A classical mechanical system is analysed which exhibits complicated scattering behaviour. In the set of all incoming asymptotes there is a fractal subset on which the scattering angle is singular. Though in the complement of this Cantor set the deflection function is regular, one can choose impact parameter intervals leading to arbitrarily complicated trajectories. We show how the complicated ...

fuzzy relation inequalities based on max-f composition are discussed, where f is a binary aggregation on [0,1]. for a fixed fuzzy relation inequalities system $ a circ^{f}textbf{x}leqtextbf{b}$, we characterize all matrices $ a^{'} $ for which the solution set of the system $ a^{' } circ^{f}textbf{x}leqtextbf{b}$ is the same as the original solution set. similarly, for a fixed matrix ...

D-decomposition technique is targeted to describe the stability domain in parameter space for linear systems, depending on parameters. The technique is very simple and effective for the case of one or two parameters. However the geometry of the arising parameter space decomposition into root invariant regions has not been studied in detail; it is the purpose of the present paper. We prove that ...

This paper addresses the problem of proving a given invariance property φ of a loop in a numeric program, by inferring automatically a stronger inductive invariant ψ. The algorithm we present is based on both abstract interpretation and constraint solving. As in abstract interpretation, it computes the effect of a loop using a numeric abstract domain. As in constraint satisfaction, it works fro...

BACKGROUND To advance asthma cohort research, we need a method that can use longitudinal data, including when collected at irregular intervals, to model multiple phenotypes of wheeze and identify both time-invariant (eg, sex) and time-varying (eg, environmental exposure) risk factors. OBJECTIVE To demonstrate the use of latent class growth analysis (LCGA) in defining phenotypes of wheeze and ...

We consider the solution of nonlinear optimal control problems subject to stochastic perturbations with incomplete observations. In particular , we generalize results obtained by Ito and Kunisch in [8] where they consider a receding horizon control (RHC) technique based on linearizing the problem on small intervals. The linear-quadratic optimal control problem for the resulting time-invariant (...

In this paper we study the system-theoretic properties of two related classes of shift-invariant two-point boundary-value descriptor systems (TPBVDSs), namely displacement systems for which Green's function is shift-invariant, and stationary systems for which the input -output map is stationary. For such systems it is possible to obtain detailed characterizations of the properties of weak reach...

Space-like and time-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances. The former are found to be Lorentz invariant –there is no 'relativistic length contraction', whereas the latter exhibit the experimentally confirmed 'time dilatation' effect, without, however, 'relativity of simultaneity'. It is shown how the spurious predictions of length...

In large-eddy simulations (LES) a computational-domain translation velocity can be used to improve performance by allowing longer time-step intervals. The continuous equations are Galilean invariant. However, standard finite-difference-based discretizations not discretely invariant with the error being proportional product of local and truncation error. Even though such numerical errors expecte...