Authors:Rajesh Joshi; Satish Kumar Abstract: Abstract In this paper, we introduce a quantity measure which is called (R, S)-norm entropy and discuss some of its major properties with Shannon’s and other entropies in the literature. Based on this (R, S)-norm entropy, we have proposed a new (R, S)-norm fuzzy information measure and discussed its validity and properties. Further, we have given its comparison with other fuzzy information measures to prove its effectiveness. Attribute weights play an important role in multiple-attribute decision-making problems. In the present communication, two methods of determining the attribute weights are introduced. First is the case when the information regarding attribute weights is incompletely known or completely unknown and second is when we have partial information about attribute weights. For the first case, the extension of ordinary entropy weight method is used to calculate attribute weights and minimum entropy principle method based on solving a linear programming model is used in the second case. Finally, two methods are explained through numerical examples. PubDate: 2017-07-29 DOI: 10.1007/s40314-017-0491-4

Authors:S. A. Shehzad; T. Hayat; A. Alsaedi Abstract: Abstract This investigation looks at the effects of thermal radiation on the magnetohydrodynamic flow of Casson fluid over a stretched surface subject to power law heat flux and internal heat generation. Conservation of mass, linear momentum and energy are used in the development of relevant flow equations. Series solutions for velocity and temperature are derived. Effects of embedded physical parameters on the velocity and temperature profiles are analyzed. Numerical values of skin-friction coefficient and local Nusselt number are examined. PubDate: 2017-07-28 DOI: 10.1007/s40314-017-0492-3

Authors:Sergio Amat; M. José Legaz Abstract: Abstract An alternative approach for the analysis and the numerical approximation of singular perturbation problems, using a variational framework, is presented. It is based on the natural idea of minimizing the residual of the differential equation measured in the \(L^2\) norm. By this strategy, the approximation is based in the solution of a set of linear problems giving the descent step directions of the problem. This is the main advantage of our approach, since we can use stable and convergent methods for linear problems (without assuming the knowledge of good initial guesses used in the approximation of the associated non-linear systems necessary in Newton-type methods). Remember that for this type of problems, we should use implicit methods. We prove that our procedure can never get stuck in local minima, and the error decreases until getting to the original solution independent of the perturbation parameter. Finally, we include some numerical examples. PubDate: 2017-07-28 DOI: 10.1007/s40314-017-0482-5

Authors:Fathi Namouni; Helena Morais Abstract: Abstract The process of capture in the coorbital region of a solar system planet is studied. Absolute capture likelihood in the 1:1 resonance is determined by randomly constructed statistical ensembles numbering \(7.24\times 10^5\) of massless asteroids that are set to migrate radially from the outer to the inner boundaries of the coorbital region of a Jupiter-mass planet. Orbital states include coorbital capture, ejection, collisions with the Sun and the planet and free-crossing of the coorbital region. The relative efficiency of retrograde capture with respect to prograde capture is confirmed as an intrinsic property of the coorbital resonance. Half the asteroids cross the coorbital region regardless of eccentricity and for any inclination less than \(120^\circ \) . We also find that the recently discovered retrograde coorbital of Jupiter, asteroid 2015 BZ509, lies almost exactly at the capture efficiency peak associated with its orbital parameters. PubDate: 2017-07-24 DOI: 10.1007/s40314-017-0489-y

Authors:W. M. Abd-Elhameed; Y. H. Youssri Abstract: Abstract The principal aim of the current paper is to present and analyze two new spectral algorithms for solving some types of linear and nonlinear fractional-order differential equations. The proposed algorithms are obtained by utilizing a certain kind of shifted Chebyshev polynomials called the shifted fifth-kind Chebyshev polynomials as basis functions along with the application of a modified spectral tau method. The class of fifth-kind Chebyshev polynomials is a special class of a basic class of symmetric orthogonal polynomials which are constructed with the aid of the extended Sturm–Liouville theorem for symmetric functions. An investigation for the convergence and error analysis of the proposed Chebyshev expansion is performed. For this purpose, a new connection formulae between Chebyshev polynomials of the first and fifth kinds are derived. The obtained numerical results ascertain that our two proposed algorithms are applicable, efficient and accurate. PubDate: 2017-07-24 DOI: 10.1007/s40314-017-0488-z

Authors:Abdul Majeed; Abd Rahni Mt Piah; Zainor Ridzuan Yahya; Johari Yap Abdullah; Muhammad Rafique Abstract: Abstract Treating trauma to the cranio-maxillofacial region is a great challenge and requires expert clinical skills and sophisticated radiological imaging. The aim of reconstruction of the facial fractures is to rehabilitate the patient both functionally and aesthetically. In this article we employed B-spline curves to construct the occipital bone fracture using Digital Imaging and Communications in Medicine (DICOM) format data. The construction of occipital bone fracture starts with the boundary extraction followed by corner detection, construction of fractured part inner outer curve for each DICOM data using B-spline curves and finally the construction of fractured part in DICOM format. Method used in this article is based on DICOM data only and does not require any technique such as mirror imaging, technical help, reference skull, or to take average thickness of skull bone. Using the proposed method, the constructed fractured implant is custom made for every individual patient. At the end of this article we present a real case, in which we have constructed the occipital bone fracture using B-spline. The proposed method has been validated using post-operation DICOM data. For practical application, Graphical User Interface (GUI) has been developed. PubDate: 2017-07-22 DOI: 10.1007/s40314-017-0487-0

Authors:Felix S. Costa; Junior C. A. Soares; Adrian R. G. Plata; Edmundo C. de Oliveira Abstract: Abstract We present and discuss the general case of a fractional nonlinear partial differential equation using similarity reductions and recover results associated with Harry Dym-type equations. Particular cases are discussed and some plots illustrate the results. The fractional derivative is considered in the Caputo sense. PubDate: 2017-07-21 DOI: 10.1007/s40314-017-0484-3

Authors:A. N. Iusem; M. I. Todorov Abstract: Abstract We introduce and study the family of sets in a finite-dimensional Euclidean space which can be written as the Minkowski sum of an open, bounded, and convex set and a closed convex cone. We establish several properties of the class of such sets, called OM-decomposable, some of which extend related properties holding for the class of Motzkin decomposable sets (i.e., those for which the convex and bounded set in the decomposition is requested to be closed, hence compact). PubDate: 2017-07-20 DOI: 10.1007/s40314-017-0486-1

Authors:Li Dong; Jingyong Tang; Xinyu Song Abstract: Abstract This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen–Harker–Kanzow–Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237–262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective. PubDate: 2017-07-20 DOI: 10.1007/s40314-017-0485-2

Authors:José Mir Justino da Costa; Helcio Rangel Barreto Orlande; Wellington Betencurte da Silva Abstract: Abstract Cancer is one of the most fatal diseases in the world. Governments and researchers from various areas have continuously concentrated efforts to better understand the disease and propose diagnostic and treatment techniques. The use of mathematical models of tumor growth is of great importance for the development of such techniques. Due to the variety of models nowadays available in the literature, the problems of model selection and parameter estimation come into picture, aiming at suitably predicting the patient’s status of the disease. As the available data on dependent variables of existing models might not justify the use of common likelihood functions, approximate Bayesian computation (ABC) becomes a very attractive tool for model selection and model calibration (parameter estimation) in tumor growth models. In the present study, a Monte Carlo approximate Bayesian computation (ABC) algorithm is applied to select among competing models of tumor growth, with and without chemotherapy treatment. Simulated measurements are used in this work. The results obtained show that the algorithm correctly selects the model and estimates the parameters used to generate the simulated measurements. PubDate: 2017-07-19 DOI: 10.1007/s40314-017-0479-0

Authors:Shuguang Li; Xiaogang Wu Abstract: Abstract In this paper, we design a compact finite difference scheme which preserves the original conservative properties to solve the generalized symmetric regularized long-wave equations. The existence of the difference solution is proved by the Brouwer fixed-point theorem. Applying the discrete energy method, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is \(O(\tau ^{2}+h^{4})\) in the \(L^{\infty }\) -norm for u and \(\rho \) . For computing the nonlinear algebraic system generated by the compact scheme, a decoupled iterative algorithm is constructed and proved to be convergent. Numerical experiment results show that the theory is accurate and the method is efficient and reliable. PubDate: 2017-07-19 DOI: 10.1007/s40314-017-0481-6

Authors:Alessandra F. S. Ferreira; Antônio F. B. A. Prado; Othon C. Winter Abstract: Abstract The Swing-By maneuver is a technique used in many space mission to modify the trajectory of a spacecraft. The most usual goal is to increase the energy of the spacecraft, but it is also possible to reduce this energy. An important application is to break a spacecraft coming to the Earth using a Swing-By with the moon, which is the example used in the present paper. Other possibilities also exist, such as reducing the velocity of a spacecraft going to the planets Mercury or Venus. The goal is to help a possible capture by the planet, or at least to provide a passage with smaller velocities to allow better observations during the passage. Therefore, the goal of the present paper is to study the energy loss that a spacecraft may have during a powered Swing-By maneuver, which is a maneuver that combines a close approach by a celestial body with the application of an impulsive maneuver. The behavior of the energy variation is analyzed as a function of the parameters related to the pure gravity maneuver: periapsis radius, angle of approach and approach velocity; and the parameters related to the impulsive maneuver: the location of application of the impulse and its direction and magnitude. The maneuver is performed in a system composed by two bodies, such as the Earth–moon system, around the secondary body, and the energy is measured with respect to the primary body of the system. This problem is solved by developing a mathematical algorithm that guides larger efforts in terms of computer simulations. The results show maps of conditions made from the numerical simulations for different points of application and direction of the impulse, where the maneuver is advantageous and how much more energy can be removed from the spacecraft. PubDate: 2017-07-17 DOI: 10.1007/s40314-017-0483-4

Authors:A. K. de Almeida; A. F. B. de Almeida Prado; R. Vilhena de Moraes; M. Lara Abstract: Abstract The present paper has the goal of studying the use of “integral indices” to quantify the effects of a perturbing force in the driven harmonic and Duffing oscillators. The main idea is to define a scalar index that can represent the cumulative effects over time that a perturbing force causes in a dynamical system. An index of this type can help to prepare “perturbation maps”, which can identify situations of larger or smaller effects. This idea appeared in the astrodynamics literature with the goal of finding less perturbed orbits for a spacecraft, but it is applied here to the driven harmonic and Duffing oscillators. The reason for those applications is that those problems have analytical solutions, which allows a better comparison of the indices. In particular, the effects of calculating this index using a perturbed and a non-perturbed trajectory are evaluated with the goal of better understanding these effects. The results show that the difference between both indices depends on the frequency and amplitude of the perturbing force. PubDate: 2017-07-13 DOI: 10.1007/s40314-017-0471-8

Authors:Yong-Xia Hao; Dianchen Lu Abstract: Abstract The goal of this paper is to develop a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant space and the balanced \(l_{1}, l_{2}\) norm minimization (named elastic net). The elastic net can be solved efficiently by an adapted split Bregman iteration algorithm. Numerical experiments indicate that by choosing appropriate regularization parameters, the model can efficiently provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. PubDate: 2017-07-12 DOI: 10.1007/s40314-017-0475-4

Authors:Iman Kazemian; Masoud Rabbani; Hamed Farrokhi-Asl Abstract: Abstract This study presents a novel approach to solve the vehicle routing problem by focusing on greenhouse gas emissions and fuel consumption aiming to mitigate adverse environmental effects of transportation. A time-dependent model with time windows is developed to incorporate speed and schedule in transportation planning. The model considers speed limits for different times of the day in a realistic delivery context. Due to the complexity of solving the model, a graph transformation approach is proposed to reduce the complexity of the problem. By means of several steps, the problem is transformed into a vehicle routing problem without time windows. In this way, we can reduce the complexity of the problem. Our method can be used in practice to decrease fuel consumption and greenhouse gas emissions, while total cost is also controlled to some extent. Finally, future research directions and conclusion remarks are provided. PubDate: 2017-07-11 DOI: 10.1007/s40314-017-0477-2

Authors:Hoang Viet Long Abstract: Abstract This paper is devoted to the study of the solvability of random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability. The notions of random fuzzy variables and fuzzy stochastic processes are developed for multivariable functions. The existence and uniqueness of two types of integral solutions generated from Darboux problem for nonlinear wave equations are proved using the successive approximations method and Gronwall’s inequality for stochastic processes. The continuous dependence on the data, the boundedness, and the stability with probability one of integral solutions are established to confirm the well posedness of our model. Some computational examples are presented to illustrate the theoretical results. PubDate: 2017-07-11 DOI: 10.1007/s40314-017-0478-1

Authors:Shulin Sun; Cuihua Guo; Xing Liu Abstract: Abstract In this paper, a chemostat model with general monotone response functions and two discrete time delays is proposed to describe the dynamical behavior about predator–prey system. First, by analyzing the characteristic equation associated with the model, we obtain the conditions of the existence and stability of extinction equilibrium and positive equilibrium. Choosing delays as bifurcation parameters, the existence of Hopf bifurcations is investigated in detail. Second, by virtue of the Poincaré normal form method and center manifold theorem, explicit formulas are derived to determine the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, some numerical simulations are carried out to illustrate the theoretical results and the biological significance. PubDate: 2017-07-07 DOI: 10.1007/s40314-017-0476-3

Authors:M. Syed Ali; N. Gunasekaran Abstract: Abstract In this paper, we consider the problem of sampled-data control for static neural networks with interval time-varying delays. As opposed to the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered neural network is derived in terms of a dynamic system with two different time-delays. By constructing a suitable Lyapunov–Krasovskii functional with double and triple integral terms and using Jensen inequality, delay-dependent criteria are presented, so that the error system is asymptotically stable. Delay-dependent asymptotically stability condition is established in terms of linear matrix inequality (LMI) framework, which can be readily solved using the LMI toolbox. Finally, three examples are given to show the effectiveness of the theoretical results. PubDate: 2017-07-06 DOI: 10.1007/s40314-017-0470-9

Authors:F. J. T. Salazar; O. C. Winter; C. R. McInnes Abstract: Abstract Terrestrial solar power is severely limited by the diurnal day–night cycle. To overcome these limitations, a Solar Power Satellite (SPS) system, consisting of a space mirror and a microwave energy generator-transmitter in formation, is presented. The microwave transmitting satellite (MTS) is placed on a planar orbit about a geostationary point (GEO point) in the Earth’s equatorial plane, and the space mirror uses the solar pressure to achieve orbits about GEO point, separated from the planar orbit, and reflecting the sunlight to the MTS, which will transmit energy to an Earth-receiving antenna. Previous studies have shown the existence of a family of displaced periodic orbits above or below the Earth’s equatorial plane. In these studies, the sun-line direction is assumed to be in the Earth’s equatorial plane (equinoxes), and at \(23.5^{\circ }\) below or above the Earth’s equatorial plane (solstices), i.e. depending on the season, the sun-line moves in the Earth’s equatorial plane and above or below the Earth’s equatorial plane. In this work, the position of the Sun is approximated by a rectangular equatorial coordinates, assuming a mean inclination of Earth’s equator with respect to the ecliptic equal to \(23.5^{\circ }\) . It is shown that a linear approximation of the motion about the GEO point yields bounded orbits for the SPS system in the Earth–satellite two-body problem, taking into account the effects of solar radiation pressure. The space mirror orientation satisfies the law of reflection to redirect the sunlight to the MTS. Additionally, a MTS on a common geostationary orbit (GEO) has been also considered to reduce the relative distance in the formation flying Solar Power Satellite (FF-SPS). PubDate: 2017-07-05 DOI: 10.1007/s40314-017-0473-6