Palindromic complexity of infinite words associated with simple Parry numbers

A simple Parry number is a real number \beta>1 such that the R\'enyi expansion of 1 is finite, of the form d_\beta(1)=t_1...t_m. We study the palindromic structure of infinite aperiodic words u_\beta that are the fixed point of a substitution associated with a simple Parry number \beta. It is shown that the word u_\beta contains infinitely many palindromes if and only if t_1=t_2= ... =t_{m-1} \geq t_m. Numbers \beta satisfying this condition are the so-called confluent Pisot numbers. If t_m=1 then u_\beta is an Arnoux-Rauzy word. We show that if \beta is a confluent Pisot number then P(n+1)+ P(n) = C(n+1) - C(n)+ 2, where P(n) is the number of palindromes and C(n) is the number of factors of length n in u_\beta. We then give a complete description of the set of palindromes, its structure and properties.Comment: 28 pages, to appear in Annales de l'Institut Fourie

Substitutions over infinite alphabet generating (-\beta)-integers

This contribution is devoted to the study of positional numeration systems with negative base introduced by Ito and Sadahiro in 2009, called (-\beta)-expansions. We give an admissibility criterion for more general case of (-\beta)-expansions and discuss the properties of the set of (-\beta)-integers. We give a description of distances within this set and show that this set can be coded by an infinite word over an infinite alphabet, which is a fixed point of a non-erasing non-trivial morphism.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Design concept three wheel small utility vehicle

Tato diplomová práce se zabývá koncepčním návrhem tříkolového užitkového vozidla s užitečným zatížením 300 kg. V úvodu je uveden stručný přehled několika vozidel podobné hmotnostní kategorie. Vlastnímu návrhu předchází analýza používaných koncepčních řešení popis, konstrukčních skupin vozidla a jejich následná volba. Poté je vytvořen 3D model v programu Pro ENGINEER a na jeho základě provedeny výpočty jízdních výkonů a napjatostní analýza vybraných dílů. Při návrhu modelu byl kladen důraz na ergonomii, vzhled, praktickou využitelnost a snadnou vyrobitelnost celé tříkolky.This diploma thesis deals with design concept of three wheel small utility vehicle with curb weight 300kg. At the beginning is short description of some similar vehicles. Analyses of used concepts and descriptions of constructions parts have preceded their choice. Then is created 3D model in PRO Engineer and calculations of driving output and stress analyses are based on it. In design concept is accent putted on ergonomics, look, practical utilization and manufacturability.

Late Quaternary slip at the Kosíř Fault of the Upper Morava Basin – an example of joint research using trenching and microseismic monitoring

Preliminary results of a research into the late Quaternary slip of a major fault in the seismically active Upper Morava Basin are given. Three trenches, up to 6 m deep, were excavated at the foot of the Kosíř Fault scarp near Stařechovice and Čelechovice. The exposed complex sequences of colluvium and loess, now only partly dated by OSL and 14C, is heavily faulted. The faulting is explained by a tectonic slip at the Kosíř Fault and, in the Stařechovice trench, also by simultaneous slope deformations. None of the faults do off set the Holocene topsoil but the youngest of them were clearly active aft er the deposition of the youngest loess and indicate the slip of up to 1.4 m in Late Pleistocene. In Čelechovice trenches the minimum vertical throw of 4 m is indicated for the lower part of the sequence with assumed Late Pleistocene age. The geometry of the deformed zone suggests an oblique normal faulting with significant strike-slip component. The sense of shearing in the horizontal plane was not resolved. Minimum tectonic slip rate of 0.1‒0.3 mm/year in Late Pleistocene is suggested but this must be confi rmed by new dating. Our observations reveal surprisingly young and large deformation which may suggest a temporary increase of tectonic activity during Late Pleistocene.Preliminary results of a research into the late Quaternary slip of a major fault in the seismically active Upper Morava Basin are given. Three trenches, up to 6 m deep, were excavated at the foot of the Kosíř Fault scarp near Stařechovice and Čelechovice. The exposed complex sequences of colluvium and loess, now only partly dated by OSL and 14C, is heavily faulted. The faulting is explained by a tectonic slip at the Kosíř Fault and, in the Stařechovice trench, also by simultaneous slope deformations. None of the faults do off set the Holocene topsoil but the youngest of them were clearly active aft er the deposition of the youngest loess and indicate the slip of up to 1.4 m in Late Pleistocene. In Čelechovice trenches the minimum vertical throw of 4 m is indicated for the lower part of the sequence with assumed Late Pleistocene age. The geometry of the deformed zone suggests an oblique normal faulting with significant strike-slip component. The sense of shearing in the horizontal plane was not resolved. Minimum tectonic slip rate of 0.1‒0.3 mm/year in Late Pleistocene is suggested but this must be confi rmed by new dating. Our observations reveal surprisingly young and large deformation which may suggest a temporary increase of tectonic activity during Late Pleistocene

Optimizing Properties of Balanced Words

In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced words as optimal. In this note we list some key results along these lines known to date.Comment: In Proceedings WORDS 2011, arXiv:1108.341