In order to obtain high-quality restoration outcomes, this paper proposed a new nonconvex variational model tailored for reconstructing blurred images corrupted by impulse noise. The newly designed optimization framework integrated nonconvex high-order total variation regularization with ℓ₀ norm data fidelity. This combination aided in overcoming the staircase artifacts and maintaining sharp contours while tackling the poor performance of ℓ₁ norm-based data fidelity in handling high-density impulse noise. To deal with the nonconvex optimization problem, we designed an efficient alternating direction method of multipliers by combining the variable splitting technique with the iteratively reweighted ℓ₁ algorithm. Finally, numerous experiments demonstrated that the suggested scheme achieves competitive performance in terms of objective metrics and visual quality.

In this paper, we propose a new preconditioner for the multi-linear systems with M-tensors by utilizing some elements in the first row and column of the majorization matrix associated with the system tensor. The new preconditioner generalizes the one proposed in (Calcolo, 57(2020) 15). Then, we establish three new preconditioned Gauss-Seidel type methods for solving the multi-linear systems with M-tensors. Theoretically, convergence theorems and comparison theorems are given, which show that the proposed methods are convergent, and the third one has the fastest convergence rate and performs better than the original Gauss-Seidel method and the one in (Calcolo, 57(2020) 15). Also, the monotonic theorem is studied. Finally, numerical experiments including some applications in the higher-order Markov chain and directed graph verify the correctness of the theoretical analyses and the effectiveness of the proposed methods, and illustrate that they are superior to the original Gauss- Seidel method and the preconditioned Gauss-Seidel methods in (Calcolo, 57(2020) 15) and (Appl. Numer. Math., 134(2018) 105–121).

We study the regularity problem with non-homogeneous terms of p-Laplacian type, which is a still unsolved problem for nonlinear elliptic equations. The main results of this work are obtained by three steps. First, we use the Hodge decomposition theorem to construct a suitable test function that satisfies the solution definition. Second, by combining the solution definition with the Hodge decomposition theorem, we establish a properly formulated inverse Hölder inequality to enhance the integrability of the very weak solutions. Finally, through an iterative process, we show that the considered very weak solutions can be improved to classical weak solutions.

The objective of this work was to provide sufficient conditions for testing the oscillatory performance of solutions of the neutral second-order differential equation with distributed deviation arguments. We derived improved relations that influence the oscillation parameters of the equation under study. We used comparison with lower-order equations and Riccati techniques to derive the oscillation parameters. Comparing our findings with earlier pertinent findings allows us to assess the advancements made in oscillation theory. Furthermore, some numerical solutions for a special case of the equation under study are presented, and the numerical and theoretical results are compared.

This research focuses on controlling fixed-time synchronization (FixTS) in a time-delayed fuzzy memristor-based neural network (TDFMNN). To achieve FixTS and improve convergence speed, a discontinuous state feedback controller (StFC) incorporating a unique exponential function is developed for the memristor-based neural network (MNN) drive-response system (DRS). The FixTS is analyzed using the indefinite derivative Lyapunov function approach. The proposed TDFMNN incorporates multiple factors, such as memristor, time-variation of coefficients, time-delay, and fuzzy elements, making the model more practical compared to existing studies. The StFC is designed using the fixed-time stability (FixS) theory of the exponential function, which requires few parameters, thereby simplifying controller design and implementation. Numerical simulations are conducted to evaluate the performance of the proposed control strategy on two-dimensional and three-dimensional TDMNNs.

In this paper, for n ≥ 2 and n ≠ 3, the module algebra structures of X_q(A₁) on the quantum n-space were discussed, where the quantum n-space is denoted by A_q(n). In particular, a complete list of X_q(A₁)-module algebra structures on the quantum plane A_q(2) was produced and the isomorphism classes of these structures were described.

The focus of this work was to establish relations between Gorenstein projective modules linked by right quasi-Frobenius extensions of rings. As applications, the right quasi-Frobenius extensions of (weakly) Gorenstein algebras, Cohen-Macaulay finite algebras and the Cohen-Macaulay free algebra were studied. Suppose that Γ was a right quasi-Frobenius extension of an Artin algebra Λ with Γ a completely faithful left Λ-module. We demonstrated that if Γ exhibited (weakly) Gorenstein properties, then Λ did so. Additionally, under the condition of Γ being a separable extension of Λ, the converse became valid.

This paper was focused on global existence for the stochastic nonlinear Schrödinger equation with time-dependent loss/gain, which read idu + (∆u + λ|u|^α u + ia(t)u)dt = dW. We proved the global existence and uniqueness of the solution in $H^{1}\left(\mathbb{R}^{N}\right)$ through the uniform boundedness of the momentum and energy functionals. The global existence result of the solution for this type of equation depended on the ranges of time-dependent loss/gain coefficient.

With a focus on image denoising applications, this paper proposed a three-term extended Rivaie-Mustafa-Ismail-Leong (RMIL) conjugate gradient projection (CGP)-based algorithm for solving constrained nonlinear equations. Unlike traditional methods, the proposed algorithm relied only on the continuity and monotonicity properties of the nonlinear equations, and did not require the more restrictive Lipschitz continuity condition. A rigorous convergence analysis was established under these relaxed assumptions. At the algorithmic level, a novel three-term search direction was constructed by extending previous two-term schemes through the introduction of a carefully designed scale factor, which effectively eliminates the need for a line search procedure. Comprehensive numerical experiments on standard benchmark problems demonstrated the algorithm’s efficiency and competitiveness, consistently outperforming comparable three-term algorithms in terms of running time in seconds, number of iterations, and function evaluations. Furthermore, the proposed algorithm has been successfully applied to image denosing problems.

This paper investigates the chaotic dynamics and control of a fractional-order energy- saving and emission-reduction (ESER) system using a high-precision method. By constructing a four-dimensional fractional-order system, the complex interactions between new energy, carbon emissions, economic growth, and carbon trading volume are studied. A novel high-precision numerical method, based on generating functions, is introduced to analyze the dynamic behaviors of the system at various fractional derivatives and parameters. Numerical simulations find all kinds of dynamic behaviors, including stable, rapid divergence, and chaotic attractors. In this study, we design feedback and adaptive control strategies to achieve chaos synchronization and system stability. The results highlight the effectiveness of the proposed control methods in stabilizing the system and synchronizing drive-response systems, underscoring the pivotal role of fractional-order derivatives in regulating system dynamics.

In recent years, Transformer-based object trackers have demonstrated exceptional performance in object tracking. However, traditional methods often employ single-scale pixel-level attention mechanisms to compute the correlation between templates and search regions, disrupting object’s integrity and positional information. To address these issues, we introduce a cyclic-shift mechanism to expand the diversity of sample positions and replace the traditional single-scale pixel-level attention mechanism with a multi-scale window-level attention mechanism. This approach not only preserves the object’s integrity but also enriches the diversity of samples. Nevertheless, the introduced cyclic-shift operation heavily burdens storage and computation. To this end, we treat the attention computation of shifted and static windows in the spatial domain as convolution. By leveraging the convolution theorem, we transform the attention computation of cyclic shift samples from the spatial domain to element-wise multiplication in the frequency domain. This approach enhances computational efficiency and reduces data storage requirements. We conducted extensive experiments on the proposed module. The results demonstrate that the proposed module outperforms multiple existing tracking algorithms regarding performance. Moreover, ablation studies show that the method effectively reduces the storage and computational burden without compromising performance.

The presence of electric bicycles in elevators poses serious safety hazards, necessitating reliable automatic detection solutions. To address these issues, this paper proposes EBike-YOLO, an enhanced real-time detection model based on YOLOv10n, specifically optimized for elevator environments. EBike-YOLO introduces three key innovations: 1) the PIoU2_NWD loss function, combining adaptive penalty mechanisms, anchor-quality-aware gradient adjustments, non-monotonic attention, and Wasserstein distance for significantly improved object localization; 2) the EnhancedPSA structure, refining self-attention and feed-forward network architectures to enhance feature extraction; and 3) the C2f_Calibration module, incorporating self-calibration operations to robustly manage diverse orientations and scales of electric bicycles. Extensive experiments on a custom elevator dataset demonstrate substantial improvements over the YOLOv10n baseline, achieving notable enhancements in precision (4.1%), recall (0.3%), F1 score (2.0%), and mAP@50 (2.23%). Further validations on standard benchmark datasets (VisDrone2019, VOC2007, VOC2012) confirm the model’s strong generalization capability, underscoring its applicability beyond specific elevator scenarios. These results clearly highlight the effectiveness, novelty, and practical value of the proposed model for diverse real-world detection tasks.

In this paper, we establish the existence of two positive solutions for a discrete mean curvature problem with Dirichlet boundary value conditions. The approach is based on a two-critical-point theorem. Our main result extends an existing conclusion in the literature. Moreover, three examples are presented to illustrate the validity and feasibility.

This study aims to investigate the qualitative behavior analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative. The equation serves as a prominent physics-based mathematical model with numerous practical uses. To analyze the studied equation, we convert it into an ordinary differential equation via traveling wave transformation and then apply the polynomial trial method to deduce its trial equation. Subsequently, the equation with periodically excited perturbation is analyzed using phase trajectory diagrams, bifurcation diagrams, and Lyapunov exponents. Additionally, by utilizing a polynomial complete discrimination system, we derive trigonometric, hyperbolic, and Jacobi elliptic function solutions, some of which are visually represented through figures. These findings enhance the theoretical understanding of the (3+1)-dimensional Kadomtsev-Petviashvili- Sawada-Kotera-Ramani equation with conformable fractional derivative and contribute to the study of nonlinear wave phenomena.

This paper studied panel interval-valued data models with individual fixed effects, in which the correlation within a group was considered and the group average method was used to eliminate the fixed effects. Then, we applied generalized estimation equations (GEEs) to analyze panel interval-valued data models and gave a computational algorithm to obtain the estimators. Some Monte Carlo simulations and real data analysis showed that, in contrast with the least-squares dummy-variable (LSDV) method, the proposed GEEs method has advantages in forecasting performance.

Wi-Fi fingerprint-based indoor localization has garnered significant attention due to its low cost, easy deployment, and high accuracy. However, indoor signal fluctuations and existing method limitations-such as single algorithm usage, low accuracy, and poor generalization-lead to suboptimal localization precision and stability. To address these issues, this paper proposes an improved dung beetle optimizer (IDBO)–stacking indoor fingerprint localization algorithm based on uncertainty estimation. In the offline phase, a hybrid filtering method combining bilateral and Gaussian filtering is first applied to the received signal strength indication (RSSI) fingerprint data for denoising and edge feature preservation, improving the stability of the fingerprint database. Next, the combination of base learners with complementary performance is constructed. An index combining the Pearson coefficient and cosine similarity (the PC index) is designed to select candidate learners with good localization performance and significant diversity as base learners. Meanwhile, IDBO is introduced, which integrates circle chaotic mapping, osprey optimization, variable spiral searching, and Gaussian–Cauchy mutation to perform hyperparameter optimization for the learners. Finally, the training of the base learners and the meta-learner is completed and saved for subsequent online localization. In the online phase, the RSSI signal of the target device is collected in real time and input into the trained base learners. Using the proposed dynamic weight allocation method with uncertainty estimation, the fusion weights of each base learner are dynamically adjusted according to their performance on different data subsets. The final positioning coordinates are output by the meta-learner. Experimental results show that the proposed algorithm achieves an average error of 1.04 m, reducing error by 13.46% to 36.54% compared with other ensemble methods and single algorithms. Moreover, the cumulative distribution function curve converges faster, demonstrating superior positioning performance and strong noise robustness. Moreover, validation in different environments further demonstrates the algorithm’s strong adaptability and generalization ability.

This paper verifies the semi-local convergence of a sixth-order iterative method for solving nonlinear systems. In the proof, the recursive relation method is used to prove the semi- local convergence of the iterative method in Banach spaces. The proof process outlined above does not necessitate the higher-order continuous differentiability of the functionL(u). The advantage of the iterative method is that by employing auxiliary sequences and functions, convergence can be established using only first-order Fréchet derivatives. The proposed sixth-order method reduces computational costs compared to existing sixth-order methods by requiring only one LU decomposition per iteration instead of two. Finally, this sixth-order iterative approach is utilized for solving Hammerstein equations along with real gas equation of state. The experimental results prove the effectiveness of the iterative method.

In this paper, we studied a generalized reaction-diffusion system that models predator-prey dynamics, incorporating prey-taxis along with a hunting cooperation effect and a logistic source for the predator population, subject to homogeneous Neumann boundary conditions. This system describes a predator-prey interaction in which the prey, via a prey-taxis mechanism, employ group defense strategies against their predators, while the predators, through their functional response and net growth rate, not only cooperate in hunting these defended prey but also exhibit logistic growth dynamics, thereby ensuring the self-regulation of the predator population. We established that solutions to the time- and space-dependent system exhibiting such ecological characteristics exist globally and remain bounded within a one-dimensional spatial domain. Furthermore, using global bifurcation theory, we proved the existence of nonconstant positive steady states. A key ingredient in this analysis is the derivation of uniforma priori estimates for positive steady-state solutions, which play a crucial role in controlling the global solution branches.

Two enhanced fifth-order weighted compact nonlinear schemes (WCNSs), namely the WCNS scheme with the modified ZN-type weights (WCNS-ZNM) and the perturbed WCNS scheme (WCNS-P), were proposed for compressible Euler equations. The WCNS-ZNM scheme incorporates an enhanced WENO-ZN-type nonlinear interpolation technique to obtain unknown flow values at cell edges. The WCNS-P scheme introduces perturbation terms containing a free parameter into the linear interpolations, effectively reducing numerical errors in smooth regions. A monotone polynomial interpolation approach was designed to enhance numerical stability by filtering out non-smooth regions and realizing the automatic switching between the WCNS-P and WCNS-ZNM schemes in smooth and non-smooth regions. Numerical results exhibit better accuracy and performance in resolving small-scale structures and shock waves, compared to the WCNS scheme with the WENO-Z and WENO-ZN weights.

This paper developed an observer design for a matrix-Lipchitz nonlinear system with measurement delay that can achieve a desired ℒ₂ performance in the presence of modeling uncertainties, input disturbance, and measurement noise. The observer was shown to be stable in the absence of disturbances and modeling uncertainties. The equations for the observer design were shown to be both necessary and sufficient. Furthermore, the observer design was formulated as linear matrix inequality (LMI) that can be solved offline using commercial solvers. Compared to previous literature, the proposed observer does not require the underlying system to be stable. The observer design procedure is demonstrated through two illustrative examples.

In this paper, we analyze, from the numerical point of view, a new thermoelastic problem involving the so-called Bresse system. The heat conduction is modeled by using the Maxwell-Cattaneo law, which is of hyperbolic type. An existence and uniqueness result and an energy decay property are recalled. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. First, we prove that the discrete solution is stable, and secondly, we provide an a priori error analysis. This allows us to conclude the linear convergence under suitable additional regularity on the continuous solution. Finally, numerical results are presented to demonstrate the convergence of the scheme and the behavior of the discrete energy.

A modified nonlinear incidence rate in an SIS epidemic model was investigated. When a new disease emerged or an old one resurged, the infectivity was initially high. Subsequently, the psychological effect attenuated the infectivity. Eventually, due to the crowding effect, the infectivity reached a saturation state. The nonlinearity of the functional form of the infection incidence was modified to enhance its biological plausibility. The stability of the associated equilibria was examined, and the basic reproduction number and the critical value that governed the dynamics of the model were deduced. Bifurcation analyses were presented, encompassing backward bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, and Hopf bifurcation. Numerical simulations were conducted to validate our findings.

For the problems of parametric uncertainties and actuator faults encountered during high-speed train operation, this paper proposes a neural network-based adaptive fault-tolerant control strategy for cooperation of multiple trains. First, a multi-train model with state constraints, disturbances, and actuator faults was established, and the radial basis function neural network was utilized to fit the unknown disturbance. Subsequently, the auxiliary control signal was introduced to compensate the impact of actuator faults on train. Then, when designing adaptive laws, the variations of basic resistance parameters were fully considered. By integrating adaptive laws with the adaptive fault-tolerant controller, the effect of disturbances on multi-train systems can be dynamically eliminated. The Lyapunov method was established to prove the stability of multi-train systems. Simulation results show that the proposed adaptive fault-tolerant control strategy can maintain the stability of multi-train systems and achieve cooperation of trains with actuator faults.

Integer programming (IP) is a fundamental combinatorial optimization problem, traditionally solved using branch-and-bound methods. However, these methods often struggle with large-scale instances as they attempt to solve the entire problem at once. Existing heuristics, such as a large neighborhood search (LNS), improve efficiency but lack a structured decomposition strategy. We have proposed a divide-and-conquer strategy for IP, which partitions decision variables based on constraint relationships, optimizes them in smaller subproblems, and progressively merges solutions while repairing constraints. This structured approach significantly enhances both solution quality and computational efficiency. Experiments on four standard benchmarks-minimum vertex cover (MVC), maximum independent set (MIS), set cover (SC), and combinatorial auction (CA)-demonstrated that our method significantly outperforms both state-of-the-art solvers (e.g., Gurobi, SCIP) and advanced LNS-based heuristics. When using Gurobi and SCIP as sub-solvers, our approach achieved up to 30× improvement in objective value on certain tasks (e.g., MIS), and reduced solution cost by over 44% compared to exact solvers in minimization settings (e.g., MVC). In addition, our method showed consistently faster convergence and better final solution quality across all tested problems. These results highlight the robustness and scalability of our divide-and-conquer strategy, establishing it as a powerful framework for solving large-scale integer programming problems beyond the capabilities of traditional and heuristic-based solvers.

Various multi-objective optimization methods are widely applied in the transportation field, enabling decision-makers to find solutions that balance trade-off objectives. Since comparing the performance of multi-objective optimization methods is generally difficult, many performance metrics are introduced to quantitatively evaluate the performance of multi-objective optimization methods. However, the effectiveness of the performance metrics needs to be further investigated. Thus, we first critically analysed a series of performance metrics, including number of solutions obtained (NOSO), overall nondominated solutions number (ONSN), normalized maximum spread (NMS), error ratio (ER), nearest ideal distance (NID), mean ideal distance (MID), spacing (SP), inverted generational distance (IGD), and hypervolume-based ratio (HR), which were extensively adopted to assess the performance of multi-objective optimization methods. We found that these performance metrics cannot always accurately reflect the quality of solutions obtained and may be misleading. Thereafter, two axioms were proposed to define the criteria for reliable performance metrics. Additionally, whether these performance metrics satisfied the two axioms was rigorously proved. The performance metrics that satisfied both axioms, i.e., NOSO, ONSN, NMS, ER, and HR, were considered reliable. Furthermore, a real-world cargo transportation case was investigated, indicating the unreliability of metrics MID and SP.

This paper explores the use of differential privacy encryption to protect against data tampering attacks in the context of finite impulse response (FIR) system identification under binary observation conditions. The study begins by introducing the core principles of differential privacy and discussing the current security challenges faced by FIR systems. It highlights the risks of data tampering and privacy leakage during the system identification process. To address these challenges, two distinct differential privacy algorithms are proposed, providing dual encryption protection for the system parameters. By integrating differential privacy mechanisms into the FIR system, the proposed approach ensures the security and privacy of both data and parameters during transmission and processing. Experimental results demonstrate that the dual differential privacy protection effectively safeguards data while providing accurate parameter estimation, validating the effectiveness of the proposed scheme.

Let $\vec{G}$ be a finite simple directed graph with $n$ vertices, and let $\Gamma$ be a finite abelian group of order $n$. A $\Gamma$-distance magic labeling is a bijection $\phi : V(\vec{G}) \to \Gamma$ for which there exists $c \in \Gamma$ such that $\sum_{y \in N^+(x)} \phi(y) - \sum_{y \in N^-(x)} \phi(y) = c$ for any $x \in V(\vec{G})$, where $N^+(x)$ and $N^-(x)$ denote the set of the head and the tail of $x$, respectively. In this paper, we obtain a necessary and sufficient condition for that there exists a $\Gamma$-distance magic labeling for the Cartesian products of two directed cycles.

In this paper, we study the solvability of positive solutions for a Caputo-type fractional- order Riemann-Stieltjes integral boundary value problem. Under some monotonicity conditions for the nonlinearity, we use the upper-lower solution method to obtain two existence theorems.

The purpose of image fusion is to combine information from different source images to produce a comprehensively representative image. Traditional autoencoder architectures often struggle to effectively extract both unique and shared features from these image types. A novel two-stage three-branch feature extraction method (TSTBFuse) was proposed in the study, specialized for the fusion of infrared and visible images. The proposed architecture employed a three-branch encoder that separately captured infrared-specific thermal radiation features, visible-specific texture details, and shared structural information. A two-stage end-to-end training strategy was introduced: the first stage focused on reconstructing the original input images to preserve modality-specific information, while the second stage leveraged the learned representations to generate high-quality fused images. we designed a comprehensive loss function combining mean squared error (MSE), structural similarity index (SSIM), and gradient loss, ensuring both pixel-level accuracy and structural integrity. Extensive experiments on public datasets (TNO, MSRS and RoadScene) demonstrated that TSTBFuse consistently outperformed seven state-of-the-art methods in both subjective and objective evaluations. Furthermore, the method exhibited strong generalization capabilities, successfully extending to challenging tasks such as magnetic resonance imaging-computed tomography (MRI-CT) medical image fusion and red-green-blue (RGB)-infrared image fusion without retraining. The code is publicly available at: https://github.com/QXinYue/TSTBFuse.