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Polynomial time primality testing
Bednaříková, Alžběta ; Žemlička, Jan (advisor) ; Čech, Martin (referee)
The topic of my thesis is the testing of prime numbers in polynomial time. The text focuses on the specific algorithm published in 2002 by Manindra Agrawal, Neeraj Kayal and Nitin Saxena and it is known as the AKS primality test. In the introduction of this work, important properties and concepts essential for the text understanding are revised. Then the basic idea of the test is explained. The description of the algorithm itself continues. The aim of the work is to prove the Theorem on the correctness of the AKS test from a gradually built-up theory and to calculate the time complexity of the algorithm. Finally, it is proved that the calculated time complexity is polynomial.
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Reasons and consequences of round goby (Neogobius melanostomus) invasion into the inland waters of Europe and North America
Starý, Vojtěch ; Čech, Martin (advisor) ; Vukićová, Jasna (referee)
Since the end of 1980s there is an ongoing massive invasion of fish from the family Gobiidae. The most widespread and aggressive of these fish is round goby (Neogobius melanostomus). Its natural habitat is area around Black and Caspian Seas, but nowadays it is already common in most of the European rivers, Baltic Sea and in the system of the North American Great Lakes. The main reason of the spreading is transport of ballast water from its natural habitat. The success of its invasion is due to the high tolerance to various factors like temperature, salinity, amount of oxygen in water, food sources and bottom substrates. Presence of the round goby in newly invaded rivers is beneficial for fish-eating predators. On the other hand competitors are highly disadvantaged as they lose in the fight with round goby over food, shelters and places for spawning and therefore, they are forced to live in less suitable habitats which leads to the decrease of their abundance. In recently colonized areas the round goby has much higher abundance than in its original habitats. The highest abundance is in the North America, where the round goby is causing the most noticeable change in the ecosystem. For this reason it is extensively studied mainly in the North America. Keywords: Gobiidae, Neogobius melanostomus,...
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The effect of barriers on riverine fish communities
Kofentová, Nikola ; Horká, Petra (advisor) ; Čech, Martin (referee)
The construction of river obstacles is considered one of the major threat to freshwater ecosystems worldwide, with a greater impact upon riverine fish than any other human activity. River obstacles, especially dams and weirs, affect the natural environment in streams and rivers, causing changes in physical, chemical and biological processes and disrupting connectivity of rivers via alternating series of lotic and lentic reaches. The effect of obstacles is further magnified by associated habitat alterations like are channelization, flow regulation, fortification and deepening of a riverbed. Orga- nisms and especially fish that live in rivers are highly sensitive to these changes, which affects them at the level of individuals, species and the whole populations. The most pronounced is the barrier-effect to upstream and downstream migration and loss of habitats. Diadromous and rheophilic species of fish are the most sensitive ones as they have complex migration strategies and habitat requirements. Fish are further affected by obstacles via many other mechanisms, such as the effect on reproduction success, growth and development, changes in the composition and trophic structure of communities and restricted response to further environmental constraints including water pollution or predicted climate...
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European catfish (Silurus glanis, Linneus 1758): Is the global warming the main reason of increasing of catches of the largest freshwater predator in Europe?
Bakeš, Michal ; Čech, Martin (advisor) ; Černý, Martin (referee)
European catfish (Silurus glanis, Linneus 1758) is our only fish which amount of catch is growing in our country in the last thirty years. The main goal of my work is to find out if global warming is essential for increasing catch of catfish, or whether rising temperatures are marginal, and the main reason is growing focus of fishermen on catfish. This thesis summarized knowledge about effect of global warming on ecosystems mainly on freshwater bodies that seem to be the most influenceable among terrestric ones. The enlarging populations of catfish in countries of south Europe (e.g. Spain, Italy) where catfish was recently introduced can be explained by the fact that warm water is suitable for catfish. However, some socioeconomic studies carried out in the Czech Republic as well as abroad clearly demonstrate that popularity of catching of catfish increases in time. I verified this idea by the results of my questionnaire survey, where 82 % of respondents approved that the popularity of catfish among fishermen is highest in the last decade. Based on the evidence we can say that increasing temperatures has a positive effect on the metapopulation of catfish in the Czech Republic, but this influence seems to be marginal. The main reason for still increasing catch is very likely the change of preferences...
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The role of fish-eating predators and socio-economic trends in recreational fishing
Lyach, Roman ; Čech, Martin (advisor) ; Adámek, Zdeněk (referee) ; Jurajda, Pavel (referee)
Recreational fishing is a very important leisure activity and one of the most important ways how humans influence freshwater habitats and wild fish populations. Both fish-eating predators and socio-economic trends play a major role in recreational fishing. This thesis found that the Eurasian otter feeds mainly of small (5-10 g) and very abundant fish species of low angling value. In this case, gudgeon Gobio gobio dominated in the otter diet. The overlap between catches of otters and anglers was very low, and commercially important salmonids made up only 10 % of the otter diet by biomass. Cormorants also prey mostly on smaller (10-100 g) a very abundant fish species. In this case, roach Rutilus rutilus dominated in the cormorant diet. The overlap between catches of cormorants and anglers was also quite low. Commercially important fish species made up less than 10 % of the cormorant diet. Even though cormorants consume mostly smaller fish, they are potentially removing fish that serve as prey for piscivores, and they are also removing smaller fish that would grow into angling size. The Atlantic salmon Salmo salar reintroduction programme has not yet been successful. However, cormorant predation is not the main reason for its low success. The main problem is somewhere on the lower River Elbe in...
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Information system for a company making parts of transportation devices
Čech, Martin ; Kofroň, Jan (advisor) ; Šerý, Ondřej (referee)
In this work we propose a specific implementation of an information system for small and middle-sized companies. Its purpose is to manage data about employees, partner institutions (both providers and customers), purchase orders and products themselves. The application consists of three parts: a database layer, application server, and client program. In addition, it focuses on the products management, division into elementary components and production processes. Another significant part is documentation of workers' production, which enables supervising the process evolution and also generation of salaries. In this work we focus especially on solution of each program part and communication among them. Powered by TCPDF (www.tcpdf.org)
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Pretentious approach to analytic number theory
Čech, Martin ; Kala, Vítězslav (advisor) ; Hančl, Jaroslav (referee)
The goal of this thesis is to present the pretentious approach to analytic number theory recently developed by Granville, Soundararajan, and others. In the first four chapters, we show the classical proof of the prime number theo- rem. We then develop the pretentious approach, explain its differences, advan- tages, and disadvantages and present another proof of the prime number theorem based on Hal'asz's theorem. This theorem is then proven using new techniques of Granville, Harper, and Soundararajan, which are substantially easier than the previous proofs. In the last chapter, we show how pretentious techniques can be used to obtain more intuitive proofs of other classical theorems or obtain new results. 1
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Ice Hockey Stadium
Čech, Martin ; Barnat, Jan (referee) ; Pilgr, Milan (advisor)
Work deals with variant design of steel structure of ice hockey stadium located in Opava. It is a three-aisled hall with shape consists of intersection of ellipse and rectangle with dimensions 70 x 82m. The roof has cylindrical shape with approx. 50 m radius. The building is about 14 m high. Object is divided to three parts – main aisle and two side aisles. The main aisle contains of a rectangle of dimensions 40 x 42 m and two semicircles of radius approx. 20 m. Frames of main aisle are made of arc roof truss connected to steel plate columns. The side aisles with rectangular shape with dimensions 15 x 42 m are connected to main aisle. The structure of side aisle is made of a sloped roof truss. Longitudinal bracing and cross bracing are used to obtain spatial rigidity of the structure. Roof and wall cladding is made of Kingspan sandwich panels.
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The Sexual Segregation of fish from family Cyprinidae in the Řimov Reservoir
Žák, Jakub ; Prchalová, Marie (advisor) ; Čech, Martin (referee)
The sexual segregation, defined as different use of space by sexes is widespread phenomenon in the animal tree of life. As a result of segregation there is a different use of resources such as habitat, prey items or different threat by predation. Nevertheless it is not well studied in fish taxa except in marine environment. The common and widespread freshwater species such as a bream (Abramis brama), a bleak (Alburnus alburnus) and a roach (Rutilus rutilus) so far have not never been studied from the perspective of sexual segregation too. This thesis aims to examine the sexual segregation of these species and to test premises of sexual segregation such as sexual size dimorphism, age composition and differences in food. Afterwards the different space use of sexes in the Římov reservoir was tested. The gillnet sampling was used to collect data. Gillnets were installed to four localities in longitudinal gradient of reservoir in epilimnion where is the highest abundance of fish. Sampling was performed in August from 2009 to 2016. Results of this thesis show that females and males have different life histories and that bleak and roach are significantly bigger and older than males. The size dimorphism in bream was confirmed but not age difference between sexes. Sexes of bream had different diet. Males...
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Importance and species composition of non-fish prey in the diet of fish-eating predators
Mach, Jakub ; Čech, Martin (advisor) ; Vejřík, Lukáš (referee)
Piscivorous birds are usually considered to be exclusive fish eaters which are responsible for signifiant numerical and economical losses to fish populations. With a method of literary research the importace and species composition of non-fish prey is determine in the diet of selected fifteen species of piscivorous birds. The aim of this work is to determine the extent of non-fish part of the diet of particular piscivorous predators and categorize them on the grounds of differences between size of this part in their diet. Another goal is to determine any effects which can influence amount and species composition of non-fish part of nourishment, and also factors, which can influence obtained results based on the chosen method of analysis. According to the data found, diet of five bird species was composed almost exclusively with fish. Eight other bird species also showed preference for fish prey, but in most of these cases was present also important part of non-fish prey. Two bird species seems to be very oportunistic in case of composition their diet. As factors that can affect the extent of non-fish part in the diet was established especially the prey availability in environment, used method for diet composition analysis, insufficient attention for parts of prey other than fish, or also less...
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