Piezoelectric composites have found a wide range of applications in smart structures and devices and effective numerical methods should be developed to simulate not only the macroscopic coupled piezoelectric performances, but also the details of the...
A multiscale analysis and computational method based on the Second-Order Two-Scale (SOTS) approach are proposed for the elastic quadratic eigenvalue problems in the periodic composite domain. Two typical quadratic eigenvalue problems with different d...
In this paper, a way to build two-dimensional Schoenberg type operators with arbitrary knots or with equidistant knots, respectively, is presented. The order of approximation reached by these operators was studied by obtaining a Voronovskaja type asy...
In this work we investigate the effectiveness of the Backward Euler-Backward Differentiation Formula (BE-BDF2) in solving unsteady compressible inviscid and viscous flows. Furthermore, to improve its accuracy and its order of convergence, we have equ...
Non-linear voter models assume that the opinion of an agent depends on the opinions of its neighbors in a non-linear manner. This allows for voting rules different from majority voting. While the linear voter model is known to reach consensus, non-li...
We introduce the problem of variable-length (VL) source resolvability, in which a given target probability distribution is approximated by encoding a VL uniform random number, and the asymptotically minimum average length rate of the uniform random n...
In this paper, we study analytical approximate solutions for second-order homogeneous differential equations with the existence of only two turning points (but without poles) by using the uniform asymptotic approximation (UAA) method. To be more conc...
In this paper, we generalize a sequence of positive linear operators introduced by Ismail and May and we study some of their approximation properties for different classes of continuous functions. First, we estimate the error of approximation in term...
An exponential-type function was discovered to transform known difference formulas by involving a shifted parameter
In this paper, a completely smooth lower-order penalty method for solving a second-order cone mixed complementarity problem (SOCMCP) is studied. Four distinct types of smoothing functions are taken into account. According to this method, SOCMCP is ap...
This paper investigates the stability of continued fractions with complex partial denominators and numerators equal to one. Such fractions are an important tool for function approximation and have wide application in physics, engineering, and mathema...
The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional d...
This work offers a (semi-analytical) solution for a second-order nonlinear differential equation associated to the dynamical Kermack–McKendrick system. The approximate closed-form solutions are obtained by means of the Optimal Homotopy Asymptot...
A standard test for weak instruments compares the first-stage F-statistic to a table of critical values obtained by Stock and Yogo (2005) using simulations. We derive a closed-form solution for the expectation from which these critical values are der...
Although robust divergence, such as density power divergence and
This paper presents a fully implicit finite difference scheme for the numerical approximation of a wave equation featuring strong damping and a distributed delay term. The discretization employs second-order accurate approximations in both time and s...
In this paper, we propose an implicit finite difference scheme for a wave equation with strong damping and a discrete delay term. Although the scheme is implicit, the use of second-order finite difference approximations for the strong damping term in...
Second-order Chebyshev–Edgeworth expansions are derived for various statistics from samples with random sample sizes, where the asymptotic laws are scale mixtures of the standard normal or chi-square distributions with scale mixing gamma or inverse e...
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations to a n...
In recent years, fractionally-differenced processes have received a great deal of attention due to their flexibility in financial applications with long-memory. This paper revisits the class of generalized fractionally-differenced processes generated...
In this research, the analytical methods of the differential transform method (DTM), homotopy asymptotic method (HAM), optimal homotopy asymptotic method (OHAM), Adomian decomposition method (ADM), variation iteration method (VIM) and reproducing ker...
In this study, a third-order linear integro-differential equation with a small parameter at two higher derivatives was considered. An asymptotic expansion of the solution to the boundary value problem for the considered equation is constructed by con...
This study proposes an investigation into the nonlinear vibration of a simply supported, flexible, uniform microbeam associated with its curvature considering the mechanical impact, the electromagnetic actuation, the nonlinear Winkler–Pasternak...
This article completes our studies on the formal construction of asymptotic approximations for statistics based on a random number of observations. Second order Chebyshev–Edgeworth expansions of asymptotically normally or chi-squared distribute...
In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust contr...
The impulse response of the fractional oscillation equation was investigated, where the damping term was characterized by means of the Riemann–Liouville fractional derivative with the order
The method of Borel transformation for the summation of asymptotic expansions with the power-law asymptotic behavior at infinity is combined with elements of scale-invariant fractional analysis with the goal of calculating the critical amplitudes. Th...
We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of th...
The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a genera...
The fractional differential equations involving different types of fractional derivatives are currently used in many fields of science and engineering. Therefore, the first purpose of this study is to investigate the qualitative properties including...
In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points He...
The paper demonstrates symmetric integral operator and interpolation based numerical approximations for linear and nonlinear ordinary differential equations (ODEs) with oscillatory factor
We introduce a generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with finite nonzero first moment and study its properties. In particular, we prove an optimal moment-type inequality for th...
This paper deals with an initial-boundary value problem modeling the unidirectional pressure-driven flow of a second grade fluid in a plane channel with impermeable solid walls. On the channel walls, Navier-type slip boundary conditions are stated. O...
In the paper, a survey of the main results concerning univariate and multivariate exponential power (EP) distributions is given, with main attention paid to mixture representations of these laws. The properties of mixing distributions are considered...
3D facial surface imaging is a useful tool in dentistry and in terms of diagnostics and treatment planning. Between-group PCA (bgPCA) is a method that has been used to analyse shapes in biological morphometrics, although various “pathologies&rd...