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Abstract: This paper is concerned with the inverse scattering problem of time-harmonic acoustic waves by a mixed-type scatterer. Such a scatterer is given as the union of an inhomogeneous medium with unknown buried objects inside and an impenetrable obstacle. Having established the well-posedness of the direct problem by the variational method, we study the factorization method for recovering the support of the inhomogeneous medium and the shape of the impenetrable obstacle simultaneously. Finally, some numerical examples are presented to illustrate the feasibility and effectiveness of the inverse algorithm. PubDate: 2021-10-13

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Abstract: In this paper, a kind of localized radial basis function-based collocation method with reproducibility has been designed for nonlocal diffusion models. The basic idea of the method is to localize the RBF shape function by a corrected kernel with compact support, and meanwhile make the interpolation function to meet the reproducing conditions by modifying the coefficient contained in such kernel. Three types of nonlocal diffusion problems including constant and singular kernels are solved by our method in numerical experiments, which indicates that our method shows almost the same convergent behavior compared with RBF collocation methods, but it is much better conditioning and more time-efficient. It also overcomes the shortcoming that the RK-enhanced RBF method is not convergent for nonlocal diffusion models. PubDate: 2021-10-13

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Abstract: The optimal control problem constrained by a fractional diffusion equation arises in a great deal of applications. Fast and efficient numerical methods for solving such kinds of problems have attracted much attention in recent years. In this paper, we consider an optimal control problem constrained by a fractional diffusion equation (FDE). After the state and costate equations are derived, the closed form of the optimal control variable is then given. The decoupled gradient projection method is applied to solve the coupled system of the state and costate equations to obtain the solution of the optimal control problem. The second-order Crank-Nicolson method as well as the weighted and shifted Grünwald difference (CN-WSGD) methods are utilized to discretize these two equations. We get the discretized state and costate equations as systems of linear equations with both coefficient matrices having the structure of the sum of a diagonal and a Toeplitz matrix. A diagonal and a R.Chan’s circulant splitting (DRCS) preconditioner is developed and combined in the Krylov subspace methods to solve the resulting discretized linear systems. Theoretical analysis of spectral distributions of the preconditioned matrix is also given. Numerical results exhibit that the proposed preconditioner can significantly improve the convergence of the Krylov subspace iteration methods. PubDate: 2021-10-12

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Abstract: This paper studies a numerical technique to solve general variable-order partial differential equations. We present a general variable-order Riemann-Liouville pseudo-operational matrix and a general variable-order fractional derivative pseudo-operational matrix for the general Lagrange scaling functions (GLSFs). These matrices are achieved generally, without considering the nodes of Lagrange polynomials. Next, by implementing the obtained pseudo-operational matrices and an optimization method, the considered problem reduces to a system of nonlinear algebraic equations. Additionally, the convergence analysis is proposed and three numerical examples illustrate its good performance. PubDate: 2021-10-12

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Abstract: In this paper, we consider the main eigenvalues of connected chain graphs. We provide some properties of the eigenvectors corresponding to the main eigenvalues, upper and lower bounds on the number of main eigenvalues in connected chain graphs as well as examples that show that these bounds are attainable. As a consequence, we show that, for any positive integer k there exists a chain graph with k main eigenvalues. We also prove that there is no connected controllable chain graph. Our results make a bridge between the spectral properties of tridiagonal matrices and of chain graphs. PubDate: 2021-10-12

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Abstract: In this paper, multiple attribute group decision making(MAGDM) problems with single-valued neutrosophic 2-tuple linguistic (SVN2TL) set information are presented based on Frank operator, extend multi-attributive border approximation area comparison (MABAC) method, and best worst method (BWM). We first give the the concept of BWM method, Frank operator, and basic operational rules on SVN2TL set with Frank t-norms and t-conorms. Then, two aggregation operators including SVN2TL Frank weighted averaging (SVN2TLFWA) operator and Frank weighted geometric (SVN2TLFWG) operator are developed, and some desirable properties are discussed as well. What’s more, an iterative algorithm is designed for the determination of decision makers’ weight based on BWM method. Subsequently, combine the extend MABAC method and proposed operators, a new approach is developed to deal MAGDM with SVN2TL information. Finally, a numerical example has been given to show the procedure of the proposed method, and some sensitivity and comparative analysis are also conducted to illustrate the effectiveness and superiority of the proposed method. PubDate: 2021-10-12

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Abstract: The emphasis of conventional survival research methods has historically been on the occurrence of failures over time. The lack of knowledge of related observed and unobserved covariates during the study of such events can have negative consequences. Frailty models are a viable option for investigating the impact of unobserved covariates in this context. In this article, we suppose that frailty multiplies the hazard rate. As a useful method to ensure the effect of unobserved heterogeneity, we propose weighted Lindley (WL) frailty models with generalized Weibull (GW) and generalized log-logistic-II (GLL2) as the baseline distributions. The Bayesian paradigm of Markov Chain Monte Carlo (MCMC) methodology is used to estimate the model parameters. Subsequently, model comparisons are performed via Bayesian comparison techniques. The popular kidney data set is considered to illustrate the results. It is shown that the new models perform better than those based on gamma and inverse Gaussian frailty distributions. PubDate: 2021-10-11

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Abstract: Inspired by the works of Siriyan and Kangtunyakarn (2018) and Yao et al. (2015), we first introduce the two-step intermixed iteration for finding a common element of the set of the solutions of the split general system of variational inequality problem (SGSV), and also, we prove strong convergence theorem of the intermixed algorithm. Using our main theorem, we prove strong convergence theorems for finding solutions to the split variational inequality problem (SVIP), the split feasibility problem (SFP), and the split common fixed point problem (SCFP). Moreover, we give three numerical examples of these classical problems introduced by the previous studies and an example that conflicts with our main theorem where some conditions fail. PubDate: 2021-10-10

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Abstract: This article is concerned with the effects of piecewise constant argument on exponential stability to a unique equilibrium state of bidirectional associative memories (BAMs) neural networks model. Based on the fixed point theorem approach and an integral inequality of Gronwall type with deviation arguments, we have derived sufficient criteria to guarantee the existence, uniqueness and global exponential stability of the equilibrium state for the BAM model. Finally, the efficiency of the theoretical results has been illustrated by providing two numerical examples with simulations. PubDate: 2021-10-08

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Abstract: In this paper, we study a class of derivative-free nonmonotone line search methods for solving nonlinear systems of equations, which includes the method N-DF-SANE proposed in Cheng and Li (IMA J Numer Anal 29:814–825, 2009). These methods correspond to derivative-free optimization methods applied to the minimization of a suitable merit function. Assuming that the mapping defining the system of nonlinear equations has Lipschitz continuous Jacobian, we show that the methods in the referred class need at most \({\mathcal {O}}\left( \log (\epsilon ) \epsilon ^{-2}\right) \) function evaluations to generate an \(\epsilon \) -approximate stationary point to the merit function. For the case in which the mapping is strongly monotone, we present two methods with evaluation-complexity of \({\mathcal {O}}\left( \log (\epsilon ) \right) \) . PubDate: 2021-10-07

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Abstract: Let \(G=(V,E)\) be a graph and \(e=uv\in E\) . Define \(n_u(e,G)\) be the number of vertices of G closer to u than to v. The number \(n_v(e,G)\) can be defined in an analogous way. The Mostar index of G is a new graph invariant defined as \(Mo(G)=\sum _{uv\in E(G)} n_u(uv,G)-n_v(uv,G) \) . The edge version of Mostar index is defined as \(Mo_e(G)=\sum _{e=uv\in E(G)} m_u(e G)-m_v(G e) \) , where \(m_u(e G)\) and \(m_v(e G)\) are the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u, respectively. Let G be a connected graph constructed from pairwise disjoint connected graphs \(G_1,\ldots ,G_k\) by selecting a vertex of \(G_1\) , a vertex of \(G_2\) , and identifying these two vertices. Then continue in this manner inductively. We say that G is a polymer graph, obtained by point-attaching from monomer units \(G_1,\ldots ,G_k\) . In this paper, we consider some particular cases of these graphs that are of importance in chemistry and study their Mostar and edge Mostar indices. PubDate: 2021-10-07

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Abstract: This work examines the existence of the solutions of a class of three-point nonlinear boundary value problems that arise in bridge design due to its nonlinear behavior. A maximum and anti-maximum principles are derived with the support of Green’s function and their constant sign. A different monotone iterative technique is developed with the use of lower solution x(z) and upper solution y(z). We have also discussed the classification of well ordered ( \(x\le y\) ) and reverse ordered ( \( y\le x\) ) cases for both positive and negative values of \( \sup \left( \frac{\partial f}{\partial w}\right) \) . Established results are verified with the help of some examples. PubDate: 2021-10-07

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Abstract: The monitoring data of landslide deformation are characterized by non-smooth, nonlinear and random changes, and the cumulative changes of the monitored objects have both monotonous growth trends and short-term fluctuations. The GM(1,1) model can get better results only when the data series are monotonous. Due to the limitations of the model, the prediction accuracy of the GM(1,1) model is limited to a certain extent. An improved algorithm based on the GM(1,1) model and the empirical mode decomposition (EMD-GM(1,1) model) for deformation prediction was presented to improve the forecast accuracy in this paper. Firstly, EMD was used to effectively separate the nonlinear high-frequency and low-frequency components hidden in the deformation sequence; then the moving average method was applied to build a prediction model for high-frequency component, and the GM(1,1) was applied to build the prediction model for low-frequency one according to the characteristics of each component; finally, the predicted value of each component was superimposed. The experimental results indicate that the optimized EMD-GM(1,1) model combines the advantages of the two models to separate effectively the different frequency components of the deformation sequence, which has higher prediction accuracy. Compared with the conventional GM(1,1) model, DGM(2,1) model and the Linear fitting model, the proposed model could satisfactorily describe the landslide deformation prediction practically. PubDate: 2021-10-07

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Abstract: In this paper, multi-objective infinite horizon optimal control problems with state constraints are investigated. First, a mono-objective auxiliary optimal control problem, free of state constraints, is introduced. The weak Pareto front of the multi-objective optimal problem is related to a set contained in the boundary of the zero level set of the value function of the auxiliary control problem. Moreover, a more detailed characterization of the Pareto front for the multi-objective problem is presented. In the infinite horizon context, the value function of the auxiliary optimal control problem satisfies a Hamilton–Jacobi–Bellman equation; however, it is not the unique solution. A semi-Lagrangian scheme, based on the Dynamic Programming Principle, is considered to compute the value function of the auxiliary optimal control problem. Furthermore, optimal Pareto trajectory reconstruction is analyzed. PubDate: 2021-10-07

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Abstract: The fractional model which played an essential role in nuclear and particle physics used to describe the nuclear element interaction is the Phi-four model. This manuscript aims to scrutinize the new numerical solution of the nonlinear time fractional Phi-four equation subject to nonhomogeneous initial-boundary conditions by means of cubic-B-spline collocation method (CBSCM). The main advantage of cubic B-spline method over existing techniques is that it efficiently provides a piecewise-continuous, closed form solution and it is simpler and easy to apply to many problems involving partial differential equations. In this approach the fractional differential equation is converted into system of equations. The non-integer derivative " \(\alpha \) " is considered in Caputo sense. The discretization of Caputo derivative is done using L1 formula, while B-spline basis functions are used for the interpolation of spatial derivative. The applicability of the proposed scheme is examined on two test problems. The influence of different parameters is studied and captured graphically and numerically. The proposed scheme is proved to be unconditionally stable. Moreover, the error norms are computed to quantify the accuracy. PubDate: 2021-09-30

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Abstract: An outbreak of coronavirus disease 2019 (COVID-19) has quickly spread worldwide from December 2019, thus characterizing a pandemic. Until August 2020, the United States of America (U.S.) accounted for almost one-fourth of the total deaths by coronavirus. In this paper, a new regression is constructed to identify the variables that affected the first-wave COVID-19 mortality rates in the U.S. states. The mortality rates in these states are computed by considering the total of deaths recorded on 30, 90, and 180 days from the 10th recorded case. The proposed regression is compared to the Kumaraswamy and unit-Weibull regressions, which are useful in modeling proportional data. It provides the best goodness-of-fit measures for the mortality rates and explains \(76.57\%\) of its variability. The population density, Gini coefficient, hospital beds, and smoking rate explain the median of the COVID-19 mortality rates in these states. We believe that this article’s results reveal important points to face pandemic threats by the State Health Departments in the U.S. PubDate: 2021-09-29

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Abstract: In this paper, we study the a posteriori error estimate corresponding to the Brinkman–Darcy–Forchheimer problem. We introduce the variational formulation discretized by using the finite element method. Then, we establish an a posteriori error estimation with two types of error indicators related to the discretization and to the linearization. Finally, numerical investigations are shown and discussed. PubDate: 2021-09-29

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Abstract: The compact method guarantees high order accuracy and comprise point stencils; however, the alternating direction implicit (ADI)-type operator splitting method is difficult to implement. Here, a non-iterative compact ADI-type operator splitting scheme with stability for the Allen–Cahn equation is presented. Operator splitting comprises temporal and spatial splitting. Temporal splitting is based on the hybrid method, which combines numerical and analytical methods to resolve the nonlinearity of the equation, and the maximum principle is maintained unconditionally. In addition, the temporal accuracy can be easily extended to the second or higher order. Spatial splitting is considered for a compact operator with a simple ADI-type implementation. This allows the Thomas algorithm, which is simple and fast, to be applied, including for solving two- and three-dimensional problems. The stability and accuracy proofs of the proposed scheme are presented. The numerical results show that the accuracy, stability, efficiency, and dynamics are consistent with theory. PubDate: 2021-09-28

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Abstract: The hub location problems deal with determining the optimal location of hub facilities and allocating the demand nodes to these hubs in such a way that the traffic between any origin–destination pair is routed effectively. This paper proposes the uncapacitated r-allocation p-hub median problem under congestion. The problem is formulated as a second-order cone programming and an efficient simulated annealing heuristic algorithm is proposed to solve the large instances of the problem. Extensive computational experiments are conducted based on three well-known data sets to demonstrate the efficiency of the proposed algorithm and also to study the effect of different input parameters on the optimal solutions. Some managerial insights are derived based on the obtained numerical results. PubDate: 2021-09-27

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Abstract: In this paper, we introduce a new modified proximal point algorithm based on M-iteration to approximate a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mapping in CAT(0) space. We also prove the \(\Delta \) -convergence of the proposed algorithm for solving common minimization problem and fixed point problem. We also provide an application and numerical results based on our proposed algorithm. PubDate: 2021-09-27