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Tenzan jutsu: Revolution in Traditional Japanese Mathematics
Vitvar, Tomáš ; Labus, David (advisor) ; Sýkora, Jan (referee)
Proposed paper is a study of historical development of wasan, i.e., traditional Japanese mathematics. I chiefly focus on the origin of tenzan jutsu, a calcula- tion method, that by its inner logic and by usage of a symbolic notation greatly resembles Western algebra. As there is no satisfying evaluation of a level of similarity of those two traditions in an existing literature, I decided to closely examine tenzan jutsu using a theory of potentialities of language of mathemat- ics proposed by Ladislav Kvasz. Comparing my examination and analysis of Western algebra done by L. Kvasz, I came to a conclusion, that although the language of tenzan jutsu is in most aspects almost identical to the language of Western algebra, there is a major difference in a way those languages developed. While the development of the Western algebra was hindered by a cultural need to interpret exponents in a geometrical context and by a strong reluctance to accept negative terms as a part of equation, the development of Japanese math- ematics, which was free of such restrictions, was considerably more dynamic. Keywords tenzan jutsu, wasan, Tokugawa, Edo, Seki Takakazu, Seki Kowa, algebra, math- ematics, tengen jutsu, Ladislav Kvasz, language of mathematics
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Political connections, public procurement and small-scale expenditures
Vitvar, Tomáš ; Palanský, Miroslav (advisor) ; Smutná, Šarlota (referee)
In this thesis, I introduce a new approach of estimating financial flows from government organisations towards its suppliers of goods and services. It is based on accounting data collected by a Ministry of Finance of the Czech Republic and unlike other available data sources offers an opportunity to study all transactions, including small-scale expenditures. Using this approach, I study the effect of an outcome of 2018 elections on the structure of municipality's suppliers. Interestingly, I find that one year after the elections there is no significant difference between municipalities with different election results. This suggests that there is either no rent-seeking activity at all, or that it takes a different form than a selection of suppliers. Also, while conducting this analysis, I quantify a link between a winning party and an affiliation of a mayor and show how it increases in municipalities where there is a dominance of one political party. Keywords political connections, public procurement, corruption, politics, government expenditures, municipality, local government, election JEL Classification D72, H72, K40
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Use of stable hydrogen and oxygen isotopes in hydrology of small catchments in the Czech and Slovak Republic
Šanda, M. ; Vitvar, T. ; Holko, L. ; Blažková, Š. ; Bůzek, F. ; Císlerová, M. ; Fottová, D. ; Kostka, Z. ; Kulasová, A. ; Kvítek, T. ; Šnytr, O. ; Tachecí, P. ; Tesař, Miroslav ; Vícha, Z. ; Žlábek, P.
The contribution summarizes the development of isotope hydrology and hydrogeology in the Czech and Slovak Republic over the past 40 years. Records of 18O and 2H in nine experimental catchments and their interpretation provide a description of runoff component mixing from various soil and rock environments, as well as a calculation of mean water residence time of 7 to 25 months. The 18O and 2H content in two profiles of the Jizera River and two boreholes in the lower reaches shows little communication of river water with the groundwater supply resources in the Lower Jizera area; the communicaton increases with pumping intensity. The 18O and 2H content in wetlands and groundwater in two catchments of the Jizera Mts. shows the differences in recharge to the wetlands via groundwater or precipitation. The isotope hydrology and hydrogeology perspectives in the ČR and SR include capacity building, cooperation of laboratories and conjunctive use of izotopic and hydrogeochemical approaches.
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