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Recycling of asphalt mixtures with higher amount of RAP
Klimek, Matěj ; Koudelka, Tomáš (referee) ; Varaus, Michal (advisor)
The theoretical part of the diploma thesis recapitulates the existing literature in the field of recycling asphalt mixtures with a higher content of RAP (Reclaimed asphalt pavement). The practical part of the diploma thesis examines changes in the properties of asphalt mixtures with a higher content of RAP, due to changes in mixing time. Five mixtures have been proposed for this research. It is an asphalt mixture intended for the road abrasive layer (ACO 11+). Reference mixture "A" without RAP, with a standard mixing time of 25 seconds. Mixture "B" with 40% RAP, without rejuvenator, with an extended mixing time of 40 seconds. Mixture "C" with 40% RAP, with rejuvenator and standard mixing time. Mixture "D" with 40% RAP with rejuvenator and extended mixing time of 40 seconds. Mixture "E" with 40% RAP, with rejuvenator and extended mixing time of 55 seconds.
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Strong stationary times and convergence of Markov chains
Suk, Luboš ; Prokešová, Michaela (advisor) ; Kříž, Pavel (referee)
In this thesis we study the estimation of speed of convergence of Markov chains to their stacionary distributions. For that purpose we will use the method of strong stationary times. We focus on irreducible and aperiodic chains only since in that case the existence of exactly one stationary distribution is guaranteed. We introduce the mixing time for a Markov chain as the time needed for the marginal distribution of the chain to be sufficiently close to the stationary dis- tribution. The distance between two distributions is measured by the total variation distance. The main goal of this thesis is to construct an appropriate strong stationary time for selected chains and then use it for obtaining an upper bound for the mixing time.
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Recycling of asphalt mixtures with higher amount of RAP
Klimek, Matěj ; Koudelka, Tomáš (referee) ; Varaus, Michal (advisor)
The theoretical part of the diploma thesis recapitulates the existing literature in the field of recycling asphalt mixtures with a higher content of RAP (Reclaimed asphalt pavement). The practical part of the diploma thesis examines changes in the properties of asphalt mixtures with a higher content of RAP, due to changes in mixing time. Five mixtures have been proposed for this research. It is an asphalt mixture intended for the road abrasive layer (ACO 11+). Reference mixture "A" without RAP, with a standard mixing time of 25 seconds. Mixture "B" with 40% RAP, without rejuvenator, with an extended mixing time of 40 seconds. Mixture "C" with 40% RAP, with rejuvenator and standard mixing time. Mixture "D" with 40% RAP with rejuvenator and extended mixing time of 40 seconds. Mixture "E" with 40% RAP, with rejuvenator and extended mixing time of 55 seconds.
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Random walks on networks and mixing of Markov chains
Gemrotová, Kateřina ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
The thesis presents the study of deriving upper bounds of the speed of convergence of reversible Markov chains with discrete time and discrete finite space state to their stationary distributions. We express the derived upper bound in terms of several variables and we make use of the theory of electrical networks, which will help us to represent random walks on a graph. The result of this thesis will be simply obtainable upper bound of mixing time of random walks on connected graphs with an arbitrary number of vertices and edges. Partial results will be demonstrated on simple examples and counterexamples. 1
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Strong stationary times and convergence of Markov chains
Suk, Luboš ; Prokešová, Michaela (advisor) ; Kříž, Pavel (referee)
In this thesis we study the estimation of speed of convergence of Markov chains to their stacionary distributions. For that purpose we will use the method of strong stationary times. We focus on irreducible and aperiodic chains only since in that case the existence of exactly one stationary distribution is guaranteed. We introduce the mixing time for a Markov chain as the time needed for the marginal distribution of the chain to be sufficiently close to the stationary dis- tribution. The distance between two distributions is measured by the total variation distance. The main goal of this thesis is to construct an appropriate strong stationary time for selected chains and then use it for obtaining an upper bound for the mixing time.
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