Abstract The purpose of this paper is to prove a priori error estimates for the completely discretized problem of the dual mixed method for the non-stationary heat diffusion equation in a polygonal domain of R 2 . Due to the geometric singularities of the domain, the exact solution is not regular in the context of classical Sobolev spaces. Instead, one must use weighted Sobolev spaces in our analysis

Abstract The estimation of a finite population distribution function is considered when there are missing data. Calibration adjustment is used for dealing with nonresponse at the estimation stage. Several procedures are proposed and compared. A numerical study is carried out to evaluate the performances of estimators. Computational problems with the implementation of the proposed calibration estimators

Abstract A method is presented for the numerical solution of odd-order nonlinear boundary value problems with complementary Lidstone boundary conditions. The approximate solution is given in terms of spline interpolation functions, written in the Lidstone second type polynomial basis. Some results on local and global errors are given. Numerical tests are presented.

Abstract This paper proposes and studies a novel test for the geometric distribution which is based on a characterization of that law in terms of the conditional expectation of the second order statistic, given the value of the first order statistic. The asymptotic null distribution of the test statistic and its limit under general conditions are derived, proving that it is consistent against fixed

Abstract In this paper, we propose an adaptive knot placement algorithm for B-Spline curve approximation to dense and noisy 2D data points. The proposed algorithm is based on a heuristic rule for knot placement. It consists in constructing a distribution knot function by blending geometric criteria such as discrete derivatives, discrete angular variations and curvature. It has been successfully compared

Abstract Functional principal component analysis (FPCA) based on Karhunen–Loeve (K–L) expansion allows to describe the stochastic evolution of the main characteristics associated to multiple systems and devices. Identifying the probability distribution of the principal component scores is fundamental to characterize the whole process. The aim of this work is to consider a family of statistical distributions

Abstract The aim of this paper is to present a family of polynomial quasi-interpolants in Bernstein basis. More precisely, we will combine the strong features of the polar forms and the symmetric polynomials to derive the coefficients of the quasi-interpolant in the Bernstein basis representation. We also derive a collection of spline quasi-interpolants that reproduce polynomial functions up to degree

Abstract Methods to analyze multicategorical variables are extensively used in sociological, medical and educational research. Nonetheless, they have a very sparse presence in finite population sampling when sensitive topics are investigated and data are obtained by means of the randomized response technique (RRT), a survey method based on the principle that sensitive questions must not be asked directly

Abstract Here, we model a thin layer of graphene located above a metal surface by means of a surface boundary condition in two different stencils, namely, a simple cubic grid (SC-Grid) and a body centered cubic grid (BCC-Grid). We extend the methodology described in the literature by taking into account the interband contribution of the graphene’s conductivity in addition to the intraband contribution

Abstract The homogeneity problem for testing if more than two different samples come from the same population is considered for the case of functional data. The methodological results are motivated by the study of homogeneity of electronic devices fabricated by different materials and active layer thicknesses. In the case of normality distribution of the stochastic processes associated with each sample

Abstract Multiphase flow equations for two components (for instance water and hydrogen) and two phases (liquid and gas), with equilibrium phase exchange, have been used to simulate the process of miscible displacement in porous media. Laboratory and field studies have shown that this assumption fails under certain circumstances especially for accurate description of the pollution and a finite transfer

Abstract Online surveys, despite their cost and effort advantages, are particularly prone to selection bias due to the differences between target population and potentially covered population (online population). This leads to the unreliability of estimates coming from online samples unless further adjustments are applied. Some techniques have arisen in the last years regarding this issue, among which

Abstract The trapezoidal formula is known to achieve exponential convergence when calculating infinite integrals of bilateral rapidly decreasing functions. Even when considering unilateral rapidly decreasing functions, the trapezoidal formula can be made to converge exponentially by applying an appropriate conformal map to the integrand, as proposed by Stenger. This study modifies the conformal map

In this paper, we develop a branch and bounds algorithm to solve bound-construction bi-objective optimization problem. The proposed algorithm allows to determine an approximation of the Pareto optimal solutions sets in both spaces: decisions and objectives ones. By running a α-dense space filling curves, we convert a multidimensional bi-objective optimization problem into a one-dimensional one. Hence

This paper studies the Mittag-Leffler stabilization for unstable infinite dimensional systems actuated by boundary controllers described by time fractional reaction diffusion equations. Via the Riesz basis method, the stable and the unstable part of the considered system are separated. The Kalman rank criterion, which is a classical linear algebra condition, guarantees the stabilizability of the unstable

A Robin boundary sub-diffusion equation is considered with fractional partial derivatives of the Caputo type. The model is an extension of various well-known equations from mathematical physics, biology, and chemistry. Initial–boundary data are imposed upon a closed and bounded spatial domain. We state and prove two main theorems in differential and difference settings to ensure the algebraic decay

This paper proposes several data-based models for solar fields (SF) of concentrating solar power (CSP) plants. The proposed models estimate SF thermal output from solar resource data and aim to replace first-principles-based SF models typical in CSP generation schedulers. The advantages of the first models as opposed to the second ones are the ease in their development and their adaptability to changes

This paper introduces the energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrödinger equation, which uses the scalar auxiliary variable approach. By a scalar variable, the system is transformed into a new equivalent system. Then applying the extrapolated Crank–Nicolson method on the temporal direction and Fourier pseudospectral method on space direction, we give a linear implicit

A dynamical network achieves generalized synchronization if there exists an asymptotically stable manifold in which the solution of each node is uniquely determine as a static function of the states of any other node in the network. For bidirectionally coupled networks, the description of a synchronization manifold changes from pairwise-explicit form to an implicit form of the relationship between

Monte Carlo Approaches for calculating Value-at-Risk (VaR) are powerful tools widely used by financial risk managers across the globe. However, they are time consuming and sometimes inaccurate. In this paper, a fast and accurate Monte Carlo algorithm for calculating VaR and ES based on Gaussian Mixture Models is introduced. Gaussian Mixture Models are able to cluster input data with respect to market’s

In this paper, the effect of viscous dissipation and Joule heating on magneto-hydrodynamic (MHD) nanofluid flow towards a vertical sinusoidal wavy surface has been investigated numerically. The wavy surface is considered to be heated with uniform flux. Effects of radiation and nanoparticle volume concentration are also considered. The fluid flow over the surface geometry is designed through the highly

An efficient numerical method based on a Sobolev gradient is presented to find the equilibrium shapes of an elastic rod resistant to bending and twisting. A Sobolev preconditioning operator is introduced based on the energy of the elastic rod that preconditions the standard conjugate gradient method and results in a speedy convergence. It outperforms the usual conjugate gradient and steepest descent

This paper deals with self-triggering adaptive optimal control for nonlinear continuous-time systems. We propose a novel self-triggering control structure concerning a special encoding mechanism, which combines the trigger time of control and sampling and reduces both the control time and the sampling time. Such a triggering structure ensures the existence of a maximum triggering time in self-triggering

This article is involved with a class of high-order proportional delayed cellular neural networks incorporating D operator. To start with, we validate the boundedness and the global existence of positive solutions. Moreover, by exploiting differential inequality techniques and with the aid of Lyapunov function method, some testable conditions are obtained to assure the positiveness and global exponential

This paper studies the delay-dependent conditions for finite-time extended dissipativity based non-fragile feedback control for neural networks with mixed interval time-varying delays. By applying Jensen’s inequality, an extended Jensen’s double integral inequality, and a free matrix form inequality to the Lyapunov–Krasovskii functional (LKF), delay-dependent conditions are derived and solved by the

In this manuscript, we mainly focus on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1

In this paper, we present a new hybrid spectral-conjugate gradient (SCG) algorithm for finding approximate solutions to nonlinear monotone operator equations. The hybrid conjugate gradient parameter has the Polak–Ribière–Polyak (PRP), Dai-Yuan (DY), Hestenes-Stiefel (HS) and Fletcher-Reeves (FR) as special cases. Moreover, the spectral parameter is selected such that the search direction has the descent

In this paper, a Gause type predator–prey system with constant-yield prey harvesting and monotone ascending functional response is proposed and investigated. We focus on the influence of the harvesting rate on the predator–prey system. First, equilibria corresponding to different situations are investigated, as well as the stability analysis. Then bifurcations are explored at nonhyperbolic equilibria

This paper proposes a new robust Discrete-Time Sliding Mode Control (dt-smc) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (ubb) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller

In the present investigation, a prey–predator model consisting of phytoplankton, susceptible zooplankton, and infected zooplankton, incorporating the response function of Holling type II, has been explored. Logistic growth is assumed to be followed by the phytoplankton species. A combined effort (E) is applied to harvest all of the three populations. Environmental toxicity is considered to affect the

The geometric properties ofr of the ensemble of numerical solutions obtained by the algorithms of different inner structure are addressed from the prospects for a posteriori error estimation. The numerical results are presented for the two-dimensional inviscid supersonic flows, containing shock waves. The truncation errors are computed using a postprocessor, the approximation errors are calculated

This paper investigates time domain model order reduction of discrete-time bilinear systems with inhomogeneous initial conditions. The state of the system is approximated by the power series associated with the Charlier polynomials and the recurrence relation of the expansion coefficients is derived. The expansion coefficients are orthogonalized to construct the projection matrix by the modified multi-order

In the paper, we convert a single nonlinear equation to a system consisting of two equations. While a quasi-linear term is added on the first equation, the nonlinear term in the second equation is decomposed at two sides through a weight parameter. After performing a linearization, an iterative scheme is derived, which is proven of third-order convergence for certain parameters. An affine quasi-linear

In this paper, we study a Susceptible–Vaccinated–Infected–Recovered (SVIR) epidemic model in a spatially heterogeneous environment under the Dirichlet boundary condition. We define the basic reproduction number ℜ0 by the spectral radius of the next generation operator, and show that it is a threshold parameter. The disease extinction and persistence in the case of a bounded domain are considered. More

This paper is devoted to a hierarchical approach of constructing a class of fractal interpolants with trigonometric basis functions and to preserve the geometric behavior of given univariate data set by these fractal interpolants. In this paper, we propose a new family of C1-rational cubic trigonometric fractal interpolation functions (RCTFIFs) that are the generalized fractal version of the classical

This article considers a generalized Logistic reaction–diffusion population model with mixed instantaneous and delayed feedback control and subject to the homogeneous Dirichlet boundary condition on the one-dimensional bounded spatial domain (0,π). Existence and asymptotic expression of the small enough positive steady state bifurcating from the zero solution are given in virtue of the implicit function

This article focuses on the synchronization problem of different chaotic systems where both the systems (i.e., master and slave) are anticipated to be perturbed with external disturbances and model uncertainties. The control problem of synchronization is addressed with a robust aggregate of backstepping with sliding mode control provided the bound of uncertainty is known and available. However, obtaining

In the present paper, we report the effect of nanoparticles in a three-species aquatic food chain model. It is assumed that due to the unavoidable interactions with nanoparticles, the growth rate of basal prey reduces. Fascinating dynamical scenarios in the model are explored in different bi-parametric spaces. We show that the model exhibits coexisting attractors of different kinds (periodic–perio

Recently a hybrid secure image encryption scheme based on Julia set and three-dimensional Lorenz chaotic system was suggested. The offered scheme was based on the multiplicative operation carried out by Julia set fractals and bitwise XOR which was implemented by the trajectories obtained from the Lorenz chaotic system. This paper presents the cryptanalysis of the scheme through a chosen-plaintext attack

The use of optimization techniques for the optimal design of roads and railways has increased in recent years. The environmental impact of a layout is usually given in terms of the land use where it runs (avoiding some ecologically protected areas), without taking into account air pollution (in these or other sensitive areas) due to vehicular traffic on the road. This work addresses this issue and

A new efficient method that combines the Puiseux series asymptotic technique with an augmented compact finite volume method is proposed to develop a numerical approximate solution for the Thomas–Fermi equation on semi-infinity domain. By using the asymptotic series of solution at infinity and the Puiseux series expansion at origin to characterize the singularities, the natural and precise boundary

Abstract Product reviews are of great commercial value for online shopping market. The identification of customer opinions from product reviews is helpful to improve the marketing decisions of customers, sellers and producers. This paper proposes a novel framework for summarizing customer opinions from product reviews. Firstly, our framework identifies grammatically and semantically meaningful phrases

The viability of finite difference stencils for higher-order derivatives of low-resolution data, encountered in various applications, is examined. This study’s illustrative example involves the evaluation of the fourth derivative of the digitized free surface radius obtained from pixelated images. Procedures to obtain an optimal approximation to the derivative are made from estimates of truncation

Using chaotic system for image encryption is a feasible and popular research interest. In this paper, a compound Sine-Piecewise Linear Chaotic Map is proposed to improve the chaotic characteristics of the original chaotic map. Compared with the original chaotic system, the proposed compound chaotic system has better dynamics performances, larger parameter space, which is more suitable for cryptographic

Recently, an exponential integrator Fourier pseudo-spectral (EIFP) scheme for the Klein–Gordon–Dirac (KGD) equation in the nonrelativistic limit regime has been proposed (Yi et al., 2019). The scheme is fully explicit and numerical experiments show that it is very efficient due to the fast Fourier transform (FFT). However, the authors did not give a strict convergence analysis and error estimate for

The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and fidelity can be deteriorated when the solutions exhibit weakly singular behaviors and this issue becomes much more severe for polynomial-based spectral methods. The eigenfunctions of the Sturm–Liouville problems of fractional order

We investigate the application of full discretization and a nonsmooth Newton method to large-scale optimal control problems. Based on a first discretize, then optimize approach, we discretize the state and control variables in time following a collocation method. Then, a nonsmooth Newton method combined with a line search globalization strategy is used to find a solution to the resulting finite-dimensional

In this paper, a mathematical model of the blade coating of the viscoelastic Carreau fluid which passes through the gap between the fixed blade and the moving substrate is constructed. The governing equations in the light of LAT (Lubrication Approximation Theory) are nondimensionalized and the solutions for the velocity, volumetric flow rate and the pressure gradient are calculated using Adomian decomposition

This paper develops a high order semi-implicit weighted compact nonlinear scheme (WCNS) for one- and two-dimensional viscous Burgers’ equations. This semi-implicit WCNS combines a fifth-order WCNS with a third-order implicit-explicit Runge–Kutta (IMEX-RK) time-stepping method. The advection terms of viscous Burgers’ equations are treated explicitly, while the viscosity terms are treated implicitly

Cooperation is a very common phenomenon in the predator population. It can also be considered as one kind of Allee effect. By cooperation, we mean that the consumption rate per predator is dependent on the density of the predator. Despite a few recent studies the study of such systems is rare in the literature. It is well known from previous studies that incorporation of Allee effect in prey population

In this paper, we consider the problems of estimating the unknown parameters as well as predicting the failure times of the removed units in multiple stages of the progressively censored sample coming from a new Pareto-type distribution. First, maximum likelihood, least squares and Bayesian methods (Lindley’s approximation and Markov chain Monte Carlo) are applied for estimating the parameters involved

In this study, for the first time, the approximate solution of Black–Scholes option pricing distributed order time-fractional partial differential equation by means of Legendre and Chebyshev wavelets is considered. The operational matrices of Legendre and Chebyshev wavelets for integer order derivative and distributed order fractional derivative are derived. Furthermore, the combination of Gauss–Legendre

A predator–prey system in discrete-time for which the predators engage in cooperative hunting and the prey population is subject to scramble intra-specific competition is developed and analyzed. We prove that the number of positive equilibrium points depends not only on the predator’s basic reproduction number but also on the intensity of predator cooperation. The model exhibits a discrete Hopf bifurcation

Model order reduction of electronic devices and on-chip interconnects plays an important role in determining the performance of very large scale IC (Integrated Circuit) designs. The ever shrinking process technology continues to increase complexity of these systems with the current Intel device technology node standing at 10 nm. In the analysis of high-speed IC interconnects, the reduced model is often

The novelty of this paper is to derive a mild solution by means of recently defined Mittag-Leffler type functions of fractional stochastic Langevin equations of orders α∈(1,2] and β∈(0,1] whose coefficients satisfy standard Lipschitz and linear growth conditions. Then, we prove existence and uniqueness results of mild solution and show the coincidence between the notion of mild solution and integral

In this paper, we study a wide spectrum of dynamical features of a prey–predator model with infection in prey population only. In the model formulation, we consider nonlinear incidence for infection transmission and Holling type II as response function of predator. We analyze the model for local stability and Hopf bifurcation, and the theoretical results are validated and extrapolated by numerical

We focus on the role of symmetries in geometric control theory from the Hamiltonian viewpoint. We demonstrate the power of Ian Anderson’s package DifferentialGeometry in CAS software Maple for dealing with control problems on Lie groups. We apply the tools to the problem of vertical rolling disc, however, anyone can modify our approach and tools to other control problems.

In this paper, we apply the high-order compact scheme coupled with alternating direction implicit (HOC–ADI) method to solve the two-dimensional Ginzburg–Landau (2D GL) equation. Five HOC–ADI schemes with second order accuracy in time and fourth order in space are proposed for 2D GL equation. Scheme I and Scheme II are both nonlinear, which need nonlinear iteration.To overcome this shortcoming, Scheme