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Ideals of Banach Spaces
Smetana, Ondřej ; Cúth, Marek (advisor) ; Rmoutil, Martin (referee)
We study a particular class of subspaces of Banach spaces called ideals. We show that the notions of ideals, locally complemented subspaces, and the existence of a Hahn-Banach extension operator coincide. We introduce and develop the method of suitable models, a set-theoretic approach which enables us to write technical proofs in simpler terms. We use the method to prove the existence of an almost isometric ideal. We present applications of almost isometric ideals and the method to the strong and local diameter two properties, and the Daugavet property.
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Control of lateral root development in response to availability of principal mineral nutrients.
Halamková, Daniela ; Tylová, Edita (advisor) ; Smetana, Ondřej (referee)
Lateral roots are, due to their large absorption surface, a part of the root system with significant importance for the plant's ingestion of water and nutrients. Their development depends on heterogeneity of soil environment, which enables the plant to optimize the acquisition of resources under current conditions. The availability of mineral nutrients (type of nutrient, form, distribution in soil and mobility) is one of key factors that determine root system morphogenesis. Another important aspect is the amount of nutrient in the plant; in other words, the plant's current demand for the element. The most important nutrients that influence the architecture of the root system are two macroelements - nitrogen and phosphorus. Both of these elements trigger positive and negative effects on the development of lateral roots. Nitrate, important source of nitrogen, induces two entirely different regulatory mechanisms of lateral root development. Under nitrogen limiting condition, a local stimulation of lateral root elongation is triggered in nitrate-rich patches. This response integrates the signalling pathways of auxin and nitrate. In contrast, high and homogenous availability of nitrate in rhizosphere (≥ 10 mM) causes inhibition of lateral root growth. This systemic inhibitory effect was similarly...
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Time optimal heating problem
Smetana, Ondřej ; Pražák, Dalibor (advisor) ; Kaplický, Petr (referee)
What is the most efficient way to control temperature in a building, which is heated to some value, and which will be abandoned for a certain period? We use ordinary differential equations and theory of control to mathematically describe the problem. We study two models describing change of the tempe- rature. Using Pontryagin Maximum Principle, we find optimal controls. We compare the two models and conduct numerical simulations.
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Control of lateral root development in response to availability of principal mineral nutrients.
Halamková, Daniela ; Tylová, Edita (advisor) ; Smetana, Ondřej (referee)
Lateral roots are, due to their large absorption surface, a part of the root system with significant importance for the plant's ingestion of water and nutrients. Their development depends on heterogeneity of soil environment, which enables the plant to optimize the acquisition of resources under current conditions. The availability of mineral nutrients (type of nutrient, form, distribution in soil and mobility) is one of key factors that determine root system morphogenesis. Another important aspect is the amount of nutrient in the plant; in other words, the plant's current demand for the element. The most important nutrients that influence the architecture of the root system are two macroelements - nitrogen and phosphorus. Both of these elements trigger positive and negative effects on the development of lateral roots. Nitrate, important source of nitrogen, induces two entirely different regulatory mechanisms of lateral root development. Under nitrogen limiting condition, a local stimulation of lateral root elongation is triggered in nitrate-rich patches. This response integrates the signalling pathways of auxin and nitrate. In contrast, high and homogenous availability of nitrate in rhizosphere (≥ 10 mM) causes inhibition of lateral root growth. This systemic inhibitory effect was similarly...
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Molecular and cellular aspects of programmed cell death in response to genotoxics in plants
Smetana, Ondřej ; Opatrný, Zdeněk (advisor) ; Havel, Ladislav (referee) ; Reichheld, Jean-Philippe (referee)
In multicellular organisms, programmed cell death (PCD) is an essential mechanism during development, morphogenesis and during the interaction with the environment. The regulation of PCD is highly regulated and conserved throughout the evolution. Animal apoptosis is the best described PCD type which is characterized by the condensation of cytoplasm, specific DNA fragmentation and the formation of apoptotic bodies which are finally engulfed by neighboring cells. Due to the structural specificities of plant cells, plant PCD exhibits rather autophagic character. In mammals, DSBs-induced PCD is mainly governed by ATM kinase. This response also involves downstream ATM effectors like p53 and E2F factors. P53 stabilization leads to the cell cycle arrest in G1/S whereas E2F can promote apoptosis by activating PCD-related genes including caspases. PCD could be induced also by E2F ectopic expression. In spite of a conservation of PCD signaling among Eukaryotes, number of animal PCD regulators was not identified in plants (caspases, p53), thus in plants the PCD response induced by DSBs is still poorly understood. On the contrary, E2F transcriptional factor is conserved between animals and plants but its role during plant PCD was not evaluated till now. The main goal of my thesis was to characterize the PCD in...
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Searching in the deep web
Smetana, Ondřej ; Pavlíček, Luboš (advisor) ; Žid, Norbert (referee)
The bachelor thesis deals with the deep web, i.e. pages not indexed by the search engines and therefore not searched, and searching in it. In the theoretical part, the deep web is analyzed and its features and tools that can be used to searching in it are described. In the practical section the selected tool are used and the difference in the search results using common search engines and metasearch engines is shown.
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