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Variations of Banach fix point theorem
Pošta, Petr ; Hušek, Miroslav (advisor) ; Lukeš, Jaroslav (referee)
\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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Solved Problems in Electromagnetism for Electronic Collection
Pošta, Petr ; Koupilová, Zdeňka (advisor) ; Ledvinka, Tomáš (referee)
This thesis is a follow-up to several bachelor and diploma theses which were dedicated to creating solved problems for Electronic Collection of Solved Problems in Electromagnetism. The first goal of this thesis was to make a short survey about electronic resources in electromagnetism, especially those which contain solved problems and provide open access to their contents. The second goal was to make a small collection of solved problems in this area which would be suitable for undergraduate students and which would fill in chapters with little amount of problems in the Electronic Collection. This Electronic Collection is openly accesible on the website of Department of Physics Education. Total of 30 solved problems have been made in this thesis, including hints, detailed solutions and suitable pictures. Methodical comments are also available for almost all problems.
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Baire and Harmonic Functions
Pošta, Petr ; Lukeš, Jaroslav (advisor)
Title: Baire and Harmonic Functions Author: Petr Pošta Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Jaroslav Lukeš, DrSc., Department of Mathematical Analysis Abstract: The present thesis consists of six research papers. The first four articles deal with topics related to potential theory, Baire-one functions and its important subclasses, in particular differences of semicontinuous functions. The first paper is devoted to the stability of the Dirichlet problem for which a new criterion in terms of Poisson equation is provided. The second paper improves the recent result obtained by Lukeš et al. It shows that the classical Dirichlet solution belongs to the B1/2 subclass of Baire-one functions. A generalization of this result to the abstract context of the Choquet theory on functions spaces is provided. Finally, an abstract Dirichlet problem for the boundary condition belonging to the class of differences of semincontinuous functions is discussed. The third paper concentrates on the Lusin-Menshov property and the approximation of Baire- one and finely continuous functions by differences of semicontinuous and finely continuous functions. It provides an exposition of topologies (various density topologies as well as the fine topologies in both linear and non-linear potential...
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Baire and Harmonic Functions
Pošta, Petr ; Lukeš, Jaroslav (advisor)
Title: Baire and Harmonic Functions Author: Petr Pošta Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Jaroslav Lukeš, DrSc., Department of Mathematical Analysis Abstract: The present thesis consists of six research papers. The first four articles deal with topics related to potential theory, Baire-one functions and its important subclasses, in particular differences of semicontinuous functions. The first paper is devoted to the stability of the Dirichlet problem for which a new criterion in terms of Poisson equation is provided. The second paper improves the recent result obtained by Lukeš et al. It shows that the classical Dirichlet solution belongs to the B1/2 subclass of Baire-one functions. A generalization of this result to the abstract context of the Choquet theory on functions spaces is provided. Finally, an abstract Dirichlet problem for the boundary condition belonging to the class of differences of semincontinuous functions is discussed. The third paper concentrates on the Lusin-Menshov property and the approximation of Baire- one and finely continuous functions by differences of semicontinuous and finely continuous functions. It provides an exposition of topologies (various density topologies as well as the fine topologies in both linear and non-linear potential...
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Baire and Harmonic Functions
Pošta, Petr ; Lukeš, Jaroslav (advisor) ; Benyaiche, Allami (referee) ; Netuka, Ivan (referee)
Title: Baire and Harmonic Functions Author: Petr Pošta Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Jaroslav Lukeš, DrSc., Department of Mathematical Analysis Abstract: The present thesis consists of six research papers. The first four articles deal with topics related to potential theory, Baire-one functions and its important subclasses, in particular differences of semicontinuous functions. The first paper is devoted to the stability of the Dirichlet problem for which a new criterion in terms of Poisson equation is provided. The second paper improves the recent result obtained by Lukeš et al. It shows that the classical Dirichlet solution belongs to the B1/2 subclass of Baire-one functions. A generalization of this result to the abstract context of the Choquet theory on functions spaces is provided. Finally, an abstract Dirichlet problem for the boundary condition belonging to the class of differences of semincontinuous functions is discussed. The third paper concentrates on the Lusin-Menshov property and the approximation of Baire- one and finely continuous functions by differences of semicontinuous and finely continuous functions. It provides an exposition of topologies (various density topologies as well as the fine topologies in both linear and non-linear potential...
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Solved Problems in Electromagnetism for Electronic Collection
Pošta, Petr ; Koupilová, Zdeňka (advisor) ; Ledvinka, Tomáš (referee)
This thesis is a follow-up to several bachelor and diploma theses which were dedicated to creating solved problems for Electronic Collection of Solved Problems in Electromagnetism. The first goal of this thesis was to make a short survey about electronic resources in electromagnetism, especially those which contain solved problems and provide open access to their contents. The second goal was to make a small collection of solved problems in this area which would be suitable for undergraduate students and which would fill in chapters with little amount of problems in the Electronic Collection. This Electronic Collection is openly accesible on the website of Department of Physics Education. Total of 30 solved problems have been made in this thesis, including hints, detailed solutions and suitable pictures. Methodical comments are also available for almost all problems.
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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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