Search Results (439)

We present here a novel approach to the analysis of common knowledge based on Category Theory. We formalize knowledge hierarchies as presheaves over a category of agent sequences. The category of these presheaves constitutes a topos. We define an unfolding monad on the resulting topos, and use a Knaster–Tarski theorem to obtain common knowledge as a greatest fixed point under natural uniformity and exchangeability conditions on agent sequences. Full article

Inertial methods are widely used to accelerate the convergence of iterative algorithms for solving fixed-point problems. However, standard inertial terms often introduce undesirable oscillations, particularly in high-dimensional settings. In this paper, we propose a novel parallel double inertial algorithm with adaptive damping control (D-DIMPMHA) for finding a common fixed point of a finite family of nonexpansive mappings in real Hilbert spaces. By integrating a double inertial step with a self-adaptive damping parameter, the proposed method effectively balances momentum and stability, thereby mitigating numerical oscillations without requiring vanishing inertial conditions. We establish the weak convergence theorem of the generated sequence under suitable control conditions. Furthermore, the practical efficiency of the algorithm is demonstrated through numerical experiments on large-scale convex feasibility problems and image restoration problems. Comparative results indicate that the proposed algorithm achieves superior convergence speed and higher restoration quality compared to existing single inertial methods and FISTA. Full article

This study examines the structure and use of Axial Parts and Relational Nouns in Italian from both a syntactic and diachronic perspective. In the first part, we argue that these elements function as nouns and establish an elementary predicate relation of inclusion with an adjacent noun. This relation can be analyzed in terms of Ground and Figure: the Axial Part acts as a possessum of the Ground linked, in turn, to a nominal phrase functioning as possessor/Figure. The interpretation of Axial Parts depends on the context, and while the predicative relation is marked by an adpositional relator, its lexical shape varies, precluding a fixed argumental or complemental relation. This Double-Relator Model contrasts with hierarchical functional projections in the PP structure. The second part supports this view with data from early Italian texts. Focusing on common nouns (e.g., front, head, foot, etc.) used as Relational Nouns or Axial Parts, we show that the Double-Relator Model captures the variability in terms of phonological realization and grammatical function of Old Italian complex PPs, at the same time making it possible to clearly analyze each component of these structures from the syntactic point of view. Full article

To address knowledge gaps in urban wetlands’ role in sustaining avian diversity along migration corridors, this study systematically surveyed three Yancheng wetland parks with a distinct habitat gradient. Monthly surveys were conducted from January to December 2024 using fixed-width line transects and point counts, with three 300 m transects set in each park and all birds within 50 m of the transect line recorded, and Shannon–Wiener, Simpson, Pielou’s Evenness, and Margalef Richness indices were employed for quantitative analysis. A total of 83 bird species across 16 orders and 41 families were documented, including the National Class I Protected and Endangered Oriental Stork and three Class II nationally protected species (Black-winged Kite, Crested Goshawk, Common Kestrel). Fengyi Lake Park, with 71 species, served as a critical migratory waterbird hub. Yandu Wetland Park sustained community stability through high habitat heterogeneity, supporting specialized breeders, and Dongfang Wetland Park, with 34 urban adaptor-dominated species, provided key autumn pulsed resources for frugivores and granivores. This study identifies habitat heterogeneity as the primary driver of avian community differentiation and highlights that the ecological functions of urban wetlands are contingent on multi-habitat complementarity. We, therefore, advocate for prioritizing the construction of heterogeneous habitat structures in urban wetland planning, enhancing functional complementarity and connectivity among distinct wetland types, and preserving the continuity of migratory bird habitat corridors along the East Asian-Australasian Flyway. These findings furnish robust scientific evidence and actionable guidance for regional green space planning and biodiversity conservation. Full article

Integral inclusion systems play a significant role in applied analysis and modeling, providing an effective framework for studying various physical, engineering, and dynamical processes. In this work, the solvability of a multidimensional integral inclusion system is investigated by applying the common fixed point technique to a pair of ${\mathbb{M}}_{\alpha }$-admissible multivalued operators. The analysis is carried out within a novel double-controlled vector-valued metric structure, in which the distance is governed by two independent matrix-valued control operators; this setting strictly extends classical Perov-type and $\mathrm{b}$-metric frameworks and offers a more flexible tool for treating multidimensional and interdependent systems. Existence results are derived under a suitable contractive condition within a generalized metric structure. Several auxiliary theorems are established to support the main conclusions. To illustrate the applicability of the theoretical findings, the obtained results are utilized to ensure the existence of solutions for a multidimensional Urysohn-type integral inclusion system. A simple example demonstrates the validity of the theoretical framework and highlights the effectiveness of the adopted approach. Full article

The purpose of this research article is to establish common fixed point results for generalized contractions defined with control functions in the framework of elliptic-valued suprametric spaces. By utilizing the structure and properties of these spaces, we develop new fixed point results that extend and unify several known theorems in the literature. The theoretical findings are illustrated through a series of non-trivial examples, demonstrating the applicability and robustness of the proposed approach. As a concrete application, we employ the established fixed point theorems to analyze the existence and uniqueness of solutions for nonlinear Volterra integral equations of the second kind. Furthermore, the results obtained herein naturally encompass a wide range of fixed point theorems previously reported in the literature as direct corollaries, emphasizing the broad applicability and flexibility of the proposed framework. Full article

The primary objective of this research article is to investigate the concept of extended $\mathcal{F}$-metric spaces and to establish a series of fixed point theorems for generalized contractions within this framework. We further introduce and analyze the notion of interpolative Kannan-type cyclic contractions in extended $\mathcal{F}$-metric spaces, deriving several novel fixed point results associated with these mappings. In addition, we obtain common fixed point theorems for rational contractions, thereby extending and unifying a variety of existing results available in the literature. To highlight the novelty and effectiveness of the proposed results, several illustrative examples are provided. Moreover, the theoretical findings are successfully applied to the solution of Atangana–Baleanu fractional integral equations as well as Volterra integral equation of Hammerstein type, demonstrating their practical significance and wide-ranging applicability. Full article

In this paper, we introduced an inertial extragradient algorithm to approximate the common solution of split fixed point, split variational inclusion and split equilibrium problems involving nonexpansive mappings and pseudomonotone Lipschitz-type bifunctions in Hilbert spaces. Moreover, using some assumptions on the control parameters, we prove the strong convergence of the proposed algorithm and then apply our main result to solve the split minimization, split feasibility and split variational inequality problems. We also present some numerical examples to show the effectiveness and applicability of the proposed scheme. We include tables illustrating the number of iterations, the CPU time for convergence, comparisons among different algorithms, and the error analysis. We apply our proposed scheme to solve the image restoration problem as another application of the result presented herein. Full article

In this study, a dielectric barrier discharge (DBD) plasma actuator was placed at the leading edge of a National Advisory Committee for Aeronautics (NACA) 0012 airfoil to act on the separation initiation point, rather than on an already separated flow farther downstream on the upper surface. The aerodynamic response was examined using complementary measurements: (i) quiescent-air thrust characterization to quantify the actuator forcing level for two dielectric configurations under voltage and frequency sweeps, (ii) wind-tunnel surface-pressure measurements on the upper and lower surfaces over an angle-of-attack sweep, and (iii) smoke-wire flow visualization. To enable consistent actuator-OFF/ON comparisons despite non-matching tap locations, a pressure-derived lift coefficient was evaluated by integrating $C_{p,l}-C_{p,u}$ over the common instrumented chordwise interval $x/c = 0.2533~0.7620$ after linear interpolation onto a common grid. The results demonstrate that a single fixed leading-edge actuation setting is not universally beneficial across the angle of attack. The actuation effect on the lift increment is small at $\alpha =4°$ and $8°$ and should be interpreted cautiously, given the pressure coefficient resolution, whereas near stall and post-stall conditions exhibit a robust redistribution of the surface-pressure field and can yield strongly negative lift increments (e.g., $\alpha =18°$). These findings highlight the need for condition-dependent evaluation and design guidelines for leading-edge DBD actuation, based on measured pressure-field changes. Full article

This study investigated the fault ride through capability of inverter-based resources in weak distribution networks and proposes a fault-oriented reactive power compensation strategy using only point of common coupling voltage measurements. The proposed strategy determines the reactive power command based on the minimum phase voltage, which represents the most severely depressed phase during unbalanced faults, without fault type detection or sequence component analysis. As a result, the same control framework can be applied to single-line-to-ground, double-line-to-ground, and three-phase faults. A detailed MATLAB/Simulink model of a Korean distribution feeder was developed using actual system parameters. The proposed strategy was compared with a no control case and a conservative fixed capacity reactive power injection scheme derived from commonly adopted power factor limits. Simulation results show that the no control case provides no voltage support, while the fixed capacity approach yields limited improvement in weak grids. In contrast, the proposed strategy maintains stable inverter operation and improves voltage recovery. At locations with an extremely low weighted short circuit ratio of 0.303, the proposed strategy prevents inverter tripping during temporary faults and satisfies low voltage ride through requirements, demonstrating its practical effectiveness. Full article

The purpose of this article is to introduce the concept of elliptic-valued suprametric spaces and to establish some common fixed point theorems within this newly proposed framework. The development of elliptic-valued suprametric spaces, along with the main results presented here, is illustrated through non-trivial examples. As applications, we employ our fixed point results to study the nonlinear Volterra integral equation of the second kind, demonstrating the existence and uniqueness of solutions under suitable conditions. In particular, we highlight the role of such equations in age-structured population models, where they serve as powerful tools for describing hereditary effects, density-dependent interactions, and delayed responses in population dynamics. This connection bridges the abstract theory with applied contexts in mathematical biology, ecology, and epidemiology, emphasizing the relevance of elliptic-valued suprametric structures in both theoretical analysis and real-world applications. Furthermore, we derive corresponding fixed point results in elliptic-valued suprametric spaces, complex-valued suprametric spaces, elliptic-valued metric spaces, and complex-valued metric spaces as corollaries of our main findings. Full article

Reliable probabilistic wind speed forecasts are essential for integrating renewable energy into power grids and managing operational uncertainty. This study compares Quantile Regression Forests (QRF), Bayesian Additive Regression Trees (BART), and Gaussian Process Regression (GPR) under at-site and regional pooled frameworks using 21 years (2000–2020) of daily wind data from eleven stations in New South Wales and Queensland, Australia. Models are evaluated via strict year-based holdout validation across seven metrics: RMSE, MAE, R², bias, correlation, coverage, and Continuous Ranked Probability Score (CRPS). Regional QRF achieves exceptional point forecast stability with minimal RMSE increase but suffers persistent under-coverage, rendering probabilistic bounds unreliable. BART attains near-nominal coverage at individual sites but experiences catastrophic calibration collapse under regional pooling, driven by fixed noise priors inadequate for spatially heterogeneous data. In contrast, GPR maintains robust probabilistic skill regionally despite larger point forecast RMSE penalties, achieving the lowest overall CRPS and near-nominal coverage through kernel-based variance inflation. Variable importance analysis identifies surface pressure and minimum temperature as dominant predictors (60–80%), with spatial covariates critical for regional differentiation. Operationally, regional QRF is prioritised for point accuracy, regional GPR for calibrated probabilistic forecasts in risk-sensitive applications, and at-site BART when local data suffice. These findings show that Bayesian machine learning methods can effectively navigate the trade-off between local specificity and regional pooling, a challenge common to wind forecasting in diverse terrain globally. The methodology and insights are transferable to other heterogeneous regions, providing guidance for probabilistic wind forecasting and renewable energy grid integration. Full article

In this article, we introduce a novel averaged-type iterative scheme designed for solving convex minimization problems over the set of common fixed points of a pair of demicontractive mappings. Under suitable assumptions, we prove that the proposed algorithm converges strongly to the solution of the considered problem in a Hilbert space setting. We further demonstrate the applicability of our method to quadratic optimization problems with a bounded linear operator. In addition, we also report the numerical experiments that were performed in order to demonstrate the convergence behavior of the algorithm and to highlight its superiority over related existing methods. Full article

Theaim of this research is to establish existence and uniqueness results for the Riemann–Liouville fractional integral equation of order $\alpha$$\varkappa \left(t\right)=f\left(t\right)+{\displaystyle \frac{\lambda }{\Gamma \left(\alpha \right)}}\underset{0}{\overset{t}{\int }}{\left(t-s\right)}^{\alpha -1}g\left(s,\varkappa \left(s\right)\right)ds,t\in [0,1],$ by developing common fixed point theorems for generalized contractions involving control functions of two variables in the framework of complex valued suprametric spaces. The proposed results extend and generalize several existing findings in the literature, and some illustrative examples are provided to demonstrate the novelty and applicability of the main theorem. Full article

Maximum power point tracking (MPPT) under partial shading is a nonconvex, rapidly varying control problem that challenges multi-agent policies deployed on photovoltaic modules. We present Fuzzy–MAT3D, a fuzzy-augmented multi-agent TD3 (Twin-Delayed Deep Deterministic Policy Gradient) controller trained under centralized training/decentralized execution (CTDE). On the theory side, we prove that differentiable fuzzy partitions of unity endow the actor–critic maps with global Lipschitz regularity, reduce temporal-difference target variance, enlarge the input-to-state stability (ISS) margin, and yield a global $L_{\infty }$$\gamma$-contraction of fixed-policy evaluation (hence, non-expansive with $\kappa =\gamma <1$). We further state a two-time-scale convergence theorem for CTDE-TD3 with fuzzy features; a PL/last-layer-linear corollary implies point convergence and uniqueness of critics. We bound the projected Bellman residual with the correct contraction factor (for $L^{\infty }$ and $L^2\left(\rho \right)$ under measure invariance) and quantified the negative bias induced by $min\{Q_1,Q_2\}$; an N-agent extension is provided. Empirically, a balanced common-random-numbers design across seven scenarios and 20 seeds, analyzed by ANOVA and CRN-paired tests, shows that Fuzzy–MAT3D attains the highest mean MPPT efficiency (92.0% ± 4.0%), outperforming MAT3D and Multi-Agent Deep Deterministic Policy Gradient controller (MADDPG). Overall, fuzzy regularization yields higher efficiency, suppresses steady-state oscillations, and stabilizes learning dynamics, supporting the use of structured, physics-compatible features in multi-agent MPPT controllers. At the level of PV plants, such gains under partial shading translate into higher effective capacity factors and smoother renewable generation without additional hardware. Full article