Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability inequalities. This fills a significant theoretical gap in the previous work [Comput. Math. Appl. 103 (2021) 1-11], which provided error estimates based on a conjecture on

The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with Lévy jump (SFDVI with Lévy jump) under some mild conditions. We verify that Mosco convergence of the perturbed set implies point convergence of the projection onto the Hilbert space consisting of special stochastic processes whose range is the perturbed

The joined effects of syntrophic relationship and substrate inhibition are considered in a diffusive model of the anaerobic digestion process. We first establish the existence and structure of coexistence solutions for the system in different growth rate parameter ranges. Numerical results suggest that the coexistence solutions of the system undergo double bifurcation in the suitable range of growth

In this article, we present a numerical scheme for solving a time-fractional stochastic Cahn–Hilliard equation driven by an additive fractionally integrated Gaussian noise. The model involves a Caputo fractional derivative in time of order α∈(0,1) and a fractional time-integral noise of order γ∈[0,1]. Our numerical approach combines a piecewise linear finite element method in space with a convolution

In modern engineering practice, there is a steady increase in the need for multi-dimensional global approximations of complex black-box functions involved in today's engineering design problems. Metamodels have been proved to be effective alternatives for analyzing and predicting highly complex original models at a lower computational cost. The Kriging model is valued for its ability to predict the

Classical spectral methods are confined to numerically solving Fredholm integro-differential equations in regular domains, such as rectangles and discs. This paper aims to numerically address two-dimensional Fredholm integro-differential equations in complex geometries by combining spectral methods with mapping techniques. Initially, we transform the computational domain into a rectangular one via

Fractional-order derivative-based modeling is crucial for describing real-world forecasting problems and analyzing proposed models. It provides an advanced framework for examining intricate variations in various systems, enhancing understanding and analysis. We present a new fractional order nonlinear model for dynamics and forecasting of nitrogen oxides (NOx) and ozone (O3) in the atmosphere, crucial

This paper explores the spatiotemporal dynamics of a three-component predator–prey model with prey-taxis. We mainly show the existence of the steady state bifurcation and the bifurcating solution. Of most interesting discovery is that only the repulsive type prey-taxis could establish the existence of the steady state bifurcation and spatial pattern formation of the system. There are no steady state

This study is devoted to the inverse spectral problems of the Sturm-Liouville operator with many frozen arguments. Under certain assumptions, the authors obtained the uniqueness theorems for recovering the operator from one spectrum. Finally, a numerical simulation of the inverse problem is given.

The main purpose of this study is to develop a numerical model of unsaturated flow in soils with plant root water uptake. The Richards equation and different sink term formulations are used in the numerical model to describe the distribution of soil moisture in the root zone. The Kirchhoff transformed Richards equation is used and the Gardner model is considered for capillary pressure. In the proposed

Systemic risks do not arise only as a result of a crisis event, and it is important to understand the ex-ante risk contagion mechanisms. There has been no research on ex-ante contagion valuation and contagion modeling of multilayer networks. This study proposes the ex-ante-contagion mechanism of a two-layer network financial system with interbank lending connections and cross-holding connections, constructs

This paper introduces balanced implicit two-step Maruyama methods for solving Itô stochastic differential equations. Such methods, compared to those corresponding standard linear two-step Maruyama methods, have better mean-square properties, which is confirmed by a comparison of the stability regions for some particular two-step Maruyama methods. Moreover, the convergence order is investigated which

This paper presents a high-precision numerical method based on spectral deferred correction (SDC) for solving the time-fractional Allen-Cahn equation. In the temporal direction, we establish a stabilized variable-step L1 semi-implicit scheme which satisfies the discrete variational energy dissipation law and the maximum principle. Through theoretical analysis, we prove that this numerical scheme is

The high-order gas-kinetic scheme (HGKS) with WENO spatial reconstruction method has been extensively validated through numerous numerical experiments, demonstrating its superior accuracy, efficiency and robustness. In comparison to WENO class schemes, TENO class schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. This paper introduces two

Isogeometric Analysis (IgA) is a spline-based approach to the numerical solution of partial differential equations. The concept of IgA was designed to address two major issues. The first issue is the exact representation of domains generated from Computer-Aided Design (CAD) software. In practice, this can be realized only with multi-patch IgA, often in combination with trimming or similar techniques

The conventional finite element method (FEM) usually fails to generate sufficiently fine numerical solutions in the analyses of Mageto-electro-elastic (MEE) structures in which three different types of physical fields are coupled together. To enhance the performance of the FEM in analyzing MEE structures, in this work a novel overlapping triangular finite element is introduced for dynamic analysis

This paper presents an effective nonlocal finite element method (FEM) for investigating the free vibration behavior of sigmoid functionally graded material (S-FGM) nanoshells using nonlocal elasticity theory. The effective nonlocal parameters via third-order shear deformation theory (TSDT) are varied along the thickness of the nanoshells following the sigmoid function. In this study, two different

Linear and nonlinear vibration absorbers are employed to achieve rapid and effective suppression of the induced vibration into structural dynamical systems to protect their structural integrity and to avoid human and economic losses. The majority of considered high performance vibration absorbers in the literature are still not capable to achieve complete vibration suppression during the first cycle

In this paper, a novel type of fractional complex networks with unbounded coupling delays (FCNUCD) is investigated. The adaptive feedback control strategy is proposed to achieve the leader-following synchronization of the FCNUCD. The leaderless synchronization of the FCNUCD is also achieved by employing the edge-based adaptive control strategy. Furthermore, a new mixed adjustment rule is proposed in

A significant limitation of conventional risk theory models in insurance is the explicit assumption that different lines of insurance business operations are uncorrelated. This paper addresses this limitation by introducing a novel multivariate size-dependent renewal risk model. The authors adopt a t-copula-based approach to model dependence structures between different types of claims, allowing for

Nonlinear energy sinks (NESs) have received widespread attention due to their broadband vibration absorption ability. This study investigates the vibration suppression of a double-cable beam structure by NES. Firstly, a mechanical model of the double cable-beam-NES structure was established, and the Hamilton principle was used to derive the motion partial differential equation of the double cable-beam-NES

This paper is concerned with the retarded reaction–diffusion equation ∂tu−Δu=f(u)+G(t,ut)+h(x) in a bounded domain. We allow both the nonlinear terms f and G to be supercritical, in which case the solutions may blow up in finite time, making it difficult to obtain global estimates. Here we employ some appropriate structure conditions to deal with this problem. In particular, we establish detailed global

In this paper, we study a posteriori error estimates of the fast L1−2 scheme for time discretization of time fractional parabolic differential equations. To overcome the huge workload caused by the nonlocality of fractional derivative, a fast algorithm is applied to the construction of the L1−2 scheme. Employing the numerical solution obtained by the fast L1−2 scheme, a piecewise continuous function

We study the numerical evaluation of the integral fractional Laplacian and its application in solving fractional diffusion equations. We derive a pseudo-spectral formula for the integral fractional Laplacian operator based on fractional order-dependent, generalized multi-quadratic radial basis functions (RBFs) to address efficient computation of the hyper-singular integral. We apply the proposed formula

Density functional theory calculations involve complex nonlinear models that require iterative algorithms to obtain approximate solutions. The number of iterations directly affects the computational efficiency of the iterative algorithms. However, for complex molecular systems, classical self-consistent field iterations either do not converge, or converge slowly. To improve the efficiency of self-consistent

A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called “Mean Field Games System” (MFGS), which is derived in the mean field games (MFG) theory. This theory has numerous applications in social sciences. The topic of Coefficient Inverse Problems (CIPs) in the MFG theory is in its infant age, both in

Without imposing light-tailed noise assumptions, we prove that Tikhonov regularization for Gaussian Empirical Gain Maximization (EGM) in a reproducing kernel Hilbert space is consistent and further establish its fast exponential type convergence rates. In the literature, Gaussian EGM was proposed in various contexts to tackle robust estimation problems and has been applied extensively in a great variety

In this paper, the issue of tracking control for nonlinear systems under external disturbances and asymmetric states-time-related full-state constraints imposed dynamically is studied. An adaptive fuzzy command filtered control method is developed. Firstly, the nonlinear nonstrict feedback system subjected to unknown disturbances and dynamic full-state constraints is modeled. Then, a fuzzy state observer

An important theorem about the spectral Turán problem of Ka,b was largely developed in separate papers. Recently it was completely resolved by Zhai and Lin [J. Comb. Theory, Ser. B 157 (2022) 184-215], which also confirms a conjecture proposed by Tait [J. Comb. Theory, Ser. A 166 (2019) 42-58]. Here, the prior work is fully stated, and then generalized with a self-contained proof. The more complete

The main contribution of this manuscript is to introduce to the scientific community the concept of maximally efficient damped composed Newton-type method and the design of two schemes of this class of orders four and six. It is obtained from a different and new extension of the vectorial optimal fourth-order Ermakov's Hyperfamily, in the sense of Cordero-Torregrosa conjecture. We call this class biparametric

Nowadays, pipelines are often used in marine engineering to effectively transport oil and natural gas due to their good continuity and high efficiency. However, the unwanted dynamics of the pipelines caused by the interaction between the external environment and internal fluid pipelines may affect their normal operation and service life. In the paper, we present a fiber-reinforced composite pipeline

The goal of this paper is to study an abstract system of nonlinear differential hemivariational inequality, which consists of nonlinear differential inclusions and evolutionary hemivariational inequalities with doubly nonlinear function. The differential inclusion is also driver by time dependent maximal monotone operators with nonlinear perturbations. Firstly, the discrete iterative problems are constructed

Deterministic growth laws, expressed by first order differential equations with time-depending intrinsic growth intensity function, are initially introduced. Such equations are then parameterized in a way to allow random fluctuations of the intrinsic growth intensity function. This procedure leads to time-inhomogeneous diffusion processes for which a detailed study of transition probability density

In this paper, we present a quadrature formula on triangular domains based on a set of simplex points. This formula is defined via the constrained mock-Waldron least squares approximation. Numerical experiments validate the effectiveness of the proposed method.

The paper develops the essentially optimal sparse tensor product finite element method for solving two scale elliptic and parabolic problems in a domain D⊂Rd, d=2,3, which is embedded with a periodic array of inclusions of microscopic sizes and spacing. The two scale coefficient is thus discontinuous in the fast variable. We obtain approximations for the solution of the homogenized equation and the

This paper considers the oscillatory flow of the Oldroyd-B fluid in a tube with a right triangular cross-section. The partial differential equation for describing the unidirectional flow of Oldroyd-B fluid is derived. For treating the triangular region, the unstructured mesh finite element method is applied. For verifying the accuracy of the finite element method, the source term is introduced and

In this paper we prove some Lp-type Heisenberg-Pauli-Weyl uncertainty principles for complex signals with respect to fractional Fourier transform, 1≤p≤2. We also discuss the effect of shifting and scaling on the uncertainty principles. Moreover, some numerical simulations are given to demonstrate our results.

In this paper, we introduce a high-precision Hermite neural network solver which employs Hermite interpolation technique to construct high-order explicit approximation schemes for fractional derivatives. By automatically satisfying the initial conditions, the construction process of the objective function is simplified, thereby reducing the complexity of the solution. Our neural networks are trained

In this paper, we focus on numerical approximations of Piecewise Diffusion Markov Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our approach is based on the thinning method for modelling the jump mechanism and combines the Euler-Maruyama scheme to approximate the underlying flow dynamics. For the proposed approximation schemes, we study both the mean-square and weak

In this paper, an online policy iteration algorithm is adopted to solve the linear quadratic tracking control problem for a class of partially unknown Markov jump singular interconnected systems. Firstly, due to the singular systems consisting of dynamic parts and static parts, Markov jump singular interconnected systems can be described as regular systems composed of dynamic parts by utilizing a linear

Image inpainting is a technique that utilizes information from surrounding areas to restore damaged or missing parts. To achieve binary image inpainting with mathematical tools and numerical techniques, an effective mathematical model and an efficient, stable numerical solver are essential. This work aims to propose a practical and unconditionally stable numerical algorithm for image inpainting. A

We study controllability and observability concepts of tempered fractional linear systems in the Caputo sense. First, we formulate a solution for the class of tempered systems under investigation by means of the Laplace transform method. Then, we derive necessary and sufficient conditions for the controllability, as well as for the observability, in terms of the Gramian controllability matrix and the

The primary purpose of this work is to consider a (2+1)-dimensional generalized KP equation via ∂̄-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the ∂̄ derivative, a ∂̄ problem arises naturally. Based on the symmetry of the Green

Cubature, i.e. multivariate numerical integration, plays a core part in the finite-element method. For a given element geometry and interpolation, it is possible to choose different cubature rules, leading to concepts like full and reduced integration. These cubature rules are usually chosen from a rather small set of existing rules, which were not specifically derived for finite-element applications

This paper proposes a numerical method for solving the time-fractional Stokes-Darcy problem using a partitioned time stepping algorithm with the Beavers-Joseph-Saffman condition. The stability of the method is established under a moderate time step restriction, τ≤C where C represents physical parameters, by utilizing a discrete fractional Gronwall type inequality. Additionally, error estimates are

We are interested in the following problem Δ2u+λu=g(u)inRN,∫RN|u|2dx=c,where N≥5, c>0 and λ∈R appears as a Lagrange multiplier. When g(u) satisfies a class of general mass supercritical conditions, we introduce one more constraint and consider the corresponding infimum. After showing that the new constraint is natural and verifying the compactness of the minimizing sequence, we obtain the existence

Existing studies have shown that asymptomatic cases might be related to short-term immunity on a timescale of weeks to months, which could have a significant impact on cholera epidemic transmission. In this paper, we are concerned with the global dynamical behavior of a cholera model with temporary immunity, which is characterized by discrete delay. The basic reproduction number of the model and the

In this paper, we establish the global stability of the spatially nonhomogeneous steady state solution of a reaction diffusion equation with nonlocal delay under the Dirichlet boundary condition. To achieve this, we obtain the global existence and nonnegativity of solutions and give an extensive study on the properties of omega limit sets.

Matrix completion is a challenging problem in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. The information on the coupling between the three channels of the color image is better utilized since the color image is treated as a whole. Due to this, researcher interest in low-rank quaternion matrix completion (LRQMC) algorithms

Let G be a graph and X⊆V(G). Then, vertices x and y of G are X-visible if there exists a shortest x,y-path where no internal vertices belong to X. The set X is a mutual-visibility set of G if every two vertices of X are X-visible, while X is a total mutual-visibility set if any two vertices from V(G) are X-visible. The cardinality of a largest mutual-visibility set (resp. total mutual-visibility set)

The partial differential equation describing equilibrium radiation diffusion is strongly nonlinear, which has been widely utilized in various fields such as astrophysics and others. The equilibrium radiation diffusion equation usually appears over multiple complicated domains, and the material characteristics vary between each domain. The diffusion coefficient near the interface is discontinuous. In

This work presents an accurate in-plane vibration analysis of functionally graded material (FGM) skew plates with elastically restrained boundaries using the variational differential quadrature method (VDQM). The weak form of the governing equations is derived by integrating two-dimensional elasticity theory with Hamilton's principle. The differential and integral operators are directly converted into

When can the input of a ReLU neural network be inferred from its output? In other words, when is the network injective? We consider a single layer, x↦ReLU(Wx), with a random Gaussian m×n matrix W, in a high-dimensional setting where n,m→∞. Recent work connects this problem to spherical integral geometry giving rise to a conjectured sharp injectivity threshold for α=m/n by studying the expected Euler

Recognizing the threshold dynamics of highly developed animals with memory is significant for the governance of species within a specific domain. To investigate how the memory threshold affects population behavior, we formulate a spatially heterogeneous predator-prey system with memory-based diffusion and hunting cooperation on predators. In homogeneous environments, the occurrence conditions of Turing

Strategy update rules play an important role in repeated Prisoner's Dilemma games. This work proposes a modified strategy update rule based on the traditional Fermi function, in which individual past performance is taken into account in strategy update. Then, the consistency aspiration α serves as a benchmark to measure an individual's past performance, and the past performance score is dynamically

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special cases. Therefore, the proposed method serves as a general framework that includes not only the classical and cubic RNMs but also a novel RNM with elastic net regularization

Let G be a graph and M⊆V(G). Vertices x,y∈M are M-visible if there exists a shortest x,y-path of G that does not pass through any vertex of M∖{x,y}. We say that M is a mutual-visibility set if each pair of vertices of M is M-visible, while the size of any largest mutual-visibility set of G is the mutual-visibility number of G. If some additional combinations for pairs of vertices x,y are required to

In the ecosystem, the chase of the predator with cooperation contributes to fear psychology in the prey, resulting in behavioral changes such as a decrease in the birth rate. We construct a spatially diffusive model with delay to investigate the combined perturbation of these factors. Initially, we establish the existence of positive solutions and examine the stability of steady-state solutions under

Understanding human responses to epidemic outbreaks—particularly to control measures such as vaccination—is essential for accurately modeling the complex interplay between epidemics and human behavior. Through the framework of evolutionary vaccination games, we explore how individuals' opinions influence vaccine uptake attitudes under imperfect vaccination and, in turn, how this affects to the spread

In the era of rapid development of the Internet, in order to reflect the evolution process of users' viewpoints on network relations, a Bayesian viewpoint evolution model based on Weibo data mining is proposed by studying the relationship between the viewpoints of the author and those of the forwarders on the Sina Weibo platform. Firstly, Python crawler technology was used to crawl the comments and