Image smoothing is a fundamental task in digital image processing with broad applications. However, traditional texture smoothing techniques often result in the loss or blurring of small structural information and contrast. In this paper, we introduce a piecewise gradient prior aimed at overcoming this drawback. The prior is based on a four-segment piecewise (FSP) penalty function, which can process

The current research introduces a new numerical iterative method that uses a quadrature formula and successive approximations to solve certain types of equations called nonlinear delay integral equations as Hammerstein Volterra type of the second kind. The convergence analysis and numerical stability of the method are also demonstrated. Additionally, by providing the numerical applications, we show

This study investigates the stabilization of generalized asynchronous Boolean control networks under noise interference. Firstly, it involves generalized asynchronous Boolean control networks unaffected by noise interference and extends the stabilization theorem of ordinary Boolean networks to them. Secondly, a theorem is provided to determine the stabilization of networks with noise interference.

The industry and investors are closely monitoring the valuation of research and development (R&D) projects related to new energy vehicles (NEVs) as their technology advances rapidly. However, standard techniques of valuation often fail to describe the full value of R&D initiatives in an uncertain market environment, due to the significant technical hazards and uncertain results associated with these

In this paper, a dual auxiliary systems-based fault-tolerant attitude turn-on/off trigger control problem is studied for the satellite. To address the flexible performance tracking control problem under any initial condition, a new prescribed performance function is designed. Furthermore, to improve the accuracy of satellite attitude tracking errors under the saturation and fault, a novel monitor auxiliary

Evolutionary games on networks often assume that individuals do not move and adopt a uniform strategy toward all neighbors. In reality, however, individuals can migrate to seek more favorable conditions and may act differently depending on whom they interact with. Here, we fill this gap by extending the spatial public goods game on a two-dimensional lattice to include both migration and node-dynamics-based

In this paper, we present an arbitrarily high-order numerical scheme for the two-component Camassa–Holm system, ensuring the preservation of three invariants: energy and two Casimir functions. The spatial discretization is achieved using Fourier–Galerkin methods, resulting in a semi-discrete system which retains a Hamiltonian structure and approximates the invariants of the original continuous system

In ecological and ecosystem studies, spatiotemporal distribution patterns are identified as crucial factors in maintaining species diversity. Specifically, spiral waves, which are a typical spatiotemporal pattern, are prevalent across various ecosystems, including both continuous and discrete-time systems. In continuous-time systems, spiral waves are commonly associated with Hopf bifurcations. This

This article is dedicated to developing a circulant and skew-circulant splitting (CSCS) iterative method for addressing a specific class of diagonal-plus-asymmetric Toeplitz systems. Theoretically, we have analyzed that the spectral radius of the convergence factor of the proposed CSCS iterative method is strictly less than 1, which implies the unconditional convergence of the proposed iterative method

This short article studies a deterministic quasi-Monte Carlo lattice rule in weighted unanchored Sobolev spaces of smoothness 1. Building on the error analysis by Kazashi and Sloan, we prove the existence of unshifted rank-1 lattice rules that achieve a worst-case error of O(n−1/4(logn)1/2), with the implied constant independent of the dimension, under certain summability conditions on the weights

In this paper, a reaction–diffusion-advection model with nonlinear boundary conditions arising from algae species is investigated. By employing the super-sub solution method, we not only establish the existence of global solutions, but also obtain the existence and global asymptotical stability of positive steady-state solutions. It is observed that the positive steady-state solution is decreasing

This study explores the use of r-adaptive mesh refinement strategies for elliptic partial differential equations (PDEs) posed on non-convex domains. We introduce an r-adaptive strategy based on a simplified optimal transport method to create a graded mesh, distributing the interpolation error evenly, considering the solution's local asymptotic behaviour. The grading ensures good mesh compression and

In this paper, we explore a class of time-dependent mixed quasi-variational-hemivariational inequality problems (TMQVHVI), which are characterized by the dependence of their constraint set on the solutions. We prove a solvability result for TMQVHVI by using a static mixed quasi-variational–hemivariational inequality and a measurable selection lemma. And, moreover, the boundedness and closedness of

We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in game theory, mathematical biology and machine learning. If one parameter is a rational number, k/n, with k,n coprime, and the second one is large enough, we prove

The Local Randomized Neural Networks with Discontinuous Galerkin (LRNN-DG) methods, introduced in Sun et al. (2024), were originally designed for solving linear partial differential equations. In this paper, we extend the LRNN-DG methods to solve nonlinear PDEs, specifically the Korteweg–de Vries (KdV) equation and the Burgers equation, utilizing a space–time approach. Additionally, we introduce adaptive

The wide class of nonlinear Schrödinger equation of the general form is studied. These nonlinear partial differential equations, depending on arbitrary functions, are not integrable by the inverse scattering transform but have exact solutions. The approach is proposed that makes it possible to find nonlinear Schrodinger equations of the general form that have exact solutions. This approach is that

The basic hyperbolic–elliptic black-oil model describes oil–water displacement in a porous medium. Given its mathematical complexity, there is a need for particular simple solutions for validation of numerical methods. We present a class of stationary solutions, which are easy to compute, and in many cases are given by explicit formulae. These solutions are constructed by a nonlinear coupling of two

In order to improve the convergence speed of the fixed point iteration method, inspired by Li and Li (2023) , we add a scaling matrix to the fixed point method and construct a new two-step fixed point iteration (NTFPI) method to solve the tensor absolute value equation and analyze the convergence of the NTFPI method. Finally, two numerical examples are given to illustrate the feasibility and effectiveness

In general, individuals with high reputation often leverage greater access to resources, influence, and opportunities, creating a differential advantage in societal hierarchies. Meanwhile, real legal systems impose stricter punishments on severe crimes to ensure proportional justice. In some social contexts, individuals who engage in punishment behavior may be perceived as more trustworthy or committed

To achieve common goals, we often use joint commitments. Our commitment helps us to coordinate with our partners and assures them that their cooperative efforts will benefit themselves. However, if one of us can exploit the other's cooperation (as in the Prisoner's Dilemma), our commitment appears less useful. It cannot remove the temptation for our partners to exploit us. Using methods from evolutionary

This paper introduces a novel varying-coefficient autoregressive model that includes an explanatory variable and a non-stationary state equation to analyze and predict complex time series data. The model incorporates a function that evolves over time, which provides a sophisticated understanding for analyzing data with nonlinear and non-stationary characteristics. Some key statistical properties of

This paper deals with an intergenerational utility maximization problem for consuming a naturally exhaustible resource. In this context, we are at odds with the unfair standard procedure of applying a time-dependent factor for discounting the utility and introducing a suitable function for penalizing overconsumption. A finite-time horizon dynamic stochastic optimization problem is presented to achieve

The Maxwell–Landau–Lifshitz equation with spin accumulation is studied in the paper. We prove the existence and uniqueness of global solutions using energy estimates method in two-dimensional space.

This work aims to construct an efficient and highly accurate numerical method to address the time singularity at t=0 involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The L2-1σ scheme is used to discretize the time-fractional operator, whereas a modified version of the composite trapezoidal approximation is employed to discretize the

Via introducing the Robin flux jump into the Galerkin scheme, this paper develops a new anisotropic trilinear immersed finite element (IFE) method for solving the magnetized plasma diffusion problem with plasma sheath interface condition under Cartesian meshes. The three-dimensional (3D) diffusion process of magnetized plasma is anisotropic and highly sensitive to magnetic fields, making it difficult

In this work, we deal with an inverse source problem for a general transport equation. First, we discuss the solvability of the problem. Next, in order to solve the problem, we propose a new hybrid numerical algorithm which is based on the finite difference method, Newton-Cotes formula, Lagrange polynomial approximation and composite trapezoidal rule. The proposed method is tested on several examples

We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional Laplacian as the exponent s→0+). Our analysis exhibits new phenomena in this setting; in particular, using recently obtained regularity results, we prove rigorous error

We discuss the synchronization control problem for a network of Euler–Bernoulli beam equations with freedom at both ends and time-varying disturbances at the boundary. First, we present the aim of the control of this paper. Next, the reference signal is provided, allowing us to transform the control objective into a form that includes the virtual reference signal. Then, by the method of active disturbance

In this study, we introduce two recent algorithms designed to solve the split variational inclusion problem in Banach spaces by using two inertial extrapolations and self-adaptive step size technique. Theoretical analysis demonstrates that the inertial Mann-type self-adaptive algorithm (IMSA) and the inertial Halpern-type self-adaptive algorithm (IHSA) generate strong convergence under the specified

This paper studies the asynchronous double-source bumpless transfer (BT) finite-time secure control issue for stochastic hidden semi-Markovian jump systems (HSMJSs) with Brownian noise. The HSMJS is assumed to suffer from deception attacks governed by Bernoulli variables, which occur randomly in both sensor-controller (SC) and controller-actuator (CA) channels. Firstly, a hidden semi-Markovian model

In this research, we mainly utilize the stationary iteration method in conjunction with Krylov subspace techniques, such as GMRES, to tackle the large indefinite least squares problem. To accomplish this, the normal equation of the large indefinite least squares problem is firstly transformed into the sparse block three-by-three linear systems with non-singular diagonal blocks, then a block upper triangular

Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently finite and smooth at the disc center (r=0), ensuring continuous differentiability along the axis. This property makes them particularly suitable for simulations, requiring

Dynamic mode decomposition (DMD) algorithm is widely applied to identify the flow characteristics of fluid dynamic field. However, for high-dimensional viscoelastic fluid systems, DMD might often result in unsatisfactory performance because of its huge computation cost. Therefore, we propose an improved dynamic mode decomposition algorithm, called sparsity promoting randomized dynamic mode decomposition

The use of conventional cubic nonlinear energy sink (NES) to mitigate vortex-induced vibrations has been widely investigated. Recently, bistable NES (BNES) has gained considerable attention owing to its ability to execute large amplitude inter-well motion and thus enhance energy transfer. But, the efficacy of BNES to mitigate self-excited vibrations in general and vortex-induced self-excited vibrations

This work presents a systematic characterization of the quasi-periodic dynamics of a uniaxial anisotropic magnetic nanoparticle under the influence of a time-varying external magnetic field. Using the Landau–Lifshitz–Gilbert (LLG) formalism, we analyze the response of the system as a function of key parameters, particularly focusing on the effects of magnetic anisotropy and dissipation. Through an

The exponential stability of the Caputo fractional order impulsive switched system (CFOISS) consisting of stable and unstable subsystems is addressed in this paper. We integrate the multiple Lyapunov function (MLFs) approach, the mode-dependent average dwell time (MDADT) method, and the fast-slow switching concept to handle the switched sequence. In order to better represent the impulse, we further

In this paper, a Nitsche's extended nonconforming virtual element method is presented to discretize biharmonic PDEs involving interfaces with a more general interface condition. By introducing some special terms on cut edges and uncut edges of interface elements, we prove the well-posedness and optimal convergence, which are independent of the location of the interface relative to the mesh and the

A novel adaptive multi-patch isogeometric approach based on truncated hierarchical NURBS (TH-NURBS) is proposed for modeling three-dimensional elasticity. The TH-NURBS are rational extension of truncated hierarchical B-splines (THB-splines) and the salient feature of the TH-NURBS is that it can exactly model complex-shaped geometries. Owing to the properties of local refinement, partition-of-unity

The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests the development of a versatile non-intrusive a posteriori error estimator. In this paper, we present a systematic approach for applying the least-squares functional

The paper compares standard iterative methods for solving the generalized Stokes problem arising from the time and space approximation of the time-dependent incompressible Navier-Stokes equations. Various preconditioning techniques are considered: (1) pressure Schur complement; (2) fully coupled system using an exact factorization as a basis for the preconditioner; (3) fully coupled system using norm

The paper is devoted to address the numerical preservation of the exponential mean-square contractive character of the dynamics of stochastic differential equations (SDEs), whose drift and diffusion coefficients are subject to non-global Lipschitz assumptions. The conservative attitude of stochastic θ-methods is analyzed both for Itô and Stratonovich SDEs. The case of systems with linear drift is also

In Wu et al. (2021), Wu et al. studied an SIR epidemic model incorporating infection–age structure and spatial diffusion. It focused on the existence of traveling wave solutions when the diffusion coefficients met a technical condition (i.e., d3≤2d2). Moreover, the question of the existence of traveling wave solutions with c=c∗ remains open. This paper employs an approach rooted in the Schauder’s fixed-point

In this work, a new QGCD iterative algorithm is presented for finding the solution of a class of quaternion matrix equation. It is proved that if the studied quaternion matrix equation is consistent, the constructed algorithm can obtain the solution within finite iterative steps in the absence of round-off errors. Moreover, if the investigated quaternion matrix equation is inconsistent, the constructed

This work presents a novel class of balanced Euler methods designed for approximating stochastic Volterra integral equations. These methods aim to address certain numerical instabilities commonly encountered with the explicit Euler approach. The study derives the convergence order and stability characteristics of the proposed schemes in the mean-square sense. Additionally, a comprehensive analytical

This work addresses the inverse problem of recovering the time-varying fractional order α(t) in a time-fractional diffusion equation, motivated by applications in subsurface flows and shale gas extraction. The fractional order α(t) plays a crucial role in modeling anomalous diffusion processes, such as those observed in complex geological formations. Prior to developing the reconstruction method, the

Based on the block Jacobi splitting, a kind of greedy partial block Jacobi (GPBJ) iteration method is constructed by greedily selecting the blocks with relatively large residuals and performing the block Jacobi iteration on the selected blocks. Theoretical analysis demonstrates that the GPBJ iteration is unconditionally convergent if the coefficient matrix of the linear system is H-matrix. Then combining

The generalization capability of Graph Convolutional Networks (GCNs) has been researched recently. The generalization error bound based on algorithmic stability is obtained for various structures of GCN. However, the generalization error bound computed by this method increases rapidly during the iteration since the algorithmic stability exponential depends on the number of iterations, which is not

For a graph G, the general Sombor (SOα) index is defined as:SOα(G)=∑vivj∈E(G)(di2+dj2)α, where α≠0 is a real number, E(G) is the edge set and di denotes the degree of a vertex vi in G. A chemical tree is a tree in which no vertex has a degree greater than 4, and a pendant vertex is a vertex with degree 1. This paper aims to completely characterize the n− vertex chemical trees with a fixed number of

Arbitrarily partitionable (AP) graphs are graphs that can have their vertices partitioned into arbitrarily many parts inducing connected graphs of arbitrary orders. Since their introduction, several aspects of AP graphs have been investigated in literature, including structural and algorithmic aspects, their connections with other fundamental notions of graph theory, and variants of the original notion

A novel high-order numerical method, specifically designed to preserve the mass and energy invariants of the coupled nonlinear Schrödinger equation (CNLS) is introduced. This algorithm integrates Gauss collocation schemes for temporal discretization with finite element methods for spatial discretization, enhanced by a post-processing correction procedure that ensures mass and energy conservation at

This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal decomposition have been widely investigated in the literature, but they usually rely on some a-priori knowledge about the bifurcating model and lack any error estimation

Metric dimension is a valuable parameter that helps address problems related to network design, localization, and information retrieval by identifying the minimum number of landmarks required to uniquely determine distances between vertices in a graph. Generalized Sierpiński graphs represent a captivating class of fractal-inspired networks that have gained prominence in various scientific disciplines

This study presents an efficient class of fourth-order iterative methods introduced by Ali Zein (2024) in a more abstract Banach space setting. The Convergence Order of this class is proved by bypassing the Taylor expansion. We use the mean value theorem and relax the differentiability assumptions of the involved function. At the outset, we provide a semilocal analysis, and then, using the results

This article proposes and analyzes fast and precise numerical methods for calculating the Bessel integral, which exhibits rapid oscillations and includes algebraic and Cauchy singularities. When a>0, we utilize the numerical steepest descent method with the Gauss-Laguerre quadrature formula to solve it. If a=0, we partition the integral into two parts, solving each part using the modified Filon-type

Individuals frequently engage in a multitude of concurrent games. Owing to the complexity of the interactions and the inherent diversity in players' preferences, this paper introduces a multi-issue game model tailored for structured populations characterized by heterogeneous preferences. The model incorporates several dimensions of preference diversity, including the relative weight accorded to different

This paper delves into the network security issues of cyber–physical systems (CPSs), where malicious agents can launch distributed denial-of service (DDoS) attacks to disrupt communication channels between sensors and remote estimator. Addressing the strategic interaction between defenders and DDoS attacker, we establish a two-player zero-sum stochastic game framework that portrays the interaction

In this paper, we propose a method of the mixture-of-experts (MoE) model embedded with physics-informed neural networks (PINNs) for the hyperbolic conservation laws. The issue on solving hyperbolic conservation laws with PINNs is still challenging since the solutions of conservation laws may contain discontinuities. PINNs, as functional approximators, nearly fail in such cases, and numerical solutions

The objective of this paper is to investigate mixed set-valued stochastic differential equations with fractional Brownian motion, where the diffusion term is also set-valued. Under the non-Lipschitz continuity conditions, firstly, some new and reliable lemmas about the set-valued stochastic integral are provided. Secondly, we justify the existence and uniqueness of solutions to considered equations

This paper establishes an AIDS model that includes both asymptomatic and symptomatic infected individuals, and we assume the transmission rate follows the log-normal Ornstein–Uhlenbeck process, which allows us to develop a stochastic model. For the stochastic model, by constructing appropriate Lyapunov functions, we derive the disease will extinct when R0e<1. The critical value R0s>1 for existence

The accurate thermal analysis of composite structures remains a challenging issue due to complicated multiscale configurations and nonlinear temperature-dependent behaviors. This work offers a novel higher-order three-scale asymptotic (HOTSA) model and corresponding numerical algorithm for accurately and efficiently simulating transient nonlinear thermal conduction problems of heterogeneous structures