Cascades-based synchronization of hyperchaotic systems: Application to Chen systems

We discuss the cascaded-based controlled synchronization method for hyperchaotic systems. The control approach is based on analysis tools for cascaded time-varying systems. That is, the closed-loop system takes the form of two subsystems which are interconnected in a manner that the state of one system enters into another but without feedback loop. The advantage of such construction is that the controller is largely simplified relative to other design methods such as backstepping. We apply the method to Chen’s hyperchaotic system and show that global synchronization is achieved via linear control. Also, we assume that only three instead of four control inputs are available. The method is tested in numerical simulations.     

Comparison of two regulatory results on functional equations with few parameters

Two methods to prove regularity properties of the linear functional equation $$f(x)=h_0(x,y)+\sum_{j=1}^n h_j(x,y)f(x+g_j(y)), $$ where ${(x,y) \in D \subset \mathbb{R}^r \times \mathbb{R}^s}$ , ${x \in \mathbb{R}^r}$ and ${y \in \mathbb{R}^s}$ , with few parameters i.e. allowing 1 ?? s < r are examined. It is proved that??under certain conditions, for some class of equations and in some sense??they are equivalent.     

LK property for σ-ideals

An ideal J of subsets of a Polish space X has (LK) property whenever for every sequence (An) of analytic sets in X, if lim supn∈HAn∉J for each infinite H then _?n∈G∉J for some infinite G. In this note we present a new class of σ-ideals with (LK) property.     

A dichotomy for the convex spaces of probability measures

We show that every nonempty compact and convex space M of probability Radon measures either contains a measure which has ‘small’ local character in M or else M contains a measure of ‘large’ Maharam type. Such a dichotomy is related to several results on Radon measures on compact spaces and to some properties of Banach spaces of continuous functions.     

Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution

The Weibull distribution is one of the most important distributions that is utilized as a probability model for loss amounts in connection with actuarial and financial risk management problems. This paper considers the Weibull distribution and its quantiles in the context of estimation of a risk measure called Value-at-Risk (VaR). VaR is simply the maximum loss in a specified period with a pre-assigned probability level. We attempt to present certain estimation methods for VaR as a quantile of a distribution and compare these methods with respect to their deficiency (Def) values. Along this line, the results of some Monte Carlo simulations, that we have conducted for detailed investigations on the efficiency of the estimators as compared to MLE, are provided.     

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.     

On sofic actions and equivalence relations

The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes? Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic.     

Chaos among self-maps of the Cantor space

Glasner and Weiss have shown that a generic homeomorphism of the Cantor space has zero topological entropy. Hochman has shown that a generic transitive homeomorphism of the Cantor space has the property that it is topologically conjugate to the universal odometer and hence far from being chaotic in any sense. We show that a generic self-map of the Cantor space has zero topological entropy. Moreover, we show that a generic self-map of the Cantor space has no periodic points and hence is not Devaney chaotic nor Devaney chaotic on any subsystem. However, we exhibit a dense subset of the space of all self-maps of the Cantor space each element of which has infinite topological entropy and is Devaney chaotic on some subsystem.     

A sufficient condition of viability for fractional differential equations with the Caputo derivative

In this paper viability results for nonlinear fractional differential equations with the Caputo derivative are proved. We give the sufficient condition that guarantees fractional viability of a locally closed set with respect to nonlinear function. As an example we discuss positivity of solutions, particularly in linear case.