Search Results (345)

We study the large-time behavior of bounded entropy solutions to a class of fractional degenerate parabolic–hyperbolic equations involving ${\Lambda }^{\alpha }={(-\Delta )}^{\alpha /2}$, $0<\alpha <2$, with initial data taken in generalized Besicovitch spaces associated with algebras possessing a mean value. The diffusion is governed by a nonlocal fractional operator and may vanish on nontrivial ranges of the solution variable, so that the equation combines hyperbolic transport with degenerate nonlocal dissipation. Under a suitable non-degeneracy condition involving the flux and the symbol of the fractional diffusion operator, we prove that the entropy solution converges, as time tends to infinity, to the mean value of the initial data in the generalized Besicovitch sense. The analysis is carried out in the framework of ergodic algebras and uses the formulation of generalized Besicovitch spaces on the corresponding compact space. In this realization, the Besicovitch mean is represented by integration on the compact space, and together with the $L^1$-mean contraction principle, it provides the main mechanism for controlling the mean distance along the evolution. After establishing the entropy formulation and the associated $L^1$-mean contraction principle, we derive a fractional kinetic representation adapted to the nonlocal diffusion and analyze a rescaled family of solutions by means of compactness tools suited to the fractional setting. This yields decay in time averages, which is then improved to full asymptotic convergence by the monotonicity of the $L^1$-mean distance to the equilibrium state. Full article

Type 1 diabetes (T1D) is a chronic autoimmune disease in which autoreactive effector T cells destroy insulin-producing pancreatic β-cells, leading to impaired insulin production and long-term metabolic complications. This study develops a mathematical model of the interactions among pancreatic β-cells, autoreactive effector T cells, regulatory T cells (Tregs), and stem cell therapy, treating stem cell administration as an immunomodulatory and regenerative strategy that suppresses autoimmune activity and promotes β-cell recovery. The existence, uniqueness, positivity, and boundedness of solutions are established. For the auxiliary subsystem with $S_{E }=0$ and constant treatment input, the disease-free equilibrium and the threshold quantity $R_{0 }$ are derived, and local asymptotic stability of the DFE is established for $R_{0 }<1$. For the full model with $S_{E }>0$, the existence of a unique biologically feasible positive equilibrium is established, together with its local asymptotic stability under constant treatment input. An optimal control problem, formulated using Pontryagin’s Maximum Principle, is used to guide therapeutic dosing, and one-year numerical simulations compare two administration protocols: high-dose pulse injections and continuous infusion. Both reduce autoimmune activity and improve β-cell dynamics, with pulse administration producing stronger transient responses and continuous infusion producing smoother treatment-period dynamics, while both protocols approach similar long-term levels. A local sensitivity analysis identifies immune activation, β-cell destruction, and regulatory T-cell activity as the parameters most strongly shaping disease progression and treatment outcomes. By unifying stem cell therapy, stability analysis, sensitivity analysis, and optimal control, and directly comparing pulse and infusion protocols, this framework offers new insight for designing stem cell-based treatments for autoimmune diabetes. Full article

Greenwashing distorts green markets and impedes sustainable development. This study develops a four-party asymmetric evolutionary game model to examine the strategic interactions among government, companies, social media, and consumers in greenwashing governance. By formulating replicator dynamics and conducting a Jacobian-based local stability analysis, the research identifies three representative locally asymptotically stable boundary equilibria under specified parameter configurations: such as dual-oversight market withdrawal, consumer-redress-driven governance, and social-media-absent regulation-driven governance. Numerical simulations examine benchmark evolutionary trajectories and selected parameter variations. The results indicate that system outcomes are sensitive to adjustments in complaint compensation, consumer complaint cost, the additional cost of genuine green production, and social media auditing costs. Specifically, high penalties for lenient auditing can induce persistent systemic fluctuations, while strict auditing alone may inadvertently stabilize a market-withdrawal outcome without prompting genuine green behavior. Under the specified parameter conditions of the model, the findings suggest that stable governance is associated with coordinated incentives for genuine production, economically viable consumer redress, and appropriately calibrated auditing policies. Full article

Bidirectional DC–DC converters are key interfaces in battery energy storage systems, electric vehicles, fuel cell vehicles, and DC microgrids, where transparent mathematical models are required for simulation, controller evaluation, and energy-flow analysis. This paper presents a hybrid index matrix framework for the Python-based modeling of a bidirectional buck–boost converter coupled to a first-order Thevenin battery model. In contrast to a classical state-space formulation, the index matrix is used as a label-aware model-assembly layer: component equations are aligned by explicit row and column identifiers and subsequently projected into ordered numerical matrices for solution. Charging, idle, and discharging equations are solved using a fixed-step backward-Euler procedure, and a PI current controller with duty-cycle saturation and anti-windup regulates the power-flow direction. A conventional switched ODE implementation is retained only as a software-level numerical-consistency check between two implementations of the same assumptions; it is not presented as experimental validation or as an independent physical benchmark. For the reported 60 s current profile, the model gives a current RMSE of 0.0863 A and a peak current of 4.3684 A, corresponding to 9.2094% overshoot at the idle-to-discharge transition. The power-integration balance is 1.6091 Wh input, 1.5868 Wh output, and 0.0223 Wh estimated loss under the adopted conduction-oriented loss model. The conditional one-step sensitivity matrices have a spectral radius of 1.00000 in all three modes; the unit eigenvalue is consistent with the slowly varying SOC state, while the remaining electrical eigenvalues lie inside the unit circle. These eigenvalue results are interpreted as local non-divergence diagnostics rather than proof of asymptotic closed-loop or switched-system stability. The framework provides a transparent and reproducible numerical workflow, while experimental validation, detailed switching-level loss modeling, step-size convergence, and formal closed-loop/switched-system stability analysis remain necessary future work. Full article

This paper investigates a distributed-order fractional SEIRS epidemic model with temporary immunity, vaccination, disease-induced mortality, and density-dependent natural mortality. The distributed-order formulation provides a flexible framework for incorporating heterogeneous memory effects into epidemic dynamics. The basic reproduction number is derived, the disease-free and endemic equilibria are characterized, and their local stability properties are investigated through the distributed-order characteristic equation. In addition, a sufficient global disease extinction criterion is established using a distributed-order Lyapunov argument, yielding global asymptotic stability of the disease-free equilibrium under an explicit transmission bound. Numerical spectral analysis shows that no oscillatory stability transition occurs within the considered parameter ranges and that the endemic equilibrium remains asymptotically stable within these ranges. Numerical simulations examine the effects of the memory interval and memory density shape on epidemic transients. Broadening the memory interval toward lower fractional orders slows convergence and increases transient persistence. For a fixed memory interval, densities concentrated near lower fractional orders produce the slowest relaxation, whereas those concentrated near higher orders, closer to the classical first-order limit, yield the fastest decay. These results show that distributed-order memory primarily regulates transient epidemic dynamics while preserving endemic equilibrium stability within the investigated parameter regimes, providing new insight into heterogeneous memory effects in fractional epidemic models. Full article

Soft exoskeletons have attracted increasing attention as wearable robotic devices for lower limb rehabilitation and assistive mobility. This study presents an integrated modelling, control, and mechanical design framework for a cable-driven soft exoskeleton operating in the sagittal plane, targeting elderly users with reduced mobility. Lower limb swing-phase dynamics were derived using the Euler–Lagrange formulation and subsequently recast via a Legendre transformation into a Hamiltonian representation of the coupled hip–knee system under tendon-driven actuation. Building upon this model, a hierarchical control architecture combining Quasi-Sliding Mode Control (QSMC) for angular regulation with Sliding Mode Control (SMC) for conjugate-momentum dynamics is developed. A Lyapunov-based stability analysis formally establishes the asymptotic stability of the closed-loop system and derives explicit gain conditions for robust tracking in the presence of bounded disturbance. In parallel, a compact winch-based actuation module was designed and geometrically optimized using a genetic algorithm to minimize the distal mass while preserving mechanical robustness and ergonomic wearability. The framework was validated through numerical simulations in MATLAB–Simulink^® and physics-based simulations in a MuJoCo–ROS2 environment, in which gravity, contact interactions, and cable compliance were considered. A modular mechanical prototype was developed and worn by users with different anthropometric characteristics for a static qualitative assessment of its fit and structural feasibility. These results establish a rigorous foundation for the future integration of embedded sensing and actuation hardware into experimental rehabilitation assessment. Full article

We study the linear continuous interior penalty finite element method (CIP-FEM) for the two-dimensional Helmholtz equation on nonconvex polygonal obstacle domains with mixed Dirichlet and impedance boundary conditions. Re-entrant corners reduce the global regularity below $H^2\left(\mathrm{\Omega }\right)$ and require a corner-sensitive treatment of the CIP stabilization term. Using a wavenumber-explicit regular–singular decomposition, we establish exact consistency of the CIP formulation under this reduced regularity. We also prove the critical-order penalty-seminorm estimate $|I_h{S}_j{|}_J \lesssim h^{{\alpha }_j}$ for the Scott–Zhang quasi-interpolant of the cut-off corner singular functions. Combining this estimate with endpoint Scott–Zhang approximation and wavenumber-explicit bounds for the regular and singular components yields ${\inf }_{v_h \in V_h}\parallel u-v_h{\parallel }_{h,k} \lesssim (kh + k^{\alpha -1/2}{h}^{\alpha }){\parallel f\parallel }_{0,\mathrm{\Omega }}$. A Schatz-type duality argument then yields the corresponding quasi-optimal error estimate $\parallel u-u_h{\parallel }_{h,k} \lesssim (kh + k^{\alpha -1/2}{h}^{\alpha }){\parallel f\parallel }_{0,\mathrm{\Omega }}$ under the sufficient resolution condition $k^{2}h \le \delta$, where $\delta$ is independent of k and h. Discrete uniqueness is proved independently of this condition. Numerical experiments support the predicted corner-singularity behavior; for the tested problems with the fixed penalty value $\gamma = 0.1$, they show smaller errors than the standard FEM on some relatively coarse meshes in the high-wavenumber pre-asymptotic regime. The present analysis does not separately identify an additive pollution error term. Full article

Due to the increase in the number of ontologies in various domains, ranking them to facilitate their selection for reuse is an important task in ontology engineering to date. To assess the multi-faceted quality configurations of candidate ontologies, Multi-Criteria Decision Making (MCDM) frameworks are used. In particular, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is an MCDM method that is widely adopted for the task of ontology ranking. However, traditional TOPSIS implementations rely almost exclusively on the Euclidean distance metric. This introduces severe rank volatilities and systematic biases when evaluating heterogeneous ontology metadata. To address these limitations, this paper introduces a novel Multi-Distance Ensemble TOPSIS (Ensemble-TOPSIS) method for robust ontology ranking. Rather than forcing a localized geometric choice, the proposed Ensemble-TOPSIS method simultaneously projects alternative ontologies through a multi-distance ensemble composed of Euclidean, Chebyshev, cosine, and Mahalanobis configurations. The Ensemble-TOPSIS method was applied to three datasets of ontologies from the artificial intelligence, agricultural, and biological domains to test its scalability and multi-domain applicability. The experimental results reveal that all the ontologies from the three domains were successfully ranked by the proposed Ensemble-TOPSIS method. Furthermore, the statistical rank correlation using Spearman’s $\rho$, Kendall’s $\tau$, and the $WS$ rank similarity coefficients was calculated between the TOPSIS variants, and the proposed Ensemble-TOPSIS method achieved the highest correlation in the majority of cases. Moreover, a comprehensive Monte Carlo simulation across 1200 stochastically generated, non-linear, and skewed multicollinear decision domains established the asymptotic stability of the proposed Ensemble-TOPSIS method, which achieved the highest global mean performance ($\overline{\rho }=0.88$, $\overline{\tau }=0.75$, $\overline{WS}=0.94$), minimized rank variance (${\sigma }^2\left(WS\right)=0.0006$), and optimally maximized the lower-bound worst-case performance profile ($\rho =0.67$) compared to individual baseline formulations. Full article

Emerging technology cultivation is formulated as a finite-time stochastic reachability problem under a budget-simplex constraint. Novelty potential, implementation feasibility, and industrial embeddedness form a three-state cascade Itô system, and success requires their joint entrance into a target set before a fixed horizon. The analysis establishes positive invariance, a unique globally attractive deterministic equilibrium, and an explicit asymptotic budget boundary whose minimum occurs at the maximizer of the knowledge-distance kernel. For specified constant-allocation rules, projected Euler–Maruyama simulation provides rule-specific node-monitoring probabilities and budget thresholds. A repeated finite-candidate sample-average approximation with independent candidate-generation, selection, and validation samples assesses the additional gain from adaptive candidate selection. The numerical results show that the deterministic grid-search rule reaches prescribed probability levels at lower intervention rates than balanced allocation, while the repeated SAA procedure yields further gains in the tested transition region. Finite-time success therefore depends on both the total budget rate and its allocation across cascade-dependent channels. Full article

In this work, we develop a projection neural network based on a second-order dynamical model (SO-PDM) for solving inverse variational inequality problems (IVIPs) in Hilbert spaces. The proposed framework incorporates inertial and damping components, resulting in improved convergence behavior while ensuring feasibility through a projection operator. Under the Lipschitz continuity assumption on the operator, the proposed SO-PDM admits a unique global trajectory. Under the additional strong monotonicity assumption and suitable parameter conditions, convergence to the unique solution of the IVIP is established. A discrete-time formulation is derived via a finite-difference scheme, leading to a projection-based inertial algorithm with relaxation. Under suitable parameter conditions, the algorithm is shown to converge linearly to the unique solution of the IVIP, and under an additional parameter condition, the global asymptotic stability of the continuous-time SO-PDM is established via Lyapunov analysis. Furthermore, a numerical comparison in a higher-dimensional setting shows that the proposed algorithm converges faster and attains higher accuracy than the existing first-order projection method. Numerical experiments further confirm the effectiveness and stability of the proposed SO-PDM, including its application to sparse signal recovery in compressed sensing. Full article

Closed droplet contours provide the geometric basis for area estimation in vision-based droplet observation. In OLED inkjet printing, droplets are deposited into pixel wells with predefined geometry; projected area is therefore a primary geometric quantity for assessing whether the deposited liquid sufficiently fills the well or risks overflow. This work formulates closed-contour sampling under a fixed sampling budget as an area-driven sampling problem. A leading-order analysis of the local arc–chord area error shows that the dominant cubic term depends jointly on curvature and segment length. Minimization of the resulting leading-order area-error functional yields an asymptotically optimal area-driven sampling density proportional to the cube root of curvature, together with a sampling-budget estimate under a target area-error tolerance. The derived sampling density is implemented on the fitted closed contour through cumulative-weight inversion. Experiments on random closed curves and the droplet dataset provide a systematic quantitative comparison with representative methods under identical fixed-budget settings, complemented by statistical analysis and evaluations of geometric fidelity, sensitivity, and computational efficiency. The proposed method achieves lower area estimation error under the tested sampling budgets, with the improvement being most pronounced at lower sampling budgets, while the reported geometric-fidelity metrics show no disproportionate degradation of contour fidelity. These results demonstrate the effectiveness of area-driven sampling for closed-contour area estimation under limited sampling budgets. Full article

Asthma is one of the most prevalent chronic respiratory diseases worldwide, and environmental pollutants such as desert dust play a significant role in triggering respiratory sensitization and aggravating asthma symptoms. In this study, a mathematical model is proposed to investigate the dynamics of dust-induced asthma progression. The population is divided into unaware susceptible individuals, aware susceptible individuals, dust-sensitized individuals, and asthmatic individuals, while two additional variables describe dust concentration in the human population and the environment. Fundamental qualitative properties of the model, including positivity, boundedness, existence of equilibria, and stability conditions, are established. It is shown that the asthma-free equilibrium is locally and globally asymptotically stable whenever the dust-induced asthma threshold is below unity, whereas a unique asthma-persistent equilibrium exists when the dust-induced asthma threshold exceeds unity. To reduce the burden of asthma, an optimal control problem is formulated by incorporating three time-dependent interventions: awareness campaigns, medical intervention for dust-sensitized individuals, and environmental dust reduction. Pontryagin’s Maximum Principle is employed to characterize the optimal controls and derive the corresponding adjoint system. Numerical simulations, performed using the forward–backward sweep method, demonstrate that the proposed interventions significantly reduce the number of asthmatic individuals compared with the uncontrolled case. Furthermore, a cost-effectiveness analysis based on the Average Cost-Effectiveness Ratio (ACER) and Incremental Cost-Effectiveness Ratio (ICER) is conducted to compare seven intervention strategies. The results indicate that the medical intervention strategy is the most economically attractive option, while the combined strategy involving all controls achieves the largest reduction in asthma burden. Full article

Excavation-induced unloading can alter soil response through both stress-path effects and material orientation. This study investigates remolded clay from Jinan using conventional consolidated undrained (CCU) and lateral unloading undrained (LUU) triaxial tests at orientation angles α = 0°, 30°, 45°, 60°, and 90° and effective consolidation pressures of 100 and 200 kPa. The measured responses were strain-hardening, with no objective yield point or distinct peak. Under CCU, the operational failure stress generally decreased from α = 0° to 60° and increased slightly at 90°, while the fitted initial tangent modulus decreased with α and the hyperbolic asymptotic deviator stress was highest at 45°. Under LUU, the terminal deviator stress showed pressure-dependent orientation effects, and the initial tangent modulus decreased with α. The apparent cohesion was lowest at 45°, whereas the apparent friction angle was lowest at 90°. An orientation-dependent Duncan–Chang extension was developed for the prescribed LUU path by parameterizing K, n, R_f, c, and φ as functions of α. An internal hold-out check at α = 60° gave parameter deviations of 2.1% or less, supporting interpolation within the investigated orientation range. Accordingly, the formulation is interpreted as an empirical fixed-orientation relation for the investigated LUU path. Full article

Ultrasonic attenuation in particle–cementitious heterogeneous media results from the coupled effects of matrix memory dissipation and particle-induced random heterogeneity, which cannot be readily distinguished using conventional homogeneous-medium models. This study develops a unified stochastic fractional wave framework that couples Caputo fractional dissipation with a random-potential representation of spatial heterogeneity. The main contribution is an analytically tractable amplitude–phase formulation that separates the leading-order roles of the two mechanisms: fractional dissipation primarily governs exponential amplitude attenuation, with $\kappa (\omega )\propto {\omega }^{\alpha -1}$, whereas the random potential mainly modulates local phase propagation and introduces finite scattering-type amplitude corrections. By transforming the governing equation into a frequency-domain Helmholtz form and applying Wentzel–Kramers–Brillouin (WKB) asymptotic analysis, explicit scaling relations are obtained for both attenuation and phase fluctuations. Two-dimensional Helmholtz simulations support the predicted attenuation law and show that the relative $L_2$ error of the WKB phase prediction decreases from 25.23% to 5.36%, while the covariance-based fixed-receiver ensemble phase-variance prediction lies within the 95% confidence interval of 30 independent realizations. Single-frequency ultrasonic transmission experiments provide complementary trend-level evidence, showing reduced tail retention and increased descriptive tail attenuation with increasing particle volume fraction. The proposed framework provides a mechanistically interpretable basis for distinguishing dissipation-dominated and heterogeneity-induced ultrasonic responses. Full article

The paper investigates the asymptotic stability for the control of systems described by multi-order fractional differential equations. By utilizing generalized Lyapunov functions and the Kalman–Yakubovich–Popov lemma, frequency-domain criteria are derived to evaluate asymptotic stability. The formulated criteria are similar to the ‘Popov Circle Criterion,’ but the circle parameters are determined by the system’s fractional order and the control parameters. Additionally, the asymptotic stability condition requires that all polar plots associated with the multi-fractional-order system lie inside the circle defining the criterion. Human–Robot System applications highlight the investigation techniques and the particularities of the presented criteria. Full article