Title: Sobolev-Type Spaces on Metric Measure Spaces Author: RNDr. Lukáš Malý Department: Department of Mathematical Analysis Supervisor: Prof. RNDr. Luboš Pick, CSc., DSc., Department of Mathematical Analysis Abstract: is thesis focuses on function spaces related to rst-order analysis in abstract metric measure spaces. In metric spaces, we can replace distributional gra- dients, whose de nition depends on the linear structure of Rn , by upper gradients that control the functions' behavior along all recti able curves. is gives rise to the so-called Newtonian spaces. e summability condition, considered in the thesis, is expressed using a general Banach function lattice quasi-norm and so an extensive framework is built. Sobolev-type spaces (mainly based on the Lp norm) on metric spaces, and Newtonian spaces in particular, have been under intensive study since the mid- s. Standard toolbox for the theory is set up in this general setting and Newto- nian spaces are proven complete. Summability of an upper gradient of a function is shown to guarantee the function's absolute continuity on almost all curves. Ex- istence of a unique minimal weak upper gradient is established. Regularization of Newtonian functions via Lipschitz truncations is discussed in doubling Poincaré spaces using weak boundedness of maximal...

The aim of this thesis is the state and the dynamics of indebtedness of territorial self-governing units in the Czech Republic to evaluate. The thesis has two parts - the theoretical part and the practical part. The important information about this issue are in the theoretical part. The information are drawn from the technical literature, the information of Ministry of Finance of the Czech Republic and the other sources. This part contains the tract on the returnable financial resources, the debt and its reporting, the causes of indebtedness, the problems, which the indebtedness of local governments will cause and the regulation of indebtedness of local governments. The practical part is divided into 5 parts - The analysis of debt of territorial self-governing units in relation to the public debt of the Czech Republic, The analysis of indebtedness of municipalities of the Czech Republic, The analysis of indebtedness of regions of the Czech Republic, The analysis of municipalities of the Czech Republic with higher measure of risk of municipal finance and The regulation of debt of local governments in the Czech Republic. For example it was discovered, that the public debt of the Czech Republic grow all the time, but the share of municipal debt and regional debt to the public debt is minimal. The municipal indebtedness of the Czech Republic has the growing trend. The municipalities use the credits often, the issue of municipal bonds and the approved returnable financial assistances. In 2012 the debt of municipalities with 5 000 and more inhabitants made up 73 per cent of total municipal debt. The regions has growing trend except 2010. The regions use the credits often and the approved returnable financial assistances. In 2011 and in 2012 the highest debt per 1 inhabitant had the Olomouc Region, the Karlovy Vary Region and the Pardubice Region. The Plzeň Region had the zero debt per 1 inhabitant. In category of municipalities with higher measure of risk of municipal finances was 47 municipalities from 6 244 monitored municipalities. The worst situation is in municipalities: Prameny, Turovice and Bublava.

This thesis investigates the impact of the fundamental news announcements on the movements of the stock indexes SAX, SaP500 and DJIA. The theoretical part of the thesis describe the basic structure and properties of these indexes. There are also presented theoretical and empirically validated relationships between different fundamental news and the indexes. These relationships are described based on the theory of efficient markets, technical, fundamental and psychological analysis. The practical part of the thesis analyze the impact of fundamental news (5 types - index SAX and 6 types- SaP500 and DJIA) 2005-2015. There is analyzed the impact of news announcements on the day of the notice and the day after the announcement. The result is there exist significant relationship between "surprise" value of inflation and interest rates news and indexes SaP500 and DJIA.

Title: Nonabsolutely convergent integrals Author: Krist'yna Kuncov'a Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Jan Mal'y, DrSc., Department of Mathematical Analysis Abstract: In this thesis we develop the theory of nonabsolutely convergent Hen- stock-Kurzweil type packing integrals in different spaces. In the framework of metric spaces we define the packing integral and the uniformly controlled inte- gral of a function with respect to metric distributions. Applying the theory to the notion of currents we then prove a generalization of the Stokes theorem. In Rn we introduce the packing R and R∗ integrals, which are defined as charges - additive functionals on sets of bounded variation. We provide comparison with miscellaneous types of integrals such as R and R∗ integral in Rn or MCα integral in R. On the real line we then study a scale of integrals based on the so called p-oscillation. We show that our indefinite integrals are a.e. approximately differ- entiable and we give comparison with other nonabsolutely convergent integrals. Keywords: Nonabsolutely convergent integrals, BV sets, Henstock-Kurzweil in- tegral, Divergence theorem, Analysis in metric measure spaces 1