Authors:Vahid Sadeghi; Farshid Farnood Ahmadi; Hamid Ebadi Pages: 825 - 842 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: 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:Davod Khojasteh Salkuyeh; Mohsen Hasani; Fatemeh Panjeh Ali Beik Pages: 877 - 883 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: 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: 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: 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: 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: 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: 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:Xiaoping Chen; Hua Dai; Wei Wei Pages: 1009 - 1021 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:Elenice W. Stiegelmeier; Vilma A. Oliveira; Geraldo N. Silva; Décio Karam Pages: 1043 - 1065 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:Abbas Saadatmandi; Zeinab Akbari Pages: 1085 - 1098 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: 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: 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:Elyse M. Garon; James V. Lambers Abstract: The goal of this paper is to develop a highly accurate and efficient numerical method for the solution of a time-dependent partial differential equation with a piecewise constant coefficient, on a finite interval with periodic boundary conditions. The resulting algorithm can be used, for example, to model the diffusion of heat energy in one space dimension, in the case where the spatial domain represents a medium consisting of two homogeneous materials. The resulting model has, to our knowledge, not yet been solved in closed form through analytical methods, and is difficult to solve using existing numerical methods, thus suggesting an alternative approach. The approach presented in this paper is to represent the solution as a linear combination of wave functions that change frequencies at the interfaces between different materials. It is demonstrated through numerical experiments that using the Uncertainty Principle to construct a basis of such functions, in conjunction with a spectral method, a mathematical model for heat diffusion through different materials can be solved much more efficiently than with conventional time-stepping methods. PubDate: 2017-06-15 DOI: 10.1007/s40314-017-0465-6

Authors:Abdallah Bradji; Jürgen Fuhrmann Abstract: This work is an improvement of the previous note (Bradji in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) which dealt with the convergence analysis of a finite volume scheme for the Poisson’s equation with a linear oblique derivative boundary condition. The formulation of the finite volume scheme given in Bradji (in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) involves the discrete gradient introduced recently in Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010). In this paper, we consider the convergence analysis of finite volume schemes involving the discrete gradient of Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010) for elliptic and parabolic equations with linear oblique derivative boundary conditions. Linear oblique derivative boundary conditions arise for instance in the study of the motion of water in a canal, cf. Lesnic (Commun Numer Methods Eng 23(12):1071–1080, 2007). We derive error estimates in several norms which allow us to get error estimates for the approximations of the exact solutions and its first derivatives. In particular, we provide an error estimate between the gradient of the exact solutions and the discrete gradient of the approximate solutions. Convergence of the family of finite volume approximate solutions towards the exact solution under weak regularity assumption is also investigated. In the case of parabolic equations with oblique derivative boundary conditions, we develop a new discrete a priori estimate result. The proof of this result is based on the use of a discrete mean Poincaré–Wirtinger inequality. Thanks to the stated a priori estimate and to a comparison with an appropriately chosen auxiliary finite volume scheme, we derive the convergence results. This work can be viewed as a continuation of the previous work (Bradji and Gallouët in Int J Finite Vol 3(2):1–35, 2006) where a convergence analysis for a finite volume scheme, based on the admissible mesh of Eymard et al. (In: Ciarlet and Lions, Handbook of numerical analysis, North-Holland, Amsterdam, 2000), for the Poisson’s equation with a linear oblique derivative boundary conditions is given. The obtained convergence results do not require any relation between the mesh sizes of the spatial and time discretizations. Some numerical tests are presented for both elliptic and parabolic equations. In particular, we present three methods to compute the discrete solution. PubDate: 2017-06-13 DOI: 10.1007/s40314-017-0463-8

Authors:Ozlem Ozturk Mizrak; Nuri Ozalp Abstract: In this paper, we introduce the fractional analog of a chemical model arouse from a mathematical paradox attributed to Dietrich Braess. Two basic examples which serve fractional kinetic models as better suited models to the real data sets than the integer-order counterparts are given. Existence and uniqueness of the rebuilt model’s solutions are proved. It is shown that asymptotic stability conditions of the solutions are provided. A comparison is made between two different solution methods and numerical simulations are also presented to exemplify the mathematical outcomes. PubDate: 2017-06-12 DOI: 10.1007/s40314-017-0462-9

Authors:Daniel A. Cervantes; Pedro González Casanova; Christian Gout; Miguel Ángel Moreles Abstract: The problem of concern in this work is the construction of free divergence fields given scattered horizontal components. As customary, the problem is formulated as a PDE constrained least squares problem. The novelty of our approach is to construct the so-called adjusted field, as the unique solution along an appropriately chosen descent direction. The latter is obtained by the adjoint equation technique. It is shown that the classical adjusted field of Sasaki’s is a particular case. On choosing descent directions, the underlying mass consistent model leads to the solution of an elliptic problem which is solved by means of a radial basis functions method. Finally, some numerical results for wind field adjustment are presented. PubDate: 2017-06-12 DOI: 10.1007/s40314-017-0461-x

Authors:Karim Samei; Mohammad Reza Alimoradi Abstract: In this paper, we study linear and cyclic codes over the ring \(F_2+uF_2+vF_2\) . The ring \(F_2+uF_2+vF_2\) is the smallest non-Frobenius ring. We characterize the structure of cyclic codes over the ring \(R=F_2+uF_2+vF_2\) using of the work Abualrub and Saip (Des Codes Cryptogr 42:273–287, 2007). We study the rank and dual of cyclic codes of odd length over this ring. Specially, we show that the equation \( C C^\bot = R ^n\) does not hold in general for a cyclic code C of length n over this ring. We also obtain some optimal binary codes as the images of cyclic codes over the ring \(F_2+uF_2+vF_2\) under a Gray map, which maps Lee weights to Hamming weights. Finally, we give a condition for cyclic codes over R that contains its dual and find quantum codes over \(F_2\) from cyclic codes over the ring \(F_2+uF_2+vF_2\) . PubDate: 2017-06-06 DOI: 10.1007/s40314-017-0460-y

Authors:N. Aslimani; R. Ellaia Abstract: Chaos optimization algorithm (COA) is a recently developed method for global optimization based on chaos theory. It has the features of easy implementation, short execution time and robust mechanisms of escaping from local optima compared with the existing stochastic searching algorithm. By integrating the gradient descent method with a new COA approach using new strategies including symmetrization and levelling, a novel hybrid method, called SCGD, is proposed in this paper. The main idea is to combine the good ability of exploitation of the gradient descent with the high ability of exploration of COA. The purpose is to avoid being trapped into local optima and to improve convergence in large space and high-dimension optimization problems. The simulation results based on a set of 50 benchmark functions with diverse properties and different dimensions show the efficiency and the abilities of the proposed method in finding the global optima compared with the existing methods. PubDate: 2017-06-01 DOI: 10.1007/s40314-017-0454-9