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: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:Fengxia Liu; Baoyindureng Wu; Jixiang Meng Pages: 90 - 95 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Fengxia Liu, Baoyindureng Wu, Jixiang Meng Let G = ( V , E ) be a graph of order n, and λ = ( λ 1 , λ 2 , … , λ p ) a sequence of positive integers. The sequence λ is admissible for G if λ 1 + ⋯ + λ p = n . Such an admissible sequence λ is said to be realizable in G if there exists a partition ( V 1 , V 2 , … , V p ) of the vertex set V such that Vi induces a connected subgraph of order ni in G for each i. If every admissible sequence is realizable in G, then we say that G is arbitrarily partitionable (AP, for short). We show that if a tree T of maximum degree at most n + 1 has a path containing all the vertices of degree n + 1 , then T □ C n has a Hamiltonian path. In particular, for any caterpillar T with maximum degree at most n + 1 , T □ C n is AP. In addition, if T is a caterpillar with Δ ( T ) ≥ n + 4 , then T □ C n is not AP. For the cases n + 2 ≤ Δ ( T ) ≤ n + 3 , we present some sufficient conditions for a caterpillar T such that T □ C n is AP.

Authors:Amanda Garcia; Amer Obeidi; Keith W. Hipel Pages: 96 - 104 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Amanda Garcia, Amer Obeidi, Keith W. Hipel An improvement in the inverse engineering of preferences approach for the Graph Model for Conflict Resolution is introduced. In addition to providing decision-makers and analysts with up-to-date preference information about opponents, the methodology is now equipped with an Advice function which enriches the decision-making process by providing important information regarding potential moves. Decision-makers who use the methods introduced in this paper are provided with the expected value of each of their possible moves, with the probability of the opponent’s next response, and with the opponent reachable states. This insightful information helps establish an accurate picture of the conflict situation and in so doing, aids stakeholders in making strategic decisions.

Authors:Gabriel J. Lord; Antoine Tambue Pages: 105 - 122 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Gabriel J. Lord, Antoine Tambue We consider the numerical approximation of a general second order semi–linear parabolic stochastic partial differential equation (SPDE) driven by additive space-time noise. We introduce a new modified scheme using linear functionals of the noise with the semi–implicit Euler–Maruyama method in time, and the finite element method in space (although extension to finite differences or finite volumes would be possible). We prove the convergence in the root mean square L 2 norm for a diffusion reaction equation and diffusion advection reaction equation with a large family of Lipschitz nonlinear functions. We present numerical results for a linear reaction diffusion equation in two dimensions as well as a nonlinear example of two-dimensional stochastic advection diffusion reaction equation. We observe from both the analysis and numerics that the proposed scheme has better convergence properties than the standard semi–implicit Euler–Maruyama method.

Authors:V.M. Silva-García; R. Flores-Carapia; C. Rentería-Márquez; B. Luna-Benoso; M. Aldape-Pérez Pages: 123 - 135 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): V.M. Silva-García, R. Flores-Carapia, C. Rentería-Márquez, B. Luna-Benoso, M. Aldape-Pérez There are procedures to encrypt images; however, sometimes there is a loss of information in the decryption process or the key set size is not specifically mentioned. In this research, substitution boxes are built for the Advanced Encryption Standard (AES) cryptosystem using Chaos, and generated by a non-linear differential equation. The boxes’ non-linearity is quantified using the Walsh function. One thousand twenty four boxes are chosen with a non-linearity of 106. To generate a pseudorandom permutation over 256 elements, an algorithm that defines a bijective function is employed. The AES utilized in this article uses 128 bit keys and applies a box in each round; that is, using an array of 10 boxes for each plaintext block of 128 bits. An encryption application for color images is presented. The degree of the encrypted images’ randomness is measured to quantify the cipher quality. Image encryption is performed without information loss. The aim in future is to design a device to encrypt video in a robust manner and in real time without loss of information.

Authors:Shuchao Cao; Libi Fu; Weiguo Song Pages: 136 - 147 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Shuchao Cao, Libi Fu, Weiguo Song An extended multi-grid model is proposed to study fire evacuation in a two-exit room. The exit selection based on random utility theory, as well as the pedestrian movement in fire, is investigated. The effects of different occupant types, the utility threshold, heat release rate of fire, burning materials and pre-movement time on evacuation are discussed. The results show that active occupants are beneficial for evacuation because of their guidance to the herding pedestrians, whereas, the existence of conservative is not always good for evacuation; a proper frequency of changing target exit can relieve congestion and optimize evacuation process; evacuation time is not monotonically increasing with the increment of heat release rate due to acceleration when pedestrians feel the incentive of high temperature within limit; the effect of burning material on evacuation is related to its thermal physical properties; the pre-movement time aggravates the difficulty of evacuation due to the bad visibility and high CO concentration in fire situation. The study may be useful to predict exit selection and pedestrian movement process, and then give suggestions to guide pedestrian evacuation under fire emergency.

Authors:Bei-Bei Hu; Tie-Cheng Xia; Wen-Xiu Ma Pages: 148 - 159 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Bei-Bei Hu, Tie-Cheng Xia, Wen-Xiu Ma In this work, we investigate the two-component modified Korteweg-de Vries (mKdV) equation, which is a complete integrable system, and accepts a generalization of 4 × 4 matrix Ablowitz–Kaup–Newell-Segur (AKNS)-type Lax pair. By using of the unified transform approach, the initial-boundary value (IBV) problem of the two-component mKdV equation associated with a 4 × 4 matrix Lax pair on the half-line will be analyzed. Supposing that the solution {u 1(x, t), u 2(x, t)} of the two-component mKdV equation exists, we will show that it can be expressed in terms of the unique solution of a 4 × 4 matrix Riemann–Hilbert problem formulated in the complex λ-plane. Moreover, we will prove that some spectral functions s(λ) and S(λ) are not independent of each other but meet the global relationship.

Authors:A.V. Porubov; R.S. Bondarenkov; D. Bouche; A.L. Fradkov Pages: 160 - 166 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): A.V. Porubov, R.S. Bondarenkov, D. Bouche, A.L. Fradkov The feedback control algorithm is applied to provide stable propagation of a two-step shock waves for nonlinear isothermal Euler equations despite the desired profile and velocity of the waves do not correspond to an analytical solution of the equations. Two cases are considered: transition to the two-step shock wave solution form the usual one-step wave and generation of a wave with a two-step front from an initially undisturbed velocity field. In both cases arising of two-step shock waves is obtained and an influence of the control algorithm coefficients on the shape of the waves is established.

Authors:Shaojun Dai; Shangzhao Li Pages: 167 - 171 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Shaojun Dai, Shangzhao Li Among the properties of homogeneity of incidence structures, flag-transitivity obviously is a particularly important and natural one. Originally, Buekenhout et al. reached a classification of flag-transitive Steiner 2-designs. Recently, Huber completely classified all flag-transitive Steiner t-designs with t ≤ 6 using the classification of the finite 2-transitive permutation groups. Hence the determination of all flag-transitive t-designs with λ ≥ 2 has remained of particular interest and has been known as a long-standing and still open problem.This article is a contribution to the study of the automorphism groups of 4-(v, k, 3) designs. Let S = ( P , B ) be a non-trivial 4- ( q + 1 , k , 3 ) design. If PSL(2, q) acts flag-transitively on S , then S is a 4-(168,12,3) design and GB is conjugate to A 4 or Z 12.

Authors:Hailong Qiu Pages: 172 - 188 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Hailong Qiu In this paper, we consider a two-grid quadratic equal-order stabilized method for the stationary incompressible Navier–Stokes equations with nonlinear slip boundary conditions. Our two-grid stabilized method consists of computing one nonlinear problem on a coarse mesh and then solving a linearization correction problem on a fine mesh. Moreover, the stability and convergence of the present method are derived. Finally, numerical experiments are performed to confirm our theoretical results.

Authors:Changqing Xu; Jianguo Li; Shan Ge Pages: 189 - 196 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Changqing Xu, Jianguo Li, Shan Ge Let G = (V(G), E(G)) be a graph and ϕ be a proper k-total coloring of G. Set f ϕ ( v ) = ∑ u v ∈ E ( G ) ϕ ( u v ) + ϕ ( v ) , for each v ∈ V(G). If fϕ (u) ≠ fϕ (v) for each edge uv ∈ E(G), the coloring ϕ is called a k-neighbor sum distinguishing total coloring of G. The smallest integer k in such a coloring of G is the neighbor sum distinguishing total chromatic number, denoted by χ Σ ″ ( G ) . In this paper, by using the famous Combinatorial Nullstellensatz, we determine χ Σ ″ ( G ) for any planar graph G with Δ(G) ≥ 13.

Authors:Jiaquan Xie; Zhibin Yao; Hailian Gui; Fuqiang Zhao; Dongyang Li Pages: 197 - 208 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Jiaquan Xie, Zhibin Yao, Hailian Gui, Fuqiang Zhao, Dongyang Li In the current study, we consider the numerical solutions of the Fokker-Planck equations of time and space fractional derivative type with variable coefficients. The proposed method is based on the two-dimensional Chebyshev wavelet basis together with their corresponding operational matrices of fractional-order integration. The convergence analysis of the proposed method is rigorously established. Numerical tests are carried out to confirm the effectiveness and feasibility of the proposed scheme.

Authors:Jingyuan Zhang Pages: 209 - 227 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Jingyuan Zhang In this paper, we present a finite difference scheme for solving the Riesz fractional advection-dispersion equations (RFADEs). The scheme is obtained by using asymmetric discretization technique and modify the shifted Grünwald approximation to fractional derivative. By calculating the unknowns in differential nodal-point sequences at the odd and even time-levels, the discrete solution of the scheme can be obtained explicitly. The computational cost for the scheme at each time step can be O(Klog K) by using the fast matrix-vector multiplication with the help of Toeplitz structure, where K is the number of unknowns. We prove that the scheme is solvable and unconditionally stable. We derive the error estimates in discrete l 2-norm, which is optimal in some cases. Numerical examples are presented to verify our theoretical results.

Authors:M. Sapagovas; T. Meškauskas; F. Ivanauskas Pages: 228 - 240 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): M. Sapagovas, T. Meškauskas, F. Ivanauskas The stability of a finite difference scheme for Schrödinger, Kuramoto–Tsuzuki and parabolic equations, subject to non-local conditions with complex coefficients, is dealt with. The stability conditions, which have to be met by complex coefficients in non-local conditions, have been determined. The main result of this study is that complex coefficients together with non-local conditions cause new effects on the stability of difference scheme. Numerical experiment has revealed additional regularities in the stability conditions.

Authors:Yujun Yang; Yuliang Cao; Haiyuan Yao; Jing Li Pages: 241 - 249 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Yujun Yang, Yuliang Cao, Haiyuan Yao, Jing Li Let G be a connected graph. The resistance distance between any two vertices of G is defined as the net effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index of G, denoted by Kf(G), is the sum of resistance distances between all pairs of vertices in G. In [28], it was conjectured that for a connected n-vertex graph G with a connected complement G ¯ , K f ( G ) + K f ( G ¯ ) ≤ n 3 − n 6 + n ∑ k = 1 n − 1 1 n − 4 sin 2 k π 2 n , with equality if and only if G or G ¯ is the path graph Pn . In this paper, by employing combinatorial and electrical techniques, we show that the conjecture is true except for a complementary pair of small graphs on five vertices.

Authors:Soriano–Sánchez A.G.; Posadas–Castillo C.; Platas–Garza M.A.; Arellano–Delgado A. Pages: 250 - 262 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Soriano–Sánchez A.G., Posadas–Castillo C., Platas–Garza M.A., Arellano–Delgado A. In this paper synchronization of fractional–order Liu chaotic oscillators is addressed. Two networks of fractional–order Liu chaotic oscillators are synchronized by appealing to results from complex systems theory for integer–order systems. We use and implement complex dynamical networks composed by nine Liu chaotic oscillators. Two scenarios are considered: (i) complex network with regular topology, and (ii) complex network with irregular topology. Synchronization of both complex networks is achieved by coupling the fractional–order chaotic oscillators through their second state. We use numerical simulations to verify the results, we also show an FPGA realization of the complex networks previously synchronized.

Authors:Liyun Tong; Yang Liu; Jungang Lou; Jianquan Lu; Fuad E. Alsaadi Pages: 263 - 275 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Liyun Tong, Yang Liu, Jungang Lou, Jianquan Lu, Fuad E. Alsaadi In this paper, we investigate the static output feedback set stabilization for context-sensitive probabilistic Boolean control networks (CS-PBCNs) via the semi-tensor product of matrices. An algorithm for finding the largest control invariant set with probability one is obtained by the algebraic representations of logical dynamics. Based on the analysis of the set stabilization, necessary and sufficient conditions for S-stabilization are obtained. Static output feedback controllers are designed to achieve S-stabilization for a CS-PBCN. At last, examples to study metastatic melanoma are given to show the effectiveness of our main results.

Authors:Anandaraman Rathinasamy; Priya Nair Pages: 276 - 303 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Anandaraman Rathinasamy, Priya Nair In this paper, the linear asymptotic mean-square stability of the weak second-order stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential equations due to Rößler (2009) and Tang and Xiao (2017) are obtained. Further, we have developed the stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential equations to the balanced stochastic Runge–Kutta methods by using the control functions. We carry out a linear stability analysis of the class of stochastic Runge–Kutta methods for the linear test equations with multiplicative noise thereby providing an explicit structure of stability matrices. Some comparisons and illustrations shows that there is an improvement in the stability and error analysis of these new balanced stochastic Runge–Kutta methods comparatively to stochastic Runge–Kutta methods and thus conforming the obtained theoretical results.

Authors:Yan Liu; Jingling Mei; Wenxue Li Pages: 304 - 315 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Yan Liu, Jingling Mei, Wenxue Li This paper aims to study the stochastic stabilization problem of complex networks without strong connectedness (CNSC). To deal with large-scale complex networks which are not strongly connected, a hierarchical method and a hierarchical algorithm are given, respectively. Meanwhile, we construct a logarithmic Lyapunov function for CNSC. Next, based on the theory of asymptotically autonomous systems, the Lyapunov method and the graph theory, the whole complex network can be stabilized by stabilizing a part of nodes. Then, stability criteria of CNSC are given, whose conditions reflect the relationship between dynamic properties and topology structure clearly. Furthermore, the theoretical results are applied to coupled oscillators on CNSC to ensure the stability. Finally, a numerical example is provided to illustrate the effectiveness and practicability of the results.

Authors:Silvana De Lillo; Marina Dolfin; Gioia Fioriti Pages: 316 - 328 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Silvana De Lillo, Marina Dolfin, Gioia Fioriti A learning dynamics on network is introduced, characterized by binary and multiple nonlinear interactions among the individuals distributed in the different nodes. A particular topology of the network is considered by introducing a leader node which influences all the other “follower” nodes without being influenced in turn. Numerical simulations are provided, particularly focusing on the effect of the network structure and of the nonlinear interactions on the emerging behaviour of the system. It turns out that the leader node always exhibits an autonomous evolution, while the follower nodes may have a regression when the interactions with the leader node are switched off. There is instead a remarkable change in the final configurations of the follower nodes, even if only one of them is connected to the leader: indeed, due to the microscopic interactions among them, all the follower nodes feel a strong “leader effect”.

Authors:Shaohui Wang; Chunxiang Wang; Jia-Bao Liu Pages: 338 - 350 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Shaohui Wang, Chunxiang Wang, Jia-Bao Liu For a (molecular) graph, the first multiplicative Zagreb index Π1 is equal to the product of squares of the vertex degrees, and the second multiplicative Zagreb index Π2 is equal to the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore the multiplicative Zagreb indices in terms of domination number. Sharp upper and lower bounds of Π1 and Π2 are given. In addition, the corresponding extreme graphs are characterized, and our conclusions enrich and extend some known results.

Authors:Hyunjin Yang; Mehrdad Massoudi Pages: 351 - 362 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Hyunjin Yang, Mehrdad Massoudi Flow and heat transfer in a suspension down an inclined plane is studied; non-linear constitutive relations for the stress tensor and the heat flux vector are used. The (material) coefficients appearing in these constitutive relations are assumed to be functions of the volume fraction. Different thermal boundary conditions including radiation boundary condition at the free surface are used and a parametric study is performed to study the impact of the dimensionless numbers on the flow and heat transfer. The dimensionless forms of the governing equations are solved numerically, and velocity, volume fraction and temperature fields are obtained.

Authors:Lei Li; Wenhai Qi; Xiaoming Chen; Yonggui Kao; Xianwen Gao; Yunliang Wei Pages: 363 - 375 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Lei Li, Wenhai Qi, Xiaoming Chen, Yonggui Kao, Xianwen Gao, Yunliang Wei This paper deals with stability analysis and control synthesis for positive semi-Markov jump systems (S-MJSs) with time-varying delay, in which the stochastic semi-Markov process related to nonexponential distribution is considered. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing have some conservation. To deal with these problems, the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition. Then, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear Lyapunov–Krasovskii functional depending on the bound of time-varying delay. Furthermore, an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable in standard linear programming. The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs with time-varying delay under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, three examples, one of which is the virus mutation treatment model, are given to demonstrate the validity of the main results.

Authors:A. Bhattacharyya; B. Mukhopadhyay Pages: 376 - 389 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): A. Bhattacharyya, B. Mukhopadhyay In this paper we have made an attempt to find a general solution of a problem of high frequency vibration in a micro-polar rectangular beam. We model the micro-polar beam problem in such a way that it can be reduced to Timoshenko beam problem in classical case. To solve the problem we adopted a methodology based on Hamiltonian principle with Legendre's transformation similar to symplectic approach. It was first applied in elasticity problem in the early 1990s by Professor W. Zhong. After achieving the Hamiltonian formulation for micro-polar beam problem we no longer follow the derivation procedure of symplectic approach but make our own way to solve it in order to reduce the complexities of the problem.

Authors:Li-Bing Wu; Heng Wang; Xi-Qin He; Da-Qing Zhang Pages: 390 - 405 Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): Li-Bing Wu, Heng Wang, Xi-Qin He, Da-Qing Zhang This paper studies the problem of decentralized adaptive tracking control for a class of nonlinear large-scale systems with unmeasurable states and actuator nonlinearities. For each subsystem, a novel decentralized disturbance rejection filter is designed to estimate both system states and external disturbances. The decentralized controller with adaptive laws is designed based on back-stepping techniques. It is proved that all the signals of the resulting closed-loop system are bounded, and the output tracking errors of subsystems converge to a desired neighborhood of origin. Simulation results illustrate the effectiveness of the method proposed in this paper.

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.

Authors:S.K. Abstract: Publication date: 1 September 2018 Source:Applied Mathematics and Computation, Volume 332 Author(s): M. Anđelić, S.K. Simić, D. Živković, E.Ć. Dolićanin The characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. Finding efficient algorithms for computing characteristic polynomial of graphs is an active area of research and for some graph classes, like threshold graphs, there exist very fast algorithms which exploit combinatorial structure of the graphs. In this paper, we put forward some novel ideas based on divisor technique to obtain fast algorithms for computing the characteristic polynomial of threshold and chain graphs.