On Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)

Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence related more general classes of regular languages with classes of more complex algebraic objects. Such generalized varieties also have natural counterparts formed by classes of finite automata equipped with a certain additional algebraic structure. In this survey, we overview several variants of such varieties of enriched automata.Comment: In Proceedings AFL 2014, arXiv:1405.527

On the insertion of n-powers

In algebraic terms, the insertion of $n$-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x^n$. We compare this pseudovariety with several other natural pseudovarieties of ordered monoids and of monoids associated with the Burnside pseudovariety of groups defined by the identity $x^n=1$. In particular, we are interested in determining the pseudovariety of monoids that it generates, which can be viewed as the problem of determining the Boolean closure of the class of regular languages closed under $n$-power insertions. We exhibit a simple upper bound and show that it satisfies all pseudoidentities which are provable from $1\le x^n$ in which both sides are regular elements with respect to the upper bound

Binary patterns in the Prouhet-Thue-Morse sequence

We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite case). This result was previously attributed to unpublished work by D. Guaiana and may also be derived from publications of A. Shur only available in Russian. We also identify the (finitely many) finite binary patterns that appear non trivially, in the sense that they are obtained by applying an endomorphism that does not map the set of all segments of the sequence into itself

The omega-inequality problem for concatenation hierarchies of star-free languages

The problem considered in this paper is whether an inequality of omega-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows that this problem is decidable for all (integer and half) levels of the Straubing-Th\'erien hierarchy

Design of steam generator tube bundle

Diplomová práce je zaměřena na analýzu stávajícího provedení a nový konstrukční návrh trubkového svazku generátoru páry na základě využití metody konečných prvků v softwaru ANSYS. Dále bude náplní práce zohledňující způsoby provozu zařízení a návrh plánu revizních kontrol míst, která budou nejkritičtější. Součástí příloh je modelová dokumentace v programu SolidWorks.Diploma thesis is focused on analisis of the steam generator tube bundle on the basis calculation by the finite elements method and softwaru ANSYS. Next it will also také account of job descriptions and methods of operation of the equipment propřed plan revision kontrol points that will be most critical. Annexes included documentary of model from the SolidWorks.

Binocular vision and anaglyph production

Tématem mé semestrální práce bylo prostudovat fyziologii binokulárního vidění pro získání prostorového vjemu z dvourozměrných obrázků pomocí brýlí s barevnými filtry, anaglyfu. Protože se to týká zrakového smyslu, na počátku jsem vysvětlil princip samotného vidění. Poté jsem popsal princip fyziologického vývoje vidění a předpokladů binokulárního vidění. Binokulární vidění je komplexní proces, probíhající i mozku. Proto je další tématem práce analýza trojrozměrných objektů, analýza prostoru, která nevědomky probíhá v našem mozku. Další kapitola pojednává o stereoskopii, technice, jež vyvolává pocit hloubky v dvourozměrném obraze. Získání prostorového vjemu pomocí brýlí s barevnými filtry je jedna z jejích technik. Sepsal sem princip získání anaglyfu, od snímání scény, přes její tvorbu až po prohlížení. Nakonec je zde uvedena ukázka programu vytvořeného v prostředí Matlab. Je to jednoduchý program na získání anaglyfu z dvou samostatných snímků.The aim of my semester work was to study the physiology of binocular vision for spatial perception of two-dimensional images using glasses with coloured filters, anaglyphs. Since the theme concerns the visual sense, I explained the principle of the vision first. Then I described the principle of physiological development of the vision and the assumptions about binocular vision. The binocular vision is a complex process ongoing in the brain. Therefore, another topic of my thesis was an analysis of three-dimensional objects, space analysis, which unknowingly takes place in our brain. The next chapter deals with stereoscopy, technology which evokes a feeling of depth in two-dimensional images. One of the techniques is obtaining spatial perception by means of glasses with colour filters. In my thesis, I summarized the knowledge about the principle of anaglyphs and I described the principle of obtaining anaglyphs, from shooting the scene, over its creation to its viewing. Finally, here is an example of the program created in Matlab. It is a simple program to obtain anaglyphs from two separate frames.

Simulation of electric machines

Tato bakalářská práce se zabývá modelováním a simulací stejnosměrných a střídavých strojů. Byly vytvořeny celkem čtyři matematické modely. Tři modely stejnosměrných motorů při různém typu buzení (kompaundní, sériový, cize buzený) a jeden model pro motor asynchronní. Všechny modely byly realizovány v prostředí MATLAB&Simulink. Po změření a zadání základních parametrů motoru, byly spuštěné simulace. Výsledky simulací jsou poté porovnány s naměřenými průběhy.This thesis deals with modeling and simulations of DC and AC machines. They were created by four mathematical models. Three models of DC motors with different type of excitation (compound, serial, derivative) and one model for asynchronous motor. All models were implemented in MATLAB & Simulink. After measuring and setting the basic parameters of the machines, simulations were running. Simulation results are then compared with measured waveforms.