Pisot unit generators in number fields

Pisot numbers are real algebraic integers bigger than 1, whose other conjugates have all modulus smaller than 1. In this paper we deal with the algorithmic problem of finding the smallest Pisot unit generating a given number field. We first solve this problem in all real fields, then we consider the analogous problem involving the so called complex Pisot numbers and we solve it in all number fields that admit such a generator, in particular all fields without CM, but not only those

Eigenvalue filtering in VAR models with application to the Czech business cycle

We propose the method of eigenvalue filtering as a new tool to extract time series subcomponents (such as business-cycle or irregular) defined by properties of the underlying eigenvalues. We logically extend the Beveridge-Nelson decomposition of the VAR time-series models focusing on the transient component. We introduce the canonical state-space representation of the VAR models to facilitate this type of analysis. We illustrate the eigenvalue filtering by examining a stylized model of inflation determination estimated on the Czech data.We characterize the estimated components of CPI, WPI and import inflations, together with the real production wage and real output, survey their basic properties, and impose an identification scheme to calculate the structural innovations. We test the results in a simple bootstrap simulation experiment. We find two major areas for further research: first, verifying and improving the robustness of the method, and second, exploring the method’s potential for empirical validation of structural economic models. JEL Classification: C32, E32Beveridge-Nelson decomposition, business cycle, eigenvalues, filtering, inflation, time series analysis

Integers in number systems with positive and negative quadratic Pisot base

We consider numeration systems with base $\beta$ and $-\beta$, for quadratic Pisot numbers $\beta$ and focus on comparing the combinatorial structure of the sets $\Z_\beta$ and $\Z_{-\beta}$ of numbers with integer expansion in base $\beta$, resp. $-\beta$. Our main result is the comparison of languages of infinite words $u_\beta$ and $u_{-\beta}$ coding the ordering of distances between consecutive $\beta$- and $(-\beta)$-integers. It turns out that for a class of roots $\beta$ of $x^2-mx-m$, the languages coincide, while for other quadratic Pisot numbers the language of $u_\beta$ can be identified only with the language of a morphic image of $u_{-\beta}$. We also study the group structure of $(-\beta)$-integers.Comment: 19 pages, 5 figure

Exchange Rate Management and Inflation Targeting: Modeling the Exchange Rate in Reduced-Form New Keynesian Models

This paper introduces a strategy for modeling the exchange rate when the monetary authority targets inflation while also managing the exchange rate using interventions. It does so in the framework of a standard reduced-form New Keynesian model of monetary transmission used in many institutions for research, forecasting, and monetary policy analysis. We propose a microfounded modification to the UIP condition which allows for modeling of informal exchange rate bands. Our modeling strategy is useful for most hybrid IT regimes, including those with imperfect control over market interest rates.IT regimes, New Keynesian model, exchange rate, UIP

Semi-detached house, Velke Mezirici

Předmětem zadání bakalářské práce, bylo navrhnout rodinný dvojdům, kde každá z částí je samostatným prostorem pro rodinné bydlení s navrhovaným počtem šesti osob. Rodinný dvojdům byl umístěn ve Velkém Meziříčí. Je řešený jako nepodsklepený se dvěma nadzemními podlažími, kde druhé nadzemní podlaží je řešeno jako obyvatelné podkroví. Objekt má sedlovou střechu se zajímavým tvarem. Byl navržen dle všech platných právních předpisů a norem.Subject of submission bachelor thesis was designed semi-detached house, which part of this building is lonely space for family housing with for six member family. Semi-detached house was placed in Velké Meziříčí. Object with two above-ground floor and has nothnig basement. Second floor is design as livable space of attic. Object has saddle roof with interesting style. Semi-detached house was designed in step with rule in operations and legal regulations.

Signal Analysis

Práce se zabývá problematikou analýzy signálu, získaného měřením rovnoměrnosti chodu harmonických a planetových převodovek. V úvodní části jsou vysvětleny některé vlastnosti FFT a pojem kepstrum. Dále je uveden přehled nejčastěji měřených parametrů uvedených převodovek a potřebné vztahy, které vyjadřují souvislosti mezi jednotlivými mechanickými částmi převodovek. Další část se zabývá popisem SW modulu vytvořeného v prostředí LabView, který je výstupním produktem práce a provádí analýzu na změřených průbězích.This thesis deals with problem of analysis signal acquiring measurement of uniformity motion harmonic drive and planetary gearboxes. In introduction part are explain some features of FFT and concept of cepstrum. Further is present overview of most often measured parameters of these gearboxes and needed formulas, which express connections among particular mechanical parts of gearboxes. The next part deals with description of SW program unit generated in LabView environment, which is output product of work and makes analysis on measured courses.

Finite beta-expansions with negative bases

The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $\beta$ having the negative finiteness property, that is the set of finite $(-\beta)$-expansions is equal to $\mathbb{Z}[\beta^{-1}]$. For a class of numbers including the Tribonacci number, we compute the maximal length of the fractional parts arising in the addition and subtraction of $(-\beta)$-integers. We also give conditions excluding the negative finiteness property

Family house

Abstrakt Předmětem této bakalářské práce je řešení rodinného domu ve městě Olomouc. Dům je částečně podsklepený s dvěmi nadzemními podlažími a obsahuje obytné prostory. Součástí objektu je i příjezdová cesta ke garáži, schody v exteriéru a garáž umístěná v přízemí obytné části domu. Půdorys domu má členitý tvar, který je zastřešen z části pultovou střechou a z části terasou, která se chová jako plochá pochozí střecha. Dům se bude nacházet na rovinném terénu. Vchod do domu je situovaný na východ. Při stavbě byl použit systém POROTHERM.Abstract The topic of this thesis is the project of a family house in Olomouc. The house is partially included with the cellar, with the ground floor, the second floor and includes living spaces. The part of the building is also the driveway to the garage, stairs outside and the garage situated on the ground floor of the living part of the house. The ground plan of the house has the indented form, which is roofed partially with the shed roof and partially with the terrace, which works as a flat walkable roof. The house will be situated on the flat terrain. The entrance into the house is located in the east. The building project was solved in the POROTHERM construction system.