396 Results Found

Identification of initial delamination is crucial to ensure the safety of the fiber-reinforced laminated composite structures. Amongst the identification approaches based on mode shapes, the concept of multiscale shear-strain gradient (MSG) has an ex...

In video processing, background initialization aims to obtain a scene without foreground objects. Recently, the background initialization problem has attracted the attention of researchers because of its real-world applications, such as video segment...

In this paper, we focus on the multiplicity of positive solutions for a singular tempered fractional initial-boundary value problem with a p-Laplacian operator and a changing-sign perturbation term. By introducing a truncation function and combing wi...

Reduced workspace is the main parallel robot disadvantage. It is generally due to the robot configuration, mainly the platform orientation constraint, the present work intends to find the maximum sphere within the orientation workspace, i.e., the sin...

In this paper, efficient methods seeking the numerical solution of a time-fractional fourth-order differential equation with Caputo’s derivative are derived. The solution of such a problem has a weak singularity near the initial time t=0. The C...

The standard ΛCDM model, despite its agreement with observational data, still has some issues unaddressed, such as the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there ap...

This paper considers impulsive systems with singularities. The main novelty of this study is that the impulses (impulsive functions) and the initial value are singular. The asymptotic convergence of the solution to a singularly perturbed initial prob...

Singular singularly-perturbed problems (SSPPs) are a powerful mathematical tool for modelling a variety of real phenomena, such as nuclear reactions, heat explosions, mechanics, and hydrodynamics. In this paper, the numerical solutions to fourth-orde...

Under some conditions, an asymptotic solution containing boundary functions was constructed in a paper by Vasil’eva and Butuzov (Differ. Uravn. 1970, 6(4), 650–664 (in Russian); English transl.: Differential Equations 1971, 6, 499–5...

In this paper, based on the L2-1σ scheme and nonconforming EQ1rot finite element method (FEM), a numerical approximation is presented for a class of two-dimensional time-fractional diffusion equations involving variable coefficients. A novel an...

This paper is devoted to proposing numerical algorithms based on the use of the tau and collocation procedures, two widely used spectral approaches for the numerical treatment of the initial high-order linear and non-linear equations of the singular...

In this article, we present up to date results on the balanced model reduction techniques for linear control systems, in particular the singular perturbation approximation. One of the most important features of this method is it allows for an a prior...

In this paper, we numerically solve the nonlinear time-fractional diffusion equation of distributed order on an unbounded domain with a weak singularity. A fully discrete implicit scheme is developed based on the L1 formula on graded meshes in time a...

Motivated by the recent interest in generalized fractional order operators and their applications, we consider some classes of integro-differential initial value problems based on derivatives of the Riemann–Liouville and Caputo form, but with n...

In this article, we focus on examining the existence, uniqueness, and continuous dependence of solutions on initial data for a specific initial boundary value problem which mainly arises from one-dimensional quasi-static contact problems in nonlinear...

We investigate the background dynamics of a class of models with noncanonical scalar field and matter both in Friedmann Lemaitre Robertson Walker (FLRW) closed and open spacetime. The detailed dynamical system analysis is carried out in a bouncing sc...

The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic sol...

The present paper deals with neural algorithms to learn the singular value decomposition (SVD) of data matrices. The neural algorithms utilized in the present research endeavor were developed by Helmke and Moore (HM) and appear under the form of two...

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation paramet...

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a...

The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent hori...

The cosmological singularity of infinite density, temperature, and spacetime curvature is the classical limit of Friedmann’s general relativity solutions extrapolated to the origin of the standard model of cosmology. Jacob Bekenstein suggests t...

There has been considerable recent interest in certain integral transform operators with non-singular kernels and their ability to be considered as fractional derivatives. Two such operators are the Caputo–Fabrizio operator and the Atangana&nda...

In this article, I mainly discuss the dynamics of the pre-inflationary Universe for the potential V ( ϕ ) ∝ ϕ n with n = 5 / 3 in the context of loop quantum cosmology, in which the big bang singularity is resolved by a non-s...

A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler&nda...

This research article introduces an efficient method for integrating Lane–Emden–Fowler equations of second-order singular initial value problems (SIVPs) using a pair of hybrid block methods with a variable step-size mode. The method pairs...

In the field of fractional calculus and applications, a current trend is to propose non-singular kernels for the definition of new fractional integration and differentiation operators. It was recently claimed that fractional-order derivatives defined...

Several real-life problems are modeled by nonlinear singular differential equations. In this article, we study a class of nonlinear singular differential equations, explore its various aspects, and provide a detailed literature survey. Nonlinear sing...

In the present work, the transmutation operator approach is employed to construct an exact solution to the initial boundary-value problem for multidimensional free transverse equation vibration of a thin elastic plate with a singular Bessel operator...

This paper presents an innovative numerical method for solving two-dimensional weakly singular Volterra integral equations, including fractional Volterra integral equations with weak singularities. Solving these equations in higher dimensions and in...

This paper describes the multilayer voting algorithm, a novel autonomous star identification method for spacecraft attitude determination. The proposed algorithm includes two processes: an initial match process and a verification process. In the init...

One of the open problems in the numerical analysis of solutions to high-dimensional nonlinear integral equations with memory kernel and proportional delay is how to preserve the high-order accuracy for nonsmooth solutions. It is well-known that the s...

This article introduces a new method for identifying anchor damage faults in fiber composite submarine cables. The method combines the Volterra model of Variation Mode Decomposition (VMD) with singular value entropy to improve the accuracy of fault i...

We study certain Volterra integral equations that extend and recover first order ordinary differential equations (ODEs). We formulate the former equations from the latter by replacing classical derivatives with nonlocal integral operators with anti-s...

This study examines the Chen–Lee–Liu dynamical equation, which represents the propagation of optical pulses in optical fibers and plasma. A new extended direct algebraic technique and Nucci’s scheme are used to find new solitary wav...

Using differential transformation method to solve the Lane-Emden equations as singular initial value problems is introduced in this study. Some numerical examples are presented to illustrate the efficiency and reliability of the method.

Based on the hydrodynamic description, the dynamics of nonlinear cylindrical waves in an isentropic plasma are investigated. The problem is considered in an electrostatic formulation for a two-dimensional plasma medium where ions form a stationary ba...

Estimation of additive white Gaussian noise levels in images has a variety of image processing applications including image enhancement, segmentation and feature extraction. Designing an algorithm with a consistent performance across a range of noise...

The determination of maximum singularity-free space is critical to structural design and motion control strategy in the Stewart platform. Nevertheless, in practical applications, there exist several limitations such as computational efficiency, calcu...

This article presents the analysis of a parallel mechanism of type 3-SPS-U. The usual singularity approach is carried out with respect to the Euler angles of the universal joint. However, this approach is computationally expensive especially when sta...

In this investigation, the adaptive fractional-order non-singular fixed-time terminal sliding mode (AFoFxNTSM) control for the uncertain dynamics of robotic manipulators with external disturbances is introduced. The idea of fractional-order non-singu...

This investigation focuses on the construction of novel dark and singular soliton solutions for the Hirota equation, which models the propagation of ultrashort light pulses in optical fibers. Initially, we employ a wave variable transformation to con...

In this paper, we explore the interior dynamics of neutral and charged black holes in f(R) gravity. We transform f(R) gravity from the Jordan frame into the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and Reissner-Nordström g...

In this paper, we have studied an anisotropic Bianchi-I cosmological model in f(R,T) gravity. To obtain the exact solutions of the field equations, we have used the condition σ/θ to be a function of the scale factor (IJTP, 54, 2740-2757,...

The orientation relationship (OR) between phases related by a phase transformation is often reproducible. This study interprets and predicts the reproducible ORs with a two-stage approach. The initial OR formed at the nucleation stage tends to allow...

In this paper, the Penrose process is used to extract rotational energy from regular black holes. Initially, we consider the rotating Simpson–Visser regular spacetime, which describes the class of geometries of Kerr black hole mimickers. The Pe...

The first part of this paper contains a brief description of the beginnings of modern cosmology, which, the author will argue, was most likely born in the year 1912. Some of the pieces of evidence presented here have emerged from recent research in t...

The goal of this paper is to give an error analysis of a finite difference method for a time-fractional Black–Scholes equation with weakly singular solutions. The time Gerasimov-Caputo derivative is discretized by the L1 scheme on a graded mesh...

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is...

When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate cal...