The reachability problem as well as the computation of the phase portrait for the class of planar hybrid systems defined by constant differential inclusions (SPDI), has been shown to be decidable. The existing reachability algorithm is based on the exploitation of topological properties of the plane which are used to accelerate certain kind of cycles. The complexity of the algorithm makes the a...

In the spring of 1910, Oskar Kokoschka painted a portrait of the eminent Swiss psychiatrist, neuroanatomist, temperance champion, and myrmecologist Auguste Forel. The painting is a remarkable psychological portrait but also appears to predict the strokes and right hemiparesis that affected Forel more than a year later. Although it is possible that Kokoschka shared a gift of psychic prediction w...

This is an extended abstract of the published paper “Approximate Similarity and Poincaré Paradox to be published in Notre Dame Journal of Formal Logic, 49, 2008”. The startin point is an observation by De Cock and Kerre, in which, in considering Poincaré paradox, one observes that the intuitive notion of “approximate similarity” cannot be adequately represented by the fuzzy equivalence relation...

Details of electronic circuitry to define Poincaré planes in the phase space of nonlinear electronic systems are presented. It allows an experimental setup to capture data at every moment the system’s orbit crosses the Poincaré plane. We illustrate how the circuit is used in an experimental setup that allows us (i) to reconstruct bifurcation cascades and to disclose induced first return chaotic...

We analyze the statistical properties of Poincaré recurrences of Homo sapiens, mammalian, and other DNA sequences taken from the Ensembl Genome data base with up to 15 billion base pairs. We show that the probability of Poincaré recurrences decays in an algebraic way with the Poincaré exponent β≈4 even if the oscillatory dependence is well pronounced. The correlations between recurrences decay ...

The bicovariant differential calculus on the three-dimensional κ-Poincaré group and the corresponding Lie-algebra structure are described. The equivalence of this Lie-algebra structure and the three-dimensional κ-Poincaré algebra is proved.

This paper proposes a new approach for estimating the failure time distribution using the indicator data. The indicators, which are checked by periodic inspection of a standby redundant system, only convey whether at least one failure occurs per interval. The estimation procedure first obtains the estimation of the forward recurrence time using the indicator data. Then the mean is estimated bas...

Abstract. We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in R via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann map. More precisely, using the full symbol of the transformed Dirichlet-to-Neumann map viewed as a semiclassical pseudodifferential operator, we give an explic...