Authors:S. Amat; A. Choutri; J. Ruiz; S. Zouaoui Pages: 16 - 26 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): S. Amat, A. Choutri, J. Ruiz, S. Zouaoui A nonlinear ternary 4-point non-interpolatory subdivision scheme is presented. It is based on a nonlinear perturbation of the 4-point subdivision scheme studied in [16]. The convergence of the scheme and the regularity of the limit function are analyzed. It is shown that the Gibbs phenomenon, that is classical in linear schemes, is eliminated. We also establish the stability of the subdivision scheme, that is not a consequence of its convergence due to its non-linearity. To the best of our knowledge, this is the first ternary non-interpolatory subdivision scheme that can be found in the literature.

Authors:Grzegorz Andrzejczak Pages: 27 - 44 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Grzegorz Andrzejczak Reproducing kernel method for approximating solutions of linear boundary value problems is valid in Hilbert spaces composed of continuous functions, but its convergence is not satisfactory without additional smoothness assumptions. We prove 2nd order uniform convergence for regular problems with coefficient piecewise of Sobolev class H 2. If the coefficients are globally of class H 2, more refined phantom boundary NSC-RKHS method is derived, and the order of convergence rises to 3 or 4, according to whether the problem is piecewise of class H 3 or H 4. The algorithms can be successfully applied to various non-local linear boundary conditions, e.g. of simple integral form. The paper contains also a new explicit formula for general spline reproducing kernels in Hm [a, b], if the inner product 〈 f , g 〉 m , ξ = ∑ i < m f ( i ) ( ξ ) g ( i ) ( ξ ) + ∫ f ( m ) g ( m ) depends on any fixed reference point ξ ∈ [a, b]. The piecewise NSC–RKHS methods are then applied to two example regular LBV problems in H 3 and H 5. Exactness of the resulting numerical solutions, the degree of convergence, and their dependency of the reference point ξ ∈ [a, b] are presented in attached figures.

Authors:Mohammed Bouchlaghem; El Bekkaye Mermri Pages: 45 - 55 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Mohammed Bouchlaghem, El Bekkaye Mermri In this paper we present a reformulation of a bilateral obstacle problem as a mixed formulation problem based on subdifferential of a continuous function of which the subdifferential can characterize the non-contact domain. Then we present the analysis of the discrete problem. We prove the convergence of the approximate solution to the exact one and we provide an error estimate. This formulation was established in an abstract way, then the theoretical results was applied to a bilateral obstacle problem.

Authors:Lang Tang; Shenglin Zhou Pages: 56 - 60 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Lang Tang, Shenglin Zhou Let D be a quasi-residual design with an automorphism group G. In this paper, we classify flag-transitive, block-primitive or point-primitive quasi-residual designs with sporadic socle. Furthermore, we show that if G is flag-transitive block-primitive with sporadic socle, then G is point-primitive.

Authors:Carlos J.S. Alves; Svilen S. Valtchev Pages: 61 - 74 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Carlos J.S. Alves, Svilen S. Valtchev Two meshfree methods are proposed for the numerical solution of boundary value problems (BVPs) for the Laplace equation, coupled with boundary conditions with jump discontinuities. In the first case, the BVP is solved in two steps, using a subtraction of singularity approach. Here, the singular subproblem is solved analytically while the classical method of fundamental solutions (MFS) is applied for the solution of the regular subproblem. In the second case, the total BVP is solved using a variant of the MFS where its approximation basis is enriched with a set of harmonic functions with singular traces on the boundary of the domain. The same singularity-capturing functions, motivated by the boundary element method (BEM), are used for the singular part of the solution in the first method and for augmenting the MFS basis in the second method. Comparative numerical results are presented for 2D problems with discontinuous Dirichlet boundary conditions. In particular, the inappropriate oscillatory behavior of the classical MFS solution, due to the Gibbs phenomenon, is shown to vanish.

Authors:Kun Shang; Zheng-Hai Huang; Wanquan Liu; Zhi-Ming Li Pages: 99 - 115 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Kun Shang, Zheng-Hai Huang, Wanquan Liu, Zhi-Ming Li For many practical face recognition problems, such as law enforcement, e-passport, ID card identification, and video surveillance, there is usually only a single sample per person enrolled for training, meanwhile the probe samples can usually be captured on the spot, it is possible to collect multiple face images per person. This is a new face recognition problem with many challenges, and we name it as the single-image-to-image-set face recognition problem (ISFR). In this paper, a customized dictionary-based face recognition approach is proposed to solve this problem using the extended joint sparse representation. We first learn a customized variation dictionary from the on-location probing face images, and then propose the extended joint sparse representation, which utilizes the information of both the customized dictionary and the gallery samples, to classify the probe samples. Finally we compare the proposed method with the related methods on several popular face databases, including Yale, AR, CMU-PIE, Georgia, Multi-PIE and LFW databases. The experimental results show that the proposed method outperforms most of these popular face recognition methods for the ISFR problem.

Authors:Yueyang Li; Shuai Liu; Maiying Zhong; Steven X. Ding Pages: 116 - 130 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Yueyang Li, Shuai Liu, Maiying Zhong, Steven X. Ding This paper deals with robust state estimation problem for a class of stochastic discrete-time systems with multiplicative noises and unknown inputs over fading channels. An unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so-called P -estimation. The filter gain matrix is derived through solving a recursive Riccati equation and a generalized Lyapunov equation. A necessary and sufficient condition that guarantees the existence of the filter is given, which establishes a fundamental limit on the mean square capacity of each fading channel. Unknown input estimation and finite horizon stability of the proposed filter are also discussed. To illustrate the effectiveness of the proposed approach, the proposed algorithm is applied to a faulty remote controlled uninterruptible power system, where both the state and the fault are estimated.

Authors:Donghui Pan; Yantao Wei; Houzhang Fang; Wenzhi Yang Pages: 131 - 141 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Donghui Pan, Yantao Wei, Houzhang Fang, Wenzhi Yang This paper proposes a reliability estimation approach based on EM algorithm and Wiener processes by considering measurement errors. Firstly, the time-transformed Wiener processes are used to model the degradation process of the product, which simultaneously consider the temporal variability, unit-to-unit heterogeneity and measurement errors. In addition, we obtain the closed-form expressions of some reliability quantities such as reliability function and probability density function of the life. Moreover, the expectation maximization algorithm is adopted to estimate the model parameters effectively. Finally, a numerical example and a practical case study for LED lamps are provided to illustrate the effectiveness and superiority of the presented approach.

Authors:Abbe Mowshowitz; Matthias Dehmer Pages: 142 - 148 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Abbe Mowshowitz, Matthias Dehmer This paper introduces a system for measuring the elegance of a graph based on the steps needed to build the graph and on its symmetry structure. The measure is designed to capture the essence of the notion of elegance in mathematics, namely, simplicity and clarity. The term “elegance” is used instead of “aesthetics” to distinguish the measure from those dependent on visual representation of a graph. Elegance is based solely on the abstract properties of a graph. A framework for measurement is defined and applied in a special case.

Authors:W. Kwon; Baeyoung Koo; S.M. Lee Pages: 149 - 157 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): W. Kwon, Baeyoung Koo, S.M. Lee This paper investigates the stability criteria of time-varying delay systems with known bounds of the delay and its derivative. To obtain a tighter bound of integral term, quadratic generalized free-weighting matrix inequality (QGFMI) is proposed. Furthermore, a novel augmented Lyapunov–Krasovskii functional (LKF) are constructed with a delay-dependent matrix, which impose the information for a bound of delay derivative. Relaxed stability condition using QGFMI and LKF provides a larger delay bound with low computational burden. The superiority of the proposed stability condition is verified by comparing to recent results.

Authors:Jinliang Liu; Jilei Xia; Engang Tian; Shumin Fei Pages: 158 - 174 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Jinliang Liu, Jilei Xia, Engang Tian, Shumin Fei This paper investigates the problem of H ∞ filter design for neural networks with hybrid triggered scheme and deception attacks. In order to make full use of the limited network resources, a hybrid triggered scheme is introduced, in which the switching between the time triggered scheme and the event triggered scheme obeys Bernoulli distribution. By considering the effect of hybrid triggered scheme and deception attacks, a mathematical model of H ∞ filtering error system is constructed. The sufficient conditions that can ensure the stability of filtering error system are given by using Lyapunov stability theory and linear matrix inequality (LMI) techniques. Moreover, the explicit expressions are provided for the designed filter parameters that is in terms of LMIs. Finally, a numerical example is employed to illustrate the design method.

Authors:Wakeel Khan; Yan Lin; Sarmad Ullah Khan; Nasim Ullah Pages: 175 - 189 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Wakeel Khan, Yan Lin, Sarmad Ullah Khan, Nasim Ullah This paper studies quantized adaptive decentralized output feedback control technique for a class of interconnected nonlinear systems with quantized input and possible number of actuator failures up to infinity. A modified backstepping approach is proposed by the use of high-gain k-filters, hyperbolic tangent function property and bound-estimation approach to compensate for the effect of possible number of actuator failures up to infinity and input quantization. It is proved both mathematically and by simulation that, all the signals of the closed-loop system are globally bounded despite of input quantization and possible number of actuator failures up to infinity.

Authors:Bart S. van Lith; Jan H.M. ten Thije Boonkkamp; Wilbert L. IJzerman Pages: 190 - 201 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Bart S. van Lith, Jan H.M. ten Thije Boonkkamp, Wilbert L. IJzerman Root-finders based on full linear multistep methods (LMMs) use previous function values, derivatives and root estimates to iteratively find a root of a nonlinear function. As ODE solvers, full LMMs are typically not zero-stable. However, used as root-finders, the interpolation points are convergent so that such stability issues are circumvented. A general analysis is provided based on inverse polynomial interpolation, which is used to prove a fundamental barrier on the convergence rate of any LMM-based method. We show, using numerical examples, that full LMM-based methods perform excellently. Finally, we also provide a robust implementation based on Brent’s method that is guaranteed to converge.

Authors:Lu Qiao; Shenggui Zhang; Jing Li Pages: 202 - 212 Abstract: Publication date: 1 March 2018 Source:Applied Mathematics and Computation, Volume 320 Author(s): Lu Qiao, Shenggui Zhang, Jing Li The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In 1940 Coulson obtained an important integral formula which makes it possible to calculate the energy of a graph without knowing its spectrum. Recently several Coulson-type integral formulas have been obtained for various energies and some other invariants of graphs based on eigenvalues. For a complex polynomial ϕ ( z ) = ∑ k = 0 n a k z n − k = a 0 ∏ k = 1 n ( z − z k ) of degree n and a real number α, the general energy of ϕ(z), denoted by Eα (ϕ), is defined as ∑ z k ≠ 0 z k α when there exists k 0 ∈ { 1 , 2 , … , n } such that z k 0 ≠ 0 , and 0 when z 1 = ⋯ = z n = 0 . In this paper we give Coulson-type integral formulas for the general energy of polynomials whose roots are all real numbers in the case that α ∈ Q . As a consequence of this result, we obtain an integral formula for the 2l-th spectral moment of a graph. Furthermore, we show that our formulas hold when α is an irrational number with 0 < α < 2 and do not hold with α > 2.

Authors:Myles Kim Pages: 1 - 11 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Myles Kim Some epithelial cells form a monolayer and individual cell in the monolayer is polarized with respect to the membrane protein location and the intracellular structure. It is observed that mitosis and cytokinesis occur in parallel to the monolayer plane so that the monolayer structure is maintained. The centrosome locations of non-mitotic cells, however, are not necessarily positioned to lead the parallel cell division. Therefore, there must be mechanisms by which centrosomes get relocated, for example in MDCK II cells, from the apical domain to lateral domain to have a proper mitosis and moved back to the apical domain after the cytokinesis. The mechanisms, however, remain poorly understood, especially the mechanical part. A computational model is constructed for centriolic microtubule asters which are driven by localized molecular motors on the cortical layer. This model shows that the interaction between the cortical bound molecular motors and microtubules can lead the two-way relocation of the centrosome. The model also shows that the microtubule dynamic instability plays an important role in initiating the relocation, the tight junction is a key element in positioning the centrosome, and the swelling nucleus can accelerate the movement of centrosome to the lateral side.

Authors:C. Coll; M. Lattanzi; N. Thome Pages: 12 - 24 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): C. Coll, M. Lattanzi, N. Thome This paper deals with weighted G-Drazin inverses, which is a new class of matrices introduced to extend (to the rectangular case) G-Drazin inverses recently considered by Wang and Liu for square matrices. First, we define and characterize weighted G-Drazin inverses. Next, we consider a new pre-order defined on complex rectangular matrices based on weighted G-Drazin inverses. Finally, we characterize this pre-order and relate it to the minus partial order and to the weighted Drazin pre-order.

Authors:Sebastião Romero Franco; Francisco José Gaspar; Marcio Augusto Villela Pinto; Carmen Rodrigo Pages: 25 - 34 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Sebastião Romero Franco, Francisco José Gaspar, Marcio Augusto Villela Pinto, Carmen Rodrigo In this work, a space-time multigrid method which uses standard coarsening in both temporal and spatial domains and combines the use of different smoothers is proposed for the solution of the heat equation in one and two space dimensions. In particular, an adaptive smoothing strategy, based on the degree of anisotropy of the discrete operator on each grid-level, is the basis of the proposed multigrid algorithm. Local Fourier analysis is used for the selection of the crucial parameter defining such an adaptive smoothing approach. Central differences are used to discretize the spatial derivatives and both implicit Euler and Crank–Nicolson schemes are considered for approximating the time derivative. For the solution of the second-order scheme, we apply a double discretization approach within the space-time multigrid method. The good performance of the method is illustrated through several numerical experiments.

Authors:Debasis Manna; Alakes Maiti; G.P. Samanta Pages: 35 - 48 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Debasis Manna, Alakes Maiti, G.P. Samanta In this paper, a predator-prey model for exploited fish populations is considered, where the prey and the predator both show schooling behavior. Due to this coordinated behavior, predator-prey interaction occurs only at the outer edge of the schools formed by the populations. Positivity and boundedness of the model are discussed. Analysis of the equilibria is presented. A criterion for Hopf bifurcation is obtained. The optimal harvest policy is also discussed using Pontryagin’s maximum principle, where the effort is used as the control parameter. Numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically.

Authors:K. Sadri; A. Amini; C. Cheng Pages: 49 - 67 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): K. Sadri, A. Amini, C. Cheng Based on Jacobi polynomials, an operational method is proposed to solve the generalized Abel’s integral equations (a class of singular integral equations). These equations appear in various fields of science such as physics, astrophysics, solid mechanics, scattering theory, spectroscopy, stereology, elasticity theory, and plasma physics. To solve the Abel’s singular integral equations, a fast algorithm is used for simplifying the problem under study. The Laplace transform and Jacobi collocation methods are merged, and thus, a novel approach is presented. Some theorems are given and established to theoretically support the computational simplifications which reduce costs. Also, a new procedure for estimating the absolute error of the proposed method is introduced. In order to show the efficiency and accuracy of the proposed method some numerical results are provided. It is found that the proposed method has lesser computational size compared to other common methods, such as Adomian decomposition, Homotopy perturbation, Block-Pulse function, mid-point, trapezoidal quadrature, and product-integration. It is further found that the absolute errors are almost constant in the studied interval.

Authors:Álvaro Leitao; Cornelis W. Oosterlee; Luis Ortiz-Gracia; Sander M. Bohte Pages: 68 - 84 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Álvaro Leitao, Cornelis W. Oosterlee, Luis Ortiz-Gracia, Sander M. Bohte In this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based financial option valuation method which assumes the availability of asset data samples: a characteristic function of the underlying asset probability density function is not required. As such, the presented technique represents a generalization of the well-known COS method [1]. The convergence of the proposed method is O ( 1 / n ) , in line with Monte Carlo methods for pricing financial derivatives. The ddCOS method is then particularly interesting for density recovery and also for the efficient computation of the option’s sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods.

Authors:Harendra Singh Pages: 85 - 100 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Harendra Singh In this paper, we present a method based on the Jacobi polynomials for the approximate solution to fractional vibration equation (FVE) of large membranes. Proposed method converts the FVE into Sylvester form of algebraic equations, whose solution gives the approximate solution. Convergence analysis of the proposed method is given. It is also shown that our approximate method is numerically stable. Numerical results are discussed for different values of wave velocities and fractional order involved in the FVE. These numerical results are shown through figures for particular cases of Jacobi polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third kind, (4) Chebyshev polynomial of fourth kind, (5) Gegenbauer polynomial. The accuracy of the proposed method is proved by comparing results of our method and other exiting analytical methods. Comparison of results are presented in the form of tables for particular cases of FVE and Jacobi polynomials.

Authors:Francisco M. Fernández; Javier Garcia Pages: 101 - 108 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Francisco M. Fernández, Javier Garcia We obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonalization of the Hamiltonian matrix (CRLM and CRCH). The other one is based on the Riccati equations for the logarithmic derivatives of factors of the wavefunction (RPM). The latter approach enabled us to obtain the most accurate results and extremely sharp resonances.

Authors:Minakshi Dhamija; Ram Pratap; Naokant Deo Pages: 109 - 120 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Minakshi Dhamija, Ram Pratap, Naokant Deo In the present article, we consider the Kantorovich type generalized Szász–Mirakyan operators based on Jain and Pethe operators [32]. We study local approximation results in terms of classical modulus of continuity as well as Ditzian–Totik moduli of smoothness. Further we establish the rate of convergence in class of absolutely continuous functions having a derivative coinciding a.e. with a function of bounded variation.

Authors:Chao-Ping Chen Pages: 121 - 128 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Chao-Ping Chen In this paper, we investigate certain asymptotic series used by Hirschhorn to prove an asymptotic expansion of Ramanujan for the nth harmonic number. We give a general form of these series with a recursive formula for its coefficients. By using the result obtained, we present a formula for determining the coefficients of Ramanujan’s asymptotic expansion for the nth harmonic number. We also give a recurrence relation for determining the coefficients aj (r) such that H n : = ∑ k = 1 n 1 k ∼ 1 2 ln ( 2 m ) + γ + 1 12 m ( ∑ j = 0 ∞ a j ( r ) m j ) 1 / r as n → ∞, where m = n ( n + 1 ) / 2 is the nth triangular number and γ is the Euler–Mascheroni constant. In particular, for r = 1 , we obtain Ramanujan’s expansion for the harmonic number.

Authors:Jing Li; Lu Qiao; Nan Gao Pages: 143 - 149 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Jing Li, Lu Qiao, Nan Gao Let G be a graph on n vertices and η 1 , η 2 , … , η n the eigenvalues of its extended adjacency matrix. The extended Estrada index EEex is defined as the sum of the terms e η i , i = 1 , 2 , … , n . In this paper we establish lower and upper bounds for EEex in terms of the number of vertices and the number of edges and characterize the extremal graphs. Also the bounds for EEex of some special graphs are obtained.

Authors:D.M. Akhmedov; A.R. Hayotov; Kh.M. Shadimetov Pages: 150 - 159 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): D.M. Akhmedov, A.R. Hayotov, Kh.M. Shadimetov In the present paper in L 2 ( m ) ( 0 , 1 ) space the optimal quadrature formulas with derivatives are constructed for approximate calculation of the Cauchy type singular integral. Explicit formulas for the optimal coefficients are obtained. Some numerical results are presented.

Authors:Francesco Asdrubali; Giorgio Baldinelli; Francesco Bianchi; Danilo Costarelli; Antonella Rotili; Marco Seracini; Gianluca Vinti Pages: 160 - 171 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Francesco Asdrubali, Giorgio Baldinelli, Francesco Bianchi, Danilo Costarelli, Antonella Rotili, Marco Seracini, Gianluca Vinti In this paper, we develop a procedure for the detection of the contours of thermal bridges from thermographic images, in order to study the energy performance of buildings. Two main steps of the above method are: the enhancement of the thermographic images by an optimized version of the mathematical algorithm for digital image processing based on the theory of sampling Kantorovich operators, and the application of a suitable thresholding based on the analysis of the histogram of the enhanced thermographic images. Finally, an improvement of the parameter defining the thermal bridge is obtained.

Authors:Raimund Bürger; Pep Mulet; Lihki Rubio; Mauricio Sepúlveda Pages: 172 - 186 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Raimund Bürger, Pep Mulet, Lihki Rubio, Mauricio Sepúlveda Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22–42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose severe stability restrictions on the time step, the novel schemes treat diffusion implicitly and convection explicitly. To avoid the need to solve the nonlinear systems appearing in the implicit treatment of the nonlinear diffusion, second-order linearly implicit-explicit Runge–Kutta schemes (LIMEX-RK schemes) are employed. Numerical experiments demonstrate that the schemes produce accurate numerical solutions with the same stability restrictions as in the purely hyperbolic case.

Authors:Falguni Roy; Dharmendra. K. Gupta Pages: 193 - 209 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Falguni Roy, Dharmendra. K. Gupta In this paper, two approaches are described to establish verifiable sufficient regularity conditions of complex interval matrices. In the first approach, a complex interval matrix is mapped to a real block interval matrix and then its sufficient regularity conditions are obtained. In the second approach, a necessary condition for the singularity of a complex interval matrix is derived and used to get its sufficient regularity conditions. As an application, the above derived sufficient regularity conditions are used to investigate the location of the outer approximations of individual eigenvalue sets of complex interval matrices. Two algorithms are proposed and results obtained are compared with those obtained by earlier methods and Monte Carlo simulations. The advantages of these algorithms are that they can detect gaps in between the approximations of the whole eigenvalue sets. The second algorithm is very effective compared to the first algorithm from the computational time point of view. Several numerical examples and statistical experiments are worked out to validate and demonstrate the efficacy of our work.

Authors:Hong Qiu; Wenmin Deng Pages: 210 - 222 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Hong Qiu, Wenmin Deng This paper systematically investigates the optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps. Under some simple assumptions, the sufficient conditions for extinction and stable in the time average of each species are established. The stability in distribution of this model is proved under our assumptions. Finally, the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained. And some numerical simulations are introduced to demonstrate the theoretical results.

Authors:C. Clavero; J. Vigo-Aguiar Pages: 223 - 233 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): C. Clavero, J. Vigo-Aguiar In this work, we are interested in approximating the solution of 2D parabolic singularly perturbed problems of convection–diffusion type. The convective term of the differential equation, associated to the initial and boundary value problem, is such that each one of its components has an interior simple turning point, which can be of attractive or repulsive type. We describe a numerical method to discretize the continuous problem, which combines the fractional implicit Euler method, defined on a uniform mesh, to discretize in time, and the classical upwind finite difference scheme, defined on a nonuniform mesh of Shishkin type, to discretize in space. The fully discrete algorithm has a low computational cost. From a numerical point of view, we see that the method is efficient and uniformly convergent with respect to the diffusion parameter in both cases when the source term is a continuous function or it has a first kind discontinuity at the turning points. Some numerical results for different test problems are showed; from them, we deduce the good properties of the numerical method.

Authors:Ran Gu; Xueliang Li; Zhongmei Qin; Yongtang Shi; Kang Yang Pages: 234 - 251 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Ran Gu, Xueliang Li, Zhongmei Qin, Yongtang Shi, Kang Yang Let ℓ and r be integers. A real number α ∈ [0, 1) is a jump for r if for any ε > 0 and any integer m, m ≥ r, any r-uniform graph with n > n 0(ε, m) vertices and at least ( α + ɛ ) ( n r ) edges contains a subgraph with m vertices and at least ( α + c ) ( m r ) edges, where c = c ( α ) is positive and does not depend on ε and m. It follows from a theorem of Erdős, Stone and Simonovits that every α ∈ [0, 1) is a jump for r = 2 . Erdős asked whether the same is true for r ≥ 3. However, Frankl and Rödl gave a negative answer by showing that 1 − 1 ℓ r − 1 is not a jump for r if r ≥ 3 and ℓ > 2r. Peng gave more sequences of non-jumping numbers for r = 4 and r ≥ 3. However, there are also a lot of unknowns on determining whether a number is a jump for r ≥ 3. Following a similar approach as that of Frankl and Rödl, we give several sequences of non-jumping numbers for r = 5 , and extend one of the results to every r ≥ 5, which generalize the above results.

Authors:Ravinder Katta; G.D. Reddy; N. Sukavanam Pages: 252 - 263 Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): Ravinder Katta, G.D. Reddy, N. Sukavanam Computing steering control for an approximately controllable linear system for a given target state is an ill-posed problem. We use a weighted Tikhonov regularization method and compute the regularized control. It is proved that the target state corresponding to the regularized control is close to the actual state to be attained. We also obtained error estimates and convergence rates involved in the regularization procedure using both the a priori and a posteriori parameter choice rule. Theory is substantiated with numerical experiments.

Authors:Guoliang Chen; Jianwei Xia; Guangming Zhuang; Junsheng Zhao Pages: 1 - 17 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Guoliang Chen, Jianwei Xia, Guangming Zhuang, Junsheng Zhao This paper focuses on the problem of delay-dependent state feedback control for a class of networked control systems (NCSs) with nonlinear perturbations and two delay components. Based on the dynamic delay interval (DDI) method and the Wirtinger integral inequality, some improved delay-dependent stability analysis are obtained. Furthermore, the results are extended to the conditions of NCSs with one time delay, and the corresponding stability analysis results and state feedback controller are obtained. Finally, some numerical examples and simulations are given to show the effectiveness of the proposed methods.

Authors:Xiaobo Yang; Anping Liao; Jiaxin Xie Pages: 18 - 24 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Xiaobo Yang, Anping Liao, Jiaxin Xie The theory and algorithms for recovering a sparse representation of multiple measurement vector (MMV) are studied in compressed sensing community. The sparse representation of MMV aims to find the K-row sparse matrix X such that Y = A X , where A is a known measurement matrix. In this paper, we show that, if the restricted isometry property (RIP) constant δ K + 1 of the measurement matrix A satisfies δ K + 1 < 1 K + 1 , then all K-row sparse matrices can be recovered exactly via the Orthogonal Matching Pursuit (OMP) algorithm in K iterations based on Y = A X . Moreover, a matrix with RIP constant δ K + 1 = 1 K + 0.086 is constructed such that the OMP algorithm fails to recover some K-row sparse matrix X in K iterations. Similar results also hold for K-sparse signals recovery. In addition, our main result further improves the proposed bound δ K + 1 = 1 K by Mo and Shen [12] which can not guarantee OMP to exactly recover some K-sparse signals.

Authors:Laihuan Chen; Jixiang Meng; Yingzhi Tian; Xiaodong Liang; Fengxia Liu Pages: 25 - 29 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Laihuan Chen, Jixiang Meng, Yingzhi Tian, Xiaodong Liang, Fengxia Liu A bipartite digraph is said to be a half vertex transitive digraph if its automorphism acts transitively on the sets of its bipartition, respectively. In this paper, bipartite double coset digraphs of groups are defined and it is shown that any half vertex transitive digraph is isomorphic to some half double coset digraph, and we show that the connectivity of any strongly connected half transitive digraph is its minimum degree.

Authors:Y. Pahamli; M.J. Hosseini; A.A. Ranjbar; R. Bahrampoury Pages: 30 - 42 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Y. Pahamli, M.J. Hosseini, A.A. Ranjbar, R. Bahrampoury This study is aimed to investigate the melting of phase change material (PCM) in a horizontal double pipe heat exchanger. The area between the pipes is filled with RT50 as PCM and water is used as a heat transfer fluid (HTF) which flows through inner pipe. The downward movement of inner pipe, inlet temperature and mass flow rate of HTF are considered and compared with the base system. The results show that inner pipe downward movement increases the convection-dominant zone which reduces melting time considerably (up to 64%). Results also indicate that by increasing the HTF inlet temperature thermal potential of the system increases which accelerates the melting process. However increasing the mass flow rate of HTF does not have significant role in melting rate.

Authors:Jianling Li; Zhenping Yang Pages: 52 - 72 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Jianling Li, Zhenping Yang In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization. At each iteration, three systems of linear equations with the same coefficient matrix are solved to yield search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for filter methods. The algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness. Finally, some preliminary numerical results are reported.

Authors:Chong-Xiao Shi; Guang-Hong Yang Pages: 73 - 88 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Chong-Xiao Shi, Guang-Hong Yang This paper studies the robust proportional-integral-derivative (PID) consensus control for a class of linear multi-agent systems (MASs) with external disturbances. Different from the existing results, both the consensus analysis and the transient performance characteristics for high-order linear MASs are considered. Based on a factorization of Laplacian matrix, the initial MAS is firstly transformed into the so-called weighted edge dynamics, and then a design equivalence between the proposed PID consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results. Furthermore, by combining Lyapunov theory and Barbalat’s Lemma, it is proved that both the stabilization of weighted edge dynamics and the consensus of MAS can be guaranteed even in the presence of external disturbances. In particular, some relationships between the transient time performance of weighted edge dynamics and the PID design parameters are given. Finally, some numerical examples on LC oscillator network are provided to illustrate the validity of theoretical results.

Authors:V.Y. Pan; F. Soleymani; L. Zhao Pages: 89 - 101 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): V.Y. Pan, F. Soleymani, L. Zhao We propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves 18th order of convergence by using only seven matrix multiplications per iteration loop. This yields a high efficiency index for that computational task. The algorithm has a relatively mild numerical instability, and we stabilize it at the price of adding two extra matrix multiplications per iteration loop. This implies an efficiency index that exceeds the known record for numerically stable iterations for this task, which means substantial acceleration of the long standing algorithms for an important problem of numerical linear algebra. Our numerical tests cover a variety of examples in the category of generalized inverses, such as Drazin case, rectangular case, and preconditioning of linear systems. The test results are in good accordance with our formal study.

Authors:Mikhail Goubko Pages: 102 - 114 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Mikhail Goubko The Wiener index is maximized over the set of trees with the given vertex weight and degree sequences. This model covers the traditional “unweighed” Wiener index, the terminal Wiener index, and the vertex distance index. It is shown that there exists an optimal caterpillar. If weights of internal vertices increase in their degrees, then an optimal caterpillar exists with weights of internal vertices on its backbone monotonously increasing from some central point to the ends of the backbone, and the same is true for pendent vertices. A tight upper bound of the Wiener index value is proposed and an efficient greedy heuristics is developed that approximates well the optimal index value. Finally, a branch and bound algorithm is built and tested for the exact solution of this NP-complete problem.

Authors:Chao Liu; Longfei Yu; Qingling Zhang; Yuanke Li Pages: 115 - 137 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Chao Liu, Longfei Yu, Qingling Zhang, Yuanke Li In this paper, we establish a double delayed hybrid bioeconomic plankton system with stochastic fluctuations and commercial harvesting on zooplankton, where maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered. Stochastic fluctuations are incorporated into the proposed system in form of Gaussian white noises to depict stochastic environmental factors in plankton system. For deterministic system without double time delays, existence of singularity induced bifurcation is studied due to variation of economic interest of commercial harvesting, and state feedback controllers are designed to eliminate singularity induced bifurcation. For deterministic system with double time delays, positivity and uniform persistence of solutions are studied, and some sufficient conditions associated with asymptotic stability of interior equilibrium are investigated. For stochastic system without double time delays, stochastic stability and existence of stochastic Hopf bifurcation are discussed based on singular boundary theory of diffusion process and invariant measure theory. For stochastic system with double time delays, existence and uniqueness of global positive solution are investigated, and asymptotic behaviors of the interior equilibrium are studied by constructing appropriate Lyapunov functions. Numerical simulations are carried out to validate theoretical analysis.

Authors:Lili Chang; Zhen Jin Pages: 138 - 154 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Lili Chang, Zhen Jin Reaction–diffusion models with time delay have been widely applied in population biology as well as epidemiology. This type of models can possibly exhibit complex dynamical behaviors such as traveling wave, self-organized spatial pattern, or chaos. Numerical methods play an essential role in the study of these dynamical behaviors. This paper concerns the finite element approximation for reaction–diffusion models with time delay. Two fully discrete schemes and corresponding a priori error estimates are derived. Generally, the research on evolution of population and epidemic needs to survey long-time dynamical behaviors of these models, so that it is important to improve the speed of numerical simulation. To this end, interpolation technique is used in our schemes to avoid numerical integration of reaction term. An outstanding advantage of using interpolation of reaction term is that it improves the operation speed greatly, meanwhile does not reduce convergence order. Applications are given to some model problems arising from population biology and epidemiology. From these simulations some interesting phenomena can be found and we try to explain them in biological significance.

Authors:Joseph Arthur; Adam Attarian; Franz Hamilton; Hien Tran Pages: 155 - 166 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Joseph Arthur, Adam Attarian, Franz Hamilton, Hien Tran The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a subset of variables. However in the case of censored observations, where measurements of the system beyond a certain detection point are impossible, the estimation problem is complicated. Without appropriate consideration, censored observations can lead to inaccurate estimates. Motivated by previous work on censored filtering in linear systems, we develop a modified version of the extended Kalman filter to handle the case of censored observations in nonlinear systems. We validate this methodology in a simple oscillator system first, showing its ability to accurately reconstruct state variables and track system parameters when observations are censored. Finally, we utilize the nonlinear censored filter to analyze censored datasets from patients with hepatitis C and human immunodeficiency virus.

Authors:Chao Luo; Xingyuan Wang; Yuanjie Zheng Pages: 174 - 185 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Chao Luo, Xingyuan Wang, Yuanjie Zheng In this article, based on interdependent networks, cooperation in spatial prisoner's dilemma game (PDG) with coevolving resources is studied. By means of a strategy-independent rule, limited resources can be continually re-allocated among different players in the same network or across different networks. The coevolution of dynamics is discussed respectively for two cases: game circumstances on two coupled networks are identical or asymmetry. In the first case, we obtain that the involvement of resources can be significantly beneficial for cooperative behaviors, and the heterogeneous distribution of resources can positively enhance interdependent network reciprocity. Furthermore, an optimal value (ρ ≈ 0.8) of the interdependent strength exists for cooperation, which is obviously larger than the previous results (ρ ≈ 0.5) without coevolving resources. Besides, we also find resources follow the power law distribution, where cooperators and interconnected players tend to obtain more resources. In the second case, we mainly focus on the flow of resources between networks as well as the intertwined effect of the interdependent strength and resources distribution on cooperation. Microscopic dynamical properties of the flow of resources jointly caused by various factors have been discussed. In certain conditions, instead of promoting the cooperation, the influx of resources could even be positive for defection.

Authors:Yuanpeng Zhu Pages: 186 - 204 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Yuanpeng Zhu A class of rational quartic/cubic interpolation spline with two local control parameters is presented, which can be C 2 continuous without solving a linear system of consistency equations for the derivative values at the knots. The effects of the local control parameters on generating interpolation curves are illustrated. For C 2 interpolation, the given interpolant can locally reproduce quadratic polynomials and has O(h 2) or O(h 3) convergence. Simple schemes for the C 2 interpolant to preserve the shape of 2D positive data are developed. Moreover, based on the Boolean sum of quintic interpolating operators, a class of bi-quintic partially blended rational quartic/cubic interpolation surfaces is also constructed. The given interpolation surface provides four local control parameters and can be C 2 continuous without using the second or higher mixed partial derivatives on a rectangular grid. Simple sufficient data dependent constraints are also derived on the local control parameters to preserve the shape of a 3D positive data set arranged over a rectangular grid.

Authors:Tae H. Lee; Ju H. Park; Hoyoul Jung Pages: 205 - 214 Abstract: Publication date: 1 January 2018 Source:Applied Mathematics and Computation, Volume 316 Author(s): Tae H. Lee, Ju H. Park, Hoyoul Jung This study considers the network-based H ∞ state estimation problem for neural networks where transmitted measurements suffer from the sampling effect, external disturbance, network-induced delay, and packet dropout as network constraints. The external disturbance, network-induced delay, and packet dropout affect the measurements at only the sampling instants owing to the sampling effect. In addition, when packet dropout occurs, the last received data are used. To tackle the imperfect signals, a compensator is designed, and then by aid of the compensator, H ∞ filter which guarantees desired performance is designed as well. A numerical example is given to illustrate the validity of the proposed methods.

Authors:Chen Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): He Chen Graph coloring problem and problem on the existence of paths and cycles have always been popular topics in graph theory. The problem on the existence of rainbow paths and rainbow cycles in edge colored graphs, as an integration of them, was well studied for a long period. In this survey, we will review known results on this subject. Because of the relationship between cycles and paths, we will review results on the existence of rainbow cycles (including rainbow Hamilton cycles, long rainbow cycles and rainbow cycles with given length) first, and then long rainbow paths (including rainbow Hamilton paths and other long rainbow paths).

Authors:Kanat Abstract: Publication date: 15 January 2018 Source:Applied Mathematics and Computation, Volume 317 Author(s): K. Kanat, M. Sofyalıoğlu In the present paper, we introduce the Stancu type generalisation of Lupaş–Schurer operators based on (p, q)-integers. We are concerned with the basic convergence of the constructed operators based on Korovkin’s type approximation theorem. Further, we obtain the rate of convergence for the new operators in terms of the modulus of continuity, with the help of functions of Lipschitz class and Peetre’s K-functionals. Then, we present three significant numerical mathematical algorithms. Finally, in order to confirm our theoretical results we obtain error estimation and illustrate the convergence of the (p, q)-Lupaş–Schurer–Stancu operators to certain functions by using MATLAB.