Decidability and Universality in Symbolic Dynamical Systems

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the `edge of chaos' and we exhibit a universal chaotic system.Comment: 23 pages; a shorter version is submitted to conference MCU 2004 v2: minor orthographic changes v3: section 5.2 (collatz functions) mathematically improved v4: orthographic corrections, one reference added v5:27 pages. Important modifications. The formalism is strengthened: temporal logic replaced by finite automata. New results. Submitte

Palladium-scavenging self-assembled hybrid hydrogels – reusable highly-active green catalysts for Suzuki–Miyaura cross-coupling reactions

A hybrid hydrogel based on 1,3:2,4-dibenzylidene sorbitol (DBS) modified with acyl hydrazides combined with agarose was used for in situ reduction and binding of palladium from aqueous mixtures without the need for an external reducing agent. Palladium uptake was monitored and the formation of Pd nanoparticles (PdNPs) trapped within the gel and located close to the nanofibres was confirmed. This gel effectively scavenges palladium from solution to concentrations 10 times). Reactions were purified by simple washing protocols, and leaching of Pd from the gels is limited (<1 ppm). The gels were also used in flow-through mode, giving efficient, rapid reactions, with easy work-up. These catalytic gels combine advantages of homogeneous and heterogeneous catalysts-they are solvent compatible with the reaction taking place in a solution-like environment, while the solid-like gel network enables catalyst recycling. In summary, these hydrogels scavenge 'waste' palladium and convert it into gel 'wealth' capable of efficient, environmentally-friendly Suzuki-Miyaura catalysis

Correction : Palladium-scavenging self-assembled hybrid hydrogels - reusable highly-active green catalysts for Suzuki-Miyaura cross-coupling reactions (Chemical Science (2019) DOI: 10.1039/c8sc04561e)

In the original article, an error was made in the placement of an oxygen atom in the structure of DBS-CONHNH2 in Fig. 1. The structure should be as shown below:. (Figure Presented). The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers

The influence of varying thermal treatment conditions on reducing zinc content from a steelmaking and blast furnace sludge

The prospects of processing blast furnace and steelmaking sludge using the Waelz process in a laboratory rotary kiln, is shown. The influence of different processing temperatures, furnace atmosphere and the type of reducing agents on the level of zinc reduction from sludges was analyzed. In general, the blast furnace sludge contains a high portion of iron (approx. 48 wt.%) and can be reused as a charge after satisfactory zinc reduction. It was found that N- atmosphere and a high content of the graphite or coke oven reducing agent in combination with high temperature can reduce the content of Zn in the sludge to 0.08 wt.% at 1200 degrees C for a mixture of steelmaking and blast furnace sludge. A significant reduction in the Zn content to 0.66 wt.% occurs at 1100 degrees C. The content and type of reducing agent plays an important role; graphite has shown a better reducing ability compared to coke oven dust. When nitrogen is used, zinc is reduced even without an additional reducing agent, since the carbon contained in the sludge is made use of for the reduction. In an air atmosphere, without the use of a reducing agent, there was no reduction in the Zn content.Web of Science1211art. no. 196

One-dimensional dynamics and factors of finite automata

We argue that simple dynamical systems are factors of finite automata, regarded as dynamical systems on discontinuum. We show that any homeomorphism of the real interval is of this class. An orientation preserving homeomorphism of the circle is a factor of a finite automaton iff its rotation number is rational. Any $S$-unimodal system on the real interval, whose kneading sequence is either periodic odd or preperiodic, is also a factor of a finite automaton, while $S$-unimodal systems at limits of period doubling bifurcations are not.Comment: Latex, 15 page

Starobní důchod v rámci sociálního zabezpečení

Import 20/04/2006Prezenční výpůjčkaVŠB - Technická univerzita Ostrava. Ekonomická fakulta. Katedra (119) práv

Dynamics of number systems: computation with arbitrary precision

This book is a source of valuable and useful information on the topics of dynamics of number systems and scientific computation with arbitrary precision. It is addressed to scholars, scientists and engineers, and graduate students. The treatment is elementary and self-contained with relevance both for theory and applications. The basic prerequisite of the book is linear algebra and matrix calculus.

Cellular automata in the Cantor, Besicovitch and Weyl spaces

The Besicovitch and Weyl pseudometrics on the space A ZZ of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from A ZZ by factoring through the equivalence of zero distance. We consider cellular automata as dynamical systems on the Besicovitch and Weyl spaces and compare their topological and dynamical properties with those in the Cantor space

Return times in dynamical systems [Temps de retour dans les systèmes dynamiques]

Dans cette thèse, deux aspects asymptotiques des temps de retour et d'entrée sont étudiés: les taux locaux de temps de retour, et les lois limites des k-ièmes temps de retour et d'entrée. Dans le cadre des "shifts" Sturmiens, des formules permettant de calculer les taux locaux de temps de retour sont développées. La classe des lois limites de premier temps d'entrée est décrite explicitement. Nous y prouvons que la classe des lois limites des k-ièmes temps de retour est la même que celle des premiers temps de retour, caractérisée par Y. Lacroix. Enfin, nous y exhibons un lien entre les lois limites des k-ièmes temps de retour et d'entrée.Several statistics of hitting and return times in dynamical systems are investigated in this thesis. It concerns local return rates and the limit laws of k-th return and hitting times. Formulas to compute the local return rates in Sturmian shifts are developed. The class of all limit laws of the first hitting times is described. The class of all limit laws of the k-th return times is shown to be the same as the class of all limit laws of the first return times, characterized by Lacroix. Last but not least, we exhibit a link between k-limit laws of return and hitting times.TOULON-BU Centrale (830622101) / SudocSudocFranceF