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Abstract: Abstract The problem of sliding mode fault-tolerant control (SMFTC) for T–S fuzzy systems is addressed in this paper. The case that the fuzzy system has different input matrices, and the input uncertainties is considered, which is more universal than the existing results. A sliding mode based observer is constructed to estimate the system states. Then, fuzzy linear sliding surfaces are constructed for the error system and the observer, and the restricted condition that all the input matrices are common existing in many results is removed. In the sequel, a singular system approach (SSA) is developed to deal with the input uncertainties. Meanwhile, an adaptive sliding mode fault-tolerant controller is constructed, which can completely compensate the effects of the fault and stabilize the fault system. Finally, the theoretical method is verified by simulation studies. PubDate: 2022-11-29

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Abstract: Abstract This paper addresses single-machine scheduling problems with truncated learning effects. The objective is to determine the optimal job schedule such that the makespan, the total weighted completion time and the maximum lateness are to be minimized. All the considered problems are NP-hard; hence, for each problem, we propose the heuristic and branch-and-bound algorithms. Extensive numerical experiments validate the efficiency of the proposed solution algorithms on a set of randomly generated instances. PubDate: 2022-11-29

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Abstract: Abstract This paper devotes to the generalized eigenvalues for even order tensors. We extend classical spectral theory for matrix pairs to the multilinear case, including the generalized Schur decomposition, the Geršgorin circle theorem, and the Bauer–Fike theorem for regular tensor pairs of even order. We introduce the backward errors and \(\epsilon \) -pseudospectrums for generalized tensor eigenvalues in normwise and componentwise, respectively, and particularize the application in stability analysis for the generalized multilinear systems. By the normwise pseudospectral theory, we obtain a lower bound for the distance from a regular tensor pair to singularity, and a formulation of the distance from a reachable multilinear time invariant control system to unreachability is given. PubDate: 2022-11-29

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Abstract: Abstract In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solution of split generalized equilibrium problem which is also a fixed point of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Our iterative method uses step-size which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We display a numerical example to illustrate the performance of our result. The result presented in this article unifies and extends several existing results in the literature. PubDate: 2022-11-29

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Abstract: Abstract Nonlinear matrix equation \(X-\sum \limits _{i = 1}^m {A_i^*{X^{-1}}{A_i} = Q} \) has wide applications in control theory, dynamic planning, interpolation theory and random filtering. In this paper, a fixed-point accelerated iteration method is proposed, and based on the basic characteristics of the Thompson distance, the convergence and error estimation of the proposed algorithm are proved. Numerical comparison experiments show that the proposed algorithm is feasible and effective. PubDate: 2022-11-28

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Abstract: Abstract This paper reports an efficient numerical method based on the Bernoulli polynomials for solving the variable-order fractional partial integro-differential equation(V-O-FPIDEs). The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann–Liouville integral operator are used in our paper. First, we prove the existence and uniqueness of the original equation by Gronwall inequality. Second, we use two-dimensional Bernoulli polynomials to approximate the unknown function of the original equation, and use the Gauss–Jacobi quadrature formula to deal with the variable-order Caputo fractional derivative operator and Riemann–Liouville integral operator. Then, the original equation is transformed into the corresponding system of algebraic equations. Furthermore, we give the convergence analysis and error estimation of the proposed method. Finally, some numerical examples illustrate the effectiveness of the method. PubDate: 2022-11-27

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Abstract: Abstract The objective of this work is to present a redefined quintic B-spline (QB-spline) collocation technique for nonlinear higher order PDEs. Two types of PDEs, viz., regularized long-wave (RLW) and Rosenau equations, are considered as these equations play a key role in the modeling of various natural phenomena in science and engineering. The time derivative is discretized by the forward difference scheme, while redefined QB-spline functions are used to integrate the spatial derivatives. Rubin–Graves-type linearization process is used to linearize the nonlinear terms. The discretization of the PDEs gives systems of linear equations. The accuracy and efficiency of the method are checked through three examples. It is found that the present method provides better results than earlier methods. The rate of convergence (ROC) of the method is obtained. The stability analysis is also discussed. PubDate: 2022-11-27

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Abstract: Abstract Release of toxic substances in water bodies from various sources is a major threat to ecologically most vulnerable aquatic food-chain. Again, planktons which hold the whole aquatic ecosystem by serving as the basic food sources, appear to be the most sensitive aquatic organisms to environmental toxins. Consequently all the fish species from prey to predator find it hard to survive in the toxic environment, severely affecting the fishing yields. The unpleasant truth is that toxicants in the environment are continuously increasing due to different natural and human activities. Thus, it is worthy to study a fishery model in the presence of environmental toxins. In this paper, we design a toxicated intraguild fishery model where the shared biotic resource fixes the logistic carrying capacities for both prey and predator fish species. We also introduce the concept of time delay to consider the gestation time for prey and predator species. We locate all the possible equilibria and then investigate the local asymptotic stable behaviour of the coexistence equilibrium point. For the delayed model, we analysis the occurrence of Hopf bifurcation by taking time delay as a bifurcation parameter. It establishes that the delayed model goes under Hopf bifurcation when the delay passes through a certain threshold value. Then, we construct a quadratic cost function to find a sustainable harvesting policy for the process of maximizing monetary profit from harvesting yields. The proposed work is finally validated by numerical simulations. Some future directions are also included after the concluding remarks. PubDate: 2022-11-27

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Abstract: Abstract In this paper, we use a metric derivative which is based on the Hausdorff distance between fuzzy numbers. Using this concept of differentiability, we study fuzzy delay differential equations and also prove a result which guarantees the existence of the approximate solutions. The proof of this result is constructive and provides a method to obtain approximate solutions based on fuzzy arithmetic. In order to illustrate the applicability of the presented results, we provide an example with Hutchinson equation and other with a two-dimensional system. PubDate: 2022-11-27

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Abstract: Abstract A Pythagorean fuzzy set outperforms fuzzy and intuitionistic fuzzy sets in solving uncertain issues. For comparing Pythagorean fuzzy sets, compatibility indices such as distance, similarity, correlation, divergence, etc. are essential. The sole compatibility metric that reveals the nature of the relationship between the Pythagorean fuzzy sets is the correlation coefficient. There are many applications for the correlation coefficient in decision-making, pattern analysis, medical diagnosis, and other areas. The novel coefficient of correlation for Pythagorean fuzzy sets that we have proposed in this study provides both the nature (positive or negative) and level of the correlation between two Pythagorean fuzzy sets. We also compared the proposed correlation coefficient to all previously calculated Pythagorean fuzzy correlation coefficients. The utility of the suggested metrics has been demonstrated in classification, medical diagnosis, and clustering problems employing Pythagorean fuzzy data. All of the Pythagorean fuzzy correlation coefficients that are currently in use have been compared to the findings of the proposed measure. In classification problems, the proposed metric has a high level of confidence. PubDate: 2022-11-24

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Abstract: Abstract A novel numerical technique based on orthogonal Laguerre polynomials called the Laguerre matrix collocation method is proposed. The motivation of the study is to reduce the computational cost in mathematical models by adapting Laguerre polynomials directly without transforming them into the truncated Taylor polynomial basis. The new approach is suitable for solving fourth-order partial differential equations arising in physics and engineering. The algorithm and error analyses are presented in general form and applied to two physical models from solid mechanics. First, the technique is used to solve the governing equation for a plate deflection under a harmonically distributed static load. Second, the algorithm is applied to the bending model of a shear deformable plate under the harmonically distributed static load. The boundary conditions of the models are specified, and the bending responses of the models are obtained. The numerical results are compared with the exact results from the literature. The comparisons show that the new approach is suitable for numerical solutions of fourth-order partial differential equations which arise in physics and engineering. PubDate: 2022-11-23

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Abstract: Abstract This paper is concerned with the robust 1-center location problems on the tree networks under minmax and minmax regret criteria, where the vertex weights and edge lengths of the underlying tree are considered as dynamic data or discrete set of scenarios. In the problem under minmax criterion, the aim is to find a point on the tree such that it minimizes the maximum cost. The problem under minmax regret asks to find a point on the tree such that minimizes the maximum regret. We develop the first optimal solution algorithms with polynomial time complexities for the problems under investigation. PubDate: 2022-11-23

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Abstract: Abstract Finite volume fitted difference schemes are constructed for one and two-dimensional air-pollution models with degenerate vertical diffusion. A weak formulation of the equations imposes the boundary conditions naturally along the boundaries, where the equation becomes degenerate. Then, we establish the energy well-posedness of the initial-boundary value problems. We prove minimum principle and show that the solution cannot attains its minimum on the boundary of degeneration and this allows us to control the positivity of its solution. To overcome the degeneracy of the vertical diffusion, we perform a local fitted space discretization. Non-negativity of numerical solutions is proved. Numerical experiments are discussed. As examples, we apply the method to study the pollution concentration to Monin–Obukhov types atmospheric models. PubDate: 2022-11-23

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Abstract: Abstract Intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets are rudimentary concepts in computational intelligence, which have a myriad of applications in fuzzy system modeling and decision-making under uncertainty. Nevertheless, all these notions have some strict restrictions imposed on the membership and non-membership grades (e.g., the sum of the grades or the sum of the squares of the grades or the sum of the qth power of the grades is less than or equal to 1). To relax these restrictions, linear Diophantine fuzzy set is a new extension of fuzzy sets, by additionally considering reference/control parameters. Thereby, the sum of membership grade and non-membership grade can be greater than 1, and even both of these grades can be 1. By selecting different pairs of reference parameters, linear Diophantine fuzzy sets can naturally categorize concerned problems and produce appropriate solutions accordingly. In this paper, the interval-valued linear Diophantine fuzzy set, which is a generalization of linear Diophantine fuzzy set, is studied. The interval-valued linear Diophantine fuzzy set is more efficient to deal with uncertain and vague information due to its flexible intervals of membership grades, non-membership grades, and reference parameters. Some basic operations on interval-valued linear Diophantine fuzzy sets are presented. We define interval-valued linear Diophantine fuzzy weighted average and interval-valued linear Diophantine fuzzy weighted geometric aggregation operators. Based on these new aggregation operators, we propose a method for multi-criteria decision-making based on supplier selection under the interval-valued linear Diophantine fuzzy environment. Besides, a real-life example, comparison study, and advantages of proposed aggregation operators are presented. We describe some correlation coefficient measures (type-1 and type-2) for the interval-valued linear Diophantine fuzzy sets and they are applied in medical diagnosis for Coronavirus Disease 2019 (COVID-19). Lastly, a comparative examination and the benefits of proposed correlation coefficient measures are also discussed. PubDate: 2022-11-23

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Abstract: Abstract The forward–backward–forward (FBF) splitting method is a popular iterative procedure for finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. In this paper, we introduce a modification of the forward–backward splitting method with an adaptive step size rule for inclusion problems in real Hilbert spaces. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish weak convergence of the proposed algorithm. Moreover, if the single-valued operator is cocoercivity, then the proposed algorithm strongly converges to the unique solution of the problem with an R-linear rate. Finally, we give several numerical experiments to illustrate the convergence of the proposed algorithm and also to compare them with others. PubDate: 2022-11-22

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Abstract: Abstract In this paper, we study the existence of even solution for a class of Schrödinger equations with Liouville–Weyl fractional derivatives $$\begin{aligned} {\left\{ \begin{array}{ll} {_{x}}D_{\infty }^{\alpha }({_{-\infty }}D_{x}^{\alpha }u) = \lambda g(u)&{}\text{ in }\quad {\mathbb {R}},\\ u\in {\mathbb {I}}_{-}^\alpha ({\mathbb {R}}), \end{array}\right. } \end{aligned}$$ where \(\alpha \in (0,\frac{1}{2})\) , \({_{-\infty }}D_{x}^{\alpha }u(\cdot ), {_{x}}D_{\infty }^{\alpha }u(\cdot )\) denote the left and right Liouville–Weyl fractional derivatives and \(g: {\mathbb {R}}\rightarrow {\mathbb {R}}\) is a continuous function satisfying suitable conditions. For the case that \(\lambda =1\) and \(g(u)= u ^{p-1}u-u\) with \(p\in (1,2_{\alpha }^*-1)\) , we show that the above problem possesses at least one nonnegative and even solution. Besides, we also investigate the existence of normalized solutions for the first time to this problem when g is the form of more general nonlinearity. PubDate: 2022-11-22

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Abstract: Abstract This article researches the approach to solving different instances of Cauchy integral equations by utilizing the Lucas polynomial technique. The technique decreases the solution of a specified singular integral equation to the solution of an array equation corresponding to a linear scheme of algebraic equations with unnamed Lucas coefficients. An evaluation of the introduced strategy has been described. Some numerical illustrates are introduced to display the accuracy and efficiency of the suggested strategy. The comparison between the results which are obtained by the Lucas polynomial method and other methods such as the Lerch polynomial method, Chebyshev polynomial method, Bernstein polynomial method, and the reproducing kernel method is represented in a group of tables. All the numerical results are obtained by using the Maple 18 program. PubDate: 2022-11-20

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Abstract: Abstract In this paper, we study and construct a higher order numerical algorithm for singularly perturbed differential-difference convection–diffusion equation with retarded term appearing in computational biological science. The solution of the considered class of problems may exhibit a boundary layer due to the presence of the perturbation parameter and retarded term. We have discussed the analytical behaviour of the exact solution and its partial derivatives. We have used Taylor’s series expansion to approximate the advance and delay terms of the model problem and then the problem is discretized using Crank–Nicolson’s method on equidistant mesh in the time direction and modified cubic B-spline basis functions on generalized Shishkin mesh in the spatial direction. We have also shown that the developed algorithm is unconditionally stable. The proposed numerical algorithm is proved to be \(\varepsilon \) -uniformly convergent of order four in the spatial direction up to a logarithmic factor and second-order convergent in the time direction. To demonstrate the accuracy and to validate the theoretical results of the proposed numerical algorithm, we have presented three numerical experiments. We have also compared our method with existing schemes in the literature to prove the accuracy of the proposed numerical algorithm. PubDate: 2022-11-19

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Abstract: Abstract In this article, we present two high-order structure-preserving difference schemes for the modified Kawahara equation, which are named as Scheme I and Scheme II, respectively. Scheme I is a compact fourth-order difference scheme with a seven-point stencil and preserves discrete mass, while Scheme II is a standard fourth-order difference scheme with a nine-point stencil and preserves discrete energy. The proposed two schemes are three-level implicit and the numerical convergence order is \(O(\tau ^{2}+h^{4})\) . The unconditional stability of Scheme I and Scheme II is proven by von Neumann’s analysis. According to the Lax equivalence theorem, the convergence of the two schemes is also presented. The errors and rates of convergence, the discrete conservative mass \(Q^{n}\) and energy \(E^{n}\) are compared with those from other schemes. At last, some numerical experiments are given to demonstrate that the two proposed schemes are accurate and efficient for handling the single and multi-solitary waves propagating over a long period. PubDate: 2022-11-19

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Abstract: Abstract We prove the finite convergence of the sequences generated by some extragradient-type methods solving variational inequalities under the weakly sharp condition of the solution set. In addition, we provide estimations for the number of iterations to guarantee the sequence converges to a point in the solution set and prove that these estimations are optimal. Numerical examples are presented to illustrate the theoretical results. PubDate: 2022-11-19