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Extremal points of convex sets and applications
Zitko, Martin ; Veselý, Jiří (referee) ; Lukeš, Jaroslav (advisor)
The thesis consists of two sections, the theoretical and the practical one. Theoretical part deals with 1. convex analysis, its important theorems including those concerning extreme points of convex sets, and also 2. mathematical solutions of fair division problems. It is shown whether and in what way are these areas related. The practical part of the work follows on results of the previous one with various exercises. Attempts have been made so as no theoretical knowledge is required to understand the formulation of the exercises.
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Toplogical properties of compact convex sets
Kačena, Miroslav ; Lukeš, Jaroslav (referee) ; Spurný, Jiří (advisor)
The first part of the thesis presents the basics of Choquet theory of function spaces needed in the next part. Text deals mainly with general function spaces, the special case of compact convex sets is considered only marginally. The main object of this investigation is an equivalence between simpliciality and some interpolation properties of a function space. The second part is engaged in research on products of function spaces. Various products are defined, the most treated being the multiaffine product. The introductory section focuses just on the connections and differences between these products. The primary goal of the work is a generalization of known results for products of compact convex sets to the context of function spaces. First, extremal sets are examined, the main result is the representation of Choquet boundary of a product space as the product of Choquet boundaries of original spaces. Simplicial spaces are studied next. It is shown, that a product of simplicial spaces is simplicial and in that case established definitions of a product space coincide for affine functions. Finally, maximal measures are investigated.
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Variations of Banach fix point theorem
Pošta, Petr ; Lukeš, Jaroslav (referee) ; Hušek, Miroslav (advisor)
\azev prace: Yariaee Banachovy vety o pevnem bode Autor: Potr Posta Katecha (ustav): Katedra malematieke analy/y Vedouci bakalarske pn'uo: prof. R.NDr. Miroslav Husek. DrSr. e-mail vedouciho: nihnsek'fika.rlin.mff.cuni.c/ Abstrakt: V predlozene pra.ci studujcmo rozlicno dusledky a /ohccnfjiii Bana- chovy vrty o pcvnrni hodr. V prvni Oasli sliulujciin' diislcdky klasickrlio Bana- cliDva prhiripu kuiitrakcc: posloiipnosti kunlraktivnicli zo)j]'ax,(ini, ru/.iie variact1 podnn'iiky koiit.rakt.iviiost.i xobra/cni. pffkladv pou/.iti v Ranacliovych prostorodi. diskrrl.ni prinrip koiilrakcc (Filriilxn'^uva a Jachyinskrho veiv.r) a tit.a/ku ckviva.- Icncc diskrutniYh vet .s Baiiachovou \vtou. V druhr casli jsou nastinriiy moxnr prfstupy k zobrcuc'-iii liaiiachovy vely: jako ph'klady jsuu dokazany ruzne vrty o pevuriu liodr (autory jsou Edrlstcin, Bailey. Civir, Kirk a dalsf), ktr.n'1 xoheciiuji Banachovii vOlu. Kh'cova sluva: Bauacliova vela u kunt.ra.kci. konl.iakcc, prvny bod, /obc'dinnr kon- Title: Variations of Bauarh iix point tluMirrin Author: Potr I'ost.a Do]>artim'iit.: Dopart.mont of iMa.lhonia.tica.l Analysis Suporvisor: prof. RNDr. Miroslav Ilvisck. DrSc. Su]>ervisor's c-niail addrcsw: Abstract: In the prosrnt \\ork wo study various consequences and generalizations of Bana.ch tixc-d point tlieor(nii. In...
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The New Use of the Courtyard in Brno-Královo Pole
Lukeš, Jaroslav ; Kramoliš, Milan (referee) ; Vojtová, Lea (advisor) ; Balíková, Jitka (advisor)
This thesis develops the original Architectural Design Studio I, which main task was interior adjustment of courtyard between the apartment blocks in Brno – Královo Pole, between the streets ‚Palackého třída‘ and ‚Kosmova‘. Nowadays there is a ground car park, smaller children’s playground and the converter station for DPMB (public transport company) used as a railway yard for tramcars in the past. Within the courtyard regeneration there was designed the reconstruction of the converter station and its transformation into sports centre, utilizable for broader neighbourhood. In the remaining part of the courtyard there will be built new underground car park which will allow to transform the courtyard into public park used mainly by residents from surrounded housing. This solution will result in increased housing quality in the area.
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