Authors:Zhang He; Junwei Lu; Yunliang Wei; Yuming Chu Abstract: Abstract This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples. PubDate: 2018-01-11 DOI: 10.1007/s40314-017-0559-1

Authors:S. Priyadharshini; R. Ponalagusamy Abstract: Abstract A mathematical model has been developed for pulsatile flow of blood through a tapered arterial stenosis in a porous medium under the influence of non-uniform magnetic field and periodic body acceleration treating blood as micropolar fluid carrying iron oxide nanoparticles. The governing equations of the system are solved numerically using finite difference schemes. The effects of stenotic height, taper angle, micropolar parameters, magnetic field, porosity, pulsatility, and magnetic nanoparticles on the flow of blood are analysed, and the results are represented graphically. It is significant to note that the flow parameters such as wall shear stress and flow resistance increase with increase in stenotic height, tapering parameter, magnetic field, pulsatile Reynolds number, time period, particle concentration, and particle mass parameters. Wall shear stress decreases with the increasing values of coupling number and it shows opposite behaviour in the case of flow resistance. Also increase in Darcy number leads to decrease in wall shear stress and flow resistance. The significance of treating blood as micropolar fluid is that the rotation of particles is taken into account. Cardiovascular diseases occur mainly due to abnormal blood flow in the arteries. To normalize the blood flow in the arteries, analysis of parameters involved in the study is essential. Hence, the present study has various applications in biomedical sciences. The effects of nanoparticles on blood flow analysed in the study have significant applications in delivery of drugs for treating cancer. PubDate: 2018-01-11 DOI: 10.1007/s40314-018-0572-z

Authors:Gang Hu; Cuicui Bo; Xinqiang Qin Abstract: Abstract Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degree (m, n) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of \({G}^{1}\) and \({G}^{2}\) continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design. PubDate: 2018-01-08 DOI: 10.1007/s40314-017-0568-0

Authors:Jianhua Guo; Hongcheng Li; Haidong Yang; Shaqing Zhang Abstract: Abstract In manufacturing industry, internal leakage of steam trap usually results in great steam waste. In particular, internal steam leakage in tyre vulcanization workshop has significant influences on its production safety and energy efficiency. In practice, internal steam leakage problem often is ignored and it tends to be difficult to detect this leakage due to lack of comprehensive flow meter or method. This paper presents a collaborative detection method for this problem in tyre vulcanization workshop with artificial immune algorithm. In the method, internal leakage of steam trap is defined as nonself antigens, and steam pressure differentials between steam pipe and steam rooms (or bladders) are extracted as epitopes of antigens. Furthermore, periodic energy efficiency and steam pressure of vulcanizer as the danger signals are simultaneously detected. Energy efficiency is represented by damaged cells which will be identified firstly for locating the leaking steam straps through antibodies. Furthermore, the self-adaptive danger thresholds for energy efficiency are evaluated through a steam consumption model and the Levenberg–Marquardt back propagation algorithm. An immune-based clustering algorithm aiNet is then adopted to generate antibodies (detectors) for detection on the steam pressure of vulcanizer. Finally, a case study is implemented to validate this method, which shows that collaborative detection method allows locating the specific leaking steam trap and is a feasible tool to reduce steam waste and ensure the safety of steam supply. PubDate: 2018-01-06 DOI: 10.1007/s40314-017-0569-z

Authors:Kang-Ya Lu Abstract: Abstract We propose three new preconditioners: diagonal and optimal-circulant splitting preconditioner, diagonal and skew-circulant splitting preconditioner, and diagonal and optimal-skew-circulant splitting preconditioner for solving the diagonal-plus-Toeplitz linear system discretized from the spatial fractional diffusion equations. Theoretical analysis shows that these three preconditioners can make the eigenvalues of the preconditioned matrices be clustered around 1, especially when the grids of the discretizations are refined. These results coincide with the one about the diagonal and circulant splitting preconditioner constructed recently by Bai et al. (Numer Linear Algebra Appl 24:e2093, 2017). Numerical experiments exhibit that the proposed preconditioners can significantly improve the convergence of the Krylov subspace iteration methods like GMRES and BiCGSTAB, and they outperform the diagonal and circulant splitting preconditioner as well. PubDate: 2018-01-05 DOI: 10.1007/s40314-017-0570-6

Authors:Asma Rouatbi; Talha Achouri; Khaled Omrani Abstract: Abstract A high-order nonlinear conservative difference scheme method is proposed to solve a model of nonlinear dispersive equation: RLW-KdV equation. The existence of the solution was proved by the Brouwer fixed point theorem. The unconditional stability besides uniqueness of the difference scheme are also obtained. The convergence of the proposed method is proved to be fourth-order in space and second-order in time in the discrete \(L^{\infty }\) -norm. An application on the RLW equation is discussed numerically in detail. Furthermore, interaction of solitary waves with different amplitudes are shown. The three invariants of the motion are evaluated to show the conservation properties of the system. The temporal evaluation of a Maxwellian initial pulse is then studied. At last some numerical examples are reported to confirm the theoretical results. PubDate: 2018-01-04 DOI: 10.1007/s40314-017-0567-1

Authors:Fakhrodin Mohammadi Abstract: Abstract In the present paper, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet basis and their properties are utilized to obtain their operational matrix of fractional integration in the Riemann–Liouville sense and delay operational matrix. Convergence and error bound of the expansion by this kind of wavelet functions are investigated. Then, these operational matrices along with the Galerkin approach have been implemented to solve systems of fractional delay differential equations (SFDDEs). The main superiority of the proposed technique is that it reduces SFDDEs to a system of algebraic equations. Moreover, accuracy and efficiency of the suggested Chelyshkov wavelet approach are verified through some linear and nonlinear SFDDEs. Finally, the obtained numerical results are compared with those previously reported in the literature. PubDate: 2018-01-03 DOI: 10.1007/s40314-017-0550-x

Authors:Xiaoyong Xu; Da Xu Abstract: Abstract In this paper, a semi-discrete scheme is presented for solving fourth-order partial integro-differential equations with a weakly singular kernel. The second-order backward difference formula is used to discretize the temporal derivatives. After discretizing the temporal derivatives, the considered problems are converted into a set of ordinary differential equations which are solved by using Legendre wavelets collocation method. The stability and convergence properties related to the time discretization are discussed and theoretically proven. Several numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. PubDate: 2018-01-03 DOI: 10.1007/s40314-017-0566-2

Authors:Iman Mohamad Sharaf Abstract: Abstract In this article, a new method is introduced to handle fuzzy multi-attribute decision-making problems. The method preserves fuzziness in the preference technique to avoid the drawbacks of defuzzification. The study modifies the technique of order preference by similarity to an ideal solution (TOPSIS) for interval-valued fuzzy numbers. The traditional TOPSIS uses the relative degree of closeness to rank the alternatives. Instead, a similarity measure based on map distance is used for preference. The degree of similarity between each attribute of an alternative and the ideal solution is computed, and a similarity matrix is formed. Then, the total degree of similarity for all the attributes of an alternative is used for ranking. The alternative corresponding to the one norm of the similarity matrix is the best alternative. Thus, the comparison is done on a fuzzy basis to avoid the loss of information due to converting the elements of the weighted normalized decision matrix to crisp values by defuzzification. An illustrative example is given to demonstrate the approach. A practical example in network selection to optimize vertical hand offs is solved where both user preferences and network parameters are treated as interval-valued fuzzy numbers. PubDate: 2017-12-30 DOI: 10.1007/s40314-017-0556-4

Authors:G. S. Seth; M. K. Mishra; R. Tripathi Abstract: Abstract A theoretical study of mixed convection stagnation point flow towards a stretching surface is presented. The governing boundary layer equations are transformed into a set of highly nonlinear ordinary differential equations using suitable similarity transforms. The semi-analytical solution is obtained using optimal homotopy analysis method (OHAM) and the numerical solution is obtained via finite element method (FEM). Solutions obtained via two different approaches are in excellent agreement, which validates the accuracy of present analysis. In a special case, the present OHAM solution is also validated with the earlier available results. Effect of pertinent flow parameters on the skin friction coefficient and Nusselt number is presented in tabular form, whereas the velocity, temperature and nanoparticle distribution are presented in graphical forms. Further, a quadratic multiple regression analysis on numeric data of skin friction coefficient and Nusselt number is performed. The findings suggest that velocity slip assists the fluid motion in presence of buoyancy forces, whereas it exhibits a retarding nature on fluid motion when no buoyancy forces exist. PubDate: 2017-12-30 DOI: 10.1007/s40314-017-0565-3

Authors:Xia Wang; Yuming Chen; Shengqiang Liu Abstract: Abstract A vector-borne disease model with general incidence rates is proposed and investigated in this paper, where both vector and host are stratified by infection ages in the form of a hyperbolic system of partial differential equations coupled with ordinary differential equations. The existence, uniqueness, nonnegativeness, and boundedness of solution of the model are studied for biologically reasonable purpose. Furthermore, a global threshold dynamics of the system is established by constructing suitable Lyapunov functionals, which is determined by the basic reproduction number \(\mathcal {R}_0\) : the infection-free equilibrium is globally asymptotically stable when \(\mathcal {R}_0<1\) while the endemic equilibrium is globally asymptotically stable when \(\mathcal {R}_0>1\) . PubDate: 2017-12-27 DOI: 10.1007/s40314-017-0560-8

Authors:Weslley Florentino de Oliveira; Giancarlo Queiroz Pellegrino Abstract: Abstract Chaos-based potentials are defined and implemented in the one-dimensional tight-binding model as a way of simulating disorder-controlled crystalline lattices. In this setting, disorder is handled with the aid of the chaoticity parameter. The inverse participation ratio (IPR) probes the response of the system to three different such potentials and shows consistent agreement with results given by the Lyapunov exponent \(\mathrm{Ly}\) : the greater \(\mathrm{Ly}(r)\) for the chaotic sequence as a function of the chaoticity parameter r, the greater the asymptotic value IPR(r) for the large-system ground state. PubDate: 2017-12-26 DOI: 10.1007/s40314-017-0561-7

Authors:Moumita Mandal; Gnaneshwar Nelakanti Abstract: Abstract In this paper, Legendre spectral projection methods are applied for the Volterra integral equations of second kind with a smooth kernel. We prove that the approximate solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the order \({\mathcal {O}}(n^{-r})\) in \(L^2\) -norm and order \({\mathcal {O}}(n^{-r+\frac{1}{2}})\) in infinity norm, and the iterated Legendre Galerkin solution converges with the order \({\mathcal {O}}(n^{-2r})\) in both \(L^2\) -norm and infinity norm, whereas the iterated Legendre collocation solution converges with the order \({\mathcal {O}}(n^{-r })\) in both \(L^2\) -norm and infinity norm, n being the highest degree of Legendre polynomials employed in the approximation and r being the smoothness of the kernels. We have also considered multi-Galerkin method and its iterated version, and prove that the iterated multi-Galerkin solution converges with the order \({\mathcal {O}}(n^{-3r})\) in both infinity and \(L^2\) norm. Numerical examples are given to illustrate the theoretical results. PubDate: 2017-12-26 DOI: 10.1007/s40314-017-0563-5

Authors:Ran Wang; Tong Kang; Yanfang Wang Abstract: Abstract We study a recovery problem for an unknown boundary coefficient relating to one material characteristic in an eddy current field. The field equations are represented in terms of the potential field method ( \(\varvec{T} - \psi \) method) and can be solved numerically by the nodal finite element method. We introduce a measurement as an additional condition and prove the existence and uniqueness of the weak solution. Further, we present an iteration algorithm for the recovery problem and validate its efficiency by two numerical experiments. PubDate: 2017-12-26 DOI: 10.1007/s40314-017-0562-6

Authors:Robert Eymard; Cindy Guichard Abstract: Abstract We include in the gradient discretisation method (GDM) framework two numerical schemes based on discontinuous Galerkin approximations: the symmetric interior penalty Galerkin (SIPG) method, and the scheme obtained by averaging the jumps in the SIPG method. We prove that these schemes meet the main mathematical gradient discretisation properties on any kind of polytopal mesh, by adapting discrete functional analysis properties to our precise geometrical hypotheses. Therefore, these schemes inherit the general convergence properties of the GDM, which hold for instance in the cases of the p-Laplace problem and of the anisotropic and heterogeneous diffusion problem. This is illustrated by simple 1D and 2D numerical examples. PubDate: 2017-12-26 DOI: 10.1007/s40314-017-0558-2

Authors:Samir Lemita; Hamza Guebbai; M. Z. Aissaoui Abstract: Abstract In this paper, we construct a generalization of the Jacobi iterative method adapted to a system of linear bounded operators. This new method is used with product integration method to solve a linear Fredholm integral equation of the second kind with a weakly singular kernel. The convergence analysis is proved. The numerical tests developed show its effectiveness. PubDate: 2017-12-22 DOI: 10.1007/s40314-017-0557-3

Authors:Yi Zuo; Yaonan Wang; Xinzhi Liu Abstract: Abstract In this paper, we propose a stable tracking control rule for rhombus-type lunar exploration wheeled mobile robot (RLEWMR) with completely unknown dynamics and unmodeled disturbance. The control system adopts a wavelet transform and probabilistic neural network (WTPNN) with accurate approximation capability to represent the unknown dynamics of the RLEWMR, and it also uses an adaptive robust compensator to confront the inevitable approximation errors due to the finite number of wavelet bases functions and to disturbances. Adaptive learning algorithms are proposed to learn the parameters of WTPNN weight and robust compensator on line. Based on the Lyapunov stability theorem, the tracking stability of the closed-loop system, the convergence of the WTPNN weight-updating process, and boundedness of WTPNN weight estimation errors are all guaranteed. The effectiveness and efficiency of the proposed controller is demonstrated by simulation and experiment studies. PubDate: 2017-12-21 DOI: 10.1007/s40314-017-0538-6

Authors:M. R. Eslahchi; Marzieh Kavoosi Abstract: Abstract This paper presents an efficient method to solve the approximation problem of the rational Bézier curve by continuous piecewise polynomial curve in \( L_{2} \) -norm. For this purpose, extended Jacobi wavelets together with the Gauss–Jacobi quadrature rules are employed. The proposed technique has some advantages such as: simplicity, high accuracy and fast computation. Also, the method in the paper performs multi-degree reduction at one time and does not need the stepwise computing. Several examples are given to illustrate the effectiveness of the algorithm. PubDate: 2017-12-21 DOI: 10.1007/s40314-017-0552-8

Authors:E. H. Doha; M. A. Abdelkawy; A. Z. M. Amin; António M. Lopes Abstract: Abstract This paper applies the shifted Jacobi–Gauss collocation (SJ–G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann–Liouville fractional derivative, \(D^{\nu (x)}\) , and integral, \(I^{\nu (x)}\) , of variable order are combined, and the SJ–G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods. PubDate: 2017-12-19 DOI: 10.1007/s40314-017-0551-9

Authors:Luiz Arthur Gagg Filho; Sandro da Silva Fernandes Abstract: Abstract A study of Earth–Moon bi-impulsive trajectories is presented in this paper. The motion of the space vehicle is described by the classic planar circular restricted three-body problem. The velocity increments are computed through analytical expressions, which are derived from the development of the Jacobi Integral expression. To determine the trajectories, a new two-point boundary value problem (TPBVP) with prescribed value of Jacobi Integral is formulated. Internal and external trajectories are determined through the solution of this new TPBVP for several times of flight. A relation between the Jacobi Integral and the Kepler’s energy at arrival is derived and several kinds of study are performed. Critical values of the Jacobi Integral, for which the Kepler’s energy of the space vehicle on the arrival trajectory becomes negative, are calculated for several configurations of arrival at the low Moon orbit in both directions: clockwise and counterclockwise. Results show that the proposed method allows the estimation of the fuel consumption before solving the TPBVP, and it facilitates the determination of trajectories with large time of flight. However, increasing values of the time of flight are not necessarily related with the increase of the Jacobi Integral value, which means that the obtaining of new trajectories becomes more difficult as the Jacobi Integral increases. Moreover, the proposed method provides results to be used as initial guess for more complex models and for optimization algorithms in order to minimize the total fuel consumption. For this case, this paper presents an example where an internal trajectory with large time of flight is optimized considering the Sun’s attraction. PubDate: 2017-12-19 DOI: 10.1007/s40314-017-0555-5