Search Results (3,168)

This article introduces a new type of contractions via $\phi$-admissibility and ${\omega }_b$-distance called generalized ${\omega }_b^{\phi }$-contractions. We prove the existence of fixed points for this type of contractions under some conditions. Moreover, we give an example to demonstrate the applications of our results. Full article

Background/Objectives: Electrical threshold testing (ETT) offers a promising method for assessing somatosensory function. Despite its growing use, fundamental aspects such as the physiological recovery time required between repeated threshold measurements remain poorly understood. This gap is critical when evaluating sensory, motor, or pain thresholds (EST, EMT, EPT) in pre–post designs or rapid intra-session protocols. The aim is to investigate the short-term recovery dynamics of electrical thresholds following electrical threshold testing, and to determine the minimum interval required for values to return to a stable baseline. Methods: In this pilot, repeated-measures study, 10 healthy adults (20 upper limbs) underwent three progressive stimulation trials (sensory, motor, and pain). Electrical thresholds were assessed at fixed recovery intervals (0–120 s), with duplicate measurements at each time point. Stability was defined as the absence of significant differences between repeated measures. Results: EST stabilized rapidly after sensory or motor stimulation, showing no significant differences beyond 0 and 15 s, respectively. Within pain stimulation, EST recovered at 60 s. EMT showed immediate recovery with motor stimulation and required longer recovery with pain stimulation, with stabilization observed at 90 s. EPT exhibited the highest variability, with the smallest time-dependent differences observed immediately after the first assessment. Conclusion: Recovery time after electrical stimulation varies by threshold type and intensity of the stimuli. EST and EMT can be reliably reassessed immediately after sensory and motor stimulation, respectively. However, when stimulation reaches EPT level, EST requires 60 s to recover and EMT needs 90 s. EPT demonstrates higher variability, indicating the need for further investigation. These findings support the implementation of standardized recovery intervals in ETT and underscore the importance of interpreting EPT results with caution during rapid assessments. Full article

This article aims to create insights concerning the remuneration of executives (also known as vice chancellors (VCs)) in higher education in South Africa. Their remuneration is a trending and contentious topic in the media and literature within the South African context. The motivation for conducting this study is that there are no clear indicators, norms, or standards to measure salaries. Therefore, this study is grounded in agency and institutional theories. Moreover, prior to this study, there were no longitudinal studies in the South African context that have analysed VCs’ salaries, using predictors like student enrolment, return on assets, debt ratio, and revenue. The research design was longitudinal, while the research approach was quantitative. The universities that did not meet the requirements for 2016 to 2023 were excluded from the analysis, which was conducted using Python, version 3.11.7, Python Software Foundation: Wilmington, DE, USA, 2025. Since the data points were small (n = 8), bootstrapping was used to resample 1000 samples. The correlation results showed a significant relationship with the fixed salary, whereas the regression results were not significant. It was found that the VCs’ salary is a larger portion of the fixed salary, and the historical data (2013 to 2016) showed an upward trend; the forecast from 2024 to 2026 showed a flat trend. The forecasts are salient and create insights that will assist remuneration practitioners to budget for VCs’ salaries in order to attract, motivate, and retain them. Full article

The design of mega-constellations poses a formidable challenge, as the selection of an optimal configuration directly governs system-level performance, while the computational efficiency of the design methodology remains a critical concern. To address this, this paper presents a high-efficiency, versatile optimization framework predicated on a genetic algorithm. The framework is architected to design diverse configurations, including Walker-$\delta$ and Rose constellations, and supports two distinct optimization objectives: the minimization of satellite count for prescribed performance requirements, or the maximization of coverage performance for a fixed number of satellites. To ensure computational tractability, the GA is holistically integrated with a rapid and accurate coverage analysis engine based on an area-adaptive uniform point distribution. The framework’s efficacy and validity are rigorously demonstrated through extensive simulations. The results exhibit strong consistency with the industry-standard Systems Tool Kit 11 software, with average deviations for key performance indicators—namely, coverage time ratio, average coverage multiplicity, and revisit time—controlled within 1%, 0.1, and 35 s, respectively. Moreover, when applied to a specific optimization task, the algorithm successfully identified a 181-satellite constellation that satisfied a given revisit requirement. The proposed method therefore constitutes an efficient, reliable, and automated tool for the design of complex mega-constellation architectures, promoting the diversified development of constellation configurations and enhancing the performance and resource optimization of satellite systems. Full article

With the advancement of intelligent technology and the rise in labor costs, manual identification and cutting of 3D cotton cup indentations can no longer meet modern demands. The increasing variety and shape of 3D cotton cups due to personalized requirements make the use of fixed molds for cutting inefficient, leading to a large number of molds and high costs. Therefore, this paper proposes a UNet-based indentation segmentation algorithm to automatically extract 3D cotton cup indentation data. By incorporating the VGG16 network and Leaky-ReLU activation function into the UNet model, the method improves the model’s generalization capability, convergence speed, detection speed, and reduces the risk of overfitting. Additionally, attention mechanisms and an Atrous Spatial Pyramid Pooling (ASPP) module are introduced to enhance feature extraction, improving the network’s spatial feature extraction ability. Experiments conducted on a self-made 3D cotton cup dataset demonstrate a precision of 99.53%, a recall of 99.69%, a mIoU of 99.18%, and an mPA of 99.73%, meeting practical application requirements. The extracted 3D cotton cup indentation contour data is automatically input into an intelligent CNC cutting machine to cut 3D cotton cup. The cutting results of 400 data points show an 0.20 mm ± 0.42 mm error, meeting the cutting accuracy requirements for flexible material 3D cotton cups. This study may serve as a reference for machine vision, image segmentation, improvements to deep learning architectures, and automated cutting machinery for flexible materials such as fabrics. Full article

Global Navigation Satellite Systems (GNSSs) are widely used in many applications but can be out of use in some critical conditions. Hybrid pseudolite systems utilize ground and aero stations as pseudolites to provide positioning signals for users within the covered area. The positioning accuracy is an important performance parameter for the pseudolite system and is decided by the layout of the pseudolites. This paper proposes a layout optimization method based on an Incremental Geometric Dilution of Precision (IGDOP) model. The IGDOP considers the GDOP value into two parts. One is the fixed part corresponding to the ground stations, and the other is the varying part related to the movable aero pseudolite stations. Thus, when the aero pseudolites’ position changes, the new GDOP value could be obtained only by calculating the varying part. Then, a Monte-Carlo Genetic Algorithm (MC-GA) is proposed for the IGDOP calculation for a minimum value. This algorithm comprises two main components: first, it leverages the random sampling capability of the Monte-Carlo Algorithm to provide sample points that satisfy the sample space for the subsequent Genetic Algorithm, which serve as individuals of the initial population; subsequently, it searches for the minimum value of IGDOP via the Genetic Algorithm and determines the optimized layout of the hybrid pseudolite system. Simulations are carried out using a hybrid pseudolite system with four fixed stations and n movable stations. The results validate the developed IGDOP model and show that the approach enables scalable optimization of n − 1 movable stations via four fixed stations, providing an efficient, low-complexity solution to the system layout optimization. Full article

Advancements in remote sensing technology have enabled the acquisition of high spatial and radiometric resolution imagery, offering abundant and reliable data sources for forest fire monitoring. In order to explore the ability of Sustainable Development Science Satellite 1 (SDGSAT-1) in wildfire monitoring, a systematic and comprehensive study was proposed on smoke detection during the wildfire early warning phase, fire point identification during the fire occurrence, and burned area delineation after the wildfire. The smoke detection effect of SDGSAT-1 was analyzed by machine learning and the discriminating potential of SDGSAT-1 burned area was discussed by Mid-Infrared Burn Index (MIRBI) and Normalized Burn Ratio 2 (NBR2). In addition, compared with Sentinel-2, the fixed-threshold method and the two-channel fixed-threshold plus contextual approach are further used to demonstrate the performance of SDGSAT-1 in fire point identification. The results show that the average accuracy of SDGSAT-1 fire burned area recognition is 90.21%, and a clear fire boundary can be obtained. The average smoke detection precision is 81.72%, while the fire point accuracy is 97.40%, and the minimum identified fire area is 0.0009 km², which implies SDGSAT-1 offers significant advantages in the early detection and identification of small-scale fires, which is significant in fire emergency and disposal. The performance of fire point detection is superior to that of Sentinel-2 and Landsat 8. SDGSAT-1 demonstrates great potential in monitoring the entire process of wildfire occurrence, development, and evolution. With its higher-resolution satellite imagery, it has become an important data source for monitoring in the field of remote sensing. 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

We consider first-order impulses for impulsive stochastic differential equations driven by fractional Brownian motion (fBm) with Hurst parameter $H\in ({\displaystyle \frac{1}{2}},1)$ involving a nonlinear $\varphi$-Laplacian operator. The system incorporates both state and derivative impulses at fixed time instants. First, we establish the existence of at least one mild solution under appropriate conditions in terms of nonlinearities, impulses, and diffusion coefficients. We achieve this by applying a nonlinear alternative of the Leray–Schauder fixed-point theorem in a generalized Banach space setting. The topological structure of the solution set is established, showing that the set of all solutions is compact, closed, and convex in the function space considered. Our results extend existing impulsive differential equation frameworks to include fractional stochastic perturbations (via fBm) and general $\varphi$-Laplacian dynamics, which have not been addressed previously in tandem. These contributions provide a new existence framework for impulsive systems with memory and hereditary properties, modeled in stochastic environments with long-range dependence. Full article

Accurate traffic forecasting underpins intelligent transportation systems. We present PTSTG, a compact spatio-temporal forecaster that couples a patch-based Transformer encoder with a data-driven adaptive adjacency and lightweight node graph blocks. The temporal module tokenizes multivariate series into fixed-length patches to capture short- and long-range patterns in a single pass, while the graph module refines node embeddings via learned inter-node aggregation. A horizon-specific head emits all steps simultaneously. On standard benchmarks (METR-LA, PEMS-BAY) and the LargeST (SD) split with horizons $\{3, 6, 12\}\to \{15, 30, 60\}$ minutes, PTSTG delivers competitive point-estimate results relative to recent temporal graph models. On METR-LA/PEMS-BAY, it remains close to strong baselines (e.g., DCRNN) without surpassing them; on LargeST, it attains favorable average RMSE/MAE while trailing the strongest hybrids on some horizons. The design preserves a compact footprint and single-pass, multi-horizon inference, and offers clear capacity-driven headroom without architectural changes. Full article

This study examines the efficiency trade-offs of Controllable Pitch Propeller (CPP) systems by comparing Combination and Fixed operation modes using real ship operational data. The analysis focuses on mechanical efficiency (η_mech), propulsive efficiency expressed through the normalized Relative Propulsive Efficiency Index (RPEI_norm), and fuel consumption. Combination mode consistently maintained higher η_mech across all load conditions, with pronounced advantages at low load and low speed (<50% load, <12 knots), where both propulsive efficiency and fuel economy improved. In contrast, Fixed mode outperformed Combination mode at high load and high speed, exceeding approximately 50% load and 12 knots, as propeller performance approached its optimal operating point despite some sacrifice in engine efficiency. To integrate these effects, a proxy overall efficiency index (η_{overall,proxy} = η_mech × RPEI_norm) was introduced, revealing a crossover point at 0.525 load where the efficiency dominance shifted between modes. These findings demonstrate that neither mode is universally superior, but rather their advantages depend on operating conditions. The results provide practical insights for adaptive operational strategies, enabling real-time switching between modes to optimize fuel consumption and overall propulsion performance while supporting compliance with environmental regulations. Full article

In this study, we investigate implicit fractional differential equations subject to anti-periodic boundary conditions. The fractional operator incorporates two distinct generalizations: the Caputo tempered fractional derivative and the Caputo fractional derivative with respect to a smooth function. We investigate the existence and uniqueness of solutions using fixed-point theorems. Stability in the sense of Ulam–Hyers and Ulam–Hyers–Rassias is also considered. Three detailed examples are presented to illustrate the applicability and scope of the theoretical results. Several existing results in the literature can be recovered as particular cases of the framework developed in this work. Full article

In this paper, we present some existence and stability results for the fixed point inclusion in the case of multi-valued self contractions, on a complete vector-valued B-metric space. Our main existence result for the fixed point problem extends to the multi-valued setting with a recent result obtained for the single-valued case. Moreover, data dependence on the operator perturbation of the fixed point set and some stability theorems (Ulam–Hyers stability, well-posedness and Ostrowski stability) are proved, in order to have a complete study of the fixed point inclusion. 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

This study develops, implements, and evaluates the Firebrand Spotting parameterization within the WRF-Fire coupled fire–atmosphere modeling system. Fire spotting is an important mechanism characterizing fire spread in wind-driven events. It can accelerate the rate of spread and enable the fire to spread over streams and barriers such as highways. Without the capability to simulate fire spotting, wind-driven fire simulations cannot accurately represent fire behavior. In the Firebrand Spotting parameterization, firebrands are generated with a set of fixed properties, from locations vertically aligned with the leading fire line. Firebrands are transported using a Lagrangian framework accounting for particle burnout (combustion) through an MPI-compatible implementation within WRF-Fire. Fire spots may occur when firebrands land on unburned grid points. The parameterization is verified through idealized simulations and its application is demonstrated for the 2021 Marshall Fire, Colorado. The simulations are assessed using the observed fire perimeter and time of arrival at multiple locations identified from social media footage and official documents. All simulations using a range of ignition thresholds outperform the control without spotting. Simulations accounting for fire spots show more accurate fire arrival times (i.e., reflecting a better fire rate of spread), despite producing a generally larger fire area. The Heidke Skill Score (Cohen’s Kappa) for the burn area ranges between 0.62 and 0.78 for simulations with fire spots compared to 0.47 for the control. These results show that the parameterization consistently improves the fire forecast verification metrics, while also underscoring future work priorities, including advancing the generation and ignition components. Full article