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On Selected Geometric Properties of Brownian Motion Paths
Honzl, Ondřej ; Rataj, Jan (advisor) ; Beneš, Viktor (referee) ; Mrkvička, Tomáš (referee)
Title: On Selected Geometric Properties of Brownian Motion Paths Author: Mgr. Ondřej Honzl E-mail Address: honzl@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Jan Rataj, CSc. E-mail Address: rataj@karlin.mff.cuni.cz Department: Mathematical Institute, Charles University Abstract: Our thesis is focused on certain geometric properties of Brownian motion paths. Firstly, it deals with cone points of Brownian motion in the plane and we show some connections between cone points and critical points of Brownian motion. The motivation of the study of critical points is provided by a pleasant behavior of the distance function outside of the set of these points. We prove the theorem on a non-existence of π+ cone points on fixed line. This statement leads us to the conjecture that there are only countably many critical points of the Brownian motion path in the plane. Next, the thesis discusses an asymptotic behavior of the surface area of r-neigh- bourhood of Brownian motion, which is called Wiener sausage. Using the proper- ties of a Kneser function, we prove the claim about the relation of the Minkowski content and S-content. As the consequence, we obtain a limit behavior of the surface area of the Wiener sausage almost surely in dimension d ≥ 3. Finally,...
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Mountain Pass Theorem and its applications
Příhoda, Vojtěch ; Černý, Robert (advisor) ; Vlasák, Václav (referee)
Cílem této práce je formulovat a dokázat Větu o horském sedle a ukázat příklady její aplikace tak, aby student třetího ročníku matematiky nebo fy- ziky, jenž absolvoval alespoň úvodní kurs funkcionální analýzy, byl schopen práci porozumět. D·kaz Věty o horském sedle provedeme s pomocí Ekelan- dova variačního principu, který si rovněž formulujeme a dokážeme. Následně si ukážeme dva příklady její aplikace na d·kaz existence netriviálního sla- bého řešení eliptické parciální diferenciální rovnice obsahující nelinearitu se subkritickým r·stem. 1
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Analysis of Critical Points in the Transportation of Hazardous Substances by Road
Fidrichová, Ivana ; Dostál, Ivo (referee) ; Adamec, Vladimír (advisor)
Diploma thesis focuses on the analysis of critical points in the transport of hazardous materials on the basis of which there is given a methodology for selecting safe routes. Thethesis includes statistical data on the total performance in the transport of hazardous materials within the EU states as well as specifies the proportion of transport performance of hazardous materials to the total performance among the individual European countries. For Czech Republic, the thesis also presents a statistical overview of the accident rate associated with this kind of transport as well as deals with the causes and consequences of the accidents occured during the transportation.
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Optimization of control system for hygiene in the selected service slaughter, cutting plant
JEŽKOVÁ, Irena
HACCP ( Hazard Analysis and Critical Control Points ) is a science-based system of food safety. This system identifies hazards and risks in food production and it proposes an effective control and monitoring procedures at points that are critical for food safety . In cases where e.g. measured values ( temperature, time) deviates from the set limits are performed specific corrective measures. Within this system of protection of food safety Two critical control points(CCP)were established in selected company and they have been set correctly . Two checkpoints (CP )in HACCP weren´t determined completely so newly designed and in five cases recommended modifications , including one designed to change the compliance time and once in imminent danger .
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"Atoms in molecules" (AIM) analysis of the Pt(II)-complexes
ŠVECOVÁ, Kristýna
AIM (Atoms in molecules) analysis of square planar trans-Pt[(NH3)2T(H2O)]n+ complexes (T = H2O, NH3, NO2-, OH-, F-, Cl-, Br-, SCN-, CN-, PH3, CO, CH3-, H-, C2H4) were performed. Electron density in critical points of the Pt-H2O bond correlates inversely proportionally with the length of this bond and with the occupation of 5d orbitals of the central platinum atom and proportionally with a total charge of the H2O ligand. The Pt-H2O bond can be supposed as a typical donor-acceptor bond. AIM analysis is a very useful method for a quantitative description of the strength of the trans-influence.
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European Policy Concerning Safety of Foods
HORÁKOVÁ, Martina
The theme of the bachelor thesis is the European policy concerning safety of foods. Its objective is to evaluate the importance of the food safety assurance for the European market and European consumers. The first part briefly summarizes the most important moments of history {--} from food sufficiency assurance for everyone to creation of elaborate system named {\clqq}from the Farm to the Fork`` which includes whole food and feed chain. This part also defines essential notions associated with given theme. Next parts involve food legislation and establishements which create legal enactments and control if these enactments are respected. The last section deals with the Rapid Alert System for Food and Feed and the Hazard Analysis Critical Control Points. Both of these systems are fundamental for assuring the consumers safety. The thesis faciliates to create the idea of current system complexity for food safety assurance.
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