
Some results in convexity and in Banach space theory
Kraus, Michal ; Lukeš, Jaroslav (advisor) ; Kalenda, Ondřej (referee) ; Smith, Richard (referee)
This thesis consists of four research papers. In the first paper we construct nonmetrizable compact convex sets with pathological sets of simpliciality, show ing that the properties of the set of simpliciality known in the metrizable case do not hold without the assumption of metrizability. In the second paper we construct an example concerning remotal sets, answering thus a question of Martín and Rao, and present a new proof of the fact that in every infinite dimensional Banach space there exists a closed convex bounded set which is not remotal. The third paper is a study of the relations between polynomials on Banach spaces and linear identities. We investigate under which conditions a linear identity is satisfied only by polynomials, and describe the space of poly nomials satisfying such linear identity. In the last paper we study the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper MatuszewskaOrlicz indices. 1

 

Integral representation theorems in noncompact cases
Kraus, Michal ; Lukeš, Jaroslav (advisor) ; Malý, Jan (referee)
Classical Choquet's theory deals with compact convex subsets of locally convex spaces. This thesis discuss some aspects of generalization of Choquet's theory for a broader class of sets, for example those which are assumed to be only closed and bounded instead of compact. Because Radon measures are usually defined for locally compact topological spaces, and this is not the case of the closed unit ball in a Banach space of infinite dimension, there are used the so called Baire measures in this setting. This thesis particularly deals with the question of existence of resultants of these measures, with the properties of the resultant map, with the analogy of Bauer's characterization of extreme points and with some other concepts known from compact theory. By using some examples we show that many of these theorems doesn't hold in noncompact setting. We also mention forms of these theorems which can be proved.


The role of mitochondrial complex II in cancer cell biology
Kraus, Michal ; Neužil, Jiří (advisor) ; Kašpárek, Petr (referee)
Mitochondria are essential organelles for most eukaryotic cells, containing intricate networks of numerous proteins. These include, among others, complexes IIV of the electron transport chain. Being at the crossroads of the tricarboxylic acid cycle and the respiratory chain, mitochondrial complex II plays a key role in cellular metabolism. The protein complex, also known as succinate dehydrogenase, is capable of not only succinate oxidation and electron transfer but also contributes to the production of reactive oxygen species. Mitochondrial complex II consists of four subunits, SDHAD, and four dedicated protein assembly factors SDHAF14 that participate in complex II biogenesis. Mutations and epigenetic modulations of genes coding for succinate dehydrogenase subunits or assembly factors are associated with pathological conditions such as neurodegenerative diseases, or may result in tumor formation. However, inborn complexIIlinked mitochondrial pathologies are rather understudied, compared to diseases with causative errors of other mitochondrial complexes, presumably due to the fact that none of complex II subunits is encoded in the mitochondrial genome. Recent studies have shown that impairment of mitochondrial complex II function or assembly leads to accumulation of alternative assembly forms...


Frequency Responses
Urbánek, Radim ; Kraus, Michal (referee) ; Kunovský, Jiří (advisor)
The aim of this MSc Thesis is to create a system for automatic generation of frequency characteristics of electrical circuits. These circuits are described by differential equations. A special simulator of RLC circuit has been created and frequence response, vector diagram can be generated. This system has been mainly suggested for application in education. The process of solving differential equations is based on the Taylor method. Systems in general is the theoretical part of this project. Different definitions of systems their divission ,basic phenomenons and mathematical devices are described there. Next chapter deals with the mathematical devices for solving differential equations which makes the basis for description of phenomenons in these systems. There are also systems TKSL and TKSL/C. In the next chapter I was investigaty the analyze of vector diagrams for simple and more difficult circuits. I have found a solution for actual circuit by this technique. The last chapter is devoted to the frequency characteristics and descriptions of simulation program for generation the frequency characteristics.


Advances in chemotherapy and novel antitumor drugs
Kraus, Michal ; Kovář, Marek (advisor) ; Koudelková, Lenka (referee)
Cancer is among the leading causes of death worldwide. While some types of cancer became almost entirely curable, majority of malignant tumors are still potentially deadly diseases due to unsensitivity of tumors to conventional chemotherapy or diversity of cancer cells within the tumor and subsequent development of resistance. The underlying mechanism of action of conventional antitumor drugs is mostly related to cell division. DNA damage, inhibition of DNA synthesis and repair or disrupted formation of mitotic spindle are the most common mechanisms. However, it implies that most of the drugs are cytotoxic for rapidly dividing cells in general which results in variety of undesirable side effects for patients. Search for novel anticancer drugs targeting cancer cells more selectively has been point of interest of researchers for decades. Hundreds of new potential anticancer drugs are being described every year, some posessing so far unrecognized mechanisms of action. Process called drug repurposing examines drugs that have already been approved for clinical use in other than oncology field and results into discovering of interesting "novel" anticancer agents. Another general trend is represented by shift towards development of targeted therapy which is slowly replacing traditional cytotoxic...


Some results in convexity and in Banach space theory
Kraus, Michal ; Lukeš, Jaroslav (advisor) ; Kalenda, Ondřej (referee) ; Smith, Richard (referee)
This thesis consists of four research papers. In the first paper we construct nonmetrizable compact convex sets with pathological sets of simpliciality, show ing that the properties of the set of simpliciality known in the metrizable case do not hold without the assumption of metrizability. In the second paper we construct an example concerning remotal sets, answering thus a question of Martín and Rao, and present a new proof of the fact that in every infinite dimensional Banach space there exists a closed convex bounded set which is not remotal. The third paper is a study of the relations between polynomials on Banach spaces and linear identities. We investigate under which conditions a linear identity is satisfied only by polynomials, and describe the space of poly nomials satisfying such linear identity. In the last paper we study the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper MatuszewskaOrlicz indices. 1


Integral representation theorems in noncompact cases
Kraus, Michal ; Malý, Jan (referee) ; Lukeš, Jaroslav (advisor)
Classical Choquet's theory deals with compact convex subsets of locally convex spaces. This thesis discuss some aspects of generalization of Choquet's theory for a broader class of sets, for example those which are assumed to be only closed and bounded instead of compact. Because Radon measures are usually defined for locally compact topological spaces, and this is not the case of the closed unit ball in a Banach space of infinite dimension, there are used the so called Baire measures in this setting. This thesis particularly deals with the question of existence of resultants of these measures, with the properties of the resultant map, with the analogy of Bauer's characterization of extreme points and with some other concepts known from compact theory. By using some examples we show that many of these theorems doesn't hold in noncompact setting. We also mention forms of these theorems which can be proved.

 

Parallel Computer Systems Based on Numerical Integrations
Kraus, Michal ; Kubátová, Hana (referee) ; Kollár,, Ján (referee) ; Kunovský, Jiří (advisor)
This thesis deals with continuous system simulation. The systems can be described by system of differential equations or block diagram. Differential equations are usually solved by numerical methods that are integrated into simulation software such as Matlab, Maple or TKSL. Taylor series method has been used for numerical solutions of differential equations. The presented method has been proved to be both very accurate and fast and also procesed in parallel systems. The aim of the thesis is to design, implement and compare a few versions of the parallel system.
