Authors:Vahid Sadeghi; Farshid Farnood Ahmadi; Hamid Ebadi Pages: 825 - 842 Abstract: Abstract Relative radiometric normalization (RRN) of multi-temporal satellite images minimizes the radiometric discrepancies between two images caused by inequalities in the acquisition conditions rather than changes in surface reflectance. In this paper, a new automatic RRN method was developed based on regression theory comprising the following techniques: Automatic detection of unchanged pixels, Histogram modeling of subject images, and Calculation of linear transformation coefficients for various categories of pixels according to their gray values in each band. The proposed method applies a new idea for unchanged pixels selection which increases the accuracy and automation level of the detection process. Also, a new idea is proposed for categorizing pixels according to their gray values. In this method, the number and interval of the categories are determined automatically and independently based on the histogram of subject images for each band. Thus, divergent influences of effective parameters such as atmosphere on different gray values are modeled. The method was implemented on two images taken by the TM sensor. Normalization results acquired by the proposed method were compared with the six conventional methods including: histogram matching, haze correction, minimum-maximum, mean-standard deviation, simple regression, no-change and modified regression using unchanged pixels. Experimental results confirmed the effectiveness of the proposed method in the automatic detection of unchanged pixels and minimizing any imaging condition effects (i.e., atmosphere and other effective parameters). PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0254-z Issue No:Vol. 36, No. 2 (2017)

Authors:Tariq Shah; Saira Jahangir; Antonio Aparecido de Andrade Pages: 843 - 857 Abstract: Abstract Substitution boxes (S-boxes) are the fundamental mechanisms in symmetric key cryptosystems. These S-boxes guarantee that the cryptosystem is cryptographically secure and make them nonlinear. The S-boxes used in conventional and modern cryptography are mostly constructed over finite Galois field extensions of binary Field \(\mathbb {F}_{2}\) . We have presented a novel construction scheme of S-boxes which is based on the elements of subgroups of multiplicative groups of units of the commutative finite chain rings of type \(\frac{\mathbb {F}_{2}[u]}{\langle u^{k}\rangle }\) , where \(2\le k\le 8\) . Majority logic criterion (MLC) is applied on the apprehended S-boxes owing to, checked their strength. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0265-9 Issue No:Vol. 36, No. 2 (2017)

Authors:Yang Xia; Guojun Zheng; Ping Hu Pages: 859 - 875 Abstract: Abstract Incompatible modes with parametric coordinates are widely used in finite element method to develop low-order elements with high accuracy. But it leads to unstable results and must be used along with the constant Jacobian matrix technique to assure convergence. The incompatible modes with Cartesian coordinates are proposed as an alternative. The advantage is that the present method can improve the accuracy, assure the convergence of the elements without additional correction technique and greatly reduce the amount of calculation. With this method, a new quadrilateral element IMQ6 is formulated within the quasi-conforming scheme. Both theoretical and numerical analyses are conducted and it is proved that the present incompatible modes improve the element’s performance in both precision and efficiency. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0262-z Issue No:Vol. 36, No. 2 (2017)

Authors:Davod Khojasteh Salkuyeh; Mohsen Hasani; Fatemeh Panjeh Ali Beik Pages: 877 - 883 Abstract: Abstract In this paper, considering a general class of preconditioners \(P(\alpha )\) , we study the convergence properties of the preconditioned AOR (PAOR) iterative methods for solving linear system of equations. It is shown that the spectral radius of the iteration matrix of the PAOR method has a monotonically decreasing property when the value of \(\alpha \) increases. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0266-8 Issue No:Vol. 36, No. 2 (2017)

Authors:Umberto Amato; Biancamaria Della Vecchia Pages: 885 - 902 Abstract: Abstract Uniform approximation error estimates for weighted Shepard-type operators more flexible than the unweighted analogues are given. Error estimates for a linear combination of their iterates faster converging than previous ones are also showed. The results are applied in CAGD to construct Shepard-type curves useful in modeling and a weighted progressive iterative approximation technique exponentially converging. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0263-y Issue No:Vol. 36, No. 2 (2017)

Authors:Riccardo Fazio; Alessandra Jannelli Pages: 903 - 913 Abstract: Abstract In this paper, we undertake a mathematical and numerical study of liquid dynamics models in a horizontal capillary. In particular, we prove that the classical model is ill-posed at initial time, and we recall two different approaches in order to define a well-posed problem. Moreover, for an academic test case, we compare the numerical approximations, obtained by an adaptive initial value problem solver based on an one-step one-method approach, with new asymptotic solutions. This is a possible way to validate the adaptive numerical approach for its application to real liquids. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0268-6 Issue No:Vol. 36, No. 2 (2017)

Authors:Akbar Mohebbi; Zahra Faraz Pages: 915 - 927 Abstract: Abstract In this work, we investigate the solitary wave solution of nonlinear Benjamin–Bona–Mahony–Burgers (BBMB) equation using a high-order linear finite difference scheme. We prove that this scheme is stable and convergent with the order of \(O(\tau ^2+h^4)\) . Furthermore, we discuss the existence and uniqueness of numerical solutions. Numerical results obtained from propagation of a single solitary and interaction of two and three solitary waves confirm the efficiency and high accuracy of proposed method. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0272-x Issue No:Vol. 36, No. 2 (2017)

Authors:Yuechao Ma; Hui Chen Pages: 929 - 953 Abstract: Abstract This paper is concerned with the problem of finite-time fault-tolerant control for one family of uncertain singular Markovian jump with bounded transition probabilities and nonlinearities systems. The actuator faults are presented as a more general and practical continuous fault model. Partially known transition rate parameters have given lower and upper bounds. Firstly, the resulting closed-loop error system is constructed based on a state estimator; sufficient criteria are provided to guarantee that the augmented system has singular stochastic finite-time boundedness and singular stochastic \(H_\infty \) finite-time boundedness in both normal and fault cases. Then, by employing a decoupling technique, the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to demonstrate the effectiveness of the proposed design approach. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0271-y Issue No:Vol. 36, No. 2 (2017)

Authors:Jean-Paul Chehab; Marcos Raydan Pages: 955 - 969 Abstract: Abstract Continuous algebraic Riccati equations (CARE) appear in several important applications. A suitable approach for solving CARE, in the large-scale case, is to apply Kleinman–Newton’s method which involves the solution of a Lyapunov equation at every inner iteration. Lyapunov equations are linear, nevertheless, solving them requires specialized techniques. Different numerical methods have been designed to solve them, including ADI and Krylov-type iterative projection methods. For these iterative schemes, preconditioning is always a difficult task that can significantly accelerate the convergence. We present and analyze a strategy for solving CARE based on the use of inexact Kleinman–Newton iterations with an implicit preconditioning strategy for solving the Lyapunov equations at each inner step. One advantage is that the Newton direction is approximated implicitly, avoiding the explicit knowledge of the given matrices. Only the effect of the matrix–matrix products with the given matrices is required. We present illustrative numerical experiments on some test problems. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0274-8 Issue No:Vol. 36, No. 2 (2017)

Authors:M. Ebrahimnejad; N. Fallah; A. R. Khoei Pages: 971 - 990 Abstract: Abstract This paper presents three schemes of 2D meshless finite volume (MFV) method, referred to as MFV with overlapping control volumes (MFV1), MFV with irregular non-overlapping control volumes (MFV2) and MFV with regular non-overlapping control volumes (MFV3). The methods utilize the local symmetric weak form of system equation and the interpolation functions constructed using the weighted multi-triangles method (WMTM) which is recently developed by the present authors. The proposed formulation involves only integrals over the boundaries of control volumes. The performance of the proposed schemes is studied in three benchmark problems. A comparative study between the predictions of the above MFV schemes and finite element method (FEM) shows the superiority of WMTM-based MFV1 and MFV2 over FEM. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0273-9 Issue No:Vol. 36, No. 2 (2017)

Authors:Andrés A. Barrea; Matias E. Hernández; Rubén Spies Pages: 991 - 1008 Abstract: Abstract We propose a model for the dynamics of an heterogeneous tumor, which consists of sensitive and resistant cells. The model is analyzed and validated using a cellular automaton whose local rules are classic and widely accepted in Biology. We then extend the model to a tumor under therapy. We consider Shannon’s entropy for the tumor and analyze the problem of minimizing this entropy. From this minimization problem, we find viable therapies that maintain at low level the entropy of the tumor. These therapies could provide a valuable tool for designing protocols for disease control, maintaining a very low growth level, while the tumor remains composed mainly of sensitive cells. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0275-7 Issue No:Vol. 36, No. 2 (2017)

Authors:Xiaoping Chen; Hua Dai; Wei Wei Pages: 1009 - 1021 Abstract: Abstract In this paper, we propose a successive mth ( \(m\ge 2\) ) approximation method for the nonlinear eigenvalue problem (NEP) and analyze its local convergence. Applying the partially orthogonal projection method to the successive mth approximation problem, we present the partially orthogonal projection method with the successive mth approximation for solving the NEP. Numerical experiments are reported to illustrate the effectiveness of the proposed methods. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0277-5 Issue No:Vol. 36, No. 2 (2017)

Authors:Ehsan Ali Askari; Mahdi Bashiri Pages: 1023 - 1041 Abstract: Abstract In this paper, the bike-sharing problem was extended by considering safety in addition to system costs. Moreover, we determined the cost and safety levels for different kinds of stations. For solving the problem of conflicting objective functions, we used the NSGA-II and MOPSO algorithms and compared them. The results confirmed that the NSGA-II algorithm performs better than MOPSO for considering different solutions to the bike-sharing system with safety design problem. In the second stage, a multi-objective model was transformed to a linear single-objective model to find a preferred solution. A genetic algorithm (GA) was developed to solve the proposed large-scale bike-sharing model, and the results were compared with the solution obtained by commercial software. The results showed that the proposed GA outperforms the commercial software solution approach in large-scale instances. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0278-4 Issue No:Vol. 36, No. 2 (2017)

Authors:Elenice W. Stiegelmeier; Vilma A. Oliveira; Geraldo N. Silva; Décio Karam Pages: 1043 - 1065 Abstract: Abstract A dynamic optimization model for weed infestation control using selective herbicide application in a corn crop system is presented. The seed bank density of the weed population and frequency of dominant or recessive alleles are taken as state variables of the growing cycle. The control variable is taken as the dose–response function. The goal is to reduce herbicide usage, maximize profit in a pre-determined period of time and minimize the environmental impacts caused by excessive use of herbicides. The dynamic optimization model takes into account the decreased herbicide efficacy over time due to weed resistance evolution caused by selective pressure. The dynamic optimization problem involves discrete variables modeled as a nonlinear programming (NLP) problem which was solved by an active set algorithm (ASA) for box-constrained optimization. Numerical simulations for a case study illustrate the management of the Bidens subalternans in a corn crop by selecting a sequence of only one type of herbicide. The results on optimal control discussed here will give support to make decision on the herbicide usage in regions where weed resistance was reported by field observations. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0280-x Issue No:Vol. 36, No. 2 (2017)

Authors:Qinglong Wang; Zhijun Liu; Xingan Zhang; Robert A. Cheke Pages: 1067 - 1084 Abstract: Abstract This article is concerned with the optimal harvesting of a predator–prey model with a prey refuge and imprecise biological parameters. We consider the model under impreciseness and introduce a parametric functional form of an interval which differs from those of models with precise biological parameters. The existence of all possible equilibria and stability of system are discussed. The bionomic equilibrium of the model is analyzed. Also, the optimal harvesting policy is derived using Pontryagin’s maximal principle. Numerical simulations are presented to verify the feasibilities of our analytical results. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0282-8 Issue No:Vol. 36, No. 2 (2017)

Authors:Abbas Saadatmandi; Zeinab Akbari Pages: 1085 - 1098 Abstract: Abstract In this paper, a weighted orthogonal system on finite interval based on the transformed Hermite functions is introduced. Some results on approximations using the Hermite functions on finite interval are obtained from corresponding approximations on infinite interval via a conformal map. To illustrate the potential of the new basis, we apply it to the collocation method for solving a class of singular two-point boundary value problems. The numerical results show that our new scheme is very effective and convenient for solving singular boundary value problems. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0284-6 Issue No:Vol. 36, No. 2 (2017)

Authors:Qinghua Wu; Guozheng Yan Pages: 1099 - 1112 Abstract: Abstract We consider the inverse scattering problem of determining the shape and position of a thin dielectric infinite cylinder having an open arc as cross section from the knowledge of the related far field data. The mathematical analysis is given to prove the validity of the factorization method for reconstructing the shape of the arc. Some numerical examples are proposed to show the efficaciousness of the algorithms. PubDate: 2017-06-01 DOI: 10.1007/s40314-015-0285-5 Issue No:Vol. 36, No. 2 (2017)

Authors:Annachiara Colombi; Marco Scianna; Alessandro Alaia Pages: 1113 - 1141 Abstract: Abstract In this article, we present a microscopic-discrete mathematical model describing crowd dynamics in no panic conditions. More specifically, pedestrians are set to move in order to reach a target destination and their movement is influenced by both behavioral strategies and physical forces. Behavioral strategies include individual desire to remain sufficiently far from structural elements (walls and obstacles) and from other walkers, while physical forces account for interpersonal collisions. The resulting pedestrian behavior emerges therefore from non-local, anisotropic and short/long-range interactions. Relevant improvements of our mathematical model with respect to similar microscopic-discrete approaches present in the literature are: (i) each pedestrian has his/her own dynamic gazing direction, which is regarded to as an independent degree of freedom and (ii) each walker is allowed to take dynamic strategic decisions according to his/her environmental awareness, which increases due to new information acquired on the surrounding space through their visual region. The resulting mathematical modeling environment is then applied to specific scenarios that, although simplified, resemble real-word situations. In particular, we focus on pedestrian flow in two-dimensional buildings with several structural elements (i.e., corridors, divisors and columns, and exit doors). The noticeable heterogeneity of possible applications demonstrates the potential of our mathematical model in addressing different engineering problems, allowing for optimization issues as well. PubDate: 2017-06-01 DOI: 10.1007/s40314-016-0316-x Issue No:Vol. 36, No. 2 (2017)

Authors:Wojciech Nawalaniec Abstract: The main goal of the paper was to develop algorithms and methods for computation of basic sums, the mathematical objects of great importance in computational materials science having applications to description of the representative volume element (RVE) and to the effective properties of 2D composites. The previously used algorithm had the exponential complexity. We propose a linearly complex algorithm. All the presented algorithms can be easily implemented in modern scientific computing packages, while maintaining both efficient calculations and a high level of abstraction. The proposed approach is applied to derivation of a polynomial approximation of the effective conductivity formula for 2D random material with non-overlapping circular inclusions with normally distributed radii. The obtained formulas are applied to the optimal packing problem of disks on the plane. PubDate: 2017-04-25 DOI: 10.1007/s40314-017-0449-6

Authors:Jorge Kennety S. Formiga; Vivian Martins Gomes; Rodolpho Vilhena de Moraes Abstract: Abstract The present paper has the goal of studying the changes of the orbital parameters of each individual element of a cloud of particles that makes a close approach with the Earth. Clouds of particles are formed when natural or man-made bodies explode for some reason. After an explosion like that, the center of mass of the cloud follows the same orbit of the body that generated the explosion, but the individual particles have different trajectories. The cloud is specified by a distribution of semi-major axis and eccentricity of their particles. This cloud is assumed to pass close to the Earth, making a close approach that modifies the trajectory of every particle that belongs to the cloud. The present paper makes simulations based in the “Patched-Conics” model to obtain the new trajectories of each particle. Then, it is possible to map the new distribution of the Keplerian elements of the particles that constituted the cloud, using the previous distribution as initial conditions. These information are important when planning satellite missions having a spacecraft passing close to a cloud of this type, because it is possible to obtain values for the density and amplitude of the cloud, so finding the risks of collision and the possible maneuvers that need to be made in the spacecraft to avoid the collisions. PubDate: 2017-04-21 DOI: 10.1007/s40314-017-0443-z