Search Results (526)

This paper introduces an application of the Chatterjea–Singh fixed-point theorem to nonlinear boundary value problems (BVPs). We define a Chatterjea–Singh mapping as one whose iterate $T^p$ satisfies a Chatterjea-type contractive condition. Under this weaker assumption than classical Banach or Chatterjea contractions, we prove the existence and uniqueness of solutions to second-order BVPs. Our method applies even when T itself does not satisfy a contraction property. Examples illustrate how iteration can recover convergence where standard conditions fail. This work extends generalized fixed-point theory in differential equations and highlights the flexibility of delayed contraction criteria. Full article

A common challenge in traditional three-dimensional grid-free localization is the struggle to balance computational efficiency with localization accuracy. To address this trade-off, a Bayesian grid-free framework with global optimization (BGG) for three-dimensional acoustic source imaging is proposed. In this method, a Bayesian inference model is established based on equivalent source theory, where the negative log-posterior of the equivalent source positions serves as the fitness function. This function is minimized using a global optimization algorithm to estimate the source locations. Subsequently, the source strengths and noise variances are inferred via fixed-point iteration and projection-based estimation. Through both simulations and experiments with spatially distributed sources, a superior balance of computational efficiency and localization accuracy is demonstrated by the proposed BGG algorithm when compared to other state-of-the-art grid-free approaches. Full article

In the field of life sciences, delay effects are often modeled with two compartments that do not model any particular organ. In this paper the use of this double counterpart model is investigated in Fixed-Point Iteration-based (FPI) Control, which was introduced in 2009 as an adaptive extension to the Computed Torque Control method. This controller is particularly sensitive to delays and measurement noise due to its iterative nature. It was recognized that, besides modeling the delay effect, this signal tackling also provided the controller with some noise filtering ability; the formerly accumulated effects of noise filtering and formally delayed sampling were avoided. This smeared delay has a noticeable effect even slightly later in time, making the adaptive method based on it more robust. This assumption was investigated both on a simulation and experimental basis. Full article

Recent developments in fixed-point theory have focused on iterative techniques for approximating solutions, yet there remain important questions about whether different methods are equivalent and how well they resist perturbations. In this study, two recently proposed algorithms, referred to as the DF and AR iteration methods, are shown to be connected by proving that they converge similarly when applied to contraction mappings in Banach spaces, provided that their control sequences meet specific, explicit conditions. This work extends previous research on data dependence by removing restrictive assumptions related to both the perturbed operator and the algorithmic parameters, thereby increasing the range of situations where the results are applicable. Utilizing a non-asymptotic analysis, the authors derive improved error bounds for fixed-point deviations under operator perturbations, achieving a tightening of these estimates by a factor of 3–15 compared to earlier results. A key contribution of this study is the demonstration that small approximation errors lead only to proportionally small deviations from equilibrium, which is formalized in bounds of the form $\parallel s^{*}-{\tilde{s}}^{*}\parallel \le O(\epsilon /(1-\lambda ))$. These theoretical findings are validated through applications involving integral equations and examples from function spaces. Overall, this work unifies the convergence analysis of different iterative methods, enhances guarantees regarding stability, and provides practical tools for robust computational methods in areas such as optimization, differential equations, and machine learning. By relaxing structural constraints and offering a detailed sensitivity analysis, this study significantly advances the design and understanding of iterative algorithms in applied mathematics. Full article

Wildfires pose a regularly increasing threat to ecosystems and critical infrastructure. The severity of this threat is steadily increasing. The growing threat necessitates the development of technologies for rapid and accurate early detection. However, the prevailing fire point detection algorithms, including several deep learning models, are generally constrained by the inherent hard threshold limitations in their decision-making logic. As a result, these methods lack adaptability and robustness in complex and dynamic real-world scenarios. To address this challenge, the present paper proposes an innovative two-stage, semi-supervised anomaly detection framework. The framework initially employs a Transformer-based autoencoder, which serves to transform raw fire-free time-series data derived from satellite imagery into a multidimensional deep anomaly feature vector. Self-supervised learning achieves this transformation by incorporating both reconstruction error and latent space distance. In the subsequent stage, a semi-supervised XGBoost classifier, trained using an iterative pseudo-labeling strategy, learns and constructs an adaptive nonlinear decision boundary in this high-dimensional anomaly feature space to achieve the final fire point judgment. In a thorough validation process involving multiple real-world fire cases in Yunnan Province, China, the framework attained an F1 score of 0.88, signifying a performance enhancement exceeding 30% in comparison to conventional deep learning baseline models that employ fixed thresholds. The experimental results demonstrate that by decoupling feature learning from classification decision-making and introducing an adaptive decision mechanism, this framework provides a more robust and scalable new paradigm for constructing next-generation high-precision, high-efficiency wildfire monitoring and early warning systems. Full article

The quest to multiply two large matrices as fast as possible is one that has already intrigued researchers for several decades. However, the ‘optimal’ algorithm for a certain problem size is still not known. The fast matrix multiplication (FMM) problem can be formulated as a non-convex optimization problem—more specifically, as a challenging tensor decomposition problem. In this work, we build upon a state-of-the-art augmented Lagrangian algorithm, which formulates the FMM problem as a constrained least squares problem, by incorporating a new, generalized cyclic symmetric (CS) structure in the decomposition. This structure decreases the number of variables, thereby reducing the large search space and the computational cost per iteration. The constraints are used to find practical solutions, i.e., decompositions with simple coefficients, which yield fast algorithms when implemented in hardware. For the FMM problem, usually a very large number of starting points are necessary to converge to a solution. Extensive numerical experiments for different problem sizes demonstrate that including this structure yields more ‘unique’ practical decompositions for a fixed number of starting points. Uniqueness is defined relative to the known scale and trace invariance transformations that hold for all FMM decompositions. Making it easier to find practical decompositions may lead to the discovery of faster FMM algorithms when used in combination with sufficient computational power. Lastly, we show that the CS structure reduces the cost of multiplying a matrix by itself. Full article

This paper investigates a simultaneous wireless information and power transfer (SWIPT) decode-and-forward (DF) relay network, where a source node transmits data to a destination node through the assistance of multi-hop passive relays. We employ the time-switching (TS) protocol, enabling the relays to harvest energy from the received previous hop signal to support data forwarding. We first prove that the system throughput monotonically increases with the transmit power of the source node. Next, by employing logarithmic transformations, we convert the non-convex problem of obtaining optimal TS ratios at each relay to maximize the system throughput into a convex optimization problem. Comprehensively taking into account the convergence rate, computational complexity per iteration, and robustness, we selected the log barrier method—a type of interior point method—to address this convex optimization problem, along with providing a detailed implementation procedure. The simulation results validate the optimality of the proposed method and demonstrate its applicability to practical communication systems. For instance, the proposed scheme achieves 1437.3 bps throughput at 40 dBm maximum source power in a 2-relay network—278.6% higher than that of the scheme with TS ratio fixed at 0.75 (379.68 bps). On the other hand, it converges within a 1.36 ms computation time for 5 relays, 6 orders of magnitude faster than exhaustive search (1730 s). Full article

In this paper, we propose a new class of self-mappings, referred to as polynomial Kannan contractions, which extend the classical Kannan contractions by incorporating higher-order polynomial distance terms with variable coefficient functions. Unlike polynomial contractions, polynomial Kannan contractions are not necessarily continuous. We establish fixed point results for such mappings under suitable conditions on the coefficient functions, in addition to presenting the error estimates for the associated Picard iteration. Furthermore, we provide some supported numerical examples to show that our extensions are proper and significant. As an application, we show that our results ensure the existence and uniqueness of solutions for a certain class of fractional differential equations. Full article

The main objective of this paper is to develop a maximum power point tracker (MPPT) for a photovoltaic module array (PVMA) under conditions of partial shading and sudden changes in solar irradiance. PVMAs exhibit nonlinear characteristics with respect to temperature and solar irradiance conditions. Therefore, when some modules in the array are shaded or when there is a sudden change in solar irradiance, the maximum power point (MPP) of the array will also change, and the power–voltage (P-V) characteristic curve may exhibit multiple peaks. Under such conditions, if the tracking algorithm employs a fixed step size, the time required to reach the MPP may be significantly prolonged, potentially causing the tracker to converge on a local maximum power point (LMPP). To address the issues mentioned above, this paper proposes a novel MPPT technique based on the nature-inspired idols algorithm (IA). The technique allows the promotion value (PM) to be adjusted through the anti-fans weight (afw) in the iteration formula, thereby achieving global maximum power point (GMPP) tracking for PVMAs. To verify the effectiveness of the proposed algorithm, a model of a 4-series–3-parallel PVMA was first established using MATLAB (2024b version) software under both non-shading and partial shading conditions. The voltage and current of the PVMAs were fed back, and the IA was then applied for GMPP tracking. The simulation results demonstrate that the IA proposed in this study outperforms existing MPPT techniques, such as particle swarm optimization (PSO), cat swarm optimization (CSO), and the bat algorithm (BA), in terms of tracking speed, dynamic response, and steady-state performance, especially when the array is subjected to varying shading ratios and sudden changes in solar irradiance. Full article

This work presents an extragradient-type iterative process combined with the viscosity method to find a common solution to a split generalized variational-like inequality, a variational inequality, and a fixed point problem associated with a family of $\epsilon$-strict pseudo-contractive mappings and a nonexpansive operator in Hilbert spaces. Strong convergence of the proposed algorithm is established, with some remarks derived from the main theorem. Numerical experiments are carried out to verify the applicability of the method and provide comparative observations. The results broaden and unify a range of existing contributions in this field. Full article

Distribution System Operators (DSOs) increasingly need planning tools that coordinate utility-influenced assets—such as electric-vehicle charging stations (EVCS) and voltage-support resources—with customer-sited distributed generation (DG). We present a Nash-equilibrium-based Iterative Best Response Algorithm (IBRA-NE) for joint planning of DG and EVCS in radial distribution networks. The framework supports two applicability modes: (i) a DSO-plannable mode that co-optimizes EVCS siting/sizing and utility-controlled reactive support (DG operated as VAR resources or functionally equivalent devices), and (ii) a customer-sited mode that treats DG locations as fixed while optimizing DG reactive set-points/sizes and EVCS siting. The objective minimizes network losses and voltage deviation while incorporating deployment costs and EV charging service penalties, subject to standard operating limits. A backward/forward sweep (BFS) load flow with Monte Carlo simulation (MCS) captures load and generation uncertainty; a Bus Voltage Deviation Index (BVDI) helps identify weak buses. On the EEU 114-bus system, the method reduces base-case losses by up to 57.9% and improves minimum bus voltage from 0.757 p.u. to 0.931 p.u.; performance remains robust under a 20% load increase. The framework explicitly accommodates regulatory contexts where DG siting is customer-driven by treating DG locations as fixed in such cases while optimizing EVCS siting and sizing under DSO planning authority. A mixed scenario with 5 DGs and 3 EVCS demonstrates coordinated benefits and convergence properties relative to PSO, GWO, RFO, and ARFO. Additionally, the proposed algorithm is also tested on the IEEE 69-bus system and results in acceptable performance. The results indicate that game-theoretic coordination, applied in a manner consistent with regulatory roles, provides a practical pathway for DSOs to plan EV infrastructure and reactive support in networks with uncertain DER behavior. Full article

Unmanned aerial vehicles (UAVs) are increasingly favored for emergency search and rescue operations due to their high adaptability to harsh environments and low operational costs. However, the dynamic nature of search path endpoints, influenced by target movement, limits the applicability of shortest path models between fixed points in moving target search problems. Consequently, the moving target search problem using UAVs in complex environments presents considerable challenges, constituting an NP-hard problem. The Grey Wolf Optimizer (GWO) is known for addressing such problems. However, it suffers from limitations, including premature convergence and instability. To resolve these constraints, a Grey Wolf Optimizer with variable population and strategy (GWO-VPS) is developed in this work. GWO-VPS implements a variable encoding scheme for UAV movement patterns, combining motion-based encoding with path-based encoding. The algorithm iteratively alternates between global optimization and local smoothing phases. The global optimization phase incorporates: (1) a Q-learning-based strategy selection; (2) position updates with obstacle avoidance and energy consumption reduction; and (3) adaptive exploration factor. The local smoothing phase employs four path smoothing operators and Q-learning-based strategy selection. Experimental results demonstrate that GWO-VPS outperforms both enhanced GWO variants and standard algorithms, confirming the algorithm’s effectiveness in UAV-based moving target search simulations. Full article

In this paper, a pattern for visualizing fractals, namely Julia and Mandelbrot sets for complex functions of the form $T\left(u\right)=u^a-\xi u^2+ru+sin{\rho }^{\sigma }\mathrm{for}\mathrm{all}u\in \mathbb{C}$ and $a\in \mathbb{N}\setminus \left\{1\right\}$, $\xi \in \mathbb{C}$, $r,\rho \in \mathbb{C}\setminus \left\{0\right\}$ are created using novel fast convergent iterative techniques. The new iteration scheme discussed in this study uses s-convexity and improves earlier approaches, including the Mann and Picard–Mann schemes. Further, the proposed approach is amplified by unique escape conditions that regulate the convergence behavior and generate Julia and Mandelbrot sets. This new technique allows greater versatility in fractal design, influencing the shape, size, and aesthetic structure of the designs created. By modifying various parameters in the suggested scheme, a significant number of visually interesting fractals can be generated and evaluated. Furthermore, we provide numerical examples and graphic demonstrations to demonstrate the efficiency of this novel technique. Full article

Spatial co-location patterns are used to describe the spatial associations between features, finding wide applications in geographic information systems, urban planning, and other fields. Traditional frameworks for mining spatial features typically consist of two stages: constructing spatial proximity relationships and discovering frequent patterns. However, existing methods have limitations: the construction of proximity relationships relies on fixed distance thresholds or clustering centers, making it difficult to adapt to spatial density heterogeneity; meanwhile, frequency metrics overly depend on participation indices, lacking quantitative analysis of the strength of geometric associations between features. To address these issues, a spatial co-location pattern mining method based on Hausdorff distance is proposed. Drawing on the concept of Hausdorff distance, this method employs Voronoi tessellation to achieve data-adaptive partitioning of the spatial domain. Combined with a K-dimensional tree, it adopts an iterative strategy of direct allocation, proportional allocation, and residual allocation to align instances, generating a spatial proximity relationship graph. Additionally, a new frequency metric based on instance distribution—alignment rate—is introduced, leveraging the decreasing trend of alignment rate in conjunction with a pruning optimization algorithm. Experimental results demonstrate that this method excels in handling noise points, effectively addressing the challenges of uneven data density distribution while enhancing the identification of weakly associated yet potentially valuable patterns. Full article

The transition to fully electric bus (EB) fleets introduces new challenges in coordinating daily operations and managing charging energy needs, while accounting for infrastructure constraints. The paper proposes a three-stage optimization framework that integrates EB scheduling with overnight charging under realistic depot layout constraints. In the first stage, a mixed-integer linear program (MILP) determines the minimum number of EBs with ample batteries and related schedules to complete all timetabled trips. With the fleet size fixed, the second stage minimizes the EB battery capacity by optimizing trip assignments. In the third stage, charging schedules are iteratively optimized for different numbers of chargers to minimize charger power capacity and charging cost, while ensuring each EB is fully recharged before its first trip on the following day. The matrix-shape depot layout imposes spatial and operational constraints that restrict the charging and movement of EBs based on their parking positions, with EBs remaining stationary overnight. The entire process is repeated by incrementing the fleet size until a saturation point is reached, beyond which no further reduction in battery capacity is observed. This results in a Pareto frontier showing trade-offs between required battery capacity, number of chargers, charger power capacity, and charging cost. The proposed method is applied to a real-world airport parking shuttle service, demonstrating its potential to reduce the battery size and charging infrastructure demands while maintaining full operational feasibility. Full article