Applied Mathematics and Computation
Journal Prestige (SJR): 1.065 Citation Impact (citeScore): 2 Number of Followers: 34 Hybrid journal (It can contain Open Access articles) ISSN (Print) 00963003 Published by Elsevier [3159 journals] 
 New examples of rank one solvable real rigid Lie algebras possessing a
nonvanishing Chevalley cohomology Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): J.M. Ancochea Bermúdez, R. CampoamorStursberg, F. Oviaño GarcíaAbstractThe class of rank one solvable Lie algebras possessing a maximal torus t with eigenvalue spectrum spec(t)=(1,4,5,…,n+2) is studied in the context of rigidity. It is shown that from the value n ≥ 18, three isomorphism classes of rigid Lie algebras exist, two of them being algebraically rigid, and the third being geometrically rigid with a twodimensional cohomology space H2(g,g).
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): J.M. Ancochea Bermúdez, R. CampoamorStursberg, F. Oviaño GarcíaAbstractThe class of rank one solvable Lie algebras possessing a maximal torus t with eigenvalue spectrum spec(t)=(1,4,5,…,n+2) is studied in the context of rigidity. It is shown that from the value n ≥ 18, three isomorphism classes of rigid Lie algebras exist, two of them being algebraically rigid, and the third being geometrically rigid with a twodimensional cohomology space H2(g,g).
 Simpson’s rule to approximate Hilbert integral and its application
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jin Li, Zhaoqing WangAbstractIn this paper, the computation of Hilbert singular integral with generalized composite Simpson’s rule for is discussed. When singular points coincide with some a priori known point, the convergence rate of Simpson’s rule higher than global one, we obtain the pointwise superconvergence phenomenon. Which means the especial function equal zero, the superconvergence points are got. Then choosing the superconvergence point as the collocation points, we get a collocation scheme for solving the relevant Hilbert integral equation. At last, some numerical examples are presented to validate the theoretical analysis.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jin Li, Zhaoqing WangAbstractIn this paper, the computation of Hilbert singular integral with generalized composite Simpson’s rule for is discussed. When singular points coincide with some a priori known point, the convergence rate of Simpson’s rule higher than global one, we obtain the pointwise superconvergence phenomenon. Which means the especial function equal zero, the superconvergence points are got. Then choosing the superconvergence point as the collocation points, we get a collocation scheme for solving the relevant Hilbert integral equation. At last, some numerical examples are presented to validate the theoretical analysis.
 Synchronization analysis of fractionalorder threeneuron BAM neural
networks with multiple time delays Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jianmei Zhang, Jianwei Wu, Haibo Bao, Jinde CaoAbstractIn this paper, we are concerned with the masterslave synchronization problem of fractionalorder threeneuron bidirectional associative memory (BAM) neural networks with multiple time delays. The linear feedback controller is designed to ensure the global synchronization of the masterslave systems. Based on the Lyapunov functionals and fractionalorder comparison theory, the corresponding synchronization conditions are derived. In the end, an example is given to further demonstrate the effectiveness of the obtained results.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jianmei Zhang, Jianwei Wu, Haibo Bao, Jinde CaoAbstractIn this paper, we are concerned with the masterslave synchronization problem of fractionalorder threeneuron bidirectional associative memory (BAM) neural networks with multiple time delays. The linear feedback controller is designed to ensure the global synchronization of the masterslave systems. Based on the Lyapunov functionals and fractionalorder comparison theory, the corresponding synchronization conditions are derived. In the end, an example is given to further demonstrate the effectiveness of the obtained results.
 Some identities of the generalized Fibonacci and Lucas sequences
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jizhen Yang, Zhizheng ZhangAbstractThe purpose of this paper is to study generalized Fibonacci and Lucas sequences. We first introduce generalized Lucas sequences. Section 2 contains a list of elementary relationships about generalized Fibonacci and Lucas sequences. In Section 3, we give a generalization of the Binet’s formulas of generalized Fibonacci, Lucas sequences and its applications. Section 4 is devote to derive many identities and congruence relations for generalized Fibonacci, Lucas sequences by using operator method.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jizhen Yang, Zhizheng ZhangAbstractThe purpose of this paper is to study generalized Fibonacci and Lucas sequences. We first introduce generalized Lucas sequences. Section 2 contains a list of elementary relationships about generalized Fibonacci and Lucas sequences. In Section 3, we give a generalization of the Binet’s formulas of generalized Fibonacci, Lucas sequences and its applications. Section 4 is devote to derive many identities and congruence relations for generalized Fibonacci, Lucas sequences by using operator method.
 Fast numerical simulation of a new timespace fractional option pricing
model governing European call option Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): H. Zhang, F. Liu, S. Chen, V. Anh, J. ChenAbstractWhen the fluctuation of option price is regarded as a fractal transmission system and the stock price follows a Lévy distribution, a timespace fractional option pricing model (TSFOPM) is obtained. Then we discuss the numerical simulation of the TSFOPM. A discrete implicit numerical scheme with a secondorder accuracy in space and a 2−γ order accuracy in time is constructed, where γ is a transmission exponent. The stability and convergence of the obtained numerical scheme are analyzed. Moreover, a fast biconjugate gradient stabilized method is proposed to solve the numerical scheme in order to reduce the storage space and computational cost. Then a numerical example with exact solution is presented to demonstrate the accuracy and effectiveness of the proposed numerical method. Finally, the TSFOPM and the above numerical technique are applied to price European call option. The characteristics of the fractional option pricing model are analyzed in comparison with the classical Black–Scholes (BS) model.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): H. Zhang, F. Liu, S. Chen, V. Anh, J. ChenAbstractWhen the fluctuation of option price is regarded as a fractal transmission system and the stock price follows a Lévy distribution, a timespace fractional option pricing model (TSFOPM) is obtained. Then we discuss the numerical simulation of the TSFOPM. A discrete implicit numerical scheme with a secondorder accuracy in space and a 2−γ order accuracy in time is constructed, where γ is a transmission exponent. The stability and convergence of the obtained numerical scheme are analyzed. Moreover, a fast biconjugate gradient stabilized method is proposed to solve the numerical scheme in order to reduce the storage space and computational cost. Then a numerical example with exact solution is presented to demonstrate the accuracy and effectiveness of the proposed numerical method. Finally, the TSFOPM and the above numerical technique are applied to price European call option. The characteristics of the fractional option pricing model are analyzed in comparison with the classical Black–Scholes (BS) model.
 On Markov’s theorem on zeros of orthogonal polynomials revisited
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): K. Castillo, M.S. Costa, F.R. RafaeliAbstractThis paper briefly surveys Markov’s theorem related to zeros of orthogonal polynomials. Monotonicity of zeros of some families of orthogonal polynomials are reviewed in detail.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): K. Castillo, M.S. Costa, F.R. RafaeliAbstractThis paper briefly surveys Markov’s theorem related to zeros of orthogonal polynomials. Monotonicity of zeros of some families of orthogonal polynomials are reviewed in detail.
 A conforming lockingfree approximation for a Koiter shell
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Hanen Ferchichi, Saloua Mani AouadiAbstractAs in the Naghdi framework, membrane locking is expected for bendingdominated Koiter shell when the thickness decreases. Inspired by Arnold and Brezzi (1997), we design a lockingfree mixed finite element method for the Koiter shell. This method is implemented, in terms of the displacement variables, as the minimization of an altered energy over a conforming finite element space. We approximate the tangential displacements by continuous piecewise polynomials augmented by bubbles and the transversal displacements by the consistent HCT (Hsieh–Clough–Tocher) element. The membrane stresses, derived from a partial integration of the membrane energy, is approximated by discontinuous piecewise polynomials. We establish optimal error estimates independent of the thickness under some restrictions which prove that the mixed solution is lockingfree. We confirm our theoretical predictions with some numerical tests, in particular, we consider a hemicylindrical shell and an hyperbolic paraboloid shell.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Hanen Ferchichi, Saloua Mani AouadiAbstractAs in the Naghdi framework, membrane locking is expected for bendingdominated Koiter shell when the thickness decreases. Inspired by Arnold and Brezzi (1997), we design a lockingfree mixed finite element method for the Koiter shell. This method is implemented, in terms of the displacement variables, as the minimization of an altered energy over a conforming finite element space. We approximate the tangential displacements by continuous piecewise polynomials augmented by bubbles and the transversal displacements by the consistent HCT (Hsieh–Clough–Tocher) element. The membrane stresses, derived from a partial integration of the membrane energy, is approximated by discontinuous piecewise polynomials. We establish optimal error estimates independent of the thickness under some restrictions which prove that the mixed solution is lockingfree. We confirm our theoretical predictions with some numerical tests, in particular, we consider a hemicylindrical shell and an hyperbolic paraboloid shell.
 Normal solutions of a boundaryvalue problem arising in free convection
boundarylayer flows in porous media Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Zhongxin ZhangAbstractThis paper is concerned with normal solutions of a twopoint boundaryvalue problem of second order which arises in the steady free convection boundarylayer flow over a vertical permeable flat plate being embedded in a saturated porous medium with both prescribed heat flux and suction rate of the plate. We use a very simple argument to prove that there exists a λmin ∈ (1.3782407, 1.4166499) such that this problem has no normal solution for all λ
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Zhongxin ZhangAbstractThis paper is concerned with normal solutions of a twopoint boundaryvalue problem of second order which arises in the steady free convection boundarylayer flow over a vertical permeable flat plate being embedded in a saturated porous medium with both prescribed heat flux and suction rate of the plate. We use a very simple argument to prove that there exists a λmin ∈ (1.3782407, 1.4166499) such that this problem has no normal solution for all λ
 Analysis on the method of fundamental solutions for biharmonic equations
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Fangfang Dou, ZiCai Li, C.S. Chen, Zhaolu TianAbstractIn this paper, the error and stability analysis of the method of fundamental solution (MFS) is explored for biharmonic equations. The bounds of errors are derived for the fundamental solutions r2ln r in bounded simplyconnected domains, and the polynomial convergence rates are obtained for certain smooth solutions. The bounds of condition number are also derived to show the exponential growth rates for disk domains. Numerical experiments are carried out to support the above analysis, which is the first time to provide the rigorous analysis of the MFS using r2ln r for biharmonic equations.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Fangfang Dou, ZiCai Li, C.S. Chen, Zhaolu TianAbstractIn this paper, the error and stability analysis of the method of fundamental solution (MFS) is explored for biharmonic equations. The bounds of errors are derived for the fundamental solutions r2ln r in bounded simplyconnected domains, and the polynomial convergence rates are obtained for certain smooth solutions. The bounds of condition number are also derived to show the exponential growth rates for disk domains. Numerical experiments are carried out to support the above analysis, which is the first time to provide the rigorous analysis of the MFS using r2ln r for biharmonic equations.
 Two iterative algorithms for stochastic algebraic Riccati matrix equations
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): AiGuo Wu, HuiJie Sun, Ying ZhangAbstractIn this paper, two iterative algorithms are proposed to solve stochastic algebraic Riccati matrix equations arising in the linear quadratic optimal control problem of linear stochastic systems with statedependent noise. In the first algorithm, a standard Riccati matrix equation needs to be solved at each iteration step, and in the second algorithm a standard Lyapunov matrix equation needs to be solved at each iteration step. In the proposed algorithms, a weighted average of the estimates in the last and the previous steps is used to update the estimate of the unknown variable at each iteration step. Some properties of the sequences generated by these algorithms under appropriate initial conditions are presented, and the convergence properties of the proposed algorithms are analyzed. Finally, two numerical examples are employed to show the effectiveness of the proposed algorithms.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): AiGuo Wu, HuiJie Sun, Ying ZhangAbstractIn this paper, two iterative algorithms are proposed to solve stochastic algebraic Riccati matrix equations arising in the linear quadratic optimal control problem of linear stochastic systems with statedependent noise. In the first algorithm, a standard Riccati matrix equation needs to be solved at each iteration step, and in the second algorithm a standard Lyapunov matrix equation needs to be solved at each iteration step. In the proposed algorithms, a weighted average of the estimates in the last and the previous steps is used to update the estimate of the unknown variable at each iteration step. Some properties of the sequences generated by these algorithms under appropriate initial conditions are presented, and the convergence properties of the proposed algorithms are analyzed. Finally, two numerical examples are employed to show the effectiveness of the proposed algorithms.
 The convergence theory for the restricted version of the overlapping Schur
complement preconditioner Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Xin Lu, Xingping Liu, Tongxiang GuAbstractThe restricted version of the overlapping Schur complement (SchurRAS) preconditioner was introduced by Li and Saad (2006) for the solution of linear system Ax=b, and numerical results have shown that the SchurRAS method outperforms the restricted additive Schwarz (RAS) method both in terms of iteration count and CPU time. In this paper, based on meticulous derivation, we give an algebraic representation of the SchurRAS preconditioner, and prove that the SchurRAS method is convergent under the condition that A is an Mmatrix and it converges faster than the RAS method.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Xin Lu, Xingping Liu, Tongxiang GuAbstractThe restricted version of the overlapping Schur complement (SchurRAS) preconditioner was introduced by Li and Saad (2006) for the solution of linear system Ax=b, and numerical results have shown that the SchurRAS method outperforms the restricted additive Schwarz (RAS) method both in terms of iteration count and CPU time. In this paper, based on meticulous derivation, we give an algebraic representation of the SchurRAS preconditioner, and prove that the SchurRAS method is convergent under the condition that A is an Mmatrix and it converges faster than the RAS method.
 Erratum to “Numerical solution of linear Fredholm integral equation by
using hybrid Taylor and BlockPulse functions” [Appl. Math. Comput. 149
(2004) 799–806] Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Mehdi SabzevariAbstractThis is an erratum to the published paper “Numerical solution of linear Fredholm integral equation by using hybrid Taylor and BlockPulse functions” by Maleknejad and Mahmoudi, where there are some scientific errors. After considering these errors we attempt to rectify them by presenting correct approach and formulae. Moreover, by means of some numerical examples, we illustrate the accuracy of solutions after applying the correct formulae.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Mehdi SabzevariAbstractThis is an erratum to the published paper “Numerical solution of linear Fredholm integral equation by using hybrid Taylor and BlockPulse functions” by Maleknejad and Mahmoudi, where there are some scientific errors. After considering these errors we attempt to rectify them by presenting correct approach and formulae. Moreover, by means of some numerical examples, we illustrate the accuracy of solutions after applying the correct formulae.
 Stability of the driftimplicit and doubleimplicit Milstein schemes for
nonlinear SDEs Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jinran Yao, Siqing GanAbstractThis paper examines the stability of numerical solutions of nonlinear stochastic differential equations (SDEs) with nonglobal Lipschitz continuous coefficients. Two implicit Milstein schemes, called driftimplicit Milstein scheme and doubleimplicit Milstein scheme, are considered to simulate the underlying SDEs. It is proved that the schemes can preserve the stability and contractivity in mean square of the underlying systems.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jinran Yao, Siqing GanAbstractThis paper examines the stability of numerical solutions of nonlinear stochastic differential equations (SDEs) with nonglobal Lipschitz continuous coefficients. Two implicit Milstein schemes, called driftimplicit Milstein scheme and doubleimplicit Milstein scheme, are considered to simulate the underlying SDEs. It is proved that the schemes can preserve the stability and contractivity in mean square of the underlying systems.
 On the lacunary sum of trinomial coefficients
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): HeXia Ni, Hao PanAbstractThe trinomial coefficient (nk)2 is given by∑k=−nn(nk)2xk=(1+x+x−1)n.In this paper, we obtain the explicit formulas for the lacunary sum∑−n≤k≤nk≡r(modm)(nk)2.For example,∑−n≤k≤nk≡1(mod12)(nk)2=2n+3n−(−1)n+6Hn12,where H0=0,H1=1 and Hn=2Hn−1+2Hn−2 for n ≥ 2.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): HeXia Ni, Hao PanAbstractThe trinomial coefficient (nk)2 is given by∑k=−nn(nk)2xk=(1+x+x−1)n.In this paper, we obtain the explicit formulas for the lacunary sum∑−n≤k≤nk≡r(modm)(nk)2.For example,∑−n≤k≤nk≡1(mod12)(nk)2=2n+3n−(−1)n+6Hn12,where H0=0,H1=1 and Hn=2Hn−1+2Hn−2 for n ≥ 2.
 Numerical solution of threedimensional Volterra–Fredholm integral
equations of the first and second kinds based on Bernstein’s
approximation Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Khosrow Maleknejad, Jalil Rashidinia, Tahereh EftekhariAbstractA new and efficient method is presented for solving threedimensional Volterra–Fredholm integral equations of the second kind (3DVFIEK2), first kind (3DVFIEK1) and even singular type of these equations. Here, we discuss threevariable Bernstein polynomials and their properties. This method has several advantages in reducing computational burden with good degree of accuracy. Furthermore, we obtain an error bound for this method. Finally, this method is applied to five examples to illustrate the accuracy and implementation of the method and this method is compared to already present methods. Numerical results show that the new method provides more efficient results in comparison with other methods.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Khosrow Maleknejad, Jalil Rashidinia, Tahereh EftekhariAbstractA new and efficient method is presented for solving threedimensional Volterra–Fredholm integral equations of the second kind (3DVFIEK2), first kind (3DVFIEK1) and even singular type of these equations. Here, we discuss threevariable Bernstein polynomials and their properties. This method has several advantages in reducing computational burden with good degree of accuracy. Furthermore, we obtain an error bound for this method. Finally, this method is applied to five examples to illustrate the accuracy and implementation of the method and this method is compared to already present methods. Numerical results show that the new method provides more efficient results in comparison with other methods.
 New multiplicative perturbation bounds for the generalized polar
decomposition Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Na Liu, Wei Luo, Qingxiang XuAbstractSome new Frobenius norm bounds of the unique solution to certain structured Sylvester equation are derived. Based on the derived norm upper bounds, new multiplicative perturbation bounds are provided both for subunitary polar factors and positive semidefinite polar factors. Some previous results are then improved.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Na Liu, Wei Luo, Qingxiang XuAbstractSome new Frobenius norm bounds of the unique solution to certain structured Sylvester equation are derived. Based on the derived norm upper bounds, new multiplicative perturbation bounds are provided both for subunitary polar factors and positive semidefinite polar factors. Some previous results are then improved.
 Dynamical behaviors analysis of memristorbased fractionalorder
complexvalued neural networks with time delay Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Yuting Zhang, Yongguang Yu, Xueli CuiAbstractThe robust stability for memristorbased fractionalorder ComplexValued Neural Networks (FCVNNs) with time delay is investigated here. In complex plane, by using the Lyapunov method, and under the sense of Filippov solutions, the existence of unique equilibrium and globally asymptotic stability for such Neural Networks (NNs) have been obtained when the nonlinear complexvalued activation functions could be split into two(real and imaginary) parts. Moreover, locally asymptotic stability for such Neural NNs have been proposed when the nonlinear complex activation functions are bounded. Lastly, three numerical examples are given to confirm the efficiency of theorems.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Yuting Zhang, Yongguang Yu, Xueli CuiAbstractThe robust stability for memristorbased fractionalorder ComplexValued Neural Networks (FCVNNs) with time delay is investigated here. In complex plane, by using the Lyapunov method, and under the sense of Filippov solutions, the existence of unique equilibrium and globally asymptotic stability for such Neural Networks (NNs) have been obtained when the nonlinear complexvalued activation functions could be split into two(real and imaginary) parts. Moreover, locally asymptotic stability for such Neural NNs have been proposed when the nonlinear complex activation functions are bounded. Lastly, three numerical examples are given to confirm the efficiency of theorems.
 A note on continuousstage Runge–Kutta methods
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Wensheng TangAbstractWe provide a note on continuousstage Runge–Kutta methods (csRK) for solving initial value problems of firstorder ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge–Kutta (RK) methods, can give us a new perspective on RK discretization and it may enlarge the application of RK approximation theory in modern mathematics and engineering fields. A highlighted advantage of investigation of csRK methods is that we do not need to study the tedious solution of multivariable nonlinear algebraic equations associated with order conditions. In this note, we will review, discuss and further promote the recentlydeveloped csRK theory. In particular, we will place emphasis on geometric integrators including symplectic methods, symmetric methods and energypreserving methods which play a central role in the field of geometric numerical integration.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Wensheng TangAbstractWe provide a note on continuousstage Runge–Kutta methods (csRK) for solving initial value problems of firstorder ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge–Kutta (RK) methods, can give us a new perspective on RK discretization and it may enlarge the application of RK approximation theory in modern mathematics and engineering fields. A highlighted advantage of investigation of csRK methods is that we do not need to study the tedious solution of multivariable nonlinear algebraic equations associated with order conditions. In this note, we will review, discuss and further promote the recentlydeveloped csRK theory. In particular, we will place emphasis on geometric integrators including symplectic methods, symmetric methods and energypreserving methods which play a central role in the field of geometric numerical integration.
 Efficient computations for generalized Zernike moments and image recovery
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): AnWen Deng, ChihYing GwoAbstractZernike moments are a set of orthogonal moments which have been successfully applied in the fields of image processing and pattern recognition. An innovative calculation method for Zernike moments, named generalized Zernike moments, is presented in this study. The generalized Zernike moment is a variant of Zernike moment. In this paper, we are proposing methods to calculate highorder generalized Zernike moments. Two kinds of recurrence for calculating generalized Zernike moments were introduced with rigorous proofs. Through the usage of the symmetries operated by the Dihedral group of order eight, the proposed method is fast and stable. The experimental results show that of the proposed method took 4.206s to compute the top 500order generalized Zernike moments of an image with 512 by 512 pixels. Furthermore, by choosing the extra parameter α in the recurrence, the method enhanced the accuracy remarkably compared to the regular Zernike moments. Its normalized mean square error is 0.00144067 when α was set to 66 and the top 500order moments were used to reconstruct the image. This error is 40.47% smaller than the one obtained by using the regular Zernike moments.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): AnWen Deng, ChihYing GwoAbstractZernike moments are a set of orthogonal moments which have been successfully applied in the fields of image processing and pattern recognition. An innovative calculation method for Zernike moments, named generalized Zernike moments, is presented in this study. The generalized Zernike moment is a variant of Zernike moment. In this paper, we are proposing methods to calculate highorder generalized Zernike moments. Two kinds of recurrence for calculating generalized Zernike moments were introduced with rigorous proofs. Through the usage of the symmetries operated by the Dihedral group of order eight, the proposed method is fast and stable. The experimental results show that of the proposed method took 4.206s to compute the top 500order generalized Zernike moments of an image with 512 by 512 pixels. Furthermore, by choosing the extra parameter α in the recurrence, the method enhanced the accuracy remarkably compared to the regular Zernike moments. Its normalized mean square error is 0.00144067 when α was set to 66 and the top 500order moments were used to reconstruct the image. This error is 40.47% smaller than the one obtained by using the regular Zernike moments.
 Estimation distribution algorithms on constrained optimization problems
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Shujun Gao, Clarence W. de SilvaAbstractEstimation distribution algorithm (EDA) is an evolution technique that uses sampling to generate the offspring. Most developed EDAs focus on solving the optimization problems which only have the constraints of variable boundaries. In this paper, EDAs are proposed for solving the constrained optimization problems (COPs) involving various types of constraints. In particular, a modified extreme elitism selection method is designed for EDAs to handle the constraints. This selection extrudes the role of some top best solutions to pull the mean vector of the Gaussian distribution towards these best solutions and makes EDAs form a primary evolutionary direction. The EDAs based on five different Gaussian distribution with this selection are evaluated using a set of benchmark functions and some engineering design problems. It is found that for solving these problems, the EDA that is based on a single multivariate Gaussian distribution model with the modified extreme elitism selection outperforms the other EDAs and some stateoftheart techniques.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Shujun Gao, Clarence W. de SilvaAbstractEstimation distribution algorithm (EDA) is an evolution technique that uses sampling to generate the offspring. Most developed EDAs focus on solving the optimization problems which only have the constraints of variable boundaries. In this paper, EDAs are proposed for solving the constrained optimization problems (COPs) involving various types of constraints. In particular, a modified extreme elitism selection method is designed for EDAs to handle the constraints. This selection extrudes the role of some top best solutions to pull the mean vector of the Gaussian distribution towards these best solutions and makes EDAs form a primary evolutionary direction. The EDAs based on five different Gaussian distribution with this selection are evaluated using a set of benchmark functions and some engineering design problems. It is found that for solving these problems, the EDA that is based on a single multivariate Gaussian distribution model with the modified extreme elitism selection outperforms the other EDAs and some stateoftheart techniques.
 A note on Katugampola fractional calculus and fractal dimensions
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): S. Verma, P. ViswanathanAbstractThe goal of this paper is to study the Katugampola fractional integral of a continuous function of bounded variation defined on a closed bounded interval. We note that the Katugampola fractional integral of a function shares some analytical properties such as boundedness, continuity and bounded variation of the function defining it. Consequently, we deduce that fractal dimensions – Minkowski dimension and Hausdorff dimension – of the graph of the Katugampola fractional integral of a continuous function of bounded variation are one. A natural question then arises is whether there exists a continuous function which is not of bounded variation with its graph having fractal dimensions one. In the last part of the article, we construct a continuous function, which is not of bounded variation and for which the graph has fractal dimensions one. The construction enunciated herein includes previous constructions found in the recent literature as special cases. The article also hints at an upper bound for the upper box dimension of the graph of the Katugampola fractional derivative of a continuously differentiable function.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): S. Verma, P. ViswanathanAbstractThe goal of this paper is to study the Katugampola fractional integral of a continuous function of bounded variation defined on a closed bounded interval. We note that the Katugampola fractional integral of a function shares some analytical properties such as boundedness, continuity and bounded variation of the function defining it. Consequently, we deduce that fractal dimensions – Minkowski dimension and Hausdorff dimension – of the graph of the Katugampola fractional integral of a continuous function of bounded variation are one. A natural question then arises is whether there exists a continuous function which is not of bounded variation with its graph having fractal dimensions one. In the last part of the article, we construct a continuous function, which is not of bounded variation and for which the graph has fractal dimensions one. The construction enunciated herein includes previous constructions found in the recent literature as special cases. The article also hints at an upper bound for the upper box dimension of the graph of the Katugampola fractional derivative of a continuously differentiable function.
 On the faulttolerant metric dimension of convex polytopes
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Hassan Raza, Sakander Hayat, XiangFeng PanAbstractA convex polytopes is a polytope that is also a convex set of points in the ndimensional Euclidean space Rn. By preserving the same adjacency relation between vertices of a convex polytope, its graph is constructed. The metric dimension problem has been extensively studied for convex polytopes and other families of graphs. In this paper, we study the faulttolerant metric dimension problem for convex polytopes. By using a relation between resolving sets and faulttolerant resolving sets of graphs, we prove that certain infinite families of convex polytopes are the families of graphs with constant faulttolerant metric dimension. We conclude the paper with some open problems.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Hassan Raza, Sakander Hayat, XiangFeng PanAbstractA convex polytopes is a polytope that is also a convex set of points in the ndimensional Euclidean space Rn. By preserving the same adjacency relation between vertices of a convex polytope, its graph is constructed. The metric dimension problem has been extensively studied for convex polytopes and other families of graphs. In this paper, we study the faulttolerant metric dimension problem for convex polytopes. By using a relation between resolving sets and faulttolerant resolving sets of graphs, we prove that certain infinite families of convex polytopes are the families of graphs with constant faulttolerant metric dimension. We conclude the paper with some open problems.
 Idea of invariant subspace combined with elementary integral method for
investigating exact solutions of timefractional NPDEs Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Weiguo RuiAbstractIn this paper, inspired by the idea of invariant subspace method and combined with elementary integral method, we introduced a novel approach for investigating exact solutions of a timefractional nonlinear partial differential equation (NPDE). Based on hypothetical structure of solution of separated variable, a timefractional NPDE defined by time and space variables can be reduced to a nonlinear ordinary differential equation (NODE) or NODEs defined by space variable alone, and then using the elementary integral method to solve the NODE or NODEs, different kinds of exact solutions of a timefractional NPDE are obtained finally. As examples, the timefractional Hunter–Saxton equation and timefractional Li–Olver equation were studied. Different kinds of exact solutions of these equations were obtained and their dynamical properties were illustrated.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Weiguo RuiAbstractIn this paper, inspired by the idea of invariant subspace method and combined with elementary integral method, we introduced a novel approach for investigating exact solutions of a timefractional nonlinear partial differential equation (NPDE). Based on hypothetical structure of solution of separated variable, a timefractional NPDE defined by time and space variables can be reduced to a nonlinear ordinary differential equation (NODE) or NODEs defined by space variable alone, and then using the elementary integral method to solve the NODE or NODEs, different kinds of exact solutions of a timefractional NPDE are obtained finally. As examples, the timefractional Hunter–Saxton equation and timefractional Li–Olver equation were studied. Different kinds of exact solutions of these equations were obtained and their dynamical properties were illustrated.
 Polychromatic colorings and cover decompositions of hypergraphs
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Tingting Li, Xia ZhangAbstractA polychromatic coloring of a hypergraph is a coloring of its vertices in such a way that every hyperedge contains at least one vertex of each color. A polychromatic mcoloring of a hypergraph H corresponds to a cover mdecomposition of its dual hypergraph H*. The maximum integer m that a hypergraph H admits a cover mdecomposition is exactly the longest lifetime for a wireless sensor network (WSN) corresponding to the hypergraph H. In this paper, we show that every hypergraph H has a polychromatic mcoloring if m≤⌊Sln(cΔS2)⌋, where 0
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Tingting Li, Xia ZhangAbstractA polychromatic coloring of a hypergraph is a coloring of its vertices in such a way that every hyperedge contains at least one vertex of each color. A polychromatic mcoloring of a hypergraph H corresponds to a cover mdecomposition of its dual hypergraph H*. The maximum integer m that a hypergraph H admits a cover mdecomposition is exactly the longest lifetime for a wireless sensor network (WSN) corresponding to the hypergraph H. In this paper, we show that every hypergraph H has a polychromatic mcoloring if m≤⌊Sln(cΔS2)⌋, where 0
 Sharp conditions for the existence of a stationary distribution in one
classical stochastic chemostat Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Dianli Zhao, Sanling YuanAbstractThis paper studies the asymptotic behaviors of one classical chemostat model in a stochastic environment. Based on the Feller property, sharp conditions are derived for the existence of a stationary distribution by using the mutually exclusive possibilities known in [11, 12] (See Lemma 2.4 for details), which closes the gap left by the Lyapunov function. Further, we obtain a sufficient condition for the extinction of the organism based on two noiseinduced parameters: an analogue of the feed concentration S* and the breakeven concentration λ. Results indicate that both noises have negative effects on persistence of the microorganism.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Dianli Zhao, Sanling YuanAbstractThis paper studies the asymptotic behaviors of one classical chemostat model in a stochastic environment. Based on the Feller property, sharp conditions are derived for the existence of a stationary distribution by using the mutually exclusive possibilities known in [11, 12] (See Lemma 2.4 for details), which closes the gap left by the Lyapunov function. Further, we obtain a sufficient condition for the extinction of the organism based on two noiseinduced parameters: an analogue of the feed concentration S* and the breakeven concentration λ. Results indicate that both noises have negative effects on persistence of the microorganism.
 The adaptive Ciarlet–Raviart mixed method for biharmonic problems with
simply supported boundary condition Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Yidu Yang, Hai Bi, Yu ZhangAbstractIn this paper, we study the adaptive fashion of the Ciarlet–Raviart mixed method for biharmonic equation/eigenvalue problem with simply supported boundary condition in Rd. We propose an a posteriori error indicator of the Ciarlet–Raviart approximate solution for the biharmonic equation and an a posteriori error indicator of the Ciarlet–Raviart approximate eigenfuction, and prove the reliability and efficiency of the indicators. We also give an a posteriori error indicator for the approximate eigenvalue and prove its reliability. We design an adaptive Ciarlet–Raviart mixed method with piecewise polynomials of degree less than or equal to m, and numerical experiments show that numerical eigenvalues obtained by the method can achieve the optimal convergence order O(dof−2md)(d=2,m=2,3;d=3,m=3).
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Yidu Yang, Hai Bi, Yu ZhangAbstractIn this paper, we study the adaptive fashion of the Ciarlet–Raviart mixed method for biharmonic equation/eigenvalue problem with simply supported boundary condition in Rd. We propose an a posteriori error indicator of the Ciarlet–Raviart approximate solution for the biharmonic equation and an a posteriori error indicator of the Ciarlet–Raviart approximate eigenfuction, and prove the reliability and efficiency of the indicators. We also give an a posteriori error indicator for the approximate eigenvalue and prove its reliability. We design an adaptive Ciarlet–Raviart mixed method with piecewise polynomials of degree less than or equal to m, and numerical experiments show that numerical eigenvalues obtained by the method can achieve the optimal convergence order O(dof−2md)(d=2,m=2,3;d=3,m=3).
 Coincidence for morphisms based on compactness conditions on countable
sets Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Donal O’ReganAbstractWe present general coincidence results for morphisms satisfying certain compactness type conditions on countable sets. Our theory is based on coincidence principles for compact morphisms.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Donal O’ReganAbstractWe present general coincidence results for morphisms satisfying certain compactness type conditions on countable sets. Our theory is based on coincidence principles for compact morphisms.
 Local RBFFD technique for solving the twodimensional modified anomalous
subdiffusion equation Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Hossein Pourbashash, Mahmood Khaksare OshaghAbstractThe main aim of this paper is to propose an efficient and suitable numerical procedure based on the local meshless collocation method for solving the twodimensional modified anomalous subdiffusion equation. The fractional derivative is based on the Riemann–Liouville fractional integral. Firstly, a finite difference scheme with O(τ) has been employed to discrete the time variable and also the local radial basisfinite difference (LRBFFD) method is used to discrete the spatial direction. For the presented numerical technique, we prove the unconditional stability and also obtain an error bound. We employ a test problem to show the accuracy of the proposed technique. Also, we solve the mentioned model on irregular domain to show the efficincy of the developed technique.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Hossein Pourbashash, Mahmood Khaksare OshaghAbstractThe main aim of this paper is to propose an efficient and suitable numerical procedure based on the local meshless collocation method for solving the twodimensional modified anomalous subdiffusion equation. The fractional derivative is based on the Riemann–Liouville fractional integral. Firstly, a finite difference scheme with O(τ) has been employed to discrete the time variable and also the local radial basisfinite difference (LRBFFD) method is used to discrete the spatial direction. For the presented numerical technique, we prove the unconditional stability and also obtain an error bound. We employ a test problem to show the accuracy of the proposed technique. Also, we solve the mentioned model on irregular domain to show the efficincy of the developed technique.
 Empirical likelihood based inference for generalized additive partial
linear models Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Zhuoxi Yu, Kai Yang, Milan ParmarAbstractEmpiricallikelihood based inference for the parameters in generalized additive partial linear models (GAPLM) is investigated. With the use of the polynomial spline smoothing for estimation of nonparametric functions, an estimated empirical likelihood ratio statistic based on the quasilikelihood equation is proposed. We show that the resulting statistic is asymptotically standard chisquared distributed and the confidence regions for the parametric components are constructed. Some simulations are conducted to illustrate the proposed methods.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Zhuoxi Yu, Kai Yang, Milan ParmarAbstractEmpiricallikelihood based inference for the parameters in generalized additive partial linear models (GAPLM) is investigated. With the use of the polynomial spline smoothing for estimation of nonparametric functions, an estimated empirical likelihood ratio statistic based on the quasilikelihood equation is proposed. We show that the resulting statistic is asymptotically standard chisquared distributed and the confidence regions for the parametric components are constructed. Some simulations are conducted to illustrate the proposed methods.
 The numerical solution of the semiexplicit IDAEs by discontinuous
piecewise polynomial approximation Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): S. PishbinAbstractIn this paper, we consider a semiexplicit form of Volterra integrodifferentialalgebraic equations (IDAEs) and investigate the existence and uniqueness of solution of these systems by using differentiability index. Numerical method based on discontinuous piecewise polynomial approximation is proposed for the solution of the semiexplicit IDAEs and global convergence results are established. The performance of the numerical scheme is illustrated by means of some test problems.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): S. PishbinAbstractIn this paper, we consider a semiexplicit form of Volterra integrodifferentialalgebraic equations (IDAEs) and investigate the existence and uniqueness of solution of these systems by using differentiability index. Numerical method based on discontinuous piecewise polynomial approximation is proposed for the solution of the semiexplicit IDAEs and global convergence results are established. The performance of the numerical scheme is illustrated by means of some test problems.
 Meansquare dissipative methods for stochastic agedependent capital
system with fractional Brownian motion and jumps Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Qiang Li, Ting Kang, Qimin ZhangAbstractIn this paper, we analyze meansquare dissipativity of numerical methods applied to a class of stochastic agedependent (vintage) capital system with fractional Brownian motion (fBm) and Poisson jumps. Some sufficient conditions are obtained for ensuring the underlying systems are meansquare dissipative. It is shown that the meansquare dissipativity is preserved by the compensated splitstep backward Euler method and compensated backward Euler method without any restriction on stepsize, while the splitstep backward Euler method and backward Euler method could reproduce meansquare dissipativity under a stepsize constraint. Those results indicate that compensated numerical methods achieve superiority over noncompensated numerical methods in terms of meansquare dissipativity. A numerical example is provided to illustrate the theoretical results.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Qiang Li, Ting Kang, Qimin ZhangAbstractIn this paper, we analyze meansquare dissipativity of numerical methods applied to a class of stochastic agedependent (vintage) capital system with fractional Brownian motion (fBm) and Poisson jumps. Some sufficient conditions are obtained for ensuring the underlying systems are meansquare dissipative. It is shown that the meansquare dissipativity is preserved by the compensated splitstep backward Euler method and compensated backward Euler method without any restriction on stepsize, while the splitstep backward Euler method and backward Euler method could reproduce meansquare dissipativity under a stepsize constraint. Those results indicate that compensated numerical methods achieve superiority over noncompensated numerical methods in terms of meansquare dissipativity. A numerical example is provided to illustrate the theoretical results.
 Orness measurements for lattice mdimensional intervalvalued OWA
operators Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): L. De Miguel, D. Paternain, I. Lizasoain, G. Ochoa, H. BustinceAbstractOrdered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks.The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggregating functions, which obviously give different results in the aggregation of the same set of data.In this paper, some possible classifications of OWA operators are suggested when they are defined on mdimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): L. De Miguel, D. Paternain, I. Lizasoain, G. Ochoa, H. BustinceAbstractOrdered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks.The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggregating functions, which obviously give different results in the aggregation of the same set of data.In this paper, some possible classifications of OWA operators are suggested when they are defined on mdimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator.
 Stability analysis for a class of neutral type singular systems with
timevarying delay Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Shaohua Long, Yunlong Wu, Shouming Zhong, Dian ZhangAbstractThis paper is concerned with the stability problem for a class of neutral type singular systems with timevarying delay. The considered systems contain delays both in their state and in their derivatives of state. Based on the singular system approach and the Lyapunov–Krasovskii functional approach, some sufficient conditions which guarantee the considered systems to be regular, impulsefree and stable are derived. Finally, some numerical examples are provided to show the effectiveness of the presented methods.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Shaohua Long, Yunlong Wu, Shouming Zhong, Dian ZhangAbstractThis paper is concerned with the stability problem for a class of neutral type singular systems with timevarying delay. The considered systems contain delays both in their state and in their derivatives of state. Based on the singular system approach and the Lyapunov–Krasovskii functional approach, some sufficient conditions which guarantee the considered systems to be regular, impulsefree and stable are derived. Finally, some numerical examples are provided to show the effectiveness of the presented methods.
 Dconvergence and conditional GDNstability of exponential Runge–Kutta
methods for semilinear delay differential equations Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jingjun Zhao, Rui Zhan, Yang XuAbstractThis paper is concerned with exponential Runge–Kutta methods with Lagrangian interpolation (ERKLMs) for semilinear delay differential equations (DDEs). Concepts of exponential algebraic stability and conditional GDNstability are introduced. Dconvergence and conditional GDNstability of ERKLMs for semilinear DDEs are investigated. It is shown that exponentially algebraically stable and diagonally stable ERKLMs with stage order p, together with a Lagrangian interpolation of order q (q ≥ p), are Dconvergent of order p. It is also shown that exponentially algebraically stable and diagonally stable ERKLMs are conditionally GDNstable. Some examples of exponentially algebraically stable and diagonally stable ERKLMs of stage order one and two are given, and numerical experiments are presented to illustrate the theoretical results.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Jingjun Zhao, Rui Zhan, Yang XuAbstractThis paper is concerned with exponential Runge–Kutta methods with Lagrangian interpolation (ERKLMs) for semilinear delay differential equations (DDEs). Concepts of exponential algebraic stability and conditional GDNstability are introduced. Dconvergence and conditional GDNstability of ERKLMs for semilinear DDEs are investigated. It is shown that exponentially algebraically stable and diagonally stable ERKLMs with stage order p, together with a Lagrangian interpolation of order q (q ≥ p), are Dconvergent of order p. It is also shown that exponentially algebraically stable and diagonally stable ERKLMs are conditionally GDNstable. Some examples of exponentially algebraically stable and diagonally stable ERKLMs of stage order one and two are given, and numerical experiments are presented to illustrate the theoretical results.
 The coefficients of the immanantal polynomial
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Guihai Yu, Hui QuAbstractAn expression of the coefficient of immanantal polynomial of an n × n matrix is present. Moreover, we give expressions of the coefficient of immanantal polynomials of combinatorial matrices (adjacency matrix, Laplacian matrix, signless Laplacian matrix). As applications, we show that the immanantal polynomials for Laplacian matrix and signless Laplacian matrix of bipartite graphs are the same. This is a generalization of the characteristic polynomial for Laplacian matrix and signless Laplacian matrix of bipartite graphs. Furthermore, we consider the relations between the characteristic polynomial and the immanantal polynomial for trees.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Guihai Yu, Hui QuAbstractAn expression of the coefficient of immanantal polynomial of an n × n matrix is present. Moreover, we give expressions of the coefficient of immanantal polynomials of combinatorial matrices (adjacency matrix, Laplacian matrix, signless Laplacian matrix). As applications, we show that the immanantal polynomials for Laplacian matrix and signless Laplacian matrix of bipartite graphs are the same. This is a generalization of the characteristic polynomial for Laplacian matrix and signless Laplacian matrix of bipartite graphs. Furthermore, we consider the relations between the characteristic polynomial and the immanantal polynomial for trees.
 Wave propagation in a nonlocal diffusion epidemic model with nonlocal
delayed effects Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Zaili Zhen, Jingdong Wei, Jiangbo Zhou, Lixin TianAbstractA nonlocal diffusion epidemic model with nonlocal delayed effects is investigated. The existence and nonexistence of the nontrivial and nonnegative traveling wave solutions for the model are obtained, respectively. It is found that the threshold dynamics of the model is determined by the basic reproduction number of the corresponding reaction system and minimal wave speed.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Zaili Zhen, Jingdong Wei, Jiangbo Zhou, Lixin TianAbstractA nonlocal diffusion epidemic model with nonlocal delayed effects is investigated. The existence and nonexistence of the nontrivial and nonnegative traveling wave solutions for the model are obtained, respectively. It is found that the threshold dynamics of the model is determined by the basic reproduction number of the corresponding reaction system and minimal wave speed.
 Reproducing kernel method for the numerical solution of the 1D
Swift–Hohenberg equation Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): P. Bakhtiari, S. Abbasbandy, R.A. Van GorderAbstractThe Swift–Hohenberg equation is a nonlinear partial differential equation of fourth order that models the formation and evolution of patterns in a wide range of physical systems. We study the 1D Swift–Hohenberg equation in order to demonstrate the utility of the reproducing kernel method. The solution is represented in the form of a series in the reproducing kernel space, and truncating this series representation we obtain the nterm approximate solution. In the first approach, we aim to explain how to construct a reproducing kernel method without using GramSchmidt orthogonalization, as orthogonalization is computationally expensive. This approach will therefore be most practical for obtaining numerical solutions. GramSchmidt orthogonalization is later applied in the second approach, despite the increased computational time, as this approach will prove theoretically useful when we perform a formal convergence analysis of the reproducing kernel method for the Swift–Hohenberg equation. We demonstrate the applicability of the method through various test problems for a variety of initial data and parameter values.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): P. Bakhtiari, S. Abbasbandy, R.A. Van GorderAbstractThe Swift–Hohenberg equation is a nonlinear partial differential equation of fourth order that models the formation and evolution of patterns in a wide range of physical systems. We study the 1D Swift–Hohenberg equation in order to demonstrate the utility of the reproducing kernel method. The solution is represented in the form of a series in the reproducing kernel space, and truncating this series representation we obtain the nterm approximate solution. In the first approach, we aim to explain how to construct a reproducing kernel method without using GramSchmidt orthogonalization, as orthogonalization is computationally expensive. This approach will therefore be most practical for obtaining numerical solutions. GramSchmidt orthogonalization is later applied in the second approach, despite the increased computational time, as this approach will prove theoretically useful when we perform a formal convergence analysis of the reproducing kernel method for the Swift–Hohenberg equation. We demonstrate the applicability of the method through various test problems for a variety of initial data and parameter values.
 The new massconserving SDDM scheme for twodimensional parabolic
equations with variable coefficients Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zhongguo Zhou, Dong Liang, Yaushu WongAbstractIn the article, a new and efficient massconserving operator splitting domain decomposition method (SDDM) is proposed and analyzed for solving two dimensional variable coefficient parabolic equations with reaction term. The domain is divided into multiple nonoverlapping blockdivided subdomains. On each blockdivided subdomain, the interface fluxes are first computed explicitly by local multipoint weighted schemes and the solutions in the interior of subdomain are computed by the onedirectional operator splitting implicit schemes at each time step. The scheme is proved to satisfy mass conservation over the whole domain of domain decomposition. By combining with some auxiliary lemmas and applying the energy method, we analyze theoretically the stability of our scheme and prove it to have second order accuracy in space step in the L2 norm. Numerical experiments are performed to illustrate its accuracy, conservation, stability, efficiency and parallelism. Our scheme not only keeps the excellent advantages of the nonoverlapping domain decomposition and the operator splitting technique, but also preserves the global mass.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zhongguo Zhou, Dong Liang, Yaushu WongAbstractIn the article, a new and efficient massconserving operator splitting domain decomposition method (SDDM) is proposed and analyzed for solving two dimensional variable coefficient parabolic equations with reaction term. The domain is divided into multiple nonoverlapping blockdivided subdomains. On each blockdivided subdomain, the interface fluxes are first computed explicitly by local multipoint weighted schemes and the solutions in the interior of subdomain are computed by the onedirectional operator splitting implicit schemes at each time step. The scheme is proved to satisfy mass conservation over the whole domain of domain decomposition. By combining with some auxiliary lemmas and applying the energy method, we analyze theoretically the stability of our scheme and prove it to have second order accuracy in space step in the L2 norm. Numerical experiments are performed to illustrate its accuracy, conservation, stability, efficiency and parallelism. Our scheme not only keeps the excellent advantages of the nonoverlapping domain decomposition and the operator splitting technique, but also preserves the global mass.
 Stochastic stability for distributed delay neural networks via augmented
Lyapunov–Krasovskii functionals Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Yonggang Chen, Zidong Wang, Yurong Liu, Fuad E. AlsaadiAbstractThis paper is concerned with the analysis problem for the globally asymptotic stability of a class of stochastic neural networks with finite or infinite distributed delays. By using the delay decomposition idea, a novel augmented Lyapunov–Krasovskii functional containing double and triple integral terms is constructed, based on which and in combination with the Jensen integral inequalities, a less conservative stability condition is established for stochastic neural networks with infinite distributed delay by means of linear matrix inequalities. As for stochastic neural networks with finite distributed delay, the Wirtingerbased integral inequality is further introduced, together with the augmented Lyapunov–Krasovskii functional, to obtain a more effective stability condition. Finally, several numerical examples demonstrate that our proposed conditions improve typical existing ones.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Yonggang Chen, Zidong Wang, Yurong Liu, Fuad E. AlsaadiAbstractThis paper is concerned with the analysis problem for the globally asymptotic stability of a class of stochastic neural networks with finite or infinite distributed delays. By using the delay decomposition idea, a novel augmented Lyapunov–Krasovskii functional containing double and triple integral terms is constructed, based on which and in combination with the Jensen integral inequalities, a less conservative stability condition is established for stochastic neural networks with infinite distributed delay by means of linear matrix inequalities. As for stochastic neural networks with finite distributed delay, the Wirtingerbased integral inequality is further introduced, together with the augmented Lyapunov–Krasovskii functional, to obtain a more effective stability condition. Finally, several numerical examples demonstrate that our proposed conditions improve typical existing ones.
 About new models of slip/noslip boundary condition in thin film flows
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): G. Bayada, M. EL Alaoui Talibi, M. HilalAbstractThe behaviour of a thin fluid film with a new slip/no slip model (The double parameter slip DPS) on a part of the boundary is studied. From the Stokes equations, the convergence of the velocity, pressure and wallstress is established. The limit problem is described in terms of a new Reynolds equation involving shear stress and associated with a variational equation. Existence and uniqueness are proved. Relation with the previously known thin film problem with Tresca boundary condition is highlighted. A numerical algorithm is proposed and numerical examples are given.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): G. Bayada, M. EL Alaoui Talibi, M. HilalAbstractThe behaviour of a thin fluid film with a new slip/no slip model (The double parameter slip DPS) on a part of the boundary is studied. From the Stokes equations, the convergence of the velocity, pressure and wallstress is established. The limit problem is described in terms of a new Reynolds equation involving shear stress and associated with a variational equation. Existence and uniqueness are proved. Relation with the previously known thin film problem with Tresca boundary condition is highlighted. A numerical algorithm is proposed and numerical examples are given.
 Nonnegative definite and Renonnegative definite solutions to a system of
matrix equations with statistical applications Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Guangjing Song, Shaowen YuAbstractNecessary and sufficient conditions are given for the existence of a nonnegative definite solution, a Renonnegative definite solution, a positive definite solution and a Repositive definite solution to the system of matrix equationsAXA*=CandBXB*=D,respectively. The expressions for these special solutions are given when the consistent conditions are satisfied. Based on the new results, the characterization of the covariance matrix such that a pair of multivariate quadratic forms are distributed as independent noncentral Wishart random matrices is derived. Many results existing in the literature are extended.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Guangjing Song, Shaowen YuAbstractNecessary and sufficient conditions are given for the existence of a nonnegative definite solution, a Renonnegative definite solution, a positive definite solution and a Repositive definite solution to the system of matrix equationsAXA*=CandBXB*=D,respectively. The expressions for these special solutions are given when the consistent conditions are satisfied. Based on the new results, the characterization of the covariance matrix such that a pair of multivariate quadratic forms are distributed as independent noncentral Wishart random matrices is derived. Many results existing in the literature are extended.
 Quasisynchronization for fractionalorder delayed dynamical networks with
heterogeneous nodes Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Fei Wang, Yongqing YangAbstractThis paper investigates the quasisynchronization problem in heterogeneous fractional order dynamic networks with timedelay. Based on comparison theorem for the fractional order differential equation, a new fractional order functional differential inequality is built at first. According to the inequality, some quasisynchronization conditions are derived via Lyapunov method, and the error bound is estimated. Then, the pinning control strategy is also considered via matrix analysis. Furthermore, the specific pinning schemes about how many nodes are needed to be selected are provided in an algorithm. Finally, two examples are given to verify the validity of our theoretical results.
 Abstract: Publication date: 15 December 2018Source: Applied Mathematics and Computation, Volume 339Author(s): Fei Wang, Yongqing YangAbstractThis paper investigates the quasisynchronization problem in heterogeneous fractional order dynamic networks with timedelay. Based on comparison theorem for the fractional order differential equation, a new fractional order functional differential inequality is built at first. According to the inequality, some quasisynchronization conditions are derived via Lyapunov method, and the error bound is estimated. Then, the pinning control strategy is also considered via matrix analysis. Furthermore, the specific pinning schemes about how many nodes are needed to be selected are provided in an algorithm. Finally, two examples are given to verify the validity of our theoretical results.
 Positive solutions to superlinear attractive singular impulsive
differential equation Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Qiuyue Li, Yaoming Zhou, Fuzhong Cong, Hu LiuAbstractIn this paper, we study positive periodic solutions to impulsive differential equation with the attractive singular perturbation. The existence theorem is proved using the Leray Schauder alternative principle and the fixed point theorem. The perturbation term in the equation we are mainly interested in is that it has not only an attractive singularity but also the superlinearity.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Qiuyue Li, Yaoming Zhou, Fuzhong Cong, Hu LiuAbstractIn this paper, we study positive periodic solutions to impulsive differential equation with the attractive singular perturbation. The existence theorem is proved using the Leray Schauder alternative principle and the fixed point theorem. The perturbation term in the equation we are mainly interested in is that it has not only an attractive singularity but also the superlinearity.
 A class of generalized Tribonacci sequences applied to counting problems
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Wojciech FlorekAbstractGeneralized Tribonacci numbers with the third order linear recurrence with constant coefficients T(k)(n)=T(k)(n−1)+T(k)(n−2)+kT(k)(n−3) for n > 2 are investigated for some sets of the initial triples (t0, t1, t2). In particular, generating functions, the Binet formula and the limit of ratio of consecutive terms T(k)(n+1)/T(k)(n) are discussed. These numbers are related to numbers of path graphs colorings with k+2 colors (or, equivalently, to counting of qary sequences of length n for q=k+2) satisfying requirements which follow the problem of degeneration in the Ising model with the second neighbor interactions. It is shown that the results obtained can be considered as the base for considerations of cycle graph colorings (cyclic qary sequences). These are counting problems, so t0, t1, t2, and k should be natural numbers, but these sequences can be considered for any real numbers. The special cases k=0,1 lead to the Fibonacci and the usual Tribonacci numbers, respectively, so the results can be applied to binary and ternary sequences.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Wojciech FlorekAbstractGeneralized Tribonacci numbers with the third order linear recurrence with constant coefficients T(k)(n)=T(k)(n−1)+T(k)(n−2)+kT(k)(n−3) for n > 2 are investigated for some sets of the initial triples (t0, t1, t2). In particular, generating functions, the Binet formula and the limit of ratio of consecutive terms T(k)(n+1)/T(k)(n) are discussed. These numbers are related to numbers of path graphs colorings with k+2 colors (or, equivalently, to counting of qary sequences of length n for q=k+2) satisfying requirements which follow the problem of degeneration in the Ising model with the second neighbor interactions. It is shown that the results obtained can be considered as the base for considerations of cycle graph colorings (cyclic qary sequences). These are counting problems, so t0, t1, t2, and k should be natural numbers, but these sequences can be considered for any real numbers. The special cases k=0,1 lead to the Fibonacci and the usual Tribonacci numbers, respectively, so the results can be applied to binary and ternary sequences.
 Spline approximation for systems of linear neutral delaydifferential
equations Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): R.H. Fabiano, Catherine PayneAbstractWe derive a new finite dimensional semidiscrete approximation scheme for systems of linear neutral delaydifferential equations and prove convergence results. Our construction extends to neutral delay equations results which were previously only available for retarded delay equations.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): R.H. Fabiano, Catherine PayneAbstractWe derive a new finite dimensional semidiscrete approximation scheme for systems of linear neutral delaydifferential equations and prove convergence results. Our construction extends to neutral delay equations results which were previously only available for retarded delay equations.
 Design of robust nonfragile fault detection filter for uncertain dynamic
systems with quantization Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Jun Xiong, XiaoHeng Chang, Xiaojian YiAbstractThis paper investigates the fault detection problem for uncertain linear systems with respect to signal quantization. The measurement output transmitted via the digital communication link is considered to be quantized by a dynamic quantizer. Moreover, different from most of existing results on fault detection where the residual generator is assumed to be realized perfectly as the designed one, this study takes the inaccuracy and uncertainty on the implementation of residual generator into account. This paper pays much attention to designing a fault detection filter with quantization as the residual generator and formulates the design problem into the H∞ framework. The objective is to guarantee the asymptotical stability and prescribed performance of the residual system. The Sprocedure and a twostep approach are adopted to handle the effects of quantization and uncertainties on residual system. Corresponding design conditions of a robust fault detection filter and a robust nonfragile ones are derived in the form of linear matrix inequalities. Finally, the efficiency of the theoretical results is illustrated by the numerical example.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Jun Xiong, XiaoHeng Chang, Xiaojian YiAbstractThis paper investigates the fault detection problem for uncertain linear systems with respect to signal quantization. The measurement output transmitted via the digital communication link is considered to be quantized by a dynamic quantizer. Moreover, different from most of existing results on fault detection where the residual generator is assumed to be realized perfectly as the designed one, this study takes the inaccuracy and uncertainty on the implementation of residual generator into account. This paper pays much attention to designing a fault detection filter with quantization as the residual generator and formulates the design problem into the H∞ framework. The objective is to guarantee the asymptotical stability and prescribed performance of the residual system. The Sprocedure and a twostep approach are adopted to handle the effects of quantization and uncertainties on residual system. Corresponding design conditions of a robust fault detection filter and a robust nonfragile ones are derived in the form of linear matrix inequalities. Finally, the efficiency of the theoretical results is illustrated by the numerical example.
 A fast energy conserving finite element method for the nonlinear
fractional Schrödinger equation with wave operator Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Meng Li, YongLiang ZhaoAbstractThe main aim of this paper is to apply the Galerkin finite element method to numerically solve the nonlinear fractional Schrödinger equation with wave operator. We first construct a fully discrete scheme combining the Crank–Nicolson method with the Galerkin finite element method. Two conserved quantities of the discrete system are shown. Meanwhile, the prior bound of the discrete solutions are proved. Then, we prove that the discrete scheme is unconditionally convergent in the senses of L2−norm and Hα/2−norm. Moreover, by the proposed iterative algorithm, some numerical examples are given to verify the theoretical results and show the effectiveness of the numerical scheme. Finally, a fast Krylov subspace solver with suitable circulant preconditioner is designed to solve above Toeplitzlike linear system. In each iterative step, this method can effectively reduce the memory requirement of the proposed iterative finite element scheme from O(M2) to O(M), and the computational complexity from O(M3) to O(MlogM), where M is the number of grid nodes. Several numerical tests are carried out to show that this fast algorithm is more practical than the traditional backslash and LU factorization methods, in terms of memory requirement and computational cost.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Meng Li, YongLiang ZhaoAbstractThe main aim of this paper is to apply the Galerkin finite element method to numerically solve the nonlinear fractional Schrödinger equation with wave operator. We first construct a fully discrete scheme combining the Crank–Nicolson method with the Galerkin finite element method. Two conserved quantities of the discrete system are shown. Meanwhile, the prior bound of the discrete solutions are proved. Then, we prove that the discrete scheme is unconditionally convergent in the senses of L2−norm and Hα/2−norm. Moreover, by the proposed iterative algorithm, some numerical examples are given to verify the theoretical results and show the effectiveness of the numerical scheme. Finally, a fast Krylov subspace solver with suitable circulant preconditioner is designed to solve above Toeplitzlike linear system. In each iterative step, this method can effectively reduce the memory requirement of the proposed iterative finite element scheme from O(M2) to O(M), and the computational complexity from O(M3) to O(MlogM), where M is the number of grid nodes. Several numerical tests are carried out to show that this fast algorithm is more practical than the traditional backslash and LU factorization methods, in terms of memory requirement and computational cost.
 Guaranteed cost consensus for secondorder multiagent systems with
heterogeneous inertias Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zhiyong Yu, Haijun Jiang, Xuehui Mei, Cheng HuAbstractIn this paper, the guaranteed cost consensus problem for secondorder multiagent systems with directed topology is considered, in which each agent has a heterogeneous inertia and control gain. The distributed control protocols with the absolute and relative velocity dampings are proposed, respectively. In each kind of protocol, both the communications with and without the input time delay are also considered. By introducing the auxiliary variables and using Lyapunov stability theory, some sufficient conditions are given to achieve the consensus. Moreover, the upper bounds of the guaranteed cost functions are obtained. Finally, some simulation examples are presented to show the effectiveness of the proposed approaches.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zhiyong Yu, Haijun Jiang, Xuehui Mei, Cheng HuAbstractIn this paper, the guaranteed cost consensus problem for secondorder multiagent systems with directed topology is considered, in which each agent has a heterogeneous inertia and control gain. The distributed control protocols with the absolute and relative velocity dampings are proposed, respectively. In each kind of protocol, both the communications with and without the input time delay are also considered. By introducing the auxiliary variables and using Lyapunov stability theory, some sufficient conditions are given to achieve the consensus. Moreover, the upper bounds of the guaranteed cost functions are obtained. Finally, some simulation examples are presented to show the effectiveness of the proposed approaches.
 Generalized system of trial equation methods and their applications to
biological systems Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Ali Ozyapici, Bülent BilgehanAbstractIt is shown that many systems of nonlinear differential equations of interest in various fields are naturally embedded in a new family of differential equations. In this paper, we improve new and effective methods for nonautonomous systems and they produce new exact solutions to some important biological systems. The exact solution of predator and prey population for different particular cases has been derived. The numerical examples show that new exact solutions can be obtained for many biological systems such as SIR model, Lotka–Volterra model. The methods perform extremely well in terms of efficiency and simplicity to solve this historical biological models.The Lotka–Volterra nonlinear differential equations for two competing species, namely X and Y, contain six independent parameters. Their general analytic solutions, valid for arbitrary values of the parameters, are at present unknown. However, when two or more of these parameters are interrelated, it is possible to obtain the exact solutions in the X, Y phase plane, and six cases of solvability are given in this paper. The dependence of the solutions on the parameters and the initial conditions can thus be readily investigated.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Ali Ozyapici, Bülent BilgehanAbstractIt is shown that many systems of nonlinear differential equations of interest in various fields are naturally embedded in a new family of differential equations. In this paper, we improve new and effective methods for nonautonomous systems and they produce new exact solutions to some important biological systems. The exact solution of predator and prey population for different particular cases has been derived. The numerical examples show that new exact solutions can be obtained for many biological systems such as SIR model, Lotka–Volterra model. The methods perform extremely well in terms of efficiency and simplicity to solve this historical biological models.The Lotka–Volterra nonlinear differential equations for two competing species, namely X and Y, contain six independent parameters. Their general analytic solutions, valid for arbitrary values of the parameters, are at present unknown. However, when two or more of these parameters are interrelated, it is possible to obtain the exact solutions in the X, Y phase plane, and six cases of solvability are given in this paper. The dependence of the solutions on the parameters and the initial conditions can thus be readily investigated.
 A numerical approach for fractional partial differential equations by
using Ritz approximation Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): M.A. Firoozjaee, S.A. YousefiAbstractIn this article, Ritz approximation have been employed to obtain numerical solutions of fractional partial differential equations (FPDEs) based on the Caputo fractional derivative. Transforming fractional partial differential equations into optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation using Mathematica7 and we have the coefficients of polynomial expansion. We extensively discuss the convergence of the method. Some numerical examples are presented which illustrate the theoretical results and the performance of the method.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): M.A. Firoozjaee, S.A. YousefiAbstractIn this article, Ritz approximation have been employed to obtain numerical solutions of fractional partial differential equations (FPDEs) based on the Caputo fractional derivative. Transforming fractional partial differential equations into optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation using Mathematica7 and we have the coefficients of polynomial expansion. We extensively discuss the convergence of the method. Some numerical examples are presented which illustrate the theoretical results and the performance of the method.
 Some notes on properties of the matrix MittagLeffler function
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Amir Sadeghi, João R. CardosoAbstractWe have come across with publications where some properties of the matrix exponential were incorrectly extended to the matrix MittagLeffler function, and then used as a key tool to solve certain linear matrix fractional differential equations. The main purpose of these notes is to give some clarifications on properties of the matrix MittagLeffler function, by explaining in detail why some identities do not hold and by providing a list of (valid) properties of this function. A sufficient condition to identify very special cases of pairs of matrices satisfying the semigroup property is given as well as examples illustrating the results.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Amir Sadeghi, João R. CardosoAbstractWe have come across with publications where some properties of the matrix exponential were incorrectly extended to the matrix MittagLeffler function, and then used as a key tool to solve certain linear matrix fractional differential equations. The main purpose of these notes is to give some clarifications on properties of the matrix MittagLeffler function, by explaining in detail why some identities do not hold and by providing a list of (valid) properties of this function. A sufficient condition to identify very special cases of pairs of matrices satisfying the semigroup property is given as well as examples illustrating the results.
 Expected hitting times for random walks on the ktriangle graph
and their applications Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Chengyong Wang, Ziliang Guo, Shuchao LiAbstractGiven a simple connected graph G, the ktriangle graph of G, written by Tk(G), is obtained from G by adding k new vertices ui1,ui2,…,uik for each edge ei=uv in G and then adding in edges uui1,uui2,…,uuik and ui1v,ui2v,…,uikv. In this paper, the eigenvalues and eigenvectors of the probability transition matrix of random walks on Tk(G) are completely determined. Then the expected hitting times between any two vertices of Tk(G) are given in terms of those of G. Using these results all the relationship on the number of spanning trees (resp. Kemeny’s constant, the degreeKirchhoff index) in Tk(G) compared to those of G is found. As well the resistance distance between any two vertices of Tk(G) is given with respect to those of G.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Chengyong Wang, Ziliang Guo, Shuchao LiAbstractGiven a simple connected graph G, the ktriangle graph of G, written by Tk(G), is obtained from G by adding k new vertices ui1,ui2,…,uik for each edge ei=uv in G and then adding in edges uui1,uui2,…,uuik and ui1v,ui2v,…,uikv. In this paper, the eigenvalues and eigenvectors of the probability transition matrix of random walks on Tk(G) are completely determined. Then the expected hitting times between any two vertices of Tk(G) are given in terms of those of G. Using these results all the relationship on the number of spanning trees (resp. Kemeny’s constant, the degreeKirchhoff index) in Tk(G) compared to those of G is found. As well the resistance distance between any two vertices of Tk(G) is given with respect to those of G.
 Corrigendum to “Richardson extrapolation technique for singularly
perturbed system of parabolic partial differential equations with
exponential boundary layers” [Applied Mathematics and Computation 333
(2018) 254–275] Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Maneesh Kumar Singh, Srinivasan Natesan
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Maneesh Kumar Singh, Srinivasan Natesan
 Convergence of a fluxsplitting finite volume scheme for conservation laws
driven by Lévy noise Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Ananta K. MajeeAbstractWe explore numerical approximation of multidimensional stochastic balance laws driven by multiplicative Lévy noise via flux splitting finite volume method. The convergence of the approximations is proved towards the unique entropy solution of the underlying problem.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Ananta K. MajeeAbstractWe explore numerical approximation of multidimensional stochastic balance laws driven by multiplicative Lévy noise via flux splitting finite volume method. The convergence of the approximations is proved towards the unique entropy solution of the underlying problem.
 Spectral radii of two kinds of uniform hypergraphs
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Liying Kang, Lele Liu, Liqun Qi, Xiying YuanAbstractLet A(H) be the adjacency tensor (hypermatrix) of uniform hypergraph H. The maximum modulus of the eigenvalues of A(H) is called the spectral radius of H, denoted by ρ(H). In this paper, a conjecture concerning the spectral radii of linear bicyclic uniform hypergraphs is solved, with these results the hypergraph with the largest spectral radius is completely determined among the linear bicyclic uniform hypergraphs. For a tuniform hypergraph G its generalized power runiform hypergraph Gr, s is defined in this paper. An exact relation between ρ(G) and ρ(Gr, s) is proved, more precisely ρ(Gr,s)=(ρ(G))tsr.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Liying Kang, Lele Liu, Liqun Qi, Xiying YuanAbstractLet A(H) be the adjacency tensor (hypermatrix) of uniform hypergraph H. The maximum modulus of the eigenvalues of A(H) is called the spectral radius of H, denoted by ρ(H). In this paper, a conjecture concerning the spectral radii of linear bicyclic uniform hypergraphs is solved, with these results the hypergraph with the largest spectral radius is completely determined among the linear bicyclic uniform hypergraphs. For a tuniform hypergraph G its generalized power runiform hypergraph Gr, s is defined in this paper. An exact relation between ρ(G) and ρ(Gr, s) is proved, more precisely ρ(Gr,s)=(ρ(G))tsr.
 Nonhydrostatic pressure shallow flows: GPU implementation using finite
volume and finite difference scheme Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): C. Escalante, T. Morales de Luna, M.J. CastroAbstractWe consider the depthintegrated nonhydrostatic system derived by Yamazaki et al. An efficient formally secondorder wellbalanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a twostep algorithm based on a projectioncorrection type scheme initially introduced by Chorin–Temam [15]. First, the hyperbolic part of the system is discretized using a Polynomial Viscosity Matrix pathconservative finite volume method. Second, the dispersive terms are solved by means of compact finite differences. A new methodology is also presented to handle wave breaking over complex bathymetries. This adapts well to GPUarchitectures and guidelines about its GPU implementation are introduced. The method has been applied to idealized and challenging experimental test cases, which shows the efficiency and accuracy of the method.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): C. Escalante, T. Morales de Luna, M.J. CastroAbstractWe consider the depthintegrated nonhydrostatic system derived by Yamazaki et al. An efficient formally secondorder wellbalanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a twostep algorithm based on a projectioncorrection type scheme initially introduced by Chorin–Temam [15]. First, the hyperbolic part of the system is discretized using a Polynomial Viscosity Matrix pathconservative finite volume method. Second, the dispersive terms are solved by means of compact finite differences. A new methodology is also presented to handle wave breaking over complex bathymetries. This adapts well to GPUarchitectures and guidelines about its GPU implementation are introduced. The method has been applied to idealized and challenging experimental test cases, which shows the efficiency and accuracy of the method.
 Strong convergence of a tamed theta scheme for NSDDEs with onesided
Lipschitz drift Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Li Tan, Chenggui YuanAbstractThis paper is concerned with strong convergence of a tamed theta scheme for neutral stochastic differential delay equations with onesided Lipschitz drift. Strong convergence rate is revealed under a global onesided Lipschitz condition, while for a local onesided Lipschitz condition, the tamed theta scheme is modified to ensure the wellposedness of implicit numerical schemes, then we show the convergence of the numerical solutions.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Li Tan, Chenggui YuanAbstractThis paper is concerned with strong convergence of a tamed theta scheme for neutral stochastic differential delay equations with onesided Lipschitz drift. Strong convergence rate is revealed under a global onesided Lipschitz condition, while for a local onesided Lipschitz condition, the tamed theta scheme is modified to ensure the wellposedness of implicit numerical schemes, then we show the convergence of the numerical solutions.
 Reaction–diffusion equation based image restoration
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Xueqing Zhao, Keke Huang, Xiaoming Wang, Meihong Shi, Xinjuan Zhu, Quanli Gao, Zhaofei YuAbstractWe present a novel restoration algorithm based on the reaction–diffusion equation theory, denominated RDER, for restoring images which are corrupted by various blur PSFs and different types of noise (including different levels of impulse noise, Gaussian noise and mixed noise). The focus of this work is to propose an image restoration method based on the reaction diffusion equation and to further extend the traditional diffusion equation. Firstly, the RDER model is constructed by using the restoration ability of the diffusion equation, and the image detail preservation ability of the reaction equation; secondly, based on the difference scheme theory, a discrete RDER model is proposed for image restoration and a RDER algorithm for restoring the image is designed; thirdly, we mathematically analyze the RDER model from the existence, stability and uniqueness of solutions of the RDER model; finally, the proposed RDER algorithm is compared with the current famous stateoftheart restoration algorithms in image restoring and image details preserving. Theoretical analysis and extensive experimental results show that the RDER is an effective image restoration algorithm for image denoising, image deblurring and image details preserving; in particular, the RDER provides a better performance in terms of the impulse noise and mixed noise.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Xueqing Zhao, Keke Huang, Xiaoming Wang, Meihong Shi, Xinjuan Zhu, Quanli Gao, Zhaofei YuAbstractWe present a novel restoration algorithm based on the reaction–diffusion equation theory, denominated RDER, for restoring images which are corrupted by various blur PSFs and different types of noise (including different levels of impulse noise, Gaussian noise and mixed noise). The focus of this work is to propose an image restoration method based on the reaction diffusion equation and to further extend the traditional diffusion equation. Firstly, the RDER model is constructed by using the restoration ability of the diffusion equation, and the image detail preservation ability of the reaction equation; secondly, based on the difference scheme theory, a discrete RDER model is proposed for image restoration and a RDER algorithm for restoring the image is designed; thirdly, we mathematically analyze the RDER model from the existence, stability and uniqueness of solutions of the RDER model; finally, the proposed RDER algorithm is compared with the current famous stateoftheart restoration algorithms in image restoring and image details preserving. Theoretical analysis and extensive experimental results show that the RDER is an effective image restoration algorithm for image denoising, image deblurring and image details preserving; in particular, the RDER provides a better performance in terms of the impulse noise and mixed noise.
 An interval algorithm for uncertain dynamic stability analysis
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Youqin HuangAbstractAnalysis on the stability of dynamic systems is a very important field in structural elasticity theory. For possible engineering situations where the system parameters are uncertain‑but‑bounded, the propagation from the initial uncertainties of parameters to the consequent uncertainty of dynamic stability of structure is elaborately investigated by interval analysis for the first time. The interval dynamic stability issue is studied through the column structure as a generalized interval eigenvalue problem, and an analytic theorem is rigorously derived and numerically verified for solving the generalized interval eigenvalue problem. Moreover, to avoid the exaggeration on actual bounds of solution, an effective approach is established to limit the dependency phenomenon in the interval dynamic stability analysis. The interval relationships of the excitation parameter and the critical load frequency with five types of system parameters are further bridged according to the interval arithmetic to propose a threestage interval scheme for evaluating the effects of interval system parameters on the dynamic stability of structures. Numerical studies demonstrate that the uncertainty of the constant part of load influences the boundaries of principal instability region much more than that of the variable part of load. Within all structural parameters, the uncertainty of column length has the most effect on the boundaries, which could make the critical frequency of load be magnified about ten times the uncertainty of parameter. In particular, if all the system parameters are interval with an identical uncertainty degree, the uncertainty of parameter would be propagated in the system of dynamic stability and enlarged as high as 20 times the uncertainty of parameter. Consequently, the impacts of parameter uncertainties on the dynamic stability of structures are fairly significant.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Youqin HuangAbstractAnalysis on the stability of dynamic systems is a very important field in structural elasticity theory. For possible engineering situations where the system parameters are uncertain‑but‑bounded, the propagation from the initial uncertainties of parameters to the consequent uncertainty of dynamic stability of structure is elaborately investigated by interval analysis for the first time. The interval dynamic stability issue is studied through the column structure as a generalized interval eigenvalue problem, and an analytic theorem is rigorously derived and numerically verified for solving the generalized interval eigenvalue problem. Moreover, to avoid the exaggeration on actual bounds of solution, an effective approach is established to limit the dependency phenomenon in the interval dynamic stability analysis. The interval relationships of the excitation parameter and the critical load frequency with five types of system parameters are further bridged according to the interval arithmetic to propose a threestage interval scheme for evaluating the effects of interval system parameters on the dynamic stability of structures. Numerical studies demonstrate that the uncertainty of the constant part of load influences the boundaries of principal instability region much more than that of the variable part of load. Within all structural parameters, the uncertainty of column length has the most effect on the boundaries, which could make the critical frequency of load be magnified about ten times the uncertainty of parameter. In particular, if all the system parameters are interval with an identical uncertainty degree, the uncertainty of parameter would be propagated in the system of dynamic stability and enlarged as high as 20 times the uncertainty of parameter. Consequently, the impacts of parameter uncertainties on the dynamic stability of structures are fairly significant.
 New complex projective synchronization strategies for driveresponse
networks with fractional complexvariable dynamics Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Quan Xu, Xiaohui Xu, Shengxian Zhuang, Jixue Xiao, Chunhua Song, Chang CheAbstractThis paper presents a fully decentralized adaptive scheme to solve the open problem of complex projective synchronization (CPS) in driveresponse fractional complexvariable networks (DRFCVNs). Based on local mismatch with the desired state and between coupled nodes, several novel fully decentralized fractional adaptive (FDFA) strategies are proposed to adjust both the feedback control strengths and the coupling weights. By employing Hermitian form Lyapunov functionals and other fractional skills, some sufficient criteria are provided for CPS. Numerical simulation examples are finally employed to illustrate the efficiency of the new synchronization strategies.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Quan Xu, Xiaohui Xu, Shengxian Zhuang, Jixue Xiao, Chunhua Song, Chang CheAbstractThis paper presents a fully decentralized adaptive scheme to solve the open problem of complex projective synchronization (CPS) in driveresponse fractional complexvariable networks (DRFCVNs). Based on local mismatch with the desired state and between coupled nodes, several novel fully decentralized fractional adaptive (FDFA) strategies are proposed to adjust both the feedback control strengths and the coupling weights. By employing Hermitian form Lyapunov functionals and other fractional skills, some sufficient criteria are provided for CPS. Numerical simulation examples are finally employed to illustrate the efficiency of the new synchronization strategies.
 The inverse spectral problem for differential pencils by mixed spectral
data Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Yu Ping WangAbstractAn inverse problem for differential pencils of second order is studied. We show that the potentials on the whole interval can be uniquely determined by partial information on potentials and parts of two spectra.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Yu Ping WangAbstractAn inverse problem for differential pencils of second order is studied. We show that the potentials on the whole interval can be uniquely determined by partial information on potentials and parts of two spectra.
 Differentialrecurrence properties of dual Bernstein polynomials
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Filip Chudy, Paweł WoźnyAbstractNew differentialrecurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourthorder differential equation satisfied by dual Bernstein polynomials has been constructed. Also, a fourthorder recurrence relation for these polynomials has been obtained; this result may be useful in the efficient solution of some computational problems.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Filip Chudy, Paweł WoźnyAbstractNew differentialrecurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourthorder differential equation satisfied by dual Bernstein polynomials has been constructed. Also, a fourthorder recurrence relation for these polynomials has been obtained; this result may be useful in the efficient solution of some computational problems.
 The Karamata integration theorem on time scales and its applications in
dynamic and difference equations Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Pavel ŘehákAbstractWe derive a time scale version of the wellknown result from the theory of regular variation, namely the Karamata integration theorem. We show an application of this theorem in asymptotic analysis of linear second order dynamic equations. We obtain a classification and asymptotic formulae for all (positive) solutions, which unify, extend, and improve the existing results. In addition, we utilize these results, in combination with a transformation between equations on different time scales, to study the critical doubleroot case in linear difference equations. This leads to solving open problems posed in the literature.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Pavel ŘehákAbstractWe derive a time scale version of the wellknown result from the theory of regular variation, namely the Karamata integration theorem. We show an application of this theorem in asymptotic analysis of linear second order dynamic equations. We obtain a classification and asymptotic formulae for all (positive) solutions, which unify, extend, and improve the existing results. In addition, we utilize these results, in combination with a transformation between equations on different time scales, to study the critical doubleroot case in linear difference equations. This leads to solving open problems posed in the literature.
 Generalized confluent hypergeometric solutions of the Heun confluent
equation Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): T.A. Ishkhanyan, A.M. IshkhanyanAbstractWe show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent equation is a nonzero integer and the accessory parameter obeys a polynomial equation. Each of the solutions can be written as a linear combination with constant coefficients of a finite number of either the Kummer confluent hypergeometric functions or the Bessel functions.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): T.A. Ishkhanyan, A.M. IshkhanyanAbstractWe show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent equation is a nonzero integer and the accessory parameter obeys a polynomial equation. Each of the solutions can be written as a linear combination with constant coefficients of a finite number of either the Kummer confluent hypergeometric functions or the Bessel functions.
 Stability and stabilization for discretetime switched systems with
asynchronism Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Shuang Shi, Zhongyang Fei, Zhenpeng Shi, Shunqing RenAbstractIn this paper, the H∞ control is investigated for a class of discretetime switched systems. The switching delay between the mode and controller, which leads to the asynchronism, is taken into consideration. The switching signal is considered to be constrained by persistent dwell time (PDT), which is known to be more general than the common used dwell time or average dwell time. Sufficient conditions to guarantee the asymptotic stability and ℓ2gain are derived under a PDT scheme. By considering that actual controllers are subjected to normbounded gain perturbations, nonfragile controllers are designed based on both state feedback and output feedback stategies. Finally, the effectiveness of the provided methods is illustrated by two examples.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Shuang Shi, Zhongyang Fei, Zhenpeng Shi, Shunqing RenAbstractIn this paper, the H∞ control is investigated for a class of discretetime switched systems. The switching delay between the mode and controller, which leads to the asynchronism, is taken into consideration. The switching signal is considered to be constrained by persistent dwell time (PDT), which is known to be more general than the common used dwell time or average dwell time. Sufficient conditions to guarantee the asymptotic stability and ℓ2gain are derived under a PDT scheme. By considering that actual controllers are subjected to normbounded gain perturbations, nonfragile controllers are designed based on both state feedback and output feedback stategies. Finally, the effectiveness of the provided methods is illustrated by two examples.
 Computer search for large trees with minimal ABC index
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Wenshui Lin, Jianfeng Chen, Zhixi Wu, Darko Dimitrov, Linshan HuangAbstractThe atombond connectivity (ABC) index of a graph G = (V, E) is defined as ABC(G)=∑vivj∈E(di+dj−2)/(didj), where V = {v0,v1,⋅⋅⋅, vn − 1} and di denotes the degree of vertex vi of G. This molecular structure descriptor found interesting applications in chemistry, and has become one of the most actively studied vertexdegreebased graph invariants. However, the problem of characterizing nvertex tree(s) with minimal ABC index remains open and was coined as the “ABC index conundrum”. In attempts to guess the general structure of such trees, several computer search algorithms were developed and tested up to n = 800. However, for large n, all current search programs seem too powerless. For example, the fastest one up to date reported recently in [30] costs 2.2 h for n = 800 on a single PC with two CPU cores. In this paper, we significantly refine the known features of the degree sequence of a tree with minimal ABC index. With the refined features a search program was implemented with OpenMP. Our program was tested on a single PC with 4 CPU cores, and identified all nvertex tree(s) with minimal ABC index up to n = 1100 within 207.1 h. Some observations are made based on the search results, which indicate some possible directions in further investigation of the problem of characterizing nvertex tree(s) with minimal ABC index.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Wenshui Lin, Jianfeng Chen, Zhixi Wu, Darko Dimitrov, Linshan HuangAbstractThe atombond connectivity (ABC) index of a graph G = (V, E) is defined as ABC(G)=∑vivj∈E(di+dj−2)/(didj), where V = {v0,v1,⋅⋅⋅, vn − 1} and di denotes the degree of vertex vi of G. This molecular structure descriptor found interesting applications in chemistry, and has become one of the most actively studied vertexdegreebased graph invariants. However, the problem of characterizing nvertex tree(s) with minimal ABC index remains open and was coined as the “ABC index conundrum”. In attempts to guess the general structure of such trees, several computer search algorithms were developed and tested up to n = 800. However, for large n, all current search programs seem too powerless. For example, the fastest one up to date reported recently in [30] costs 2.2 h for n = 800 on a single PC with two CPU cores. In this paper, we significantly refine the known features of the degree sequence of a tree with minimal ABC index. With the refined features a search program was implemented with OpenMP. Our program was tested on a single PC with 4 CPU cores, and identified all nvertex tree(s) with minimal ABC index up to n = 1100 within 207.1 h. Some observations are made based on the search results, which indicate some possible directions in further investigation of the problem of characterizing nvertex tree(s) with minimal ABC index.
 On the superconvergence of some quadratic integrosplines at the midknots
of a uniform partition Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): FengGong Lang, XiaoPing XuAbstractIn this paper, we illustrate some new superconvergence of four kinds of quadratic integrosplines. It is proved that these quadratic integrosplines possess superconvergence in function values approximation (fourth order convergent) and in secondorder derivatives approximation (second order convergent) at the midknots of a uniform partition.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): FengGong Lang, XiaoPing XuAbstractIn this paper, we illustrate some new superconvergence of four kinds of quadratic integrosplines. It is proved that these quadratic integrosplines possess superconvergence in function values approximation (fourth order convergent) and in secondorder derivatives approximation (second order convergent) at the midknots of a uniform partition.
 Numerical analysis of the impact of pollutants on water vapour
condensation in atmospheric air transonic flows Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Sławomir Dykas, Mirosław Majkut, Krystian Smołka, Michał StrozikAbstractThe paper presents a developed numerical tool in the form of a CFD code solving Reynoldsaveraged Navier–Stokes equations for transonic flows of a compressible gas which is used to model the process of atmospheric air expansion in nozzles. The numerical model takes account of condensation of water vapour contained in atmospheric air. The paper presents results of numerical modelling of both homo and heterogeneous condensation taking place as air expands in the nozzle and demonstrates the impact of the air relative humidity and pollutants on the condensation process.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Sławomir Dykas, Mirosław Majkut, Krystian Smołka, Michał StrozikAbstractThe paper presents a developed numerical tool in the form of a CFD code solving Reynoldsaveraged Navier–Stokes equations for transonic flows of a compressible gas which is used to model the process of atmospheric air expansion in nozzles. The numerical model takes account of condensation of water vapour contained in atmospheric air. The paper presents results of numerical modelling of both homo and heterogeneous condensation taking place as air expands in the nozzle and demonstrates the impact of the air relative humidity and pollutants on the condensation process.
 Quickest drift change detection in Lévytype force of mortality model
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Michał Krawiec, Zbigniew Palmowski, Łukasz PłociniczakAbstractIn this paper, we give solution to the quickest drift change detection problem for a Lévy process consisting of both a continuous Gaussian part and a jump component. We consider here Bayesian framework with an exponential a priori distribution of the change point using an optimality criterion based on a probability of false alarm and an expected delay of the detection. Our approach is based on the optimal stopping theory and solving some boundary value problem. Paper is supplemented by an extensive numerical analysis related with the construction of the Generalized ShiryaevRoberts statistics. In particular, we apply this method (after appropriate calibration) to analyse Polish life tables and to model the force of mortality in this population with a drift changing in time.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Michał Krawiec, Zbigniew Palmowski, Łukasz PłociniczakAbstractIn this paper, we give solution to the quickest drift change detection problem for a Lévy process consisting of both a continuous Gaussian part and a jump component. We consider here Bayesian framework with an exponential a priori distribution of the change point using an optimality criterion based on a probability of false alarm and an expected delay of the detection. Our approach is based on the optimal stopping theory and solving some boundary value problem. Paper is supplemented by an extensive numerical analysis related with the construction of the Generalized ShiryaevRoberts statistics. In particular, we apply this method (after appropriate calibration) to analyse Polish life tables and to model the force of mortality in this population with a drift changing in time.
 Multipoint secant and interpolation methods with nonmonotone line search
for solving systems of nonlinear equations Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Oleg Burdakov, Ahmad KamandiAbstractMultipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasiNewton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the information about the Jacobian matrix gathered at the previous iterations, these methods are especially efficient in the case of expensive functions. They are known to be local and superlinearly convergent. We combine these methods with the nonmonotone line search proposed by Li and Fukushima (2000), and study global and superlinear convergence of this combination. Results of numerical experiments are presented. They indicate that the multipoint secant and interpolation methods tend to be more robust and efficient than Broyden’s method globalized in the same way.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Oleg Burdakov, Ahmad KamandiAbstractMultipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasiNewton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the information about the Jacobian matrix gathered at the previous iterations, these methods are especially efficient in the case of expensive functions. They are known to be local and superlinearly convergent. We combine these methods with the nonmonotone line search proposed by Li and Fukushima (2000), and study global and superlinear convergence of this combination. Results of numerical experiments are presented. They indicate that the multipoint secant and interpolation methods tend to be more robust and efficient than Broyden’s method globalized in the same way.
 Enumeration of perfect matchings of lattice graphs by Pfaffians
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Xing Feng, Lianzhu Zhang, Mingzu ZhangAbstractEnumeration of perfect matchings in general graphs (even in bipartite graphs) is #Pcomplete. In this paper, we obtain explicit expressions of the number of perfect matchings of 8.6.4 lattices with toroidal boundary by enumerating Pfaffians.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Xing Feng, Lianzhu Zhang, Mingzu ZhangAbstractEnumeration of perfect matchings in general graphs (even in bipartite graphs) is #Pcomplete. In this paper, we obtain explicit expressions of the number of perfect matchings of 8.6.4 lattices with toroidal boundary by enumerating Pfaffians.
 Evaluating the apparent shear stress in prismatic compound channels using
the Genetic Algorithm based on MultiLayer Perceptron: A comparative study
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Hossein Bonakdari, Zohreh Sheikh Khozani, Amir Hossein Zaji, Navid AsadpourAbstractApparent shear stress acting on a vertical interface between the main channel and floodplain in a compound channel is used to quantify the momentum transfer between these subareas of a cross section. In order to simulate the apparent shear stress, two soft computing techniques, including the Genetic AlgorithmArtificial Neural Network (GAANN) and Genetic Programming (GP) along with Multiple Linear Regression (MLR) were used. The proposed GAANN is a novel selfhidden layer neuron adjustable hybrid method made by combining the Genetic Algorithm (GA) with the MultiLayer Perceptron Artificial Neural Network (MLPANN) method. In order to find the optimum condition of the methods considered in modeling apparent shear stress, various input combinations, fitness functions, transfer functions (for the GAA method), and mathematical functions (for the GP method) were investigated. Finally, the results of the optimum GAA and GP methods were compared with the MLR as a basic method. The results show that the hybrid GAA method with RMSE of 0.5326 outperformed the GP method with RMSE of 0.6651. In addition, the results indicate that both GAA and GP methods performed significantly better than MLR with RMSE of 1.5409 in simulating apparent shear stress in symmetric compound channels.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Hossein Bonakdari, Zohreh Sheikh Khozani, Amir Hossein Zaji, Navid AsadpourAbstractApparent shear stress acting on a vertical interface between the main channel and floodplain in a compound channel is used to quantify the momentum transfer between these subareas of a cross section. In order to simulate the apparent shear stress, two soft computing techniques, including the Genetic AlgorithmArtificial Neural Network (GAANN) and Genetic Programming (GP) along with Multiple Linear Regression (MLR) were used. The proposed GAANN is a novel selfhidden layer neuron adjustable hybrid method made by combining the Genetic Algorithm (GA) with the MultiLayer Perceptron Artificial Neural Network (MLPANN) method. In order to find the optimum condition of the methods considered in modeling apparent shear stress, various input combinations, fitness functions, transfer functions (for the GAA method), and mathematical functions (for the GP method) were investigated. Finally, the results of the optimum GAA and GP methods were compared with the MLR as a basic method. The results show that the hybrid GAA method with RMSE of 0.5326 outperformed the GP method with RMSE of 0.6651. In addition, the results indicate that both GAA and GP methods performed significantly better than MLR with RMSE of 1.5409 in simulating apparent shear stress in symmetric compound channels.
 Threedimensional Green’s function approach for analysis of dispersion
and attenuation curve in fibrereinforced heterogeneous viscoelastic layer
due to a point source Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Santimoy Kundu, Alka Kumari, Shishir GuptaAbstractThe present paper deals with the propagation of Love waves due to the presence of a point source in the fibrereinforced heterogeneous viscoelastic medium with the aid of Green’s function technique. The physical parameters, i.e. rigidity and density are assumed to be exponentially and linearly varying function of depth for medium and halfspace, respectively. Threedimensional Green’s function representation for stresses and displacements are derived in complexplane lineintegral. The frequency equations of Lovetype waves are derived relating the dependence complex wave numbers after developing the mathematical model with the help of Green’s function and Fourier transformation. This representation is useful in various elastodynamic as well as elastostatic problems. The complex expansion of frequency equation is derived to define the phase velocity and attenuation coefficient of Love waves in the proposed model. Dispersion and attenuation curves are plotted by taking different variations in the reinforcement, inhomogeneity and viscoelastic parameters. The results indicate that the effect of these parameters are very pronounced. The final conclusion can be used to understand the nature of propagation of Love waves in the introduced model.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Santimoy Kundu, Alka Kumari, Shishir GuptaAbstractThe present paper deals with the propagation of Love waves due to the presence of a point source in the fibrereinforced heterogeneous viscoelastic medium with the aid of Green’s function technique. The physical parameters, i.e. rigidity and density are assumed to be exponentially and linearly varying function of depth for medium and halfspace, respectively. Threedimensional Green’s function representation for stresses and displacements are derived in complexplane lineintegral. The frequency equations of Lovetype waves are derived relating the dependence complex wave numbers after developing the mathematical model with the help of Green’s function and Fourier transformation. This representation is useful in various elastodynamic as well as elastostatic problems. The complex expansion of frequency equation is derived to define the phase velocity and attenuation coefficient of Love waves in the proposed model. Dispersion and attenuation curves are plotted by taking different variations in the reinforcement, inhomogeneity and viscoelastic parameters. The results indicate that the effect of these parameters are very pronounced. The final conclusion can be used to understand the nature of propagation of Love waves in the introduced model.
 Bounds for variable degree rational L
∞ approximations to the matrix
exponential Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Ch. Tsitouras, I.Th. FamelisAbstractIn this work we derive new alternatives for efficient computation of the matrix exponential which is useful when solving Linear Initial Value Problems, vibratory systems or after semidiscretization of PDEs. We focus especially on the two classes of normal and nonnegative matrices and we present intervals of applications for rational L∞ approximations of various degrees for these types of matrices in the lines of [7, 8]. Our method relies on Remez algorithm for rational approximation while the innovation here is the choice of the starting set of nonsymmetrical Chebyshev points. Only one Remez iteration is then usually enough to quickly approach the actual L∞ approximant.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Ch. Tsitouras, I.Th. FamelisAbstractIn this work we derive new alternatives for efficient computation of the matrix exponential which is useful when solving Linear Initial Value Problems, vibratory systems or after semidiscretization of PDEs. We focus especially on the two classes of normal and nonnegative matrices and we present intervals of applications for rational L∞ approximations of various degrees for these types of matrices in the lines of [7, 8]. Our method relies on Remez algorithm for rational approximation while the innovation here is the choice of the starting set of nonsymmetrical Chebyshev points. Only one Remez iteration is then usually enough to quickly approach the actual L∞ approximant.
 On a hydrodynamic permeability of a system of coaxial partly porous
cylinders with superhydrophobic surfaces Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Anatoly Filippov, Yulia KorolevaAbstractThe paper considers a Stokes–Brinkman’s system with varying viscosity that describes the continuous flow of viscous incompressible liquid along an ensemble of partially porous cylindrical particles using the cell approach. The analytical solution for the considered system was derived and analyzed for a particular case of Brinkman’s viscosity which illustrates the presence of superhydrophobic surfaces in a porous system. Some numerical validation of the derived results are done and the hydrodynamic permeability of the porous system was calculated and analyzed depending on geometrical and physicochemical parameters. Our analysis of the problem shows that the bigger the impermeable core the less the coefficient of hydrodynamic permeability what agrees with the physical process of the filtration. In addition, the bigger the specific permeability of porous layer the greater the hydrodynamic permeability of the porous medium.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Anatoly Filippov, Yulia KorolevaAbstractThe paper considers a Stokes–Brinkman’s system with varying viscosity that describes the continuous flow of viscous incompressible liquid along an ensemble of partially porous cylindrical particles using the cell approach. The analytical solution for the considered system was derived and analyzed for a particular case of Brinkman’s viscosity which illustrates the presence of superhydrophobic surfaces in a porous system. Some numerical validation of the derived results are done and the hydrodynamic permeability of the porous system was calculated and analyzed depending on geometrical and physicochemical parameters. Our analysis of the problem shows that the bigger the impermeable core the less the coefficient of hydrodynamic permeability what agrees with the physical process of the filtration. In addition, the bigger the specific permeability of porous layer the greater the hydrodynamic permeability of the porous medium.
 Global Mittag–Leffler stabilization of fractionalorder complexvalued
memristive neural networks Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Wenting Chang, Song Zhu, Jinyu Li, Kaili SunAbstractThis paper presents the theoretical results about global Mittag–Leffler stabilization for a class of fractionalorder complexvalued memristive neural networks with the designed two types of control rules. As the extension of fractionalorder realvalued memristive neural networks, fractionalorder complexvalued memristive neural networks have complexvalued states, synaptic weights, and the activation functions. By utilizing the setvalued maps, a generalized fractional derivative inequality as well as fractionalorder differential inclusions, several stabilization criteria for global Mittag–Leffler stabilization of fractionalorder complexvalued memristive neural networks are established. A numerical example is provided here to illustrate our theoretical results.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Wenting Chang, Song Zhu, Jinyu Li, Kaili SunAbstractThis paper presents the theoretical results about global Mittag–Leffler stabilization for a class of fractionalorder complexvalued memristive neural networks with the designed two types of control rules. As the extension of fractionalorder realvalued memristive neural networks, fractionalorder complexvalued memristive neural networks have complexvalued states, synaptic weights, and the activation functions. By utilizing the setvalued maps, a generalized fractional derivative inequality as well as fractionalorder differential inclusions, several stabilization criteria for global Mittag–Leffler stabilization of fractionalorder complexvalued memristive neural networks are established. A numerical example is provided here to illustrate our theoretical results.
 Exact and nonstandard numerical schemes for linear delay differential
models Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): M.A. García, M.A. Castro, J.A. Martín, F. RodríguezAbstractDelay differential models present characteristic dynamical properties that should ideally be preserved when computing numerical approximate solutions. In this work, exact numerical schemes for a general linear delay differential model, as well as for the special case of a pure delay model, are obtained. Based on these exact schemes, a family of nonstandard methods, of increasing order of accuracy and simple computational properties, is proposed. Dynamic consistency of the new nonstandard methods are proved, and illustrated with numerical examples, for asymptotic stability, positive preserving properties, and oscillation behaviour.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): M.A. García, M.A. Castro, J.A. Martín, F. RodríguezAbstractDelay differential models present characteristic dynamical properties that should ideally be preserved when computing numerical approximate solutions. In this work, exact numerical schemes for a general linear delay differential model, as well as for the special case of a pure delay model, are obtained. Based on these exact schemes, a family of nonstandard methods, of increasing order of accuracy and simple computational properties, is proposed. Dynamic consistency of the new nonstandard methods are proved, and illustrated with numerical examples, for asymptotic stability, positive preserving properties, and oscillation behaviour.
 Further analytical bifurcation analysis and applications of coupled
logistic maps Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): A.A. Elsadany, A.M. Yousef, Amr ElsonbatyAbstractIn this work, we extend further the analytical study of complex dynamics exist in two coupled logistic maps. New results about the occurrence of various types of bifurcation in the system, including flip bifurcation, pitchfork bifurcation and Neimark–Sacker bifurcation are presented. To the best of authors’ knowledge, the presence of chaotic dynamics in system’s behavior has been investigated and proved analytically via Marotto’s approach for first time. Numerical simulations are carried out in order to verify theoretical results. Furthermore, chaos based encryption algorithm for images is presented as an application for the coupled logistic maps. Different scenarios of attacks are considered to demonstrate its immunity and effectiveness against the possible attacks. Finally, a circuit realization for the coupled logistic maps is proposed and utilized in a suggested real time text encryption system.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): A.A. Elsadany, A.M. Yousef, Amr ElsonbatyAbstractIn this work, we extend further the analytical study of complex dynamics exist in two coupled logistic maps. New results about the occurrence of various types of bifurcation in the system, including flip bifurcation, pitchfork bifurcation and Neimark–Sacker bifurcation are presented. To the best of authors’ knowledge, the presence of chaotic dynamics in system’s behavior has been investigated and proved analytically via Marotto’s approach for first time. Numerical simulations are carried out in order to verify theoretical results. Furthermore, chaos based encryption algorithm for images is presented as an application for the coupled logistic maps. Different scenarios of attacks are considered to demonstrate its immunity and effectiveness against the possible attacks. Finally, a circuit realization for the coupled logistic maps is proposed and utilized in a suggested real time text encryption system.
 Two lower bounds for generalized 3connectivity of Cartesian product
graphs Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Hui Gao, Benjian Lv, Kaishun WangAbstractThe generalized kconnectivity κk(G) of a graph G, which was introduced by Chartrand et al. (1984) is a generalization of the concept of vertex connectivity. Let G and H be nontrivial connected graphs. Recently, Li et al. (2012) gave a lower bound for the generalized 3connectivity of the Cartesian product graph G□H and proposed a conjecture for the case that H is 3connected. In this paper, we give two different forms of lower bounds for the generalized 3connectivity of Cartesian product graphs. The first lower bound is stronger than theirs, and the second confirms their conjecture.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Hui Gao, Benjian Lv, Kaishun WangAbstractThe generalized kconnectivity κk(G) of a graph G, which was introduced by Chartrand et al. (1984) is a generalization of the concept of vertex connectivity. Let G and H be nontrivial connected graphs. Recently, Li et al. (2012) gave a lower bound for the generalized 3connectivity of the Cartesian product graph G□H and proposed a conjecture for the case that H is 3connected. In this paper, we give two different forms of lower bounds for the generalized 3connectivity of Cartesian product graphs. The first lower bound is stronger than theirs, and the second confirms their conjecture.
 Nonconforming quasiWilson finite element method for 2D multiterm time
fractional diffusionwave equation on regular and anisotropic meshes Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Z.G. Shi, Y.M. Zhao, F. Liu, F.L. Wang, Y.F. TangAbstractThe paper mainly focuses on studying nonconforming quasiWilson finite element fullydiscrete approximation for two dimensional (2D) multiterm time fractional diffusionwave equation (TFDWE) on regular and anisotropic meshes. Firstly, based on the Crank–Nicolson scheme in conjunction with L1approximation of the time Caputo derivative of order α ∈ (1, 2), a fullydiscrete scheme for 2D multiterm TFDWE is established. And then, the approximation scheme is rigorously proved to be unconditionally stable via processing fractional derivative skillfully. Moreover, the superclose result in broken H1norm is deduced by utilizing special properties of quasiWilson element. In the meantime, the global superconvergence in broken H1norm is derived by means of interpolation postprocessing technique. Finally, some numerical results illustrate the correctness of theoretical analysis on both regular and anisotropic meshes.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Z.G. Shi, Y.M. Zhao, F. Liu, F.L. Wang, Y.F. TangAbstractThe paper mainly focuses on studying nonconforming quasiWilson finite element fullydiscrete approximation for two dimensional (2D) multiterm time fractional diffusionwave equation (TFDWE) on regular and anisotropic meshes. Firstly, based on the Crank–Nicolson scheme in conjunction with L1approximation of the time Caputo derivative of order α ∈ (1, 2), a fullydiscrete scheme for 2D multiterm TFDWE is established. And then, the approximation scheme is rigorously proved to be unconditionally stable via processing fractional derivative skillfully. Moreover, the superclose result in broken H1norm is deduced by utilizing special properties of quasiWilson element. In the meantime, the global superconvergence in broken H1norm is derived by means of interpolation postprocessing technique. Finally, some numerical results illustrate the correctness of theoretical analysis on both regular and anisotropic meshes.
 Simulation of thin film flows with a moving mesh mixed finite element
method Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Hong Zhang, Paul Andries ZegelingAbstractWe present an efficient mixed finite element method to solve the fourthorder thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. (2001,2002). To achieve a high quality mesh, we adopt an adaptive monitor function and smooth it based on a diffusive mechanism. A variety of numerical tests are performed to demonstrate the accuracy and efficiency of the method. The moving mesh refinement accurately resolves the overshoot and downshoot structures and reduces the computational cost in comparison to numerical simulations using a fixed mesh.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Hong Zhang, Paul Andries ZegelingAbstractWe present an efficient mixed finite element method to solve the fourthorder thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. (2001,2002). To achieve a high quality mesh, we adopt an adaptive monitor function and smooth it based on a diffusive mechanism. A variety of numerical tests are performed to demonstrate the accuracy and efficiency of the method. The moving mesh refinement accurately resolves the overshoot and downshoot structures and reduces the computational cost in comparison to numerical simulations using a fixed mesh.
 Efficient Krylovbased exponential time differencing method in application
to 3D advectiondiffusionreaction systems Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): H.P. Bhatt, A.Q.M. Khaliq, B.A. WadeAbstractThe number of ordinary differential equations generally increases exponentially as the partial differential equation is posed on a domain with more dimensions. This is, of course, the curse of dimensionality for exponential time differencing methods. The computational challenge in applying exponential time differencing methods for solving partial differential equations in high spatial dimensions is how to compute the matrix exponential functions for very large matrices accurately and efficiently. In this paper, our main aim is to design a Krylov subspace approximationbased locally extrapolated exponential time differencing method and compare its performance in terms of accuracy and efficiency to the already available method in the literature for solving a threedimensional nonlinear advectiondiffusionreaction systems. The fundamental idea of the proposed method is to compute only the action of the matrix exponential on a given state vector instead of computing the matrix exponential itself, and then multiplying it with given vector. The stability and local truncation error of the proposed method have been examined. Calculation of local truncation error and empirical convergence analysis indicate the proposed method is secondorder accurate in time. The performance and reliability of this novel method have been investigated by testing it on systems of the threedimensional nonlinear advectiondiffusionreaction equations and threedimensional viscous nonlinear Burgers’ equation.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): H.P. Bhatt, A.Q.M. Khaliq, B.A. WadeAbstractThe number of ordinary differential equations generally increases exponentially as the partial differential equation is posed on a domain with more dimensions. This is, of course, the curse of dimensionality for exponential time differencing methods. The computational challenge in applying exponential time differencing methods for solving partial differential equations in high spatial dimensions is how to compute the matrix exponential functions for very large matrices accurately and efficiently. In this paper, our main aim is to design a Krylov subspace approximationbased locally extrapolated exponential time differencing method and compare its performance in terms of accuracy and efficiency to the already available method in the literature for solving a threedimensional nonlinear advectiondiffusionreaction systems. The fundamental idea of the proposed method is to compute only the action of the matrix exponential on a given state vector instead of computing the matrix exponential itself, and then multiplying it with given vector. The stability and local truncation error of the proposed method have been examined. Calculation of local truncation error and empirical convergence analysis indicate the proposed method is secondorder accurate in time. The performance and reliability of this novel method have been investigated by testing it on systems of the threedimensional nonlinear advectiondiffusionreaction equations and threedimensional viscous nonlinear Burgers’ equation.
 A numerically efficient Hamiltonian method for fractional wave equations
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): J.E. MacíasDíazAbstractIn this work, we consider a partial differential equation that extends the well known wave equation. The model under consideration is a multidimensional equation which includes the presence of both a damping term and a fractional Laplacian of the Riesz type. Homogeneous Dirichlet boundary conditions on a closed and bounded spatial interval are considered in this work. The mathematical model has a fractional Hamiltonian which is conserved when the damping coefficient is equal to zero, and dissipated otherwise. Motivated by these facts, we propose a finitedifference method to approximate the solutions of the continuous model. The method is an implicit scheme which is based on the use of fractional centered differences to approximate the spatial fractional derivatives of the model. A discretized form of the Hamiltoninan is also proposed in this work, and we prove analytically that the method is capable of preserving/dissipating the discrete energy when the continuous model preserves/dissipates the energy. We establish rigorously the properties of consistency, stability and convergence of the method, and provide some a priori bounds for the numerical solutions. Moreover, we prove the existence and the uniqueness of the numerical solutions as well as the unconditional stability of the method in the linear regime. Some computer simulations that assess the capability of the method to preserve/dissipate the energy are carried out for illustration purposes.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): J.E. MacíasDíazAbstractIn this work, we consider a partial differential equation that extends the well known wave equation. The model under consideration is a multidimensional equation which includes the presence of both a damping term and a fractional Laplacian of the Riesz type. Homogeneous Dirichlet boundary conditions on a closed and bounded spatial interval are considered in this work. The mathematical model has a fractional Hamiltonian which is conserved when the damping coefficient is equal to zero, and dissipated otherwise. Motivated by these facts, we propose a finitedifference method to approximate the solutions of the continuous model. The method is an implicit scheme which is based on the use of fractional centered differences to approximate the spatial fractional derivatives of the model. A discretized form of the Hamiltoninan is also proposed in this work, and we prove analytically that the method is capable of preserving/dissipating the discrete energy when the continuous model preserves/dissipates the energy. We establish rigorously the properties of consistency, stability and convergence of the method, and provide some a priori bounds for the numerical solutions. Moreover, we prove the existence and the uniqueness of the numerical solutions as well as the unconditional stability of the method in the linear regime. Some computer simulations that assess the capability of the method to preserve/dissipate the energy are carried out for illustration purposes.
 Macroeconomic models with long dynamic memory: Fractional calculus
approach Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Vasily E. Tarasov, Valentina V. TarasovaAbstractThis article discusses macroeconomic models, which take into account effects of powerlaw fading memory. The powerlaw long memory is described by using the mathematical tool of fractional calculus that includes the fractional derivatives and integrals of noninteger orders. We obtain solutions of the fractional differential equations of these macroeconomic models. Examples of dependence of macroeconomic dynamics on the memory effects are suggested. Asymptotic behaviors of the solutions, which characterize the rate of technological growth with memory, are described. We formulate principles of economic dynamics with oneparametric and multiparametric memory. It has been shown that the effects of fading long memory can change the economic growth rate and change dominant parameters, which determine growth rates.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Vasily E. Tarasov, Valentina V. TarasovaAbstractThis article discusses macroeconomic models, which take into account effects of powerlaw fading memory. The powerlaw long memory is described by using the mathematical tool of fractional calculus that includes the fractional derivatives and integrals of noninteger orders. We obtain solutions of the fractional differential equations of these macroeconomic models. Examples of dependence of macroeconomic dynamics on the memory effects are suggested. Asymptotic behaviors of the solutions, which characterize the rate of technological growth with memory, are described. We formulate principles of economic dynamics with oneparametric and multiparametric memory. It has been shown that the effects of fading long memory can change the economic growth rate and change dominant parameters, which determine growth rates.
 Finitetime tracking control for stochastic nonlinear systems with full
state constraints Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Jing Zhang, Jianwei Xia, Wei Sun, Guangming Zhuang, Zhen WangAbstractIn this paper, an adaptive finitetime controller is constructed for stochastic nonlinear systems with parametric uncertainties. All the states in the systems are constrained in a bounded compact set. By constructing a tantype Barrier Lyapunov Function, the scheme we proposed deals with the finitetime tracking control problem and all the state in the stochastic systems are not violated. Tracking error can converge into a small neighborhood of zero and all the signals in the closedloop system are bounded. Simulation results demonstrate the effectiveness of the presented approach.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Jing Zhang, Jianwei Xia, Wei Sun, Guangming Zhuang, Zhen WangAbstractIn this paper, an adaptive finitetime controller is constructed for stochastic nonlinear systems with parametric uncertainties. All the states in the systems are constrained in a bounded compact set. By constructing a tantype Barrier Lyapunov Function, the scheme we proposed deals with the finitetime tracking control problem and all the state in the stochastic systems are not violated. Tracking error can converge into a small neighborhood of zero and all the signals in the closedloop system are bounded. Simulation results demonstrate the effectiveness of the presented approach.
 Regular nonhamiltonian polyhedral graphs
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Nico Van Cleemput, Carol T. ZamfirescuAbstractInvoking Steinitz’ Theorem, in the following a polyhedron shall be a 3connected planar graph. From around 1880 till 1946 Tait’s conjecture that cubic polyhedra are hamiltonian was thought to hold—its truth would have implied the Four Colour Theorem. However, Tutte gave a counterexample. We briefly survey the ensuing hunt for the smallest nonhamiltonian cubic polyhedron, the LederbergBosákBarnette graph, and prove that there exists a nonhamiltonian essentially 4connected cubic polyhedron of order n if and only if n ≥ 42. This extends work of Aldred, Bau, Holton, and McKay. We then present our main results which revolve around the quartic case: combining a novel theoretical approach for determining nonhamiltonicity in (not necessarily planar) graphs of connectivity 3 with computational methods, we dramatically improve two bounds due to Zaks. In particular, we show that the smallest nonhamiltonian quartic polyhedron has at least 35 and at most 39 vertices, thereby almost reaching a quartic analogue of a famous result of Holton and McKay. As an application of our results, we obtain that the shortness coefficient of the family of all quartic polyhedra does not exceed 5/6. The paper ends with a discussion of the quintic case in which we tighten a result of Owens.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Nico Van Cleemput, Carol T. ZamfirescuAbstractInvoking Steinitz’ Theorem, in the following a polyhedron shall be a 3connected planar graph. From around 1880 till 1946 Tait’s conjecture that cubic polyhedra are hamiltonian was thought to hold—its truth would have implied the Four Colour Theorem. However, Tutte gave a counterexample. We briefly survey the ensuing hunt for the smallest nonhamiltonian cubic polyhedron, the LederbergBosákBarnette graph, and prove that there exists a nonhamiltonian essentially 4connected cubic polyhedron of order n if and only if n ≥ 42. This extends work of Aldred, Bau, Holton, and McKay. We then present our main results which revolve around the quartic case: combining a novel theoretical approach for determining nonhamiltonicity in (not necessarily planar) graphs of connectivity 3 with computational methods, we dramatically improve two bounds due to Zaks. In particular, we show that the smallest nonhamiltonian quartic polyhedron has at least 35 and at most 39 vertices, thereby almost reaching a quartic analogue of a famous result of Holton and McKay. As an application of our results, we obtain that the shortness coefficient of the family of all quartic polyhedra does not exceed 5/6. The paper ends with a discussion of the quintic case in which we tighten a result of Owens.
 Numerical simulation of gasliquid twophase flow in wellbore based on
drift flux model Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Na Wei, Chaoyang Xu, Yingfeng Meng, Gao Li, Xiao Ma, Anqi LiuAbstractA general model and computational code for transient gasliquid twophase flow in wellbore are developed in this paper. The model consists of mass conservation equation for each phase and mixture momentum conservation equation. The interactions of each phase are taken into account by invoking the Shi slip relation in the proposed model. The model is numerically solved by the second order AUSMV scheme, which is obtained by using classical MUSCL technique. The computational code is validated by the classical numerical cases, Zuber–Findlay tube and complex mass transport problem. The simulation results show good agreement with the references which are obtained by using firstorder fluxlimited Roe scheme with refined grids. The computational code also succeeds in obtaining the transient behavior of each phase for a normal gaskick occurrence in wellbore. The simulation results illustrate the degree of pressure variation in the upper wellbore is greater than that in the lower wellbore. The pressures of wellbore increase before the corresponding gas mass flow rate reach max inlet gas mass flow rate, then decrease.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Na Wei, Chaoyang Xu, Yingfeng Meng, Gao Li, Xiao Ma, Anqi LiuAbstractA general model and computational code for transient gasliquid twophase flow in wellbore are developed in this paper. The model consists of mass conservation equation for each phase and mixture momentum conservation equation. The interactions of each phase are taken into account by invoking the Shi slip relation in the proposed model. The model is numerically solved by the second order AUSMV scheme, which is obtained by using classical MUSCL technique. The computational code is validated by the classical numerical cases, Zuber–Findlay tube and complex mass transport problem. The simulation results show good agreement with the references which are obtained by using firstorder fluxlimited Roe scheme with refined grids. The computational code also succeeds in obtaining the transient behavior of each phase for a normal gaskick occurrence in wellbore. The simulation results illustrate the degree of pressure variation in the upper wellbore is greater than that in the lower wellbore. The pressures of wellbore increase before the corresponding gas mass flow rate reach max inlet gas mass flow rate, then decrease.
 The collective behavior of shear strain localizations in dipolar materials
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): N.A. Kudryashov, R.V. Muratov, P.N. RyabovAbstractWe study the collective behavior of shear bands in HY100 steel and OFHC copper taking into account the dipolar effects. Starting from mathematical model, we present new numerical methodology that allows one to simulate the processes of shear strain localization in nonpolar and dipolar materials. The verification procedure was performed to prove the efficiency and accuracy of the proposed method. Using the proposed algorithm we investigate the statistical characteristics of the shear strain localization processes in dipolar materials and compare results with nonpolar case. In particular, we obtain the statistical distributions of the width of localization zones and distance between them.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): N.A. Kudryashov, R.V. Muratov, P.N. RyabovAbstractWe study the collective behavior of shear bands in HY100 steel and OFHC copper taking into account the dipolar effects. Starting from mathematical model, we present new numerical methodology that allows one to simulate the processes of shear strain localization in nonpolar and dipolar materials. The verification procedure was performed to prove the efficiency and accuracy of the proposed method. Using the proposed algorithm we investigate the statistical characteristics of the shear strain localization processes in dipolar materials and compare results with nonpolar case. In particular, we obtain the statistical distributions of the width of localization zones and distance between them.

( n − 1 )  Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Shengjie He, RongXia Hao, Liancui ZuoAbstractA linear kforest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear karboricity of G, denoted by lak(G), is the minimum number of linear kforests needed to partition the edge set E(G) of G. In this paper, the exact values of the linear (n−1)arboricity of lexicographic product graphs Kn ○ Kn, n and Kn, n ○ Kn are obtained. Furthermore, lak(Kn,n□Kn,n) are also derived for the Cartesian product graph of two copies of Kn, n. These results confirm the conjecture about the upper bound lak(G) given in [Discrete Math. 41(1982)219220] for Kn ○ Kn, n, Kn, n ○ Kn and Kn,n□Kn,n.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Shengjie He, RongXia Hao, Liancui ZuoAbstractA linear kforest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear karboricity of G, denoted by lak(G), is the minimum number of linear kforests needed to partition the edge set E(G) of G. In this paper, the exact values of the linear (n−1)arboricity of lexicographic product graphs Kn ○ Kn, n and Kn, n ○ Kn are obtained. Furthermore, lak(Kn,n□Kn,n) are also derived for the Cartesian product graph of two copies of Kn, n. These results confirm the conjecture about the upper bound lak(G) given in [Discrete Math. 41(1982)219220] for Kn ○ Kn, n, Kn, n ○ Kn and Kn,n□Kn,n.
 Taking control of initiated propagating wave in a neuronal network using
magnetic radiation Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zahra Rostami, VietThanh Pham, Sajad Jafari, Fatemeh Hadaeghi, Jun MaAbstractThe effect of magnetic radiation is essential to be studied due to its favorable or unfavorable influences especially when it comes to biological systems. In this study, some effects of an external timevarying magnetic induction on the formation of spatiotemporal patterns in a model of excitable tissue are investigated. We have designed a twodimensional neuronal network, in which the local dynamics of the neurons are governed by the fourvariable magnetic Hindmarsh–Rose (HR) neuronal model. Besides, each neuron is set to be in chaotic regime. We have examined some values of the bifurcation parameters, namely the frequency and the amplitude of the external magnetic radiation. The resulting evolutionary spatiotemporal patterns have showed that an extremely low frequency provides the tissue more opportunity to support propagation process, while low frequency confines the evolution of the wave fronts. Moreover, higher amplitude of the sinusoidal radiation caused the wave propagation be impeded by an inherent obstacle that could limit the ultimate radius of the propagated wave. The resulting collective response of the designed neuronal network is represented in snapshots and the time series of a sampled neuron are plotted, as well.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zahra Rostami, VietThanh Pham, Sajad Jafari, Fatemeh Hadaeghi, Jun MaAbstractThe effect of magnetic radiation is essential to be studied due to its favorable or unfavorable influences especially when it comes to biological systems. In this study, some effects of an external timevarying magnetic induction on the formation of spatiotemporal patterns in a model of excitable tissue are investigated. We have designed a twodimensional neuronal network, in which the local dynamics of the neurons are governed by the fourvariable magnetic Hindmarsh–Rose (HR) neuronal model. Besides, each neuron is set to be in chaotic regime. We have examined some values of the bifurcation parameters, namely the frequency and the amplitude of the external magnetic radiation. The resulting evolutionary spatiotemporal patterns have showed that an extremely low frequency provides the tissue more opportunity to support propagation process, while low frequency confines the evolution of the wave fronts. Moreover, higher amplitude of the sinusoidal radiation caused the wave propagation be impeded by an inherent obstacle that could limit the ultimate radius of the propagated wave. The resulting collective response of the designed neuronal network is represented in snapshots and the time series of a sampled neuron are plotted, as well.
 A High Resolution EquiGradient scheme for convective flows
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): T. ChourushiAbstractNumerical performance of CFD codes in convection dominated flows where in diffusion is feeble, rely majorly on the numerical scheme. In such cases, numerical schemes play a very important role in the prediction of flow property, depending upon their order. To overcome this inadequacy, a new numerical scheme is presented which is in context of finite volume method. The proposed scheme possesses high accuracy as it depends on the contribution from faroff neighboring grid points and thus advects better flow property than lowerorder schemes. Furthermore, the scheme is formulated based on the symmetric limiter property and minimized downwind effect, which ensures a better convergence than the existing higherorder schemes. The presented scheme is henceforth named as High Resolution EquiGradient (HREG) scheme. Pure advection tests are conducted to assess the performance of this scheme with the existing schemes. Results clearly suggest that the HREG scheme advects accurate and symmetric profiles. Further , to assess the convergence behaviour of the proposed scheme, incompressible Newtonian and nonNewtonian fluids are being studied. Results generated strongly depict that the HREG scheme can be used as a substitute over existing schemes for studying highly convective flows.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): T. ChourushiAbstractNumerical performance of CFD codes in convection dominated flows where in diffusion is feeble, rely majorly on the numerical scheme. In such cases, numerical schemes play a very important role in the prediction of flow property, depending upon their order. To overcome this inadequacy, a new numerical scheme is presented which is in context of finite volume method. The proposed scheme possesses high accuracy as it depends on the contribution from faroff neighboring grid points and thus advects better flow property than lowerorder schemes. Furthermore, the scheme is formulated based on the symmetric limiter property and minimized downwind effect, which ensures a better convergence than the existing higherorder schemes. The presented scheme is henceforth named as High Resolution EquiGradient (HREG) scheme. Pure advection tests are conducted to assess the performance of this scheme with the existing schemes. Results clearly suggest that the HREG scheme advects accurate and symmetric profiles. Further , to assess the convergence behaviour of the proposed scheme, incompressible Newtonian and nonNewtonian fluids are being studied. Results generated strongly depict that the HREG scheme can be used as a substitute over existing schemes for studying highly convective flows.
 A collocation approach for solving twodimensional secondorder linear
hyperbolic equations Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Şuayip YüzbaşıAbstractIn this study, a collocation approach is introduced to solve secondorder twodimensional hyperbolic telegraph equation under the initial and boundary conditions. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. The method is constructed in four steps for the considered problem. In first step we construct the fundamental relations for the solution method. By using the collocation points and matrix operations, second step gives the constructing of the main matrix equation. In third step, matrix forms are created for the initial and boundary conditions. We compute the approximate solutions by combining second and third steps. Algorithm of the proposed method is given. Later, error estimation technique is presented and the approximate solutions are improved. Numerical applications are included to demonstrate the validity and applicability of the presented method.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Şuayip YüzbaşıAbstractIn this study, a collocation approach is introduced to solve secondorder twodimensional hyperbolic telegraph equation under the initial and boundary conditions. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. The method is constructed in four steps for the considered problem. In first step we construct the fundamental relations for the solution method. By using the collocation points and matrix operations, second step gives the constructing of the main matrix equation. In third step, matrix forms are created for the initial and boundary conditions. We compute the approximate solutions by combining second and third steps. Algorithm of the proposed method is given. Later, error estimation technique is presented and the approximate solutions are improved. Numerical applications are included to demonstrate the validity and applicability of the presented method.
 A preprocessed multistep splitting iteration for computing PageRank
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Chuanqing Gu, Xianglong Jiang, Ying Nie, Zhibing ChenAbstractThe PageRank algorithm plays an important role in determining the importance of Web pages. The multistep splitting iteration (MSPI) method for calculating the Pagerank problem is an iterative framework of combining the multistep classical power method with the innerouter method. In this paper, we present a preprocessed MSPI method called the ArnoldiMSPI iteration, which is the MSPI method modified with the thick restarted Arnoldi algorithm. The implementation and convergence of the new method are discussed in detail. Numerical experiments are given to show that our method has a good computational effect when the damping factor is close to 1.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Chuanqing Gu, Xianglong Jiang, Ying Nie, Zhibing ChenAbstractThe PageRank algorithm plays an important role in determining the importance of Web pages. The multistep splitting iteration (MSPI) method for calculating the Pagerank problem is an iterative framework of combining the multistep classical power method with the innerouter method. In this paper, we present a preprocessed MSPI method called the ArnoldiMSPI iteration, which is the MSPI method modified with the thick restarted Arnoldi algorithm. The implementation and convergence of the new method are discussed in detail. Numerical experiments are given to show that our method has a good computational effect when the damping factor is close to 1.
 Reduced order Kalman filter for a continuoustime fractionalorder system
using fractionalorder average derivative Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zhe GaoAbstractThis paper investigates two kinds of reduced order Kalman filters for a continuoustime fractionalorder system with uncorrelated and correlated process and measurement noises. The fractionalorder average derivative is adopted to enhance the discretization accuracy for the investigated continuoustime fractionalorder system. The uncorrelated and correlated cases for the process and measurement noises are treated by the reduced order Kalman filters to achieve the robust estimation for a part of states of a fractionalorder system. The truncation issue is considered to implement the practical application of the proposed state estimation algorithm. Finally, two examples for uncorrelated and correlated noises are offered to verify the effectiveness of the proposed reduced order Kalman filters.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Zhe GaoAbstractThis paper investigates two kinds of reduced order Kalman filters for a continuoustime fractionalorder system with uncorrelated and correlated process and measurement noises. The fractionalorder average derivative is adopted to enhance the discretization accuracy for the investigated continuoustime fractionalorder system. The uncorrelated and correlated cases for the process and measurement noises are treated by the reduced order Kalman filters to achieve the robust estimation for a part of states of a fractionalorder system. The truncation issue is considered to implement the practical application of the proposed state estimation algorithm. Finally, two examples for uncorrelated and correlated noises are offered to verify the effectiveness of the proposed reduced order Kalman filters.
 Reversibility in polynomial systems of ODE’s
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Maoan Han, Tatjana Petek, Valery G. RomanovskiAbstractFor a given family of real planar polynomial systems of ordinary differential equations depending on parameters, we consider the problem of how to find the systems in the family which become timereversible after some affine transformation. We first propose a general computational approach to solve this problem, and then demonstrate its usage for the case of the family of quadratic systems.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Maoan Han, Tatjana Petek, Valery G. RomanovskiAbstractFor a given family of real planar polynomial systems of ordinary differential equations depending on parameters, we consider the problem of how to find the systems in the family which become timereversible after some affine transformation. We first propose a general computational approach to solve this problem, and then demonstrate its usage for the case of the family of quadratic systems.
 A hybrid binomial inverse hypergeometric probability distribution: Theory
and applications Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Herbert Jodlbauer, Matthias Dehmer, Sonja StrasserAbstractIn this paper, we define a novel probability distribution triggered by a due date setting problem from a multiitem single level production system. As a result, we derive a recurrence relation for the underlying distribution function and, finally, we also infer the novel discrete distribution function. We underpin our analytical findings by numerical results when computing the distribution function, the expected value as well as the variance. In order to apply and translate our apparatus to other problems, we come up with an application when determining due dates for a production system with sequencedependent setup costs.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Herbert Jodlbauer, Matthias Dehmer, Sonja StrasserAbstractIn this paper, we define a novel probability distribution triggered by a due date setting problem from a multiitem single level production system. As a result, we derive a recurrence relation for the underlying distribution function and, finally, we also infer the novel discrete distribution function. We underpin our analytical findings by numerical results when computing the distribution function, the expected value as well as the variance. In order to apply and translate our apparatus to other problems, we come up with an application when determining due dates for a production system with sequencedependent setup costs.
 Existence of periodic solutions for a class of secondorder
pLaplacian systems Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Xiang LvAbstractIn this paper, the existence of periodic solutions are obtained for a class of nonautonomous secondorder pLaplacian systems by the least action principle.
 Abstract: Publication date: 1 December 2018Source: Applied Mathematics and Computation, Volume 338Author(s): Xiang LvAbstractIn this paper, the existence of periodic solutions are obtained for a class of nonautonomous secondorder pLaplacian systems by the least action principle.