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Construction of a von Koch snowflake
Bouchala, Ondřej ; Hencl, Stanislav (advisor) ; Vlasák, Václav (referee)
A Mapping from C onto C is quasiconformal, if it maps "infinitesimally small circles" onto "infinitesimally small ellipses". In other words, its real derivative in almost every point (which is for each point linear mapping from plane to plane) maps circles to ellipses with bounded ratio of axes. Koch snowflake is well-known inductively defined fractal: Using Beurling-Ahlfors extension we will prove, that there exists quasi- conformal mapping from the plane onto the plane, which maps unit disk onto Koch snowflake. 1
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Collections of compact sets in descriptive set theory
Vlasák, Václav ; Zelený, Miroslav (advisor)
1 Title: Collections of compact sets in descriptive set theory Author: Václav Vlasák Department: Department of Mathematical Analysis Supervisor: Doc. RNDr. Miroslav Zelený, Ph.D. Author's e-mail address: vlasakmm@volny.cz Abstract: This work consists of three articles. In Chapter 2, we dissert on the connections between complexity of a function f from a Polish space X to a Polish space Y and complexity of the set C(f) = {K ∈ K(X); f K is continuous}, where K(X) denotes the space of all compact subsets of X equipped with the Vietoris topology. We prove that if C(f) is analytic, then f is Borel; and assuming ∆1 2-Determinacy we show that f is Borel if and only if C(f) is coanalytic. Similar results for projective classes are also presented. In Chapter 3, we continue in our investigation of collection C(f) and also study its restriction on convergent sequences (C(f)). We prove that C(f) is Borel if and only if f is Borel. Similar results for projective classes are also presented. The Chapter 4 disserts on HN -sets, which form an important subclass of the class of sets of uniqueness for trigonometric series. We investigate the size of these classes which is reflected by the family of measures called polar which annihilate all the sets belonging to the given class. The main aim of this chapter is to answer in...
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Collections of compact sets in descriptive set theory
Vlasák, Václav ; Zelený, Miroslav (advisor) ; Holický, Petr (referee) ; Tišer, Jaroslav (referee)
1 Title: Collections of compact sets in descriptive set theory Author: Václav Vlasák Department: Department of Mathematical Analysis Supervisor: Doc. RNDr. Miroslav Zelený, Ph.D. Author's e-mail address: vlasakmm@volny.cz Abstract: This work consists of three articles. In Chapter 2, we dissert on the connections between complexity of a function f from a Polish space X to a Polish space Y and complexity of the set C(f) = {K ∈ K(X); f K is continuous}, where K(X) denotes the space of all compact subsets of X equipped with the Vietoris topology. We prove that if C(f) is analytic, then f is Borel; and assuming ∆1 2-Determinacy we show that f is Borel if and only if C(f) is coanalytic. Similar results for projective classes are also presented. In Chapter 3, we continue in our investigation of collection C(f) and also study its restriction on convergent sequences (C(f)). We prove that C(f) is Borel if and only if f is Borel. Similar results for projective classes are also presented. The Chapter 4 disserts on HN -sets, which form an important subclass of the class of sets of uniqueness for trigonometric series. We investigate the size of these classes which is reflected by the family of measures called polar which annihilate all the sets belonging to the given class. The main aim of this chapter is to answer in...
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Mountain Pass Theorem and its applications
Příhoda, Vojtěch ; Černý, Robert (advisor) ; Vlasák, Václav (referee)
Cílem této práce je formulovat a dokázat Větu o horském sedle a ukázat příklady její aplikace tak, aby student třetího ročníku matematiky nebo fy- ziky, jenž absolvoval alespoň úvodní kurs funkcionální analýzy, byl schopen práci porozumět. D·kaz Věty o horském sedle provedeme s pomocí Ekelan- dova variačního principu, který si rovněž formulujeme a dokážeme. Následně si ukážeme dva příklady její aplikace na d·kaz existence netriviálního sla- bého řešení eliptické parciální diferenciální rovnice obsahující nelinearitu se subkritickým r·stem. 1
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Financing of small and medium size enterprizes with use of factoring
Vlasák, Václav ; Sato, Alexej (advisor) ; Černohlávková, Eva (referee) ; Králová, Lenka (referee)
The main goal of the thesis is to assess factoring as a tool for small and medium size enterprises financing. Factoring offers receivables management, securing of debtors risk and support of national and international trade. The target is to sum up theoretical approaches in Czech as well as international literature and connect them with practice knowledge and experience that the author have learned during expert experience. Factoring was successfully offered in course of bad economic times during worldwide recession mainly to due easy availability in the markets. Financing via factoring expresses lower risk for financing party, due to transaction risk spread being on the more debtors. In contrast, there is higher demand on administration of every single invoice of company to its debtors. This logically brings higher cost of manpower on the financing party site that has to deal with high proportion of invoices. The thesis is divided into five parts. First parts is taking care about state and private trade supporting tools including Czech Export Bank and its role in creating space for national exporters. Second part deals with forms, in which small and medium size enterprise can find the suitable financial tools and products. Receivables and its main features, receivables live cycle and tools for effective use of receivable in asset based financing, that is all proceeded in part with number three. Whereas chapter four analyze current latest experience with factoring, its forms and way of use including legal and accountancy view. Fifth chapter summarizes theoretical background and uses the application of theory in practice and presents examples, how factoring can help. The thesis found out, that factoring is a suitable financing tool in times of economic crisis and general downturn. The number of factoring transaction grew, as well as the total turnover, but average transaction price went down due to lower cost of traded goods, that was financed via factoring. Thesis also proved that factoring financing is easy to get in the market, as there is large scale of big and small factoring financing providers. Factoring did not improve all significant financial ratios, but increased turnover of assets, mainly receivables, decreased the ratio of indebtedness. Thesis introduced the factoring financing, its use, forms and pros as well as cons. Factoring provided to be sufficient substitute for conventional credit, but bears differences, that have to be taken into account, when deciding on suitable form of receivable financing.
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SKODA AUTO Export strategy
Řezáčová, Petra ; Černohlávková, Eva (advisor) ; Vlasák, Václav (referee)
This bachelor's thesis deals with the topic of export strategy of the biggest Czech car manufacturer - SKODA AUTO. It mainly focuses on strategic markets that will be crucial for the company in next years. The tool used in this thesis is SWOT analysis (analysis of strengths, weaknesses, opportunities and threats). Moreover, the first two chapters deal with current information concerning the company's performance and its Strategy of growth.
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Vyhodnocení produkce vánočních stromků z plantáží v majetku Martina Langa
Vlasák, Václav
This bachelor thesis deals with the production of Christmas trees on plantations owned by Martin Lang. Here are described natural conditions and history of Christmas tree production on the before mentioned properties. A description of tree types grown on the plantations follows. A one year evaluation on monthly basis was carried out assessing work processes. Further individual activities such as soil preparation, tree planting, shaping of trees, fertilization and logging of the trees are briefly described. It is a comparison of two plantations, where two types of Christmas trees are grown, eight year old Abies nordmanniana (Stev.) Spach. provenience Ambrolauri -- Nordmann Fir and Picea pungens Engelm. var. Kaibab -- Blue Spruce.
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