Oscillation criteria for higher order nonlinear dynamic equations

In this paper, we will consider the higher‐order functional dynamic equations of the form on an above‐unbounded time scale , where and , . The function is a rd‐continuous function such that . The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.     

On compact semisimple Lie groups as 2-plectic manifolds

In this paper a compact and semisimple Lie group G is considered endowed with a 2-plectic structure ω, induced by the Killing form. We show that the Lie group of 2-plectomorphisms of G is finite dimensional and compact, and hence the Darboux’s theorem fails to be true for this 2-plectic structure. Also it is shown that ω induces a left-invariant \({\mathfrak{g}^{*}}\) valued 2-form which is proportional to dΘ, where Θ is the Cartan–Maurer 1-form on G. At last we consider the action of G on its tangent bundle which is furnished with the 2-plectic structure ω ^c , the complete lift of ω, and calculate covariant momentum map of this action.     

A new multiobjective allocator of capacitor banks and distributed generations using a new investigated differential evolution

This article has investigated a new multiobjective allocation of optimal sizing and sitting of distributed generation (DG) units and capacitor banks in simultaneous mode to improve reliability and reduce energy losses. The proposed method consists of four objectives, that is, cost of energy not supplied, system average interruption duration index, costs of energy loss and investment. A novel structure differential evolution has been suggested to solve this nonlinear complex problem and its results are compared with related values of genetic algorithm and simple differential evolutionary algorithm. In addition to the novel objective function, the other contribution of this article is proposing a new model for load and energy cost. Three types of DGs, that is, wind turbine, solar cell, and diesel generator have been used in placement process. To verify the comprehensiveness of the proposed function, three scenarios have been introduced: scenario i: first, placement of DGs, then capacitor banks, scenario ii: first, placement of capacitor banks, and then DGs, and scenario iii: simultaneous placement of DGs and capacitor banks. Simulations have been carried out on one part of practical distribution network in Metropolitan Tabriz in North West of Iran. The results of simulations have been discussed and analyzed using the five novel indices. The obtained simulation results using proposed function shows that the simultaneous placement of DGs and capacitor banks results in more reduction of the energy losses and increase improvements of reliability indices as well as voltage profile. © 2013 Wiley Periodicals, Inc. Complexity 19: 40–54, 2014     

Chaotic fractional‐order model for muscular blood vessel and its control via fractional control scheme

This article studies the chaotic and complex behavior in a fractional‐order biomathematical model of a muscular blood vessel (MBV). It is shown that the fractional‐order MBV (FOMBV) model exhibits very complex and rich dynamics such as chaos. We show that the corresponding maximal Lyapunov exponent of the FOMBV system is positive which implies the existence of chaos. Strange attractors of the FOMBV model are depicted to validate the chaotic behavior of the system. We change the fractional order of the model and investigate the dynamics of the system. To suppress the chaotic behavior of the model, we propose a single input fractional finite‐time controller and prove its stability using the fractional Lyapunov theory. In addition, the effects of the model uncertainties and external disturbances are taken into account and a robust fractional finite‐time controller is constructed. The upper bound of the chaos suppression time is also given. Some computer simulations are presented to illustrate the findings of this article. © 2014 Wiley Periodicals, Inc. Complexity 20: 37–46, 2014     

Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups

In this paper, we propose a new general iterative scheme based on the viscosity approximation method for finding a common element of the set of solutions of the generalized mixed equilibrium problem and the set of all common fixed points of a finite family of nonexpansive semigroups. Then, we prove the strong convergence of the iterative scheme to find a unique solution of the variational inequality that is the optimality condition for the minimization problem. Our results extend and improve some recent results of Cianciaruso et al. (J. Optim. Theory Appl. 146:491–509, 2010), Kamraksa and Wangkeeree (J. Glob. Optim. 51:689–714, 2011), and many others.     

Estimation of mutual information by the fuzzy histogram

Mutual Information (MI) is an important dependency measure between random variables, due to its tight connection with information theory. It has numerous applications, both in theory and practice. However, when employed in practice, it is often necessary to estimate the MI from available data. There are several methods to approximate the MI, but arguably one of the simplest and most widespread techniques is the histogram-based approach. This paper suggests the use of fuzzy partitioning for the histogram-based MI estimation. It uses a general form of fuzzy membership functions, which includes the class of crisp membership functions as a special case. It is accordingly shown that the average absolute error of the fuzzy-histogram method is less than that of the naïve histogram method. Moreover, the accuracy of our technique is comparable, and in some cases superior to the accuracy of the Kernel density estimation (KDE) method, which is one of the best MI estimation methods. Furthermore, the computational cost of our technique is significantly less than that of the KDE. The new estimation method is investigated from different aspects, such as average error, bias and variance. Moreover, we explore the usefulness of the fuzzy-histogram MI estimator in a real-world bioinformatics application. Our experiments show that, in contrast to the naïve histogram MI estimator, the fuzzy-histogram MI estimator is able to reveal all dependencies between the gene-expression data.     

Cellular articular cartilage replacement tissues: Modeling and analysis

Long-term studies reveal that mechanical stimulation causes growth and remodeling phenomena within biological tissues. The main aim of this research is to fully understand and control these phenomena. For accomplishing that, two steps are considered: first, we determine a suitable numerical model based on different approaches by a comparative study using experimental validations, and second, investigate the mechanical properties of the tissue specimens after a remodeling process. We start with the first step by choosing a convenient model that mimics the biotissue for running the numerical simulations in the second step. There are different models available that determine the mechanical properties of soft replacement tissues seeded with human chondrocytes in modern medical applications. It is our objective to achieve a common methodology of theory and experiments that allows the determination of the mechanical properties of the native material. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A symmetric generalization of Sturm–Liouville problems in q-difference spaces

Classical Sturm–Liouville problems of q-difference variables are extended for symmetric discrete functions such that the corresponding solutions preserve the orthogonality property. Some illustrative examples are given in this sense.     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015