the groundwork for optimizing MC that balances vibration mitigation with structural capacity. Full article

Background/Objectives: Dental caries (DCs) and type 2 diabetes share common risk factors. Dental caries risk in type 2 diabetics (T2DM) shows contradictory results. The aim of this study was to determine if there is a difference in DC prevalence in adults with and without T2DM and whether body mass index (BMI) classes or glycated hemoglobin (HbA1c) levels interfere in that difference. Methods: A total of 666 adults (n(T2DM) = 343; n(nT2DM) = 323), from Espinho Primary Health Care Center, were interviewed by calibrated observers. Data from clinical records were collected and oral health status was registered using WHO criteria. Inference analysis was conducted using non-parametric tests (α = 0.05). Results: A similar caries prevalence was found between the T2DM (98.2%) and nT2DM (98.8%) groups, with the T2DM group showing significantly higher tooth loss (p < 0.001), higher caries experience rerted as mean ± sd (17.7 ± 8.3 vs. 15.9 ± 7.8, p = 0.005), fewer decayed teeth (p < 0.001) and filled teeth (p = 0.016) compared to nT2DM. The most frequently identified comorbidity was hypertension (53.6%). Tobacco use (12.9%) was lower in T2DM (p < 0.001). The restorative and treatment indices indicated a significantly higher proportion of use of oral care services (p < 0.001) in T2DM individuals. The prevalence of the higher classes of BMI indicative of pre-obesity or obesity shows significant differences (p < 0.001). The differences found in the DMFT or each of its components for the prevalence or for the mean in HbA1c control were not statistically significant (p = 0.368, and 0.524, respectively). Conclusions: Adults with T2DM and higher BMI classes could be associated with a greater prevalence of DCs. The glycemic control of T2DM does not significantly influence DMFT score or each of its components. Full article

In ultra-relativistic heavy-ion collisions, the study of muons from kaon (K) and pion ($\pi$) decays provides insights into hadron production and propagation in the Quark–Gluon Plasma (QGP). This paper investigates muon yields from K and $\pi$ decays in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV using a fast simulation method. We employ a fast Monte Carlo procedure to estimate muon yields from charged kaons and pions. The simulation involves generating pions and kaons with uniform $p_{\mathrm{T}}$ and y distributions, simulating their decay kinematics via PYTHIA, and reweighting to match the physical spectra. Our results show the transverse momentum distributions of muons from K and $\pi$ decays at forward rapidity ($2.5<y<4.0$) for different centrality classes. The systematic uncertainties are primarily from the mid-rapidity charged K/$\pi$ spectra and rapidity-dependent $R_{\mathrm{AA}}$ uncertainties. The muon yields from pion and kaon decays exhibit consistency across centrality classes in the $p_{\mathrm{T}}$ range of 3–10 GeV/c. This study contributes to understanding hadronic interactions and decay kinematics in heavy-ion collisions, offering references for investigating pion and kaon decay channels and hot medium effects. Full article

We investigate an inverse problem involving source and damping term with variable-exponent nonlinearities. We establish adequate conditions on the initial data for the decay of solutions as the integral overdetermination approaches zero over time within an acceptable range of variable exponents. This class of inverse problems, where internal terms such as source and damping are to be determined from indirect measurements, has significant relevance in real-world applications—ranging from geophysical prospecting to biomedical engineering and materials science. The accurate identification of these internal mechanisms plays a crucial role in optimizing system performance, improving diagnostic accuracy, and constructing predictive models. Therefore, the results obtained in this study not only contribute to the theoretical understanding of nonlinear dynamic systems but also provide practical insights for reconstructive analysis and control in applied settings. The asymptotic behavior and decay conditions we derive are expected to be of particular interest to researchers dealing with stability, uniqueness, and identifiability in inverse problems governed by nonstandard growth conditions. Full article

(1) Background: This study aimed to develop a deep learning model using a convolutional neural network (CNN) to automate Risser grade assessment from pelvic radiographs. (2) Methods: We used 1619 pelvic radiographs from patients aged 12–18 years with scoliosis to train two CNN models—one for the right pelvis and one for the left. A multimodal approach incorporated 224 × 224-pixel regions of interest from radiographs, alongside patient age and gender. The models were optimized with Adam, weight decay, rectified linear unit (ReLU) activation, dropout, and batch normalization, while synthetic data augmentation addressed class imbalance. Performance was evaluated through accuracy, precision, recall, F1-score, and area under the receiver operating characteristic curve (ROC AUC). (3) Results: The right pelvis model achieved 83.64% accuracy; the left pelvis model reached 80.56%. Both models performed well for Risser Grades 0, 2, and 4, with the right pelvis model achieving a microaverage F1-score of 0.836 and ROC AUC of 0.895. The left pelvis model achieved a microaverage F1-score of 0.806 and ROC AUC of 0.872. Challenges arose from class imbalance in less frequent grades. (4) Conclusions: CNN models effectively automated Risser grade assessment, reducing clinician workload and variability. Full article

We consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes can be introduced by using the general framework of the weighted matrices approach to ultradifferentiable functions. We examine alternative descriptions of Gelfand–Shilov spaces related to the extended Gevrey regularity and derive their nuclearity. In addition to the Fourier transform invariance property, we present their corresponding symmetric characterizations. Finally, we consider some time–frequency representations of the introduced classes of ultradifferentiable functions. Full article