Search Results (360)

We study a modified-degenerate version of the $W_{\alpha ,\beta ,\nu }$-factorial and the associated exponential, trigonometric, and hyperbolic families obtained by replacing the Euler gamma function with the modified-degenerate gamma function ${\Gamma }_{\lambda }^{*}$, where $\lambda \in (0,1)$. A main conclusion of this paper is that this construction does not generate a genuinely new transcendental family. Indeed, since ${\Gamma }_{\lambda }^{*}\left(s\right)=b_{\lambda }^s\Gamma \left(s\right),b_{\lambda }={\displaystyle \frac{\lambda }{log(1+\lambda )}},$ all modified-degenerate W-functions reduce to exact rescalings of their non-degenerate counterparts. The novelty of the present work is therefore operational rather than structural. We formulate this transport principle explicitly, derive the corresponding modified-degenerate Laplace-transform identities directly in the spectral variable s, establish the induced convolution rule, and obtain first-order asymptotic expansions as $\lambda \to 0^{+}$. We further show that the associated W-derivative is a formal coefficient-shift operator, and conjugate it to the non-degenerate one under the scaling map. As an application, we present a complete Volterra integral-equation example with polynomial memory, including an explicit resolvent representation for the case $m=1$, together with convergence and residual-error checks supporting the numerical illustrations. Full article

This study proposes a new strongly convergent iterative framework obtained by combining a Krasnosel’skiǐ–Mann type subgradient extragradient process with a hybrid projection strategy and an inertial extrapolation mechanism. The method is applied to address hierarchical fixed-point problems (HFPPs) for nonexpansive and quasi-nonexpansive mappings as well as variational inequality problems (VIPs) involving a pseudomonotone operator in real Hilbert spaces. The proposed scheme employs step sizes that are restricted by the inverse of the Lipschitz constant of the underlying cost operator. Strong convergence of the iterates is achieved under mild hypotheses on the inertial parameter and control sequences. The method is further applied to problems arising in optimization and monotone operator theory. The results show that the proposed framework generalizes and integrates a number of existing approaches while offering improved computational performance. Full article

Certain extensions of $F$-controlled self-mappings in metric spaces to the, as called in this manuscript, ${ F}_{\tau \prime \tau }$ and modified $\ast F_{\tau \prime \tau }$ controlled self-mappings, which are parameterized by two parameters, are addressed. Those parameters govern the properties of local expansivity, asymptotic nonexpansivity, and contractivity properties of the generated sequences. Also, further generalizations to parameterizations by two real sequences of parameters, which are referred to as $F_{{\left\{{\tau }_j^{\prime }\right\}}_{j=0}^{\infty }{\left\{{\tau }_j\right\}}_{j=0}^{\infty }}$-controlled self-mappings, are studied. The main formulated results rely on the asymptotic contractivity and the asymptotic nonexpansivity in metric spaces and some of their relevant properties. In particular, the properties of boundedness of the sequences of distances, as well as those of boundedness of the elements of the sequences themselves, are investigated under asymptotic contractivity or nonexpansivity related to the various types of the above-mentioned $F_{\left(.\right)}$-controlled self-mappings. Also, existence and uniqueness results of fixed points are proved if the metric space is complete, and the resulting Cauchyness properties of sequences and properties of the convergence of such sequences to fixed points are also proved. Finally, two illustrative examples are described if the $F_{\left(.\right)}$-controlled self-mappings are of a cyclic nature when defined using the union of two nonempty closed subsets of the metric space, in the case that those sets intersect, and also in the case when they are disjointed. Full article

Addressing high dynamics, stringent non-holonomic constraints, and limited onboard computation in cooperative online trajectory planning for multiple fixed-wing UAVs in complex 3D obstacle environments, this paper proposes a Cooperative-3D-Quick-Dubins-RRT*. First, an offline motion-primitive database is engineered to align with RRT* mechanics: an unconstrained expansion mode facilitates rapid space exploration, while a constrained rewiring mode ensures kinodynamic continuity. This architecture, synergized with four targeted acceleration strategies (dimensionality reduction, elliptical sampling, tree pruning, and pre-discretized collision checking), significantly accelerates convergence. Second, a Dubins-detour-based time-coordination mechanism is designed to map cooperative timing constraints into controllable path-length adjustments, and the feasible adjustment range is analyzed to ensure realizability. Finally, simulations and hardware-in-the-loop experiments across a variety of representative scenarios are conducted for validation. The results show that, compared with the classical Dubins-RRT*, the proposed method achieves clear advantages in planning time and path length, demonstrating its suitability for online cooperative obstacle-avoidance planning of multiple UAVs. Full article

Exploring the evolutionary dynamics of urban, agricultural, and ecological spaces is critical for regional sustainable development and spatial governance. However, traditional spatial simulation methods based on Cellular Automata often struggle to accommodate top-down spatial regulation, non-linear development patterns, and coordinated regional growth. The objective of this scientific research is to address these limitations by proposing a deep learning-based framework for simulating the future distribution of these three spaces. Utilizing the Unet++ model and integrating empirical data sources including multi-period remote sensing land-use mapping and prefecture-level socioeconomic statistical data, the framework predicts regional spatial patterns for the year 2030. Empirical results from the Yangtze River Economic Belt demonstrate that the model achieves high precision in large-scale spatial forecasting (with an average test accuracy of 99.32%) and effectively captures non-linear evolutionary characteristics. Predictions across various growth scenarios reveal that a moderate socioeconomic growth rate facilitates ecological preservation; controlling the expansion of urban space to approximately 20% by 2030 can prevent excessive resource depletion and regional imbalances. Consequently, it is recommended to implement the construction land increment targets outlined in current spatial planning to achieve a balance between economic growth and ecological protection. Full article

In 2024, Kimura proposed the modified shrinking method without assuming the existence of a common fixed point for a family of nonexpansive mappings defined on a complete geodesic space with a nonpositive upper curvature bound. In this paper, we discuss this method for vicinal mappings in an admissible complete geodesic space whose upper curvature bound is an arbitrary real number. Moreover, we investigate the convex minimization problem by using the main result and a resolvent for convex functions. Full article

Accurate correction of radial lens distortion is a fundamental requirement in computer vision and photogrammetry, as geometric inaccuracies directly affect 3D reconstruction, mapping, and geospatial measurements, particularly in high-precision imaging systems. In this study, we propose a fully analytical, non-iterative method for truncated inverse modeling of radial lens distortion, applicable to general radial distortion polynomials that contain constant terms. Unlike classical truncated Lagrange series reversion, which relies on recursive expansion and combinatorial series construction, the proposed formulation determines inverse distortion coefficients directly through a system of constrained algebraic inverse polynomials. This enables deterministic computation of inverse parameters without iterative refinement, numerical root finding, or combinatorial complexity. The method was evaluated using ultra-wide-angle smartphone camera imagery exhibiting severe barrel distortion modeled by an eighth-degree depressed radial distortion polynomial. Its performance was compared with a commonly used iterative inverse modeling approach. The analytical formulation demonstrated improved numerical stability and substantially reduced reprojection errors when correcting highly nonlinear distortion profiles, achieving sub-pixel accuracy in image rectification. In contrast, the iterative approach exhibited instability and significantly larger reprojection errors under identical conditions. These results demonstrate that the proposed framework provides a general, robust, and repeatable solution for inverse radial distortion modeling, particularly for high-order polynomial models. The method offers clear practical advantages for camera calibration pipelines in photogrammetry, remote sensing, robotics, and other applications requiring high-fidelity imaging. Full article

Mountain ecosystems are susceptible to climate change, and alpine treeline ecotones (ATEs) represent one of the significant responsive indicators of climate-driven environmental change. This study examines long-term spatiotemporal dynamics of the ATE across the Eastern Slopes of the Canadian Rocky Mountains (ESCR) from 1984 to 2023, with the objective of assessing whether regional climate warming has influenced ATE extent and elevation across different aspects and watersheds. Multi-decadal Landsat imagery, ERA5-Land temperature data, and topographic variables were integrated within a Google Earth Engine (GEE) framework to map ATEs using the Alpine Treeline Ecotone Index (ATEI), a probabilistic approach designed to capture transitional vegetation zones. Temporal trends were evaluated using non-parametric statistics, correlation analyses, and watershed- and aspect-based comparisons. Results indicate that the total alpine treeline ecotone (ATE) area in the ESCR was approximately 13.3% larger in 2023 than in 1984. However, the temporal evolution of ATE extent and elevation was non-monotonic, and linear trend analyses did not detect statistically significant increasing or decreasing trends over the full study period. ATE elevation and expansion exhibited pronounced spatial heterogeneity, with greater changes occurring on north- and northwest-facing slopes and within selected watersheds. In contrast, summer (July–September) temperatures increased significantly (+2.84 °C), exceeding global land-only warming rates, and vegetation greenness (NDVI) showed a strong, statistically significant positive relationship with temperature. These findings show that while climate warming has clearly increased vegetation productivity, elevational ATE dynamics remain spatially heterogeneous and temporally non-synchronous with summer temperature trends. Full article

Building upon classical fixed point theory, the concept of enriched contractions introduces a new class of mappings. For a normed linear space $(X,\parallel ·\parallel )$, a mapping $T:X\to X$ is called an enriched contraction if there exist $b\in [0,\infty )$ and $\theta \in [0,b+1)$ such that $\parallel b(x-y)+Tx-Ty\parallel \le \theta \parallel x-y\parallel ,\forall x,y\in X.$ This class of mappings includes both the well-known Picard–Banach contraction and certain nonexpansive mappings. In this paper, we extend the definition by allowing $b\in \mathbb{R}\backslash \{-1\}$ instead of $b\in [0,\infty )$. This extension enables the condition to cover both contraction and certain nonexpansive mappings. We establish results on the existence and uniqueness of fixed points and present the Krasnosel’skii iteration for approximating such points. An example is provided to demonstrate mapping that meets the extended condition but not the original. 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

In this paper, we present approximation results for a generalized $\alpha$-non-expansive multi-valued mapping using a four-step iteration scheme introduced in the context of a convex metric space. We extend some recent results about generalized $\alpha$-non-expansive multi-valued mappings from the Banach space setting to a convex metric space. Two examples of generalized $\alpha$-non-expansive multi-valued mappings are presented, and it is numerically shown that our iteration scheme enables faster convergence than other well-known schemes in the literature. To demonstrate the application of one of our results, we provide the solution of a non-linear integral equation. Full article

Gabon harbors one of Africa’s richest assemblages of non-human primates (NHPs), yet integrated national-scale evidence on their conservation status remains limited. To inform conservation strategies, we conducted the first nationwide assessment integrating habitat dynamics, the geographic distribution of species, and the effectiveness of the protected-area network in the country. We harmonized 300 m land-cover maps (ESA CCI 1992; Copernicus 2022), compiled 481 georeferenced occurrences, and identified concentration areas using kernel density estimation and Getis–Ord Gi* analysis. We quantified land-cover transitions with a per-pixel transition matrix and assessed protected-area capture using Monte Carlo randomization. Ten fully protected species are confirmed, including Gorilla gorilla and Pan troglodytes. Occurrences concentrate mainly in the Ogooué-Ivindo and Haut-Ogooué Provinces; ~10% of the national territory lies above the 90th kernel density percentile (≈26,700 km²), and 1.5% of cells qualify as hotspots at the 99% threshold. Primate records are strongly associated with evergreen broadleaved forests (87.9% of points), which remained persistent from 1992 to 2022 (forest-to-forest = 223,476 km²; 98.13%) with a net decline (−2571.66 km²; −1.19%). Gross losses (4046.58 km²) were mainly attributable to agricultural conversion (68.63%; χ² = 31,525; p < 0.001). Over 90% of records fall in areas stable across 1992–2022. Protected areas (PAs) captured more occurrences (observed 40.1% vs. expected 18.47%; p < 0.001), yet gaps remain for some taxa (e.g., Allochorocebus solatus, 86% outside PAs). Overall, Gabon retains an extensive core of suitable habitat, but targeted action outside PAs and maintenance of landscape connectivity are needed to secure populations where agricultural expansion and fragmentation are intensifying. Full article

Weakly nonlinear oscillators display complex behavior that perturbation methods struggle to analyze, particularly near critical thresholds. The non-perturbation approach (NPA) offers a unified, parameter-agnostic approach that is effective in strongly resonant situations, accurately capturing global phase space structures, and directly addressing chaotic transitions, providing predictive insights where traditional methods fail. The NPA as a novel technique successfully converts the nonlinear weakly oscillator of the ordinary differential equation (ODE) into a linear issue. Theoretical findings are confirmed through a numerical comparison using Mathematica Software (MS). The results of the numerical solution (NS) show excellent agreement. It is commonly acknowledged that all conventional perturbation methods utilize Taylor expansion to augment restoring forces, hence optimizing the usual conditions. A comprehensive analysis of the issue’s stability is easily achievable via NPA. Accordingly, when evaluating NS estimates of weakly nonlinear oscillators, NPA occupations serve as a more useful form of responsibility. Additionally, the stability analysis is easily accomplished via NPA. The system’s dynamics are examined by chaotic analyses, incorporating bifurcation diagrams (BDs), Poincaré maps (PMs), and Lyapunov exponents (LEs). This analysis identifies transitions between regular and complicated behavior and thoroughly examines the system’s stability features. The results provide a comprehensive understanding of the fundamental nonlinear dynamics and offer significant insights for future research on analogous systems. Full article

In China, ports have long served as a key engine of growth for coastal cities. Increases in coastal port throughput inevitably lead to port spatial expansion, which in turn drives construction land expansion in port cities. Consequently, ports are a critical factor shaping construction land expansion in coastal cities, with direct implications for spatial planning and sustainable development in coastal port cities. Therefore, it is necessary to examine how ports influence construction land expansion in coastal cities. This paper using multiple linear regression and binary logistic regression models and incorporating landscape metrics explores the impacts of ports on the expansion of urban construction land in coastal port cities. The findings reveal distinct characteristics of land expansion in port cities compared to non-port cities: (1) Macro-level changes: The expansion of construction land is driven by industrial restructuring, real estate development, port cargo traffic, population growth, and GDP growth. Industrial restructuring is the primary driver, while real estate development plays a significant role in land expansion. Port cargo demand serves as a unique driving factor compared to non-port cities, whereas population and GDP growth have minimal effects. (2) Micro-level spatial expansion: Land expansion is influenced by proximity to port shorelines, transportation infrastructure, and the degree of base construction land expansion. Expansion tends to concentrate along the port shoreline, transport hubs, and established urban areas. Elevation and slope are significant factors for coastal port cities, while rivers and proximity to core urban areas predominantly impact estuarine port cities. (3) Temporal patterns of expansion: Port development follows a phased pattern of land expansion: “Decline → Increase → Decline”. Ports also influence landscape patterns, with increased distance from the port shoreline leading to decreased patch density and higher landscape fragmentation. The results of this paper help to address gaps in existing research on how ports shape the spatial expansion of coastal cities. Furthermore, this paper provides insights for effective land use strategies, spatial planning, and port-city management, promoting coordinated land and marine development. It offers a foundation for addressing the integration of land and sea spatial planning in the “One Map” initiative. Full article

The rapid expansion of distributed cloud platforms introduces critical security challenges, specifically non-deterministic race conditions like Time-of-Check to Time-of-Use (TOCTOU) vulnerabilities. Traditional passive detection methods often fail to identify these transient “Heisenbugs” due to the asynchronous nature of multi-threaded control planes. To address this, we propose a novel DAG-Guided Active Fuzzing framework. Our approach constructs a Directed Acyclic Graph (DAG) to map causal dependencies of API operations and implements deterministic proactive scheduling. By injecting microsecond-level delays into identified race windows, the system enforces adversarial interleavings to expose hidden order and atomicity violations. Validated on 32 verified vulnerabilities across six distributed systems (including Hadoop and OpenStack), our method achieves an overall Recall (Detection Rate) of 68.8% across the entire dataset and a peak Precision of 92% in reproducibility tests, significantly outperforming random fuzzing baselines ($p<0.01$). Furthermore, the framework maintains a low runtime overhead of 11.5%. These findings demonstrate a favorable trade-off between detection depth and system efficiency, establishing the approach as a robust toolchain for transforming theoretical concurrency risks into reproducible security findings in large-scale cloud infrastructure. Full article