In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay. Keywords—Caputo derivative, delay, stability, chaos.

We present a list of measures for a single trajectory, including measures that require the presence of other trajectories, such as the centrality of a trajectory amidst other trajectories. Then, we introduce three different views in order to extend measures of a single trajectory to a group, namely the representative view, the complete view and the area view. Furthermore, we give measures that ...

We study the formation of cartels within two di¤erent contexts. First, we consider internal-external stability based models which, due to …rms’ free-riding incentives, lead to the inexistence of stable cartels. Second, we introduce the dynamic aspect of coalition formation. That is, when considering a cartel we consider also any cartel that can be reached through a succession of moves. Despite ...

ZIF-8 as a promising storage material was investigated at high pressures up to ~39 GPa by in situ FTIR spectroscopy for the first time. Structural modifications are found to be reversible in a low-pressure region but irreversible in a high-pressure region. Overall, the ZIF-8 framework exhibits an unusual chemical stability even under extreme compression.

This note describes probabilistic properties of optimal price sample paths in a dynamic pricing model with a finite horizon and limited stock. We assume that customer arrivals follow a nonhomogeneous Poisson process. We show that if customers’ willingness-to-pay increases rapidly over time, then the optimal price process follows a submartingale, which implies an upward price trend. Alternativel...

We consider linear deterministic systems on real Hilbert spaces which are subjected to a nite number (N) of stochastic, structured, Lipschitzian perturbations. A stability radius is deened and is completely characterized via an N-parameter minimization of the norm of a family of bounded operators. This is in contrast to the determin-istic case where the stability radius is determined by the-fun...

For symmetric inde®nite tridiagonal matrices, block LDL factorization without interchanges is shown to have excellent numerical stability when a pivoting strategy of Bunch is used to choose the dimension (1 or 2) of the pivots. Ó 1999 Elsevier Science Inc. All rights reserved. AMS classi®cation: 65F05; 65G05

Cationic triangulenes and helicenes are highly stable carbocations with planar and helical conformations respectively. These moieties are effective dyes with original absorption and emission properties. Over the last decade, they have received greater attention and are considered as valuable tools for the development of innovative applications. In this review, the synthesis of these unique comp...

where p(t) and q(t) are real-valued functions and p(t) 6= 0 for any t ∈ R. In what follows we assume that a(t), b(t), and c(t) satisfy the periodicity conditions a(t+ T ) = a(t), b(t+ T ) = b(t), c(t+ T ) = c(t), t ∈ R. The system (2) (or (3)) is said to be stable if all solutions are bounded on R, unstable if all nontrivial solutions are unbounded on R, and conditionally stable if there exits ...