An efficient and secure Diffie–Hellman key agreement protocol based on Chebyshev chaotic map

This paper proposes a new efficient and secure Diffie–Hellman key agreement protocol based on Chebyshev chaotic map. The proposed key agreement protocol uses the semi-group property of Chebyshev polynomials to agree Diffie–Hellman based session key. The proposed protocol provides strong security compared with the previous related protocols. In addition, the proposed protocol does not require any timestamp information and greatly reduces computational costs between communication parties. As a result, the proposed protocol is more practical and provides computational/communicational efficiency compare with several previously proposed key agreement protocols based on Chebyshev chaotic map.     

Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control

This paper aims at synchronization and anti-synchronization between Lu chaotic system, a member of unified chaotic system, and recently developed Bhalekar–Gejji chaotic system, a system which cannot be derived from the member of unified chaotic system. These synchronization and anti-synchronization have been achieved by using nonlinear active control since the parameters of both the systems are known. Lyapunov stability theory is used and required condition is derived to ensure the stability of error dynamics. Controller is designed by using the sum of relevant variables in chaotic systems. Simulation results suggest that proposed scheme is working satisfactorily.     

Design PD controller for master–slave synchronization of chaotic Lur’e systems with sector and slope restricted nonlinearities

In this paper, design PD controller for master–slave synchronization of chaotic Lur’e systems with sector and slope restricted nonlinearities is presented. A new synchronization criterion is proposed based on Lyapunov functions with quadratic form of states and nonlinear functions of the systems. Sector and slope bounds are employed to the Lyanunov–Krasovskii functional through convex representation of the nonlinearities so that less conservative stability conditions are obtained. The criteria is given in terms of linear matrix inequalities (LMIs) by using Finsler’s lemma. A numerical example is provided to illustrate the effectiveness of the method.     

Comments on: “Synchronization of N-coupled fractional-order chaotic systems with ring connection” [Commun Nonlinear Sci Numer Simulat 2010;15:401–12]

In this note, we present some points to paper [Tang Yang, Fang Jian-an, Synchronization of N-coupled fractional-order chaotic systems with ring connection. Commun Nonlinear Sci Numer Simulat 2010;15:401–12].     

An extension of Krasnoselskii’s fixed point theorem and its application to nonlocal problems for implicit fractional differential systems with uncertainty

The traditional Krasnoselskii’s fixed point theorem in Banach spaces does not reproduce the rich and varied forms of operator equations in abstract spaces which are not linear structure. Consequently, its applications to integral equations and differential equations have met many obstacles. The present alternative Krasnoselskii’s fixed point theorem in generalized semilinear Banach spaces overcomes this deficiency and opens up for profitable investigation such as differential systems with uncertainty. An application to the existence of solutions of nonlocal problems for fuzzy implicit fractional differential systems under Caputo generalized Hukuhara differentiability with demonstrated example is given to validate the effectiveness of our theoretical results.     

An extension theorem in SBV and an application to the homogenization of the Mumford–Shah functional in perforated domains

The aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a noncoercive homogenization problem.     

Comments on “Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control” [Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762]

In this note some points to paper [L. Pan, W. Zhou, J. Fang, D. Li, Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762] are presented. Hereby, we illustrate that the way that authors in [1] treat with fractional version of Lyapunov stability theorem suffers lack of a correct justification.     

Ecological modernization in the electrical utility industry: An application of a bads–goods DEA model of ecological and technical efficiency

Newly-developed data envelopment analysis techniques permit simultaneous consideration of ‘good and bad’ outputs in evaluating efficiency. We use these techniques to determine joint ecological and technical efficiencies of the 437 largest fossil-fueled electricity-generating plants in the United States. Utilizing the EPA’s E-Grid and Clean Air Markets databases and drawing on ecological modernization theory we evaluate whether innovations in organizational practices and technological solutions help achieve joint technical and environmental performance efficiencies.     

Complement to ‘Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties’ [Commun Nonlinear Sci Numer Simulat 15 (2010) 3241–3247]

Owing to the singularity problem having not been considered in control design process, we present some points to improve the results of paper [Wei Xiang, Yugao Huangpu, second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties, Commun Nonlinear Sci Numer Simulat 15 (2010) 3241–3247].     

Comment on “Parameter identification and synchronization of fractional-order chaotic systems” [Commun Nonlinear Sci Numer Simulat 2012;17:305–16]

This paper comments on the recently published work related to parameter identification of fractional-order chaotic systems [1]. In this note, it is shown that according to the sensitivity issues of chaotic systems to their initial conditions, the criteria for the cost function to be acceptable are not satisfied.     

Obtaining confidence limits for safe creep life in the presence of multi batch hierarchical databases: An application to 18Cr–12Ni–Mo steel

The creep and creep rupture properties of 18Cr–12Ni–Mo steel tubes have been analysed using the Wilshire equations. The observed behaviour patterns are then briefly discussed in terms of the dislocation processes governing creep strain accumulation. A suitable statistical framework for analysing both the single and multi batch data available on this material is then specified. It is shown that ignoring the hierarchical nature present in many creep data bases, which has been the approach used until now when using the Wilshire equations, leads to a serious and significant underestimate of the predicted safe life for this material. The model allows accurate predictions, with associated levels of confidence, of long-term properties by extrapolation of short-term test results for this steel.     

An Algorithm for the Computation of Hermite–Padé Approximations to the Exponential Function: Divided Differences and Hermite–Padé Forms

We present the first of two different algorithms for the explicit computation of Hermite–Padé forms (HPF) associated with the exponential function. Some roots of the algebraic equation associated with a given HPF are good approximants to the exponential in some subsets of the complex plane: they are called Hermite–Padé approximants (HPA) to this function. Our algorithm is recursive and based upon the expression of HPF as divided differences of the function texp(xt) at multiple integer nodes. Using this algorithm, we find again the results obtained by Borwein and Driver for quadratic HPF. As an example, we give an interesting family of quadratic HPA to the exponential.     

An extension of Krugman’s core–periphery model to the case of a continuous domain: Existence and uniqueness of solutions of a system of nonlinear integral equations in spatial economics

We consider a model that is an extension of Krugman’s core–periphery model to the case of a bounded closed domain included in a Euclidean space. We can describe the relation of the density of workers, the density of nominal wages, and the density of real wages by the system of nonlinear integral equations of the model. If we obtain a solution of the system under the condition that the density of workers is given, then the solution is called a short-run equilibrium. In this paper we prove that this model has a short-run equilibrium, and we obtain a sufficient condition for its uniqueness. Moreover we obtain upper and lower estimates for short-run equilibria, and we construct a useful iteration scheme to numerically obtain short-run equilibria.     

Corrigendum to the paper: Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792–834

In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792-834]. In fact, in this corrigendum we present the correct hypotheses and results, and highlight that the results can be proved using the same method used in the original work. The main feature is that we used a result which has been proved only when the diffusion term does not depend on the unknown.