| A number of mathematical tools are used for analysing nonlinear over-ow eeects in digital lters. In our investigations we found if useful to use the probabilis-tic approach and the circle-map theory in the analysis of complex behaviour in second-order digital lter. In the rst part we introduce some deenition (rotation number, nonwander-ing and chain recurrent points, mixing, exact-ness) and p...

BACKGROUND Epinephrine and more recently arginine vasopressin (AVP) alone or in combination have been proposed in patients with anaphylactic shock, but few experimental data exist. The authors investigated the effects of epinephrine only, AVP only, or epinephrine followed by AVP in a model of anaphylactic shock. METHODS Ovalbumin-sensitized Brown Norway rats were anesthetized, intubated, and ...

Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show these purely singular continuous with respect Lebesgue measure their distribution satisfy super-polynomial asymptotics near origin, thus providing a family extremal examples measures, including Thue–Morse measure.

In this note we prove that reconstruction from magnitudes of frame coefficients (the so called ”phase retrieval problem”) can be performed using Lipschitz continuous maps. Specifically we show that when the nonlinear analysis map α : H → R is injective, with (α(x))k = |〈x, fk〉| , where {f1, . . . , fm} is a frame for the Hilbert space H, then there exists a left inverse map ω : R → H that is Li...

In this note we show that reconstruction from magnitudes of frame coefficients (the so called “phase retrieval problem”) can be performed using Lipschitz continuous maps. Specifically we show that when the nonlinear analysis map α : H → Rm is injective, with (α(x))k = |〈x, fk〉|, where {f1, · · · , fm} is a frame for the Hilbert space H, then there exists a left inverse map ω : Rm → H that is Li...

The aim of this paper is to prove the following results: a continuous map f : [0, 1]→ [0, 1] is chaotic iff the shift map σf : lim ← ([0, 1], f)→ lim ← ([0, 1], f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. σf : lim ← ([0, 1], f) → lim ← ([0, 1], f) is chaotic iff there exists an increasing sequence of positive integers A such that the topological s...

A Markov switching position dependent random map is a random map of a finite number of measurable transformations where the probability of switching from one transformation to another is controlled by a position dependent irreducible stochastic matrix W . Existence of absolutely continuous invariant measures (acim) for a Markov switching position dependent random map was proved in [1] using spe...