Search Results (164)

We examine a Szász–Mirakyan–Durrmeyer type operator that reproduces the functions 1 and $e^{2ax}$ for a fixed parameter $a>0.$ While its exponential reproduction property has been described in the classical literature, the effect of exponential weights on its approximation behavior has not been studied. In this work, we provide a detailed analysis of the operator in weighted spaces and show that combining exponential reproduction with weighted norms improves the approximation behavior for exponentially growing functions. We also prove that the corresponding sequence of operator norms remains uniformly bounded for a family of exponential weights, ensuring the stability of the operators in the weighted framework. Moreover, we establish new Korovkin-type approximation theorems involving weighted convergence and obtain sharp uniform error estimates in the presence of exponential weights. These results extend the classical theory to weighted exponential settings and highlight several quantitative features that do not arise in the classical case. Full article

This paper focuses on analyzing and implementing a numerical technique using the Petrov–Galerkin technique (PGT) to solve the time fractional cable problem (TFCP). The trial functions are a modified set of shifted Legendre polynomials ($\mathsf{LPs}$). An appropriate numerical approach can be used to solve the linear algebraic equations resulting from the application of the PGT. With error bounds, we discuss the truncation estimation and stability in the $L_2$ norm. We apply some inequalities on the modified set of shifted $\mathsf{LPs}$ to this research. Numerical experiments include benchmark issues for which exact solutions are presented to show how efficient and accurate the method is. Comparisons with different techniques in the literature are used to support our examples. Full article

Synthetic Aperture Radar (SAR) images generated via range-Doppler (RD) model-based geometric correction often suffer from non-negligible systematic geolocation errors due to cumulative impacts of platform positioning inaccuracies, payload time synchronization offsets, and atmospheric propagation delays. These errors limit the applicability of SAR data in high-precision geometric applications, especially in scenarios where ground control points (GCPs)—traditionally used for calibration—are inaccessible or costly to acquire. To address this challenge, this study proposes a novel GCP-free high-precision geolocation method based on multi-view SAR image fusion, integrating outlier detection, weighted fusion, and refined estimation strategies. The method first establishes a positioning error correlation model for homologous point pairs in multi-view SAR images. Under the assumption of approximately equal positioning errors, initial systematic error estimates are obtained for all arbitrary dual-view combinations. It then identifies and removes outlier images with inconsistent systematic errors via coefficient of variation analysis, retaining a subset of multi-view images with stable calibration parameters. A weighted fusion strategy, tailored to the geometric error propagation model, is applied to the optimized subset to balance the influence of angular relationships on error estimation. Finally, the minimum norm least-squares method refines the fusion results to enhance consistency and accuracy. Validation experiments on both simulated and actual airborne SAR images demonstrate the method’s effectiveness. For actual measured data, the proposed method achieves an average positioning accuracy improvement of 84.78% compared with dual-view fusion methods, with meter-level precision. Ablation studies confirm that outlier removal and refined estimation contribute 82.42% and 22.75% to accuracy gains, respectively. These results indicate that the method fully leverages multi-view information to robustly estimate and compensate for 2D systematic errors (range and azimuth), enabling high-precision planar geolocation of airborne SAR images without GCPs. Full article

This study aimed to assess the potential of machine learning models applied to high spatial resolution images from UAVs for estimating the aboveground biomass (AGB) of forage grass cultivated in the Brazilian semiarid region. The fresh and dry AGB were determined in Cenchrus ciliare plots with an area of 0.04 m². Spectral data were obtained using a multispectral sensor (Red, Green, and NIR) mounted on a UAV, from which 45 vegetation indices were derived, in addition to a structural variable representing plant height (H95). Among these, H95, GDVI, GSAVI2, GSAVI, GOSAVI, GRDVI, and CTVI exhibited the strongest correlations with biomass. Following multicollinearity analysis, eight variables (R, G, NIR, H95, CVI, MCARI, RGR, and Norm G) were selected to train Random Forest (RF), Support Vector Machine (SVM), and XGBoost models. RF and XGBoost yielded the highest predictive performance, both achieving an R² of 0.80 for AGB—Fresh. Their superiority was maintained for AGB—Dry estimation, with R² values of 0.69 for XGBoost and 0.67 for RF. Although SVM produced higher estimation errors, it showed a satisfactory ability to capture variability, including extreme values. In modeling, the incorporation of plant height, combined with spectral data obtained from high spatial resolution imagery, makes AGB estimation models more reliable. The findings highlight the feasibility of integrating UAV-based remote sensing and machine learning algorithms for non-destructive biomass estimation in forage systems, with promising applications in pasture monitoring and agricultural land management in semi-arid environments. Full article

In mineral processing and metallurgy, total iron grade serves as a critical indicator guiding the entire production chain from crushing to smelting, directly influencing the quality and yield of steel products. To address the limitations of conventional matrix effect correction methods in X-ray fluorescence (XRF) analysis—such as low accuracy, high time consumption, and labor-intensive procedures—this study proposes a novel hybrid model (DSCN-LS) integrating least squares (LS) with dynamically regularized stochastic configuration networks (DSCNs) for total iron ore grade quantification. Through feature analysis, we decompose the grade modeling problem into a linear structural component and nonlinear residual terms. The linear component is resolved by means of LS, while the nonlinear terms are processed by the DSCN with a dynamic regularization strategy. This strategy implements node-specific weighted regularization: weak constraints preserve salient features in high-weight-norm nodes, while strong regularization suppresses redundant information in low-weight-norm nodes, collectively enhancing model generalizability and robustness. Notably, the model was trained and validated using datasets collected directly from industrial sites, ensuring that the results reflect real-world production scenarios. Industrial validation demonstrates that the proposed method achieves an average absolute error of 0.3092, a root mean square error of 0.5561, and a coefficient of determination (R²) of 99.91% in total iron grade estimation. All metrics surpass existing benchmarks, confirming significant improvements in accuracy and operational practicality for XRF detection under complex industrial conditions. Full article

Multiple regression analysis has a wide range of applications. The analysis of error structures in regression model $\mathit{Y}=\mathbf{\Gamma }\mathit{X}+\mathit{Z}$ has also attracted much attention. This paper focuses on large-scale precision matrix of the error vector that only has lower polynomial moments. We mainly study upper bounds of the proposed estimator under different norms in term of the probability estimation. It is shown that our estimator achieves the same optimal convergence order as under Gaussian assumption on the data. Simulation experiments further validate that our method has advantages. Full article

Accurate trajectory tracking is crucial for fixed-wing unmanned aerial vehicles (UAVs) in executing diverse missions. However, the inherent strong nonlinearities, parametric uncertainties, and external disturbances in the UAV model present significant challenges for controller design. To address these challenges, this paper proposes a robust adaptive control strategy based on the backstepping technique. The proposed strategy effectively addresses a class of uncertainties with norm bounds that are unknown and state-dependent. An adaptive law is constructed to estimate the unknown parameters online, thereby enabling compensation for the effects of these uncertainties. Furthermore, to mitigate chattering, the controller is modified to generate smooth control inputs, ensuring that the steady-state tracking error is ultimately bounded and converges to an arbitrarily small neighborhood of zero. Simulation results demonstrate that, under realistic flight control sampling frequencies, the proposed controller achieves accurate trajectory tracking and eliminates the chattering phenomenon. Full article

This paper investigates the asymptotic behavior of kernel-based estimators for the error distribution in a first-order autoregressive model with dependent errors. The model assumes that the error terms form an $\alpha$-mixing sequence with an unknown cumulative distribution function (CDF) and finite second moment. Due to the unobservability of true errors, we construct kernel-smoothed estimators based on residuals obtained via least squares. Under mild assumptions on the kernel function, bandwidth selection, and mixing coefficients, we establish a logarithmic law of the iterated logarithm (LIL) for the supremum norm difference between the residual-based kernel estimator and the true distribution function. The limiting bound is shown to be $1/2$, matching the classical LIL for independent samples. To support the theoretical results, simulation studies are conducted to compare the empirical and kernel distribution estimators under various sample sizes and error term distributions. The kernel estimators demonstrate smoother convergence behavior and improved finite-sample performance. These results contribute to the theoretical foundation for nonparametric inference in autoregressive models with dependent errors and highlight the advantages of kernel smoothing in distribution function estimation under dependence. Full article

In this article, we present an efficient numerical strategy for the two-dimensional nonlinear Schrödinger equation, focusing on its development and analysis. Our approach begins with proposing a nonlinear, energy-conservative, fourth-order, compact, alternating-direction, implicit (ADI) scheme. To boost efficiency when solving the associated nonlinear system, we then implement this scheme using a temporal two-mesh (TTM) algorithm. Under discretization with coarse time step ${\tau }_C$, fine time step ${\tau }_F$, and spatial mesh size h, the numerical scheme exhibits a convergence rate of order $\mathcal{O}({\tau }_C^4+{\tau }_F^2+h^4)$ in both the discrete $L_2$-norm and $H_1$-norm. To facilitate the convergence analysis under fine time discretization, we propose a novel technique along with several supporting lemmas that enable the estimation of the discrete $L_4$-norm error term over the temporal coarse mesh. Numerical experiments are then performed to validate the theoretical results and demonstrate the effectiveness of the proposed algorithm. The numerical results show that the new algorithm produces highly accurate results and preserves the conservation laws of mass and energy. Compared with the fully nonlinear compact ADI scheme, it reduces computational time while maintaining accuracy. Full article

The goal of this paper is to give an error analysis of a finite difference method for a time-fractional Black–Scholes equation with weakly singular solutions. The time Gerasimov-Caputo derivative is discretized by the L1 scheme on a graded mesh designed to compensate for the initial singularities, and a standard finite difference method is used for spatial discretization on a uniform mesh. A discrete comparison principle is presented for the fully discrete scheme, and stability and convergence of the scheme in maximum norm are established by constructing some appropriate barrier functions. Furthermore, an $\alpha$-robust pointwise error estimate of the fully discrete scheme on a uniform mesh is given. Finally, some numerical results are presented to show the sharpness of the error estimate. Full article

With the widespread adoption of space–air–ground integrated networks (SAGINs) in next-generation wireless communications, intelligent reflecting surfaces (IRSs) have emerged as a key technology for enhancing system performance through passive link reinforcement. This paper addresses the prevalent issue of channel state information (CSI) uncertainty in practical systems by constructing an IRS-assisted multi-hop SAGIN communication model. To capture the performance degradation caused by channel estimation errors, a norm-bounded uncertainty model is introduced. A simulated annealing (SA)-based phase optimization algorithm is proposed to enhance system robustness and improve worst-case communication quality. Simulation results demonstrate that the proposed method significantly outperforms traditional multiple access strategies (SDMA and NOMA) under various user densities and perturbation levels, highlighting its stability and scalability in complex environments. Full article

While autonomous vehicles (AVs) are increasingly integrated into urban mobility, little is known about how digital capability shapes elderly pedestrians’ willingness to share roads with these technologies. This is especially true in the absence of explicit vehicle–pedestrian communication mechanisms. To address this gap, we combine the Theory of Planned Behavior (TPB) with the Pedestrian Behavior Questionnaire (PBQ) and segment elderly pedestrians using Latent Class Analysis (LCA). A sample of 750 older adults in Wuhan, China, was divided into two latent groups: digitally disengaged (70.8%) and digitally engaged (29.2%). Classification was based on four indicators: smart device usage, online social interaction, online entertainment, and online economic behavior. We then applied ordered logit models to estimate group-specific determinants of AV road-sharing acceptance. Results reveal clear heterogeneity across digital capability levels. For digitally disengaged seniors, positive pedestrian behaviors significantly increased willingness (β = 0.316, p = 0.001). Prior accident experience reduced willingness (0 accident: β = 0.435, p = 0.021; 1–2 accidents: β = −0.518, p = 0.012). For digitally engaged seniors, perceived behavioral control showed a marginally positive effect (β = 0.353, p = 0.066). Errors had a significant positive effect (β = 0.540, p = 0.009). Positive behaviors had a significant negative effect (β = −0.414, p = 0.007). These patterns indicate that digital capability not only modulates the strength of TPB pathways but also reshapes behavior–intention linkages captured by PBQ dimensions. Methodologically, the study contributes an integrated TPB–PBQ–LCA–OLM framework. This framework identifies digital capability as a critical moderator of AV acceptance among elderly pedestrians. Practically, the findings suggest differentiated strategies. For digitally disengaged users, interventions should build digital literacy and reinforce safe walking norms. For digitally engaged users, strategies should prioritize transparent AV intent signaling and features that enhance perceived control. Full article

Aerodynamic ablation of external control surfaces and structural complexity in hypersonic reentry vehicles (HRVs) pose significant challenges for maneuverability and system reliability. To address these issues, this study develops a novel bank-to-turn (BTT) control strategy integrating a single internal moving mass with differential ailerons, eliminating reliance on ablation-prone elevators/rudders while enhancing internal space utilization. A coupled 7-DOF dynamics model explicitly quantifies inertial-rolling interactions induced by the moving mass, revealing critical stability boundaries for roll maneuvers. To ensure robustness against aerodynamic uncertainties, aileron failures, and high-frequency mass-induced disturbances, a dynamic inversion controller is augmented with an L1 adaptive layer decoupling estimation from control for improved disturbance rejection. Monte Carlo simulations demonstrate: (1) a 20.6% reduction in roll-tracking error (L₂-norm) under combined uncertainties compared to dynamic inversion control, and (2) a 72% suppression of oscillations under aerodynamic variations. Comparative analyses confirm superior transient performance and robustness in worst-case scenarios. This work offers a practical solution for high-maneuverability hypersonic vehicles, with potential applications in reentry vehicle design and multi-actuator system optimization. Full article

This paper proposes a robust blind algorithm for direction of arrival (DOA) estimation in challenging acoustic environments. The method introduces a novel Time Difference of Arrival (TDOA) consensus framework that effectively identifies and filters outliers using Median and Median Absolute Deviation (MAD) statistics. By combining this consensus approach with whitening transformation and Lawson norm optimization, the algorithm achieves superior performance in noisy and reverberant conditions. Comprehensive simulations demonstrate that the proposed method significantly outperforms traditional approaches and modern alternatives such as SRP-PHAT and robust MUSIC, particularly in environments with high reverberation times and low signal-to-noise ratios. The algorithm’s robustness to impulsive noise and varying microphone array configurations is also evaluated. Results show consistent improvements in DOA estimation accuracy across diverse acoustic scenarios, with root mean square error (RMSE) reductions of up to 30% compared to standard methods. The computational complexity analysis confirms the algorithm’s feasibility for real-time applications with appropriate implementation optimizations, showing significant improvements in estimation accuracy compared to conventional approaches, particularly in highly reverberant conditions and under impulsive noise. The proposed algorithm maintains consistent performance without requiring prior knowledge of the acoustic environment, making it suitable for real-world applications. Full article

This work investigates the solutions of fractional integro-differential equations (FIDEs) using a unique kernel operator within the Caputo framework. The problem is addressed using both analytical and numerical techniques. First, the two-step Adomian decomposition method (TSADM) is applied to obtain an exact solution (if it exists). In the second part, numerical methods are used to generate approximate solutions, complementing the analytical approach based on the Adomian decomposition method (ADM), which is further extended using the Sumudu and Shehu transform techniques in cases where TSADM fails to yield an exact solution. Additionally, we establish the existence and uniqueness of the solution via fixed-point theorems. Furthermore, the Ulam–Hyers stability of the solution is analyzed. A detailed error analysis is performed to assess the precision and performance of the developed approaches. The results are demonstrated through validated examples, supported by comparative graphs and detailed error norm tables ($L_{\infty }$, $L_2$, and $L_1$). The graphical and tabular comparisons indicate that the Sumudu-Adomian decomposition method (Sumudu-ADM) and the Shehu-Adomian decomposition method (Shehu-ADM) approaches provide highly accurate approximations, with Shehu-ADM often delivering enhanced performance due to its weighted formulation. The suggested approach is simple and effective, often producing accurate estimates in a few iterations. Compared to conventional numerical and analytical techniques, the presented methods are computationally less intensive and more adaptable to a broad class of fractional-order differential equations encountered in scientific applications. The adopted methods offer high accuracy, low computational cost, and strong adaptability, with potential for extension to variable-order fractional models. They are suitable for a wide range of complex systems exhibiting evolving memory behavior. Full article