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Extremal points of convex sets and applications
Zitko, Martin ; Lukeš, Jaroslav (advisor) ; Veselý, Jiří (referee)
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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Ecological factors influencing variability of ultraviolet colouration of flowers
Zitko, Martin ; Kleisner, Karel (advisor) ; Neustupa, Jiří (referee)
Ultraviolet colouration of flowers varies both among and within species. The significance of these patterns and differences among them was usually associated with a visual per- ception of pollinators. In this study we examine the variation of marsh marigold's (Caltha palustris) bull's-eye pattern on a basis of 289 observed individuals from 32 distinct locati- ons. The variation of this pattern is shown to be quite large within separate locations and the pattern is predictably changing according to latitude. This trend of darker colouration towards the equator is an another example of a more widely understood Gloger's rule in the plant kingdom. The effect of ultraviolet radiation appears to be one of the most likely causes of this phenomenon. Hereafter we analyse the weakness of this explanation, the gaps in current knowledge and propose possible directions of further research. Keywords: ultraviolet, bull's-eye, marsh marigold, Caltha palustris, Gloger's rule
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Ecological factors influencing variability of ultraviolet colouration of flowers
Zitko, Martin ; Kleisner, Karel (advisor) ; Neustupa, Jiří (referee)
Ultraviolet colouration of flowers varies both among and within species. The significance of these patterns and differences among them was usually associated with a visual per- ception of pollinators. In this study we examine the variation of marsh marigold's (Caltha palustris) bull's-eye pattern on a basis of 289 observed individuals from 32 distinct locati- ons. The variation of this pattern is shown to be quite large within separate locations and the pattern is predictably changing according to latitude. This trend of darker colouration towards the equator is an another example of a more widely understood Gloger's rule in the plant kingdom. The effect of ultraviolet radiation appears to be one of the most likely causes of this phenomenon. Hereafter we analyse the weakness of this explanation, the gaps in current knowledge and propose possible directions of further research. Keywords: ultraviolet, bull's-eye, marsh marigold, Caltha palustris, Gloger's rule
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Ultraviolet patterns in flowers and their significance as a signal to pollinators
Zitko, Martin ; Pecháček, Pavel (advisor) ; Janeček, Štěpán (referee)
Various animals are sensitive to ultraviolet light and many angiosperms make use of this ability to communicate with their pollinators. Therefore plants often dis- play patterns on their flowers and inflorescences visible only in ultraviolet light. The origin of these patterns is both pigment-based and structural-based, resulting in UV absorbing or UV reflecting flower. The main goal of this thesis is to give a summary of ultraviolet light as well as explore how plants produce ultraviolet pat- terns and present their actual appearance. I also pay attention to the characteristics of pollinators' vision with emphasis on ultraviolet light, and to the biological signifi- cance of ultraviolet flower signals for the pollinators. Gaps in knowledge are implied as well. The result of the thesis shows that ultraviolet light has an unquestionable significance in the relationship of angiosperms and their pollinators. It also shows a coevolution of ultraviolet patterns and pollinators' preferences for them. Keywords: ultraviolet, flower pattern, bull's eye, signalisation, pollinator
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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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