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Abstract: Abstract In this paper, we set an impulsive boundary value problem for matrix valued Schrödinger equation on the semi axis. We first introduce some solutions of mentioned problem so that we can obtain Jost solution, Jost function, scattering function and resolvent of corresponding impulsive operator. Moreover, investigating analytical and asymptotic properties of the Jost solution enables us to find the discrete spectrum of matrix Schrödinger operator and to study characteristic properties of the scattering matrix. PubDate: 2022-09-19

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Abstract: Abstract This paper deals with the periodic unfolding for sequences defined on one dimensional lattices in \({\mathbb {R}}^N\) . In order to transfer the known results of the periodic unfolding in \({\mathbb {R}}^N\) to lattices, the investigation of functions defined as interpolation on lattice nodes play the main role. The asymptotic behavior for sequences defined on periodic lattices with information until the first and until the second order derivatives are shown. In the end, a direct application of the results is given by homogenizing a 4th order Dirichlet problem defined on a periodic lattice. PubDate: 2022-09-09

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Abstract: Abstract Disturbances propagating through an unsteady, inviscid non-ideal gas under the influence of magnetic field are analysed. Various cases keeping the shock amplitude as finite, small and not so small are studied using the technique of relatively undistorted waves. Further an asymptotic solution valid upto first and second order approximations is found out using the theory of weakly nonlinear geometrical optics and the effects of wave front configuration, non-ideal parameter and magnetic pressure on the formation and subsequent propagation of shock waves are considered. Our results are found in good agreement with the known results. The asymptotic decay laws for weak shocks in the absence of a magnetic field are exactly recovered for an ideal gas as well as a non-ideal gas. The last section of the paper is devoted to the study of resonantly interacting waves leading to the derivation of certain transport equations for waves that are mutually coupled and interact with each other resonantly. PubDate: 2022-09-09

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Abstract: Abstract We propose an alternate overlapping Schwarz method to solve the singularly perturbed problems of convection-diffusion type. The method decomposes the original domain into two overlapping subdomains; one subdomain is known as the outside boundary layer subdomain and the other subdomain is known as the inside boundary layer subdomain, which contains the boundary layer. On the outside boundary layer subdomain, a combination of the compact difference scheme and the central difference scheme with uniform mesh is considered, while on the inside boundary layer subdomain, a combination of the compact difference scheme and the central difference scheme with a special type of piecewise-uniform mesh is considered. The convergence analysis is given and the method is shown to have almost second order global parameter-uniform convergence. The method is then extended to a weakly coupled system of \(M(\ge 2)\) singularly perturbed convection-diffusion problems. Numerical experiments are given in support of the theoretical findings. PubDate: 2022-09-09

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Abstract: Abstract This research looks at the Hall and Ion-slip currents with time variation in an unstable, incompressible, viscous fluid electrically conducting free convection flow that passes over an electrically non-conducting inclined plate in the presence of an inclined magnetic field. The fluid flow is generated by the moving and oscillating plate, and it is also influenced by the magnetic force, gravitational force, and viscous force. The buoyancy forces are produced by temperature and concentration variance in the gravity field due to the oscillating plate in its own plane. The governing equations are derived from the Navier–Stokes equation, energy equation, and concentration equation and then applied to the boundary layer approximation. The magnetic Reynolds number of flows is kept relatively small, so this analysis has not used the magnetic induction equation. On the velocity distribution, the angle of inclination has a retarding impact. The results of this study have been shown to explain the drag on flow at inclined surfaces instantly. The impact of the relevant parameters on fluid velocity, temperature, and concentration distributions has been explained and visualized using graphs. Numerical data for skin friction, rate of heat transmission, and mass transfer in terms of shear stress, Nusselt, and Sherwood numbers are visualized graphically. PubDate: 2022-09-09

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Abstract: Abstract We discuss some optimal control problem for the evolutionary Perona–Malik equations with the Neumann boundary condition. The control variable v is taken as a distributed control. The optimal control problem is to minimize the discrepancy between a given distribution \(u_d\in L^2(\Omega )\) and the current system state. Since we cannot expect to have a solution of the original boundary value problem for each admissible control, we make use of a variant of its approximation using the model with fictitious control in coefficients of the principle elliptic operator. We introduce a special family of regularized optimization problems for linear parabolic equations and show that each of these problems is consistent, well-posed, and their solutions allow to attain (in the limit) an optimal solution of the original problem as the parameter of regularization tends to zero. PubDate: 2022-09-09

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Abstract: Abstract We propose a kinetic model describing a polyatomic gas undergoing resonant collisions, in which the microscopic internal and kinetic energies are separately conserved during a collision process. This behaviour has been observed in some physical phenomena, for example in the collisions between selectively excited CO \(_2\) molecules. We discuss the model itself, prove the related H-theorem and show that, at the equilibrium, two temperatures are expected. We eventually present a numerical illustration of the model and its main properties. PubDate: 2022-09-09

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Abstract: Abstract In this paper, we consider the (p, q)-Laplacian problem $$\begin{aligned} -\Delta _{p}u-\mu \Delta _{q}u+\theta (x) u^{p-1}=\beta (x) u^{p-1}+\lambda a(x) u^{-\gamma }+b(x)u^{r-1}, \end{aligned}$$ with homogeneous Dirichlet boundary condition and \(u > 0 \) in \( \Omega \) , where \(\Omega \subset \mathbb {R}^N\) is an open bounded domain with smooth boundary. The existence of an interval for \(\lambda \) in which the problem has at least two positive weak solutions is proved. The main tools are Nehari manifold and the fibering method. PubDate: 2022-09-09

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Abstract: Abstract The Sarmanov family of bivariate distributions is considered as the most flexible and efficient extended families of the traditional Farlie–Gumbel–Morgenstern family. The goal of this work is twofold. The first part focuses on revealing some novel aspects of the Sarmanov family’s dependency structure. In the second part, we study the Fisher information (FI) related to order statistics (OSs) and their concomitants about the shape-parameter of the Sarmanov family. The FI helps finding information contained in singly or multiply censored bivariate samples from the Sarmanov family. In addition, the FI about the mean and shape parameter of exponential and power distributions in concomitants of OSs is evaluated, respectively. Finally, the cumulative residual FI in the concomitants of OSs based on the Sarmanov family is derived. PubDate: 2022-09-03

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Abstract: Abstract In this paper, a collocation method based on the Pell-Lucas polynomials is presented for the numerical solution of the Abel equation of the second kind. Abel equation of the second kind corresponds to a nonlinear differential equation. As a first step, the matrix forms of the Pell-Lucas polynomials and the assumed solution form are constructed. Then, the first derivative of solution, the nonlinear terms and the initial condition are introduced in matrix forms. By using the evenly spaced collocation points and the matrix relations, nonlinear problem is transformed to a system of the nonlinear algebraic equations. Consequently, the solution of this system gives the coefficients of the assumed approximate solution. In addition, the error analysis is done. Accordingly, an upper bound of the errors is stated. Besides, error estimation technique and the residual improvement technique are presented by using residual function. Moreover, the method is applied to two examples and the comparisons are made with the results of other methods in tables to show the computational efficiency of present method. The code of method and the presented graphics are constituted by using Matlab program. PubDate: 2022-08-02

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Abstract: Abstract This paper concerns the ground state solutions for the partial differential equations known as the Dirac equations. Under suitable assumptions on the nonlinearity, we show the existence of nontrivial and ground state solutions. PubDate: 2022-08-02

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Abstract: Abstract Spiral waves are a mathematical concept that organizes spatio-temporal dynamics in dissipative, spatially extended biological, physical and chemical systems. They support a variety of important phenomena, such as re-entrant cardiac arrhythmias and spatial patterns in chemical reactions. In this paper we consider a two-dimensional (2D) disturbance wave that can make the pulse wave travel around the disturbance and generate a self-sustaining spiral wave. The use of a region temporarily refractory as a disturbance in format wave is a novel mechanism for generating activity in spiral shape. In addition, it is robust for a wide variety of refractory areas and geometry shapes. This situation models the appearance of abnormal electrical activity in the heart, where the disturbance is a cardiac tissue in damage. We present a Finite Element Method (FEM) scheme for the two-dimensional FitzHugh-Nagumo (FHN) system to simulate the spiral-generation mechanism in cardiac tissue. This scheme is based on the semi implicit Eyres algorithm and we present some numerical results to demonstrate the effectiveness and usefulness of the present technique. PubDate: 2022-07-25

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Abstract: Abstract Using the notion of n-stability of a support on a ring that we owe to Coquand, we show that if \(\mathbf{R}\) is a ring of Krull dimension \(\le 0\) , or a domain of Krull dimension 1 such that \(\mathrm{Rad}(\mathbf{R})\ne \{ 0\}\) (for example, a local domain of Krull dimension 1), or a ring with finite prime spectrum, then for any finitely-generated projective \(\mathbf{R}[X_1,\ldots ,X_n]\) -module M of rank \(r\ge n+1\) , we have \(M\cong N \oplus \mathbf{R}^{r-n}\) where N is isomorphic to the image of a matrix of rank n. PubDate: 2022-07-13 DOI: 10.1007/s11587-022-00724-2

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Abstract: Abstract Our aim in this note is to establish Hardy-Sobolev inequalities for double phase functionals \(\Phi (t,r)= r^p + (b(t) r)^q\) on the half space, as a continuation of our paper (Mizuta and Shimomura in Rocky Mount. J. Math.), where \(1 \le p < q\) , b is non-negative and Hölder continuous in \([0,\infty )\) of order \(\theta \in (0,1]\) . The Sobolev conjugate for \(\Phi \) is given by \(\Phi ^*(t,r)= r^{p^*} + (b(t) r)^{q^*}\) , where \(p^*\) and \(q^*\) denote the Sobolev exponent of p and q, respectively, that is, \(1/p^* = 1/p - 1/n\) and \(1/q^* = 1/q - 1/n\) . As applications, we study the boundary behavior of Sobolev functions on the half space. PubDate: 2022-07-12 DOI: 10.1007/s11587-022-00686-5

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Abstract: Abstract The main object of the present paper is the study of thermoelastic laminated beam with structural damping, where the heat conduction is given by the classical Fourier’s law and acting on both the rotation angle and the transverse displacements. We establish an exponential stability result for the considered problem in case of equal wave speeds. In the opposite case, we show the lack of exponential stability. Furthermore, a polynomial stability result is established. PubDate: 2022-07-11 DOI: 10.1007/s11587-022-00708-2

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Abstract: Abstract Awareness plays a vital role in informing and educating people about infection risk during an outbreak and hence helps to reduce the epidemic’s health burden by lowering the peak incidence. Therefore, this paper studies a susceptible-aware-infected-recovered (SAIR) epidemic model with the novel combinations of Michaelis-Menten functional type nonlinear incidence rates for unaware and aware susceptible with the inclusion of time delay as a latent period and a saturated treatment rate for infected people. The model is analyzed mathematically to describe disease transmission dynamics in two obtained equilibria: disease-free and endemic. We derive the basic reproduction number \(R_0\) and investigate the local and global stability behavior of obtained equilibria for the time delay . A bifurcation analysis is performed using center manifold theory when there is no time delay, revealing the forward bifurcation when \(R_0\) varies from unity. Moreover, the presence of Hopf bifurcation around EE is shown depending on the bifurcation parameter time delay. Lastly, the numerical simulations validate the analytical findings. PubDate: 2022-07-11 DOI: 10.1007/s11587-022-00720-6

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Abstract: Abstract We study the stabilization of non-homogeneous viscoelastic waves for the vibrations of a flexible structure with thermodiffusion effect and a distributed forcing term as input disturbance. The coupled heat conduction is governed by Cattaneo-Vernotte’s law. Using the semigroup theory, we prove the existence and the uniqueness of the solution. Under construction of a suitable Lyapunov functional, it is shown that the amplitude of such vibrations is bounded for admissible bounded input disturbances. An estimate of the total energy of the system over a time interval is obtained directly with a tolerance level of the disturbance. Finally, in the absence of input disturbance, the uniform exponential decay of solution with an explicit form of energy decay estimate is achieved directly. PubDate: 2022-07-06 DOI: 10.1007/s11587-022-00722-4

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Abstract: Abstract In this paper, we prove that the solutions to the problem determined by an elastic material with \(n^2\) coupling dissipative mechanisms decay in an exponential way for every (bounded) geometry of the body, where n is the dimension of the domain, and whenever the coupling coefficients satisfy a suitable condition. We also give several examples where the solutions do not decay when the rank of the matrix of the coupling mechanisms is less than \(n^2\) (2 in dimension 2 and 6 in dimension 3). PubDate: 2022-07-06 DOI: 10.1007/s11587-022-00719-z

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Abstract: Abstract In this article, we compute the distance, distance Laplacian, and distance signless Laplacian eigenvalues of central vertex and central edge join of two graphs \(G_1\) and \(G_2\) , when \(G_1\) is triangle-free regular and \(G_2\) is regular. These results enable us to determine infinitely many pairs of distance, distance Laplacian and distance signless Laplacian cospectral graphs. In addition, we obtain some lower and upper bounds for the distance spectral radius of the central graph of a triangle-free regular graph. As an application, we construct some new classes of non D-cospectral D-equienergetic graphs. PubDate: 2022-07-03 DOI: 10.1007/s11587-022-00721-5

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Abstract: Abstract The closeness or similarity between two populations is usually assessed by means of overlap measures based on their probability distributions. Matusita’s measure, Morisita’s measure and Weitzman’s measure are three commonly used overlap measures. These measures are defined based on the probability density functions of the two distributions. There are several probability distributions that do not have a tractable probability density function, though the corresponding quantile density function has an explicit form. In such cases, the traditional approach fails and the overlap measures need to be defined in terms of quantile functions. The present paper considers a quantile-based study of the overlap measures. We also illustrate the usefulness of the proposed quantile-based overlap measures using several examples. PubDate: 2022-06-25 DOI: 10.1007/s11587-022-00712-6