In this paper, which can be considered as an extension of our previous publication (Liu and Yu in Fract Calc Appl Anal 25:2040-2061, 2022) in same journal, we analyze the stability and synchronization for the discrete fractional-order neural network systems with mixed time delays. By new techniques, we give the proof of the discrete fractional-order Halanay inequality with mixed time delays, which

In this work, we are interested in a class of numerical schemes for certain phase field models. It is well known that unconditional energy stability (energy decays in time regardless of the size of the time step) provides a fidelity check in practical numerical simulations. In recent work (Li, D. (2022b, Why large time-stepping methods for the Cahn–Hilliard equation is stable. Math. Comp., 91, 2501–2515))

In‐situ stress condition is an important aspect of buried unpressurized pipelines. Empirical approaches used for preliminary design are usually based on observations, which may be associated with some errors related to the measurement method. The photoelastic approach represents an alternative, nonintrusive measurement technique to model the plane stress‐strain behavior of buried pipes under different

We consider a p-fractional Choquard-type equation $$\begin{aligned} (-\varDelta )_p^s u+a|u|^{p-2}u=b(K*F(u))F'(u)+\varepsilon _g |u|^{p_g-2}u \quad \text {in } \mathbb {R}^N, \end{aligned}$$ where \(0

We are concerned with a space-time fractional parabolic initial-boundary value problem of Sturm-Liouville type in a general star graph with mixed Dirichlet and Neumann boundary controls. We first give several existence, uniqueness and regularity results of weak and very-weak solutions. Using the notion of no-regret control introduced by Lions, we prove the existence, uniqueness, and characterize the

To better understand the strain‐softening effect and its implications for coal construction and extraction, this paper utilizes a numerical simulation method to investigate the deformation stability of gas extraction holes with consideration for strain softening. The study further analyzes the strain‐softening effect on effective stress, gas pressure, and plastic failure mode by comparing models with

We construct and analyse finite element approximations of the Einstein tensor in dimension $N \ge 3$. We focus on the setting where a smooth Riemannian metric tensor $g$ on a polyhedral domain $\varOmega \subset \mathbb{R}^{N}$ has been approximated by a piecewise polynomial metric $g_{h}$ on a simplicial triangulation $\mathcal{T}$ of $\varOmega $ having maximum element diameter $h$. We assume that

Optimal-order convergence in the $H^{1}$ norm is proved for an arbitrary Lagrangian–Eulerian (ALE) interface tracking finite element method (FEM) for the sharp interface model of two-phase Navier–Stokes flow without surface tension, using high-order curved evolving mesh. In this method, the interfacial mesh points move with the fluid’s velocity to track the sharp interface between two phases of the

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 619-640, April 2025. Abstract. Mesh quality is crucial in the simulation of surface evolution equations using parametric finite element methods (FEMs). Energy-diminishing schemes may fail even when the surface remains smooth due to poor mesh distribution. In this paper, we aim to develop mesh-preserving and energy-stable parametric finite

In seismic tunnel lining design, most existing studies have focused on circular and box‐type tunnels, while the response of subrectangular tunnel linings under seismic loading, especially in imperfect soil‐lining conditions, remains underexplored. The present paper aims to address this gap by investigating the behavior of subrectangular tunnel lining subjected to seismic loadings in full‐slip condition

Explicit strategies for shell dynamics are presented using 7-parameter shell elements and the Central Difference scheme. The formulation of the 7-parameter shell element is based on the widely used Enhanced Assumed Strain (EAS), allowing the use of a 3D constitutive law in the shell element without the need to condense the transverse normal stress component in the material law. The 7-parameter shell

We introduce a novel class of stochastic partial differential equations (SPDEs) driven by space-only fractional Lévy noise. In contrast to the prevalent focus on space-time noise in the existing literature, our work explores the unique challenges and opportunities presented by purely spatial perturbations. We establish the existence and uniqueness of the solution to the stochastic heat equation by

We introduce an efficient discretisation of a novel fractional-order adaptive exponential (FrAdEx) integrate-and-fire model, which is used to study the fractional-order dynamics of neuronal activities. The discretisation is based on an extension of L1-type methods that can accurately handle exponential growth and the spiking mechanism of the model. This new method is implicit and uses adaptive time

In this paper, we investigate various classes of the abstract multi-term fractional difference equations and the abstract higher-order difference equations with integer order derivatives. The abstract difference equations under our consideration can be unsolvable with respect to the highest derivative. We use the Riemann-Liouville and Caputo fractional derivatives, provide some new applications of

In this article, we consider a multi-term \(\varphi \)-Caputo fractional dynamical system with non-instantaneous impulses. Firstly, we derive the solution for the linear \(\varphi \)-Caputo fractional differential equation by using the generalized Laplace transform. Then, some necessary and sufficient conditions have been examined for the controllability of the linear multi-term \(\varphi \)-Caputo

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the second-order total variation of each trainable activation. The slope constraints allow us to impose properties such as 1-Lipschitz stability, firm non-expansiveness

Deep learning still has drawbacks regarding trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obligations associated with trustworthiness have been proposed via regulatory guidelines, e.g., in the European AI Act. Therefore, a central question is to what extent trustworthy deep learning can be realized. Establishing the described

Temperature effects become important in a number of geotechnical applications, such as nuclear waste disposal facilities, buried high‐voltage cables, pavement, energy geostructures and geothermal energy. On the other hand, soft soils act time‐ and strain rate dependent. Both temperature and strain rate influence soil behavior, affecting stiffness, strength, and deformation even under constant stress

Complex Gaussian quadrature rules for oscillatory integral transforms have the advantage that they can achieve optimal asymptotic order. However, their existence for Hankel transform can only be guaranteed when the order of the transform belongs to $[0,1/2]$. In this paper we introduce a new family of Gaussian quadrature rules for Hankel transforms of integer order. We show that, if adding certain

The vibrational response of mechanical systems including four-point contact slewing bearings is heavily influenced by the stiffness and damping properties of the bearing joint itself. As an initial approach to study the dynamic response of these components, in this work several aspects are addressed. With a view toward dynamic modelling, first, a FE-based modification of the force-deflection Hertz

The fractional Laplacian and fractional gradient are operators which play fundamental role in modeling of anomalous diffusion in d-dimensional space with the fractional exponent \(\alpha \in (1,2)\). The principal-value integrals are split into singular and regular parts where we avoid using any weight function for the approximation in the singularity neighborhood. The resulting approximation coefficients

For an arbitrary given span of high dimensional multivariate Chebyshev polynomials, an approach to construct spatial discretizations is presented, i.e., the construction of a sampling set that allows for the unique reconstruction of each polynomial of this span.

In this paper, we study direct and inverse problems for Dirac systems with complex-valued potentials on p-star-shaped graphs. More precisely, we firstly obtain sharp 2-term asymptotics of the corresponding eigenvalues. We then formulate and address a Horváth-type theorem, specifically, if the potentials on p−1 edges of the p-star-shaped graph are predetermined, we demonstrate that the remaining potential

This paper presents a semi‐analytical method for the stress and displacement of a shallow buried lined tunnel based on the complex variable method under the full‐slip contact condition, that is, along the interface between the surrounding rock/soil mass and lining, the radial stresses and radial displacements are continuous, and the shear stresses are equal to zero. In the presented solution, the interaction

Let \(\{e^{-t{\mathcal {L}}^{\alpha }}\}_{t>0}\) be the heat semigroup related to the fractional Schrödinger operator \(\mathcal {L}^{\alpha }:=(-\varDelta +V)^{\alpha }\) with \(\alpha \in (0,1)\), where V is a non-negative potential belonging to the reverse Hölder class. In this paper, we analyze the convergence of the following type of the series $$\begin{aligned} T_{N,t}^{\alpha ,\beta }(f)=\sum

In this paper, we introduce a concept of the nth-level general fractional derivatives that combine the Djrbashian–Nersessian fractional derivatives and the general fractional derivatives with the Sonin kernels in one definition. Then some basic properties of these fractional derivatives including the fundamental theorems of fractional calculus and a formula for their Laplace transform are presented

This study examines the controllability criteria for linear and semilinear fractional dynamical systems with delays in both state and control variables in the framework of the Caputo fractional derivative. To establish the controllability criteria for linear fractional dynamical systems, the study derives necessary and sufficient conditions by employing the positive definiteness of the Grammian matrix

This study focuses on the existence, uniqueness, and quenching behavior of solution to the time-space fractional Kawarada problem, where the time derivative is the Caputo-Hadamard derivative and the spatial derivative is the fractional Laplacian. The mild solution represented by Fox H-function, based on the fundamental solution, is considered in space \(C\left( [a, T], L^r(\mathbb {R}^d)\right) \)

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 588-618, April 2025. Abstract. The multiscale hybrid-mixed (MHM) method for the Stokes operator was formally introduced in [R. Araya et al., Comput. Methods Appl. Mech. Engrg., 324, pp. 29–53, 2017] and numerically validated. The method has face degrees of freedom associated with multiscale basis functions computed from local Neumann problems

This paper provides an error estimate for the u-series method of the Coulomb interaction in molecular dynamics simulations. We show that the number of truncated Gaussians M in the u-series and the base of interpolation nodes b in the bilateral serial approximation are two key parameters for the algorithm accuracy, and that the errors converge as O(b−M) for the energy and O(b−3M) for the force. Error

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 564-587, April 2025. Abstract. In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for quasiperiodic systems with concentrated spectral point distribution. Based on the projection method (PM), IWFPM filters out dominant spectral points by defining an irrational window and uses a corresponding

In the construction process of the artificial ground freezing (AGF), the utilization of the temperature field to determine the freezing time is crucial for the safe construction. While the thermal parameter is the core parameter of the temperature field calculation. How to obtain the joint probability distribution of thermal parameters of frozen soil under limited test data is essential to improve

The utilization of cemented tailings backfill (CTB) presents distinct advantages in managing tailings and underground mining voids, occasionally incorporating coarse aggregate. In this study, the particle swarm optimization (PSO) algorithm was employed to optimize the extreme gradient boosting (XGBoost) model for predicting the unconfined compressive strength (UCS) of CTB containing coarse aggregate

Concrete piers located in steep mountainous regions are highly susceptible to damage from debris flows. Existing studies often oversimplify debris flows as particle flows or equivalent fluids, neglecting their multiphase characteristics. In this paper, a three‐dimensional numerical model of debris flow‐bridge piers interaction is established based on the coupled CFD‐DEM approach. The Hertz–Mindlin

We consider the numerical approximation for a class of radial Dunkl processes corresponding to arbitrary (reduced) root systems in $\mathbb{R}^{d}$. This class contains well-known processes such as Bessel processes, Dyson’s Brownian motions and square root of Wishart processes. We propose some semi-implicit and truncated Euler–Maruyama schemes for radial Dunkl processes and study their convergence

Annual precipitation and its intensity have increased worldwide since the start of the 20th century and represent two weather and climate change indicators related to rainfall‐induced landslides. Although these landslides can occur in a very short time, the hydro‐mechanical conditions that precede them can take several hours or days to develop. In this context, understanding the mechanisms of rainfall‐induced

With increasing mining depth, the mining methods for steeply inclined medium‐thick ore bodies have become unsuitable. In this paper, by integrating the roof‐pillar induced caving technology, through technical fusion and reconstruction, a combined mining method of roof‐pillar induced caving and non‐pillar sublevel caving has been formulated. The five core parameters of the combined mining method (the

This paper is concerned with the study of a poroelastic soil layer under impulsive horizontal loading. Building upon Biot's general theory of poroelasticity, a comprehensive set of governing equations addressing three‐dimensional transient wave propagation problem are established. Explicit general solutions for displacements and pore‐pressures are derived by employing a sophisticated mathematical approach

We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphism from an appropriately defined graph space to $L^{2}$. The results rely on well-posedness and stability of the weak and ultraweak formulation of the second-order wave equation. As an application, we define and analyze a space-time least-squares finite element method

We prove rigorous a-posteriori error estimates for first-order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dimension. Our estimators rely on recent stability results by Bressan, Chiri and Shen, a new way to localize residuals and a novel method to compute negative-order norms of these local residuals. Computing negative-order norms becomes possible

In this paper, we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method that is capable to capture properly the divergence at discrete level and the eigenvalues and eigenfunctions. Under the compact theory for operators, we prove convergence and

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 542-563, April 2025. Abstract. Efficient simulation of stochastic partial differential equations (SPDEs) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a semilinear stochastic reaction-advection-diffusion equation on a convex

We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressible Stokes equations. We propose a diffuse interface model in which a phase field function is used to write each integral in the weak formulation of the coupled problem on the entire domain containing both the Stokes and Biot

In Heimann, Lehrenfeld, and Preuß (2023, SIAM J. Sci. Comp., 45(2), B139–B165), new geometrically unfitted space–time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and time have been introduced. For geometrically higher-order accuracy a parametric mapping on a background space–time tensor-product mesh has been used. In this paper

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 520-541, April 2025. Abstract. Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank structure in the form of a sum of discrete multipole terms and continuum predictors

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 495-519, April 2025. Abstract. Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation

In this paper, we are concerned with 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems with Laplacian damping terms and nonlinear sources terms. The global well-posedness is proved by using the theory of maximal monotone operators. And then we get the Lipschtiz stability of the solution. By establishing the existence of pullback absorbing sets and pullback asymptotic compactness of the process

This article studies topological properties of the solution set for a class of Caputo fractional delayed evolution inclusions. Firstly, in the scenario when the cosine family is noncompact, the compactness and \(R_{\delta }\)-property are obtained for the mild solution set. Then, as an application of the above obtained results, the approximative controllability is demonstrated. Finally, an example

In this paper, we provide new multiplicity results for a class of impulsive fractional Schrödinger-Kirchhoff-type equations involving p-Laplacian and Riemann-Liouville derivatives. By using the variational method and critical point theory, we obtain that the impulsive fractional problem has infinitely many solutions under appropriate hypotheses when the parameter \(\lambda \) lies in different intervals

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 469-494, April 2025. Abstract. In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde matrix is smaller than the reciprocal of machine epsilon. This leads to a practical algorithm for piecewise polynomial interpolation

We introduce the definition of tensorized block rational Krylov subspace and its relation with multivariate rational functions, extending the formulation of tensorized Krylov subspaces introduced in Kressner, D. & Tobler, C. (2010) Krylov subspace methods for linear systems with tensor product structure. SIAM J. Matrix Anal. Appl., 31,$1688$–$1714$. Moreover, we develop methods for the solution of

We consider an extension of the Newton-MR algorithm for nonconvex unconstrained optimization to the settings where Hessian information is approximated. Under a particular noise model on the Hessian matrix, we investigate the iteration and operation complexities of this variant to achieve appropriate sub-optimality criteria in several nonconvex settings. We do this by first considering functions that

A convincing feature of least-squares finite element methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to discontinuous finite element ansatz functions, this paper introduces a least-squares principle on piecewise Sobolev functions by the example of the Poisson model problem with mixed boundary conditions. It allows for fairly

This paper presents an efficient two‐and‐a‐half dimensional (2.5D) numerical approach for analysing the long‐term settlement of a tunnel‐soft soil system under cyclic train loading. Soil deformations from train loads are divided into shear deformation under undrained conditions and volumetric deformation from excess pore water pressure (EPWP) dissipation. A 2.5D numerical model was employed to provide

Traditional bilinear isoparametric coordinate systems exhibit sensitivity to mesh distortion due to their fully high-order polynomials being only equivalent to first-order polynomials in Cartesian coordinate systems when confronted with mesh distortion. This paper combines the concept of 3- and 6-component volume coordinate systems (VCS) with the generalized mixed element method to develop a novel

We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity $$\begin{aligned} \mathfrak {M}\left( \int _{Q}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right) (-\Delta )_{p}^{s} u&=\frac{\lambda }{u^{\gamma }}+u^{p_s^*-1}~\text {in}~\Omega ,\\ u&>0~\text {in}~\Omega ,\\ u&=0~\text {in}~\mathbb {R}^N\setminus \Omega , \end{aligned}$$ where \(\mathfrak {M}\)

The paper addresses structural properties of distributed order controllers. A Distributed Order PID (DOPID) controller is a control structure in which a continuum of “differintegral” actions of orders between -1 and 1 are integrated together, and where relative contributions of different orders is determined by a weighting function. This stands in sharp contrast to conventional proportional-integral-derivative

SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 461-467, February 2025. Abstract. Various nonlinear Schwarz domain decomposition methods were proposed to solve the one-dimensional equidistribution principle in [M. J. Gander and R. D. Haynes, SIAM J. Numer. Anal., 50 (2012), pp. 2111-2135]. A corrected proof of convergence for the linearized Schwarz algorithm presented in section 3.2, under

SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 437-460, February 2025. Abstract. We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total variation term with Raviart–Thomas functions, which is known from the