Authors:Baoqin Chen; Zhenyu Zhao; Zhi Li; Zehong Meng Pages: 1 - 10 Abstract: Publication date: 1 October 2018 Source:Applied Mathematics and Computation, Volume 334 Author(s): Baoqin Chen, Zhenyu Zhao, Zhi Li, Zehong Meng Based on the idea of Fourier extension, we develop a new method for numerical differentiation. The Tikhonov regularization method with a super-order penalty term is presented to deal with the illposdness of the problem and the regularization parameter can be chosen by a discrepancy principle. For various smooth conditions, the solution process of the new method is uniform and order optimal error bounds can be obtained. Numerical experiments are also presented to illustrate the effectiveness of the proposed method.

Authors:Xin-Guang Yang; Lu Li; Yongjin Lu Pages: 11 - 29 Abstract: Publication date: 1 October 2018 Source:Applied Mathematics and Computation, Volume 334 Author(s): Xin-Guang Yang, Lu Li, Yongjin Lu In this paper, we study the large time behavior for 3D viscoelastic incompressible fluid flow subject to Kelvin–Voigt damping and a time varying external force. The evolution of the dynamic is governed by a 3D non-autonomous Navier–Stokes–Voigt (NSV) equation. We assume that the external force is in the space of translation bounded functions (or its sub-spaces) that requires less compactness than the space of translation compact functions. We formulate the system in the framework of skew product flow. By defining an appropriate energy space that incorporates the Kelvin–Voigt damping, we established the existence of regular strong uniform attractor for the NSV equation in energy space W ˜ and provide a description of the general structure of the uniform attractor. Our result improves the H 0 1 regularity of global attractor of the system under study.

Authors:Zujin Zhang; Chupeng Wu; Zheng-an Yao Pages: 1 - 7 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Zujin Zhang, Chupeng Wu, Zheng-an Yao We investigate the Cauchy problem for the 3D MHD system with damping terms u α − 1 u and b β − 1 b (α, β ≥ 1), and show that the strong solution exists globally and uniquely if one of the following four conditions holds, (1) 3 ≤ α ≤ 27 8 , β ≥ 4 ; (2) 27 8 < α ≤ 7 2 , β ≥ 7 2 α − 5 ; (3) 7 2 < α < 4 , β ≥ 5 α + 7 2 α ; (4) α ≥ 4, β ≥ 1. This improves the previous results significantly.

Authors:Xiao-Yong Xiao; Hong-Wei Yin Pages: 8 - 19 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Xiao-Yong Xiao, Hong-Wei Yin In this paper, for solving systems of nonlinear equations, we develop a family of two-step third order methods and introduce a technique by which the order of convergence of many iterative methods can be improved. Given an iterative method of order p ≥ 2 which uses the extended Newton iteration as a predictor, a new method of order p + 2 is constructed by introducing only one additional evaluation of the function. In addition, for an iterative method of order p ≥ 3 using the Newton iteration as a predictor, a new method of order p + 3 can be extended. Applying this procedure, we develop some new efficient methods with higher order of convergence. For comparing these new methods with the ones from which they have been derived, we discuss the computational efficiency in detail. Several numerical examples are given to justify the theoretical results by the asymptotic behaviors of the considered methods.

Authors:Dazhong Ma; Xiaoyu Li; Qiuye Sun; Xiangpeng Xie Pages: 20 - 31 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Dazhong Ma, Xiaoyu Li, Qiuye Sun, Xiangpeng Xie This paper is concerned with the fault tolerant synchronization of the master-slave chaotic system. Based on the double event-triggered scheme, the sampled controller, which yellow includes the fault compensator and state feedback controller, is designed to achieve the fault tolerant synchronization. When the fault exceeds the threshold value, the fault compensator can eliminate its effect in synchronized chaotic system. The double event-triggered scheme is composed of the system trigger and fault trigger, which can judge whether or not the newly sampled signal should be transmitted to the fault compensator and state feedback controller. It can make more appropriate use of network resources and increase the robustness of synchronized chaotic system. Based on the input delay method, the solution of the controller is converted to guarantee the stability of chaotic errors system. By constructing the Lyapunov–Krasovskii functional and employing the Wirtingerbrk inequality, sufficient conditions for asymptotical stability of the chaotic error system are derived for achieving the fault tolerant synchronization through linear matrix inequality approach. Finally, a numerical simulation example is discussed to prove the practical utility of this method.

Authors:Yujie Zhou; Fanfan Chen; Jiaxiang Cai; Hua Liang Pages: 32 - 41 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Yujie Zhou, Fanfan Chen, Jiaxiang Cai, Hua Liang Two efficient splitting schemes are developed for 3D Maxwell’s equations. The schemes are energy-preserving and unconditionally stable, while being implemented explicitly. Rigorous optimal error estimates are established for the proposed schemes, and especially the constant in the error estimates is only O ( T ) . Numerical results confirm the theoretical analysis, and numerical comparison with some existing methods shows the good performance of the present schemes.

Authors:D.E. Ferreyra; F.E. Levis; N. Thome Pages: 42 - 52 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): D.E. Ferreyra, F.E. Levis, N. Thome This paper derives some further results on recent generalized inverses studied in the literature, namely core EP, DMP, and CMP inverses. Our main aim is to develop maximal classes of matrices for which their representations remain valid.

Authors:Beniamin Bogosel Pages: 61 - 75 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Beniamin Bogosel We present an amelioration of current known algorithms for minimizing functions depending on the eigenvalues corresponding to a partition of a given domain. The idea is to use the advantage of a representation using density functions on a fixed grid while decreasing the computational time. This is done by restricting the computation to neighbourhoods of regions where the associated densities are above a certain threshold. The algorithm extends and improves known methods in the plane and on surfaces in dimension 3. It also makes possible to make computations of optimal volumic 3D spectral partitions on sufficiently important discretizations.

Authors:Yongchao Yu; Jigen Peng Pages: 76 - 94 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Yongchao Yu, Jigen Peng In this paper, we first present a modified Chambolle–Pock primal-dual method (MCPPDM) to solve a convex composite optimization problem which minimizes the sum of two convex functions with one composed by a linear operator. It is well known that the Chambolle–Pock primal-dual method (CPPDM) with the combination parameter being 1 is an application of the proximal point algorithm and thus is convergent, however, when the combination parameter is not 1, the method may be not convergent. To choose flexibly the combination parameter, we develop a slightly modified version with little additional computation cost. In CPPDM, one variable is updated twice but another variable is updated only once at each iteration. However, in the modified version, two variables are respectively updated twice at each iteration. Another main task of this paper is that we reformulate some well-known sparse recovery problems as special cases of the convex composite optimization problem and then apply MCPPDM to address these sparse recovery problems. A large number of numerical experiments have demonstrated that the efficiency of the proposed method is generally comparable or superior to that of existing well-known methods such as the linearized alternating direction method of multipliers and the graph projection splitting algorithm in terms of solution quality and run time.

Authors:M. De Lorenzo; M. Pelanti; Ph. Lafon Pages: 95 - 117 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): M. De Lorenzo, M. Pelanti, Ph. Lafon The present article deals with the numerical integration of a six-equation single-velocity two-phase flow model with stiff mechanical relaxation. This model can be employed to approximate efficiently the well known single-velocity single-pressure five-equation model of Kapila et al. (2001). Work in the literature has shown the efficiency of the six-equation model in simulating complex two-phase flows involving cavitation and evaporation processes. The aim of this work is to present and discuss various numerical schemes for this two-phase model focusing on the integration of the nonconservative terms appearing in the phasic energy equations. In fact, previous work has suggested that the choice of the discretization method for the nonconservative terms often does not play a significant role. Two new methods are proposed: a path-conservative HLLC-type scheme that is based on the Dal Maso–LeFloch–Murat theory, and a generalized HLLC-type scheme that is based on a Suliciu’s Riemann solver. The latter scheme has the important property of preserving the positivity of the intermediate states of the conserved quantities. Moreover, we also approximate solutions of the six-equation model by applying two path-conservative schemes recently proposed in the literature, which have been derived from the Osher and HLLEM Riemann solvers. We show comparisons of the different numerical schemes for several test cases, including cavitation problems and shock tubes. An efficiency study for first and second order schemes is also presented. Numerical results show that different methods corresponding to different numerical treatments of the nonconservative terms give analogous results and they are all able to produce accurate approximations of solutions of the Kapila’s five-equation model, except, as expected, for shocks in two-phase mixtures with very high pressure ratios.

Authors:I. Kusbeyzi Aybar; O.O. Aybar; M. Dukarić; B. Ferčec Pages: 118 - 132 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): I. Kusbeyzi Aybar, O.O. Aybar, M. Dukarić, B. Ferčec In this paper we investigate the dynamical properties of a two prey-one predator system with quadratic self interaction represented by a three-dimensional system of differential equations by using tools of computer algebra. We first investigate the stability of the singular points. We show that the trajectories of the solutions approach to stable singular points under given conditions by numerical simulation. Then, we determine the conditions for the existence of the invariant algebraic surfaces of the system and we give the invariant algebraic surfaces to study the flow on the algebraic invariants which is a useful approach to check if Hopf bifurcation exists.

Authors:Huicheng Feng; Teck Neng Wong Pages: 133 - 144 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Huicheng Feng, Teck Neng Wong This paper reports an analytical study on the induced-charge electro-osmosis (ICEO) within a leaky dielectric annulus subjected to an AC electric field. An interesting non-monotonic variation of the ICEO flow with the increasing AC frequency is revealed. This is different from the monotonic decrease of the ICEO flow around a cylinder submerged in an unbounded electrolyte solution upon increasing the AC frequency. Moreover, the ICEO flow is significantly reduced and may reverse direction due to the existence of the outer cylinder, depending on the charging responses of the annulus and the electrolyte solution, and the annulus geometry. In this analysis, we consider both the space charge layers (SCLs) and the electric double layers (EDLs) established within the solid and the liquid sides of the solid–liquid interfaces, respectively. The ICEO flow forms eight vortices within the annulus, which show a potential for mixing enhancement in micro/nanofluidics. As the AC phase increases, the ICEO flow changes periodically with a period half of the AC period. The outer cylinder presents a significant influence on the ICEO flow within the annulus since it affects the local electric fields and the induced zeta potentials of the cylinders. The present study may provide references for microchip fabrications with non-contact electrodes and biocell manipulations by electric fields.

Authors:Yaonan Shan; Kun She; Shouming Zhong; Qishui Zhong; Kaibo Shi; Can Zhao Pages: 145 - 168 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Yaonan Shan, Kun She, Shouming Zhong, Qishui Zhong, Kaibo Shi, Can Zhao This paper is concerned with exponential stability and extended dissipativity criteria for generalized discrete-time neural networks (GDNNs) with additive time-varying delays. The generalized dissipativity analysis combines a few previous results into a framework, such as l 2 − l ∞ performance, H ∞ performance, passivity performance, strictly ( Q , S , R ) − γ − dissipative and strictly ( Q , S , R ) − dissipative. The definition of exponential stability for GDNNs is given with a new and more appropriate expression. A novel augmented Lyapunov-Krasovskii functional (LKF) which involves more information about the additive time-varying delays is constructed. By introducing more zero equalities and using a new double summation inequality together with Finsler’s lemma, an improved delay-dependent exponential stability and extended dissipativity criterion are derived in terms of convex combination technique (CCT). Finally, numerical examples are given to illustrate the usefulness and advantages of the proposed methods.

Authors:Josef Diblík; Rigoberto Medina Pages: 169 - 186 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Josef Diblík, Rigoberto Medina The paper considers a generalized Dickman equation t x ˙ ( t ) = − ∑ i = 1 s a i x ( t − τ i ) for t → ∞ where s ∈ N , ai > 0, τi > 0, i = 1 , … , s and ∑ i = 1 s a i = 1 . It is proved that there are two mutually disjoint sets of positive decreasing solutions such that, for every two solutions from different sets, the limit of their ratio for t → ∞ equals 0 or ∞. The asymptotic behavior of such solutions is derived and a structure formula utilizing such solutions and describing all the solutions of a given equation is discussed. In addition, a criterion is proved giving sufficient conditions for initial functions to generate solutions falling into the first or the second set. Illustrative examples are given. Some open problems are suggested to be solved.

Authors:Mengmeng Zhou; Jianlong Chen Pages: 187 - 193 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Mengmeng Zhou, Jianlong Chen In this paper, we present integral representations for the DMP and core-EP inverse, which based on the full-rank decomposition of a given matrix. In particular, integral representations of the core and dual core inverse are given. All of these integral representations do not require any restriction on the spectrum of a certain matrix.

Authors:Abhirup Bandyopadhyay; Samarjit Kar Pages: 194 - 212 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Abhirup Bandyopadhyay, Samarjit Kar Emergence of synchronization is a remarkable collective phenomena between apparently independent agents in numerous multilevel and complex systems. The evidence of synchronization ranges from the elementary biological organisms to the most sophisticated human societies. In this paper, the problem of synchronization of nonlinearly coupled dynamical networks of Hindmarsh–Rose neurons with a sigmoidal coupling function is addressed. Sufficient condition for synchrony in terms of network structure is developed. A study on the basis of attraction of the complete synchronization is carried out for different structured networks. Also the phase synchronization of dynamical network of Hindmarsh–Rose neurons are studied. The impact of different structural properties of complex network on the phase synchronization are analyzed. The synchronization of Hindmarsh–Rose neurons are evaluated and compared on different structured network like random, regular, small-world, scale-free and modular networks. Interestingly, it was found that networks with high clustering coefficient and neutral degree mixing pattern promote better synchronization. Some chimera like state are also found in different structural networks. Further the effect of time delay dynamics on the synchronization of nonlinearly coupled network of Hindmarsh–Rose neurons are illustrated.

Authors:Zeting Liu; Shujuan Lü; Fawang Liu Pages: 213 - 224 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Zeting Liu, Shujuan Lü, Fawang Liu We consider the initial boundary value problem of the time fractional nonlinear Sine–Gordon equation and the fractional derivative is described in Caputo sense with the order α(1 < α < 2). Two fully discrete schemes are developed based on Legendre spectral approximation in space and finite difference discretization in time for smooth solutions and non-smooth solutions, respectively. Numerical stability and convergence are analysed. Numerical experiments for both the fully discrete schemes are presented to confirm our theoretical analysis.

Authors:Shouqiang Shen; Weijun Liu; Lihua Feng Pages: 225 - 230 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Shouqiang Shen, Weijun Liu, Lihua Feng For a ring R (not necessarily commutative) with identity, the comaximal right ideal graph of R, denoted by G ( R ) , is a graph whose vertices are the nonzero proper right ideals of R, and two distinct vertices I and J are adjacent if and only if I + J = R . In this paper we consider a subgraph G * ( R ) of G ( R ) induced by V ( G ( R ) ) ∖ J ( R ) , where J ( R ) is the set of all proper right ideals contained in the Jacobson radical of R. We prove that if R contains a nontrivial central idempotent, then G * ( R ) is a star graph if and only if R is isomorphic to the direct product of two local rings, and one of these two rings has unique maximal right ideal {0}. In addition, we also show that R has at least two maximal right ideals if and only if G * ( R ) is connected and its diameter is at most 3, then completely characterize the diameter of this graph.

Authors:Higinio Ramos; M.A. Rufai Pages: 231 - 245 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Higinio Ramos, M.A. Rufai This paper is devoted to the development and analysis of a modified family of Falkner-type methods for solving differential systems of second-order initial-value problems. The approaches of collocation and interpolation are adopted to derive the new methods. These modified methods are implemented in block form to obtain the numerical solutions to the considered problems. The study of the properties of the proposed block Falkner-type methods reveals that they are consistent and zero-stable, and thus, convergent. From the stability analysis, it could be seen that the proposed Falkner methods have non-empty stability regions for k = 2 , 3 , 4 . Some numerical test are presented to illustrate the efficiency of the proposed family.

Authors:Ashim Kumar; João R. Cardoso Pages: 246 - 253 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Ashim Kumar, João R. Cardoso The main goal of this paper is the numerical computation of solutions of the so-called Yang–Baxter-like matrix equation A X A = X A X , where A is a given complex square matrix. Two novel matrix iterations are proposed, both having second-order convergence. A sign modification in one of the iterations gives rise to a third matrix iteration. Strategies for finding starting approximations are discussed as well as a technique for estimating the relative error. One of the methods involves a very small cost per iteration and is shown to be stable. Numerical experiments are carried out to illustrate the effectiveness of the new methods.

Authors:Maneesh Kumar Singh; Srinivasan Natesan Pages: 254 - 275 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Maneesh Kumar Singh, Srinivasan Natesan In this article, we propose a higher-order uniformly convergent numerical scheme for singularly perturbed system of parabolic convection-diffusion problems exhibiting overlapping exponential boundary layers. It is well-known that the the numerical scheme consists of the backward-Euler method for the time derivative on uniform mesh and the classical upwind scheme for the spatial derivatives on a piecewise-uniform Shishkin mesh converges uniformly with almost first-order in both space ant time. Richardson extrapolation technique improves the accuracy of the above mentioned scheme from first-order to second-order uniformly convergent in both time and space. This has been proved mathematically in this article. In order to validate the theoretical results, we carried out some numerical experiments.

Authors:D. Boyadzhiev; D.N. Georgiou; A.C. Megaritis; F. Sereti Pages: 276 - 285 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): D. Boyadzhiev, D.N. Georgiou, A.C. Megaritis, F. Sereti Indubitably, the notion of covering dimension of frames was, extensively, studied. Many searches such as Charalambous, Banashewski and Gilmour (see, for example (Charalambous, 1974; Charalambous, 1974 [11]; Banaschewski and Gilmour, 1989 [12]) studied this dimension. Also, in the study [5], the covering dimension of finite lattices has been characterized by using the so called minimal covers. This approach gave the motive to other searches such as Zhang et al., to study properties of this dimension (see Zhang et al. (2017) [9]). In this paper, we study the covering dimension of finite lattices in combination with matrix theory. Essentially, we characterize the minimal covers of finite lattices and the order of those covers using matrices and we compute the covering dimension of the corresponding finite lattices.

Authors:Elliot J. Carr; Nathan G. March Pages: 286 - 303 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Elliot J. Carr, Nathan G. March We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [Appl. Math. Model., 46:450–464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work.

Authors:Naveed Ahmed; Volker John; Gunar Matthies; Julia Novo Pages: 304 - 324 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Naveed Ahmed, Volker John, Gunar Matthies, Julia Novo A local projection stabilization (LPS) method in space is considered to approximate the evolutionary Oseen equations. Optimal error bounds with constants independent of the viscosity parameter are obtained in the continuous-in-time case for both the velocity and pressure approximation. In addition, the fully discrete case in combination with higher order continuous Galerkin–Petrov (cGP) methods is studied. Error estimates of order k + 1 are proved, where k denotes the polynomial degree in time, assuming that the convective term is time-independent. Numerical results show that the predicted order is also achieved in the general case of time-dependent convective terms.

Authors:R. Ponalagusamy; S. Priyadharshini Pages: 325 - 343 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): R. Ponalagusamy, S. Priyadharshini A mathematical model on the pulsatile flow of a Casson fluid through a porous stenosed artery with bifurcation in the presence of magnetic field and periodic body acceleration has been developed in the present study. The governing equation is expressed in terms of shear stress and the resulting momentum equation with the initial and boundary conditions is solved numerically by adopting finite difference schemes. The velocity distribution is obtained at different locations of the artery for various values of parameters involved in the study. The combined effects of bifurcation angle, stenotic height, yield stress, Hartmann number, Darcy number and time period on flow variables such as velocity, wall shear stress and resistive impedance have been observed. The shear stress along the outer wall of the parent artery is less than its corresponding value on the inner wall of the daughter artery. The shear stress along the outer wall of the parent artery and the inner wall of the daughter artery increase as Hartmann number increases. It is of interest to note that the flow resistance has a decreasing trend with the increasing value of half of the bifurcation angle and Darcy number. The wall shear stress and flow resistance are increased when the rheology of blood is changed from Newtonian to Casson fluid. It is worthwhile to note that the presence of magnetic field and porous medium increases the plug core radius which is for the first time, added to the literature. The plug core radius increases with increase in yield stress and decrease in stenotic height.

Authors:Xiaoqing Xiao; Ju H. Park; Lei Zhou Pages: 344 - 352 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Xiaoqing Xiao, Ju H. Park, Lei Zhou The event-triggered control problem for discrete-time switched linear systems with packet losses is addressed in this paper. It is assumed that, at each event-triggered instant transmitted successfully, the controller can only access the transmitted information of system state and mode. In both cases of packet losses and no packet losses, mode dependent event-triggered transmission schemes are proposed. And the closed-loop system is modeled as a switched system with augmented switching signal. Then, based on the multiple Lyapunov function method, in the case of packet losses, exponential stability conditions are given with constraint of the maximum allowable number of successive packet losses, and design methods for state feedback controller gains and mode dependent event-triggered parameters are obtained. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example.

Authors:Tadeja Kraner Šumenjak; Douglas F. Rall; Aleksandra Tepeh Pages: 353 - 361 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Tadeja Kraner Šumenjak, Douglas F. Rall, Aleksandra Tepeh In this paper, we define a new domination invariant on a graph G, which coincides with the ordinary independent domination number of the generalized prism G □ K k , called the k-rainbow independent domination number and denoted by γ rik (G). Some bounds and exact values concerning this domination concept are determined. As a main result, we prove a Nordhaus–Gaddum-type theorem on the sum for 2-rainbow independent domination number, and show if G is a graph of order n ≥ 3, then 5 ≤ γ ri 2 ( G ) + γ ri 2 ( G ¯ ) ≤ n + 3 , with both bounds being sharp.

Authors:Shuang Zhao; Jixiang Meng Pages: 362 - 368 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Shuang Zhao, Jixiang Meng Let H be a connected hypergraph. H is said to be linear if any two edges of H share at most one vertex. If all edges of H have the same cardinality, then H is uniform. We call H maximally edge-connected if the edge-connectivity of H attains its minimum degree. In this paper, we present some sufficient conditions for linear uniform hypergraphs to be maximally edge-connected that generalize the corresponding well-known results for graphs.

Authors:Hui Li; Ye-Zhou Li Pages: 369 - 375 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Hui Li, Ye-Zhou Li In this work, abundant meromorphic exact solutions of two kinds of extended (3+1)-dimensional Jimbo–Miwa equations are obtained by making use of the complex method, which contain rational solutions, exponential function solutions and elliptic function solutions. The properties of the results are also shown by some figures.

Authors:Aymen Laadhari Pages: 376 - 400 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Aymen Laadhari We present a numerical methodology based on the use of the Newton and level set methods and tailored for the simulation of incompressible immiscible two-fluid flows with moving hyperelastic membrane. The method features the use of implicit time integration schemes and is based on a consistent Newton–Raphson linearization. The performances are enhanced by using the Kou’s method (Kou et al., 2006) which features a third-order convergence behavior without requiring higher order derivatives. To overcome numerical instability issues related to the explicit decoupling, a fully monolithic strategy and a partitioned implicit strategy are devised. We investigate the main features of the proposed strategies, and we report several numerical experiments with the aim of illustrating their robustness and accuracy. We show numerically that the monolithic strategy performs better and remains stable when considering relatively small viscosities or large stiffness, for which the partitioned approach depicts a slow convergence or even fails to converge. However, the partitioned strategy features significant computational savings when it converges within a reasonable number of sub-iterations. Graphical abstract

Authors:M. Oulghelou; C. Allery Pages: 416 - 434 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): M. Oulghelou, C. Allery Classical adjoint-based optimization approach for the optimal control of partial differential equations is known to require a large amount of CPU time and memory storage. In this article, in order to reduce these requirements, a posteriori and a priori model order reduction techniques such as POD (Proper Orthogonal Decomposition) and PGD (Proper Generalized Decomposition) are used. As a matter of fact, these techniques allows a fast access to the temporal dynamics of a solution approximated in a suitable subspace of low dimension, spanned by a set of basis functions that form a reduced basis. The costly high fidelity model is then projected onto this basis and results in a system of ordinary differential equations which can be solved in quasi-real time. A disadvantage of considering a fixed POD basis in a suboptimal control loop, is basically the dependence of such bases on a posteriori information coming from high fidelity simulations. Therefore, a non robustness of the POD basis can be expected for certain perturbations in the original parameter for which it was built. As a result, update the reduced bases with respect to each variation in the control parameter using the POD method is still costly. To get over this difficulty, we equip the usual reduced optimal control algorithm with an intermediate basis adaptation step. The first proposed approach consists in adapting the reduced basis for a new control parameter by interpolating over a set of POD bases previously computed for a range of control parameters. To achieve that, an interpolation technique based on properties of the tangent subspace of the Grassmann manifold (ITSGM) is considered. The second approach is the PGD method, which by nature, enrich a space time decomposition trying to enhance the approximation by learning from its own errors. Relaying on this property, this method is employed in the control loop as a basis corrector, in such a way the given spatial basis is adapted for the new control parameter by performing just few enrichments. These two approaches are applied in the sub-control of the two dimensional non-linear reaction-diffusion equations and Burgers equations.

Authors:Qingqiong Cai; Fuyuan Cao; Tao Li; Hua Wang Pages: 435 - 442 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Qingqiong Cai, Fuyuan Cao, Tao Li, Hua Wang The study of extremal problems on various graph invariants has received great attention in recent years. Among the most well known graph invariants is the sum of distances between all pairs of vertices in a graph. This is also known as the Wiener index for its applications in Chemical Graph Theory. Many interesting properties related to this concept have been established for extremal trees that maximize or minimize it. Recently a vertex-weighted analogue of sum of distances is introduced for vertex weighted trees. Some extremal results on (vertex-weighted) trees were obtained, by Goubko, for trees with a given degree sequence. In this note we first analyze the behavior of vertex-weighted distance sum in general, identifying the “middle part” of a tree analogous to that with respect to the regular distance sum. We then provide a simpler approach (than that of Goubko’s) to obtain a stronger result regarding the extremal tree with a given degree sequence. Questions and directions for potential future study are also discussed.

Authors:Dinh Kien Nguyen; Khoa Viet Nguyen; Van Manh Dinh; Buntara S. Gan; Sergei Alexandrov Pages: 443 - 459 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Dinh Kien Nguyen, Khoa Viet Nguyen, Van Manh Dinh, Buntara S. Gan, Sergei Alexandrov Nonlinear bending of elastoplastic functionally graded (FG) ceramic-metal beams subjected to nonuniform distributed loads is investigated by the finite element method. A bilinear stress-strain relation with isotropic hardening is assumed for elastoplastic behavior of metal, and the elastoplastic properties of the FG ceramic-metal material are evaluated by using Tamura–Tomota–Ozawa (TTO) model. Based on Euler–Bernoulli beam theory, a nonlinear finite element formulation, taking the effect of plastic deformation into account, is derived and used in the investigation. The formulation employing nonlinear von Kámán strain-displacement relationship is derived by using the physical neutral surface as reference plane. An incremental-iterative procedure based on Newton–Raphson method, in which the plastic equation is solved at Gauss points for updating the stress and evaluating the element formulation, is employed to solve nonlinear equilibrium equations. The elastoplastic behavior is illustrated for a FG beam composed of TiB and Ti. The numerical results show that yielding in the FG beam occurs at the layer near the ceramic surface earlier than it does at the layer near the metal surface. The effect of the material distribution, plastic deformation on the nonlinear behavior of the beam with various end conditions is investigated in detail. The formation and propagation of plastic zone inside the beam during the loading process is also examined and highlighted.

Authors:Rodica Cimpoiasu Pages: 460 - 466 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Rodica Cimpoiasu In this paper a new perspective upon generating arbitrage-free stock price models is proposed. The generalized conditional symmetry (GCS) method is applied to the governing second order ( 1 + 1 ) partial differential equation which does contain a rational parameter p drawn from the interval [ 1 2 , 1 ] . We investigate the conditions that yield the concerned equation admitting a special class of second-order GCSs. The determining system is solved in several special cases and, from invariance surface condition associated to each of the GCS operator, for all values of p, some invariant solutions are pointed out. New candidate models for arbitrage-free stock price are derived.

Authors:Osmanbey Uzunkol; Mehmet Sabır Kiraz Pages: 467 - 479 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Osmanbey Uzunkol, Mehmet Sabır Kiraz Recently many pairing-based cryptographic protocols have been designed with a wide variety of new novel applications including the ones in the emerging technologies like cloud computing, internet of things (IoT), e-health systems, and wearable technologies. There have been, however, a wide range of incorrect use of these primitives mainly because of their use in a “black-box” manner. Some new attacks on the discrete logarithm problem lead to either totally insecure or highly inefficient pairing-based protocols, and extend considerably the issues related to pairings originally pointed out by Galbraith et al. (2008). Other reasons are the implementation attacks, the minimal embedding field attacks, and the issues due to the existence of auxiliary inputs. Although almost all these issues are well-known to mathematical cryptographers, there is no state-of-the-art assessment covering all these new issues which could be used by the applied cryptography researchers and the IT-security developers. In order to illustrate this point, we give a list of recent papers having either wrong security assumptions or realizability/efficiency issues. Furthermore, we give a compact and an state-of-the-art recipe of the correct use of pairings for the correct design with a view towards efficient and secure implementation of security solutions using these primitives.

Authors:Yiqiao Wang; Weifan Wang; Ying Wang Pages: 480 - 489 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Yiqiao Wang, Weifan Wang, Ying Wang The star chromatic index χ st ′ ( G ) of a graph G is the smallest integer k for which G has a proper edge k-coloring without bichromatic paths or cycles of length four. The strong chromatic index χ s ′ ( G ) of G is the smallest integer k for which G has a proper edge k-coloring such that any two edges at distance at most two get distinct colors. In this paper, we prove that if a graph G can be edge-partitioned into two graphs F and H, then χ st ′ ( G ) ≤ χ st ′ ( F ) + χ s ′ ( H G ) , where χ s ′ ( H G ) denotes the strong chromatic index of H restricted on G. Using this result, we give some upper bounds of the star chromatic index for planar graphs. Precisely, we show that (1) if G is a planar graph with maximum degree Δ, then χ st ′ ( G ) ≤ 2.75 Δ + 18 ; (2) if G is a planar graph without 4-cycles, then χ st ′ ( G ) ≤ ⌊ 1.5 Δ ⌋ + 18 ; (3) if G is a planar graph of girth at least 8, then χ st ′ ( G ) ≤ ⌊ 1.5 Δ ⌋ + 3 ; (4) if G is a K 4-minor free graph, then χ st ′ ( G ) ≤ 2.25 Δ + 6 ; and (5) if G is an outerplanar graph, then χ st ′ ( G ) ≤ ⌊ 1.5 Δ ⌋ + 5 , which improves a result in Bezegová et al. [2], which says that χ st ′ ( G ) ≤ ⌊ 1.5 Δ ⌋ + 12 for an outerplanar graph G.

Authors:Mats Gyllenberg; Francesca Scarabel; Rossana Vermiglio Pages: 490 - 505 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Mats Gyllenberg, Francesca Scarabel, Rossana Vermiglio We address the problem of the numerical bifurcation analysis of general nonlinear delay equations, including integral and integro-differential equations, for which no software is currently available. Pseudospectral discretization is applied to the abstract reformulation of equations with infinite delay to obtain a finite dimensional system of ordinary differential equations, whose properties can be numerically studied with well-developed software. We explore the applicability of the method on some test problems and provide some numerical evidence of the convergence of the approximations.

Authors:Bo Zhang; Hui Li; Shengguo Li; Jin Peng Pages: 506 - 520 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Bo Zhang, Hui Li, Shengguo Li, Jin Peng Emergency facilities location and vehicle routing are two of the most challenging issues in emergency logistics. This paper presents an exploration of the sustainable multi-depot emergency facilities location-routing problem with uncertain information. An uncertain multi-objective location-routing programming model is constructed for emergency response with consideration of travel time, emergency relief costs and carbon dioxide emissions via uncertainty theory. By implementing the main-objective method, the uncertain multi-objective model can be rebuilt as an uncertain single-objective optimization model. The properties of the model are discussed in the framework of uncertainty theory. A hybrid intelligent algorithm that integrates uncertain simulation and a genetic algorithm is designed to solve the proposed model. Finally, numerical examples are presented to illustrate the optimization ideas and the robustness and effectiveness of the proposed algorithm.

Authors:Qiaoping Li; Sanyang Liu; Yonggang Chen Pages: 521 - 535 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Qiaoping Li, Sanyang Liu, Yonggang Chen In this paper, the networked synchronization communication for nonlinear uncertain fractional-order chaotic systems is investigated. Notice that the network transmission capacity is limited, a novel combination event-triggered mechanism is designed. Based on the fractional Lyapunov stability criterion and adaptive control technique, an event-triggered adaptive controller is constructed and a sufficient networked synchronization condition for the above-mentioned fractional-order chaotic systems with uncertainties and disturbances is attained. The detailed theoretical derivation and specific numerical simulation demonstrate that the proposed networked synchronization strategy can reduce the burden of network bandwidth effectively without losing the desired synchronization performance. Meanwhile, Zeno phenomenon is excluded.

Authors:Jialing Zhang; Kun Qian Pages: 536 - 546 Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Jialing Zhang, Kun Qian Harmonic map is the critical point of the corresponding integral with respect to the square norm of the gradient or energy density. The harmonic energy defined on Riemann surfaces will decrease along its gradient line direction and reduce to the limit conformal map. Harmonic map between surfaces is a diffeomorphism which is associated to a unique Beltrami differential. So a harmonic diffeomorphism sequence corresponds to an Beltrami differential sequence. When boundary map is restricted on a unit circle, the Beltrami differential sequence changes with constant conformal modulus. In this paper, we consider the conformal map between surfaces by the Beltrami differential sequence with constant conformal modulus, which is equivalent to a decreasing harmonic energy sequence with fixed boundary correspondence, and provide the corresponding algorithms for numerical computation. Furthermore, we will discuss the convergence of proposed algorithms, which provides theoretical foundation for numerical experiments.

Authors:Zhichao Geng; Jinjiang Yuan; Junling Yuan Pages: 1 - 18 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Zhichao Geng, Jinjiang Yuan, Junling Yuan In this paper, we consider several scheduling problems on a serial-batch machine for scheduling jobs with or without precedence relations. Under the serial-batch setting, the jobs in a batch are processed in succession and are removed until the last job in this batch finishes its processing. Thus, the processing time of a batch is equal to the sum of processing times of jobs in the batch. When a new batch starts, a constant setup time is required for the machine. The objectives of the problems involve minimizing makespan and a maximum cost. For these problems, we either present polynomial-time algorithms to generate all Pareto optimal points and find a corresponding Pareto optimal schedule for each Pareto optimal point, or give the strong NP-hardness proof. Experimentation results show that the proposed algorithms for the considered problems are very efficient.

Authors:Jonathan D. Hauenstein; Margaret H. Regan Pages: 19 - 34 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Jonathan D. Hauenstein, Margaret H. Regan Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing computations on an adaptively chosen affine coordinate patch. Second, for parameterized systems which are overdetermined, we investigate options for adaptively selecting a well-constrained subsystem to restore numerical stability. Finally, since one is typically interested in only computing real solutions for parameterized problems which arise from applications, we investigate a scheme for heuristically identifying solution paths which appear to be ending at nonreal solutions and truncating them. We demonstrate these three aspects on two problems arising in computer vision.

Authors:Fu-Tao Hu; Lu Li; Jia-Bao Liu Pages: 35 - 41 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Fu-Tao Hu, Lu Li, Jia-Bao Liu The total domination number of a graph G without isolated vertices is the minimum number of vertices that dominate all vertices in G. The total bondage number of G is the minimum number of edges whose removal enlarges the total domination number. In this paper, we establish a tight lower bound for the total bondage number of a vertex-transitive graph. We also obtain upper bounds for regular graphs by investigating the relation between the total bondage number and the efficient total domination. As applications, we study the total bondage numbers for some circulant graphs and toroidal meshes by characterizing the existence of efficient total dominating sets in these graphs.

Authors:Pengfei Wan; Jianhua Tu; Shenggui Zhang; Binlong Li Pages: 42 - 47 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Pengfei Wan, Jianhua Tu, Shenggui Zhang, Binlong Li In the theory and applications of graphs, it is a basic problem to compute the numbers of independent sets and matchings of given sizes. Since the problem of computing the total number of independent sets and that of matchings of graphs is #P-complete, it is unlikely to give efficient algorithms to find the numbers of independent sets and matchings of given sizes. In this paper, for graphs with order n and treewidth at most p, we present two dynamic algorithms to compute the numbers of independent sets of all sizes with runtime O(2 p · pn 3) and the numbers of matchings of all sizes with runtime O(22p · pn 3), respectively. By the algorithms presented in this paper, for graphs with small treewidths, the numbers of independent sets and matchings of all possible sizes can be computed efficiently.

Authors:Quanwei Ren; Hongjiong Tian Pages: 48 - 57 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Quanwei Ren, Hongjiong Tian In this paper, we propose generalized two-step Maruyama methods for solving Itô stochastic differential equations. Numerical analysis concerning consistency, convergence and numerical stability in the mean-square sense is presented. We derive sufficient and necessary conditions for linear mean-square stability of the generalized two-step Maruyama methods. We compare the stability region of the generalized two-step Maruyama methods of Adams type with that of the corresponding two-step Maruyama methods of Adams type and show that our proposed methods have better linear mean-square stability. A numerical example is given to confirm our theoretical results.

Authors:Xu Yang; Weidong Zhao Pages: 58 - 75 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Xu Yang, Weidong Zhao In this paper, we investigate the mean square error of numerical methods for SPDEs driven by Gaussian and non-Gaussian noises. The Gaussian noise considered here is a Hilbert space valued Q-Wiener process and the non-Gaussian noise is defined through compensated Poisson random measure associated to a Lévy process. As the models consider the influences of Gaussian and non-Gaussian noises simultaneously, this makes the models more realistic when the models are also influenced by some randomly abrupt factors, but more complicated. As a consequence, the numerical analysis of the problems becomes more involved. We first study the regularity for the mild solution. Next, we propose a semidiscrete finite element scheme in space and a fully discrete linear implicit Euler scheme for the SPDEs, and rigorously obtain their error estimates. Both the regularity results of the mild solution and error estimates obtained in the paper are novel.

Authors:Lukas Einkemmer; Martina Moccaldi; Alexander Ostermann Pages: 76 - 89 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Lukas Einkemmer, Martina Moccaldi, Alexander Ostermann Strang splitting is a well established tool for the numerical integration of evolution equations. It allows the application of tailored integrators for different parts of the vector field. However, it is also prone to order reduction in the case of non-trivial boundary conditions. This order reduction can be remedied by correcting the boundary values of the intermediate splitting step. In this paper, three different approaches for constructing such a correction in the case of inhomogeneous Dirichlet, Neumann, and mixed boundary conditions are presented. Numerical examples that illustrate the effectiveness and benefits of these corrections are included.

Authors:Valero Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): Valentín Valero The concept of process similarity has attracted the attention of many researchers in the recent literature, since it measures the degree of proximity of processes. Similarities are therefore useful for the efficient management of large repositories, since they allow us to find the appropriate process models among hundreds or thousands of possible candidates. However, time constraints are usually omitted when these similarity measures are defined, so in this paper two similarity measures are defined over a timed extension of Petri nets, the so-called timed-arc Petri nets, in which tokens are assigned an age indicating the time elapsed from creation, and PT-arcs (place to transition arcs) are labeled with time intervals that are used to restrict the age of the tokens that can be used to fire the adjacent transition.

Authors:Zafer Abstract: Publication date: 15 September 2018 Source:Applied Mathematics and Computation, Volume 333 Author(s): S. Doğru Akgöl, A. Zafer We obtain sufficient conditions which guarantee the existence of a solution of a class of second order nonlinear impulsive differential equations with fixed moments of impulses possessing a prescribed asymptotic behavior at infinity in terms of principal and nonprincipal solutions. An example is given to illustrate the relevance of the results.