|
|
Some topics of topological measure theory with application in stochastic analysis
Kříž, Pavel ; Beneš, Viktor (advisor) ; Riečan, Beloslav (referee) ; Seidler, Jan (referee)
Title: Some topics of topological measure theory with application in stochastic analysis Author: Pavel Kříž Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Josef Štěpán, DrSc., Department of Probability and Mathematical Statistics Abstract: This work studies identifications of values of probability limits based on trajectories of convergent (random) sequences. The key concept is the so called Probability Limit Identification Function (PLIF). The main concern is focused on the existence of PLIFs, mainly those, which are measurable and adapted. We also study in more detail special cases, when the convergence in probability and the convergence almost surely coincide. Furthermore, possible applications of the PLIF concept in stochastic analysis (path-wise representations of stochastic integrals and weak solutions of the stochastic differential equations), as well as in estimation theory (the existence of strongly consistent estimators) are outlined. The achieved results are based on analyses of the topologies on spaces of measures, spaces of random variables and spaces of real-valued functions. Keywords: Probability Limit, Identification, Almost-sure Convergence 1
|
|
|
Fractional Brownian motion
Rubín, Tomáš ; Maslowski, Bohdan (advisor) ; Kříž, Pavel (referee)
Fractional Brownian motion is a nontrivial generalization of standard Brownian motion (Wie- ner process). Definition leaves independence of increments, whereas dependence is controlled by the Hurst index. This paper deals with proofs of fractional Brownian motion's properties such as correlation of increments, selfsimilarity, long-range dependence and analytical pro- perties of its paths, i.e. Hölder continuity and nondifferentiability. Furthermore, the proof of the theorem about nondifferentiability is presented in a stronger form than it is usual in published papers about fractional Brownian motion. Further topics are simulations of the process's paths, suitable even for general Gaussian processes, and point estimators of the Hurst index. 1
|
|
|
System to support decision making in dental implantology - quality of life of patients with dental implants
Kříž, Pavel ; Dostálová, Taťjána (advisor) ; Mazánek, Jiří (referee) ; Zvárová, Jana (referee)
Title: System to support decission making in dental implantology - quality of life of patients with dental implants Author: MUDr. Pavel Kříž Department: Paediatric Stomatology of 2nd Medical School and Faculty Hospital Motol, V Úvalu 84, 150 06 Prague 5 Supervisor: Prof. MUDr. Taťjana Dostálová, DrSc., MBA Supervisor's e-mail: tatjana.dostalova@fnmotol.cz Dental implants are the method of choice in the treatment of missing tooth/teeth replacement. Implant therapy must be preceded by a detailed examination and the overall treatment plan. As an aid for decision-making for dentists was created decision-making scheme, which gradually, logically and schematically guides the dentists in this particular situation. Health is closely related to the quality of life. Our work evaluates the oral health-related quality of life (OHRQoL) of patients with dental implants. The aim of our study was to determine whether treatment with a dental implant(s) improve(s) OHRQoL. We created a questionnaire to determine the quality of life before and after implantation. In our study, we evaluated only patients who were treated by the only one implantological system to eliminate the influence of other systems on the quality of the results of the study; we evaluated a total of 297 implants. It was assessed a total of 97...
|
|
|
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.
|
|
|
The police provocation in the light of court of general nature findings, Institutional court, European court for human rights with the focus on the right for the fair trial
Kříž, Pavel ; Herczeg, Jiří (advisor) ; Zeman, Pavel (referee)
The abstrakt "The police provocation in the light of court of general nature findings, Institutional court, European court for human rights with the focus on the right for the fair trial" The connection of the criminal law with the democracy is firstly about guarancy of the space of one to the other. In this connection the criminal law never intervenes into the social, political and economic life to see different purpose than the protection against the crime. The subjective rights must form the basis of each legal state and in each democratic legal code, the elementary human and civil rights have to have the exceptional place. This piece of work is focused on the one of the fundamental civil rights within the meaning of Convention of the civil rights and fundamental liberties protection, which is the right for the fair trial considering the police provocation. Human and civil rights have the borders not only in the criminal-law level. Hence one of the function of the criminal law is to set these borders in this level. The setting of the borders in the precise way are the guarantee of the civil rights and liberties. Regarding the chosen topic of my work, I am trying to define these bordrers.
|
|
| |
|
|
The identification function for the convergence in probability with an application in the estimation theory
Kříž, Pavel ; Hlubinka, Daniel (referee) ; Štěpán, Josef (advisor)
In the present work we introduce the concept of probability limit identification function (PLIF) as it is done in [6]. This function identifies almost surely the value of the probability limit of a sequence of random variables on the basis of one realization of the sequence. According to the same article we show the construction of PLIF for real valued random variables from the special PLIF for 0-1 valued random variables. Following the method described in [8] we prove the existence of the universal PLIF for real valued random variables under the continuum hypothesis. Next we show that there are no borel measurable special PLIFs for 0-1 valued random variables (as well as PLIFs for real valued random variables). We use the proof that is published in [2]. Then we extend the construction of PLIF from R to any separable metrizable topological space. This PLIF may be used e.g. for creating functional representations of stochastic integrals and weak solutions of stochastic differential equations.
|
|
|
Using thermoelectric generator to increase the efficiency of the radiator
Kříž, Pavel ; Janák, Luděk (referee) ; Vlach, Radek (advisor)
This diploma thesis deals with a design layout of the fan power supply that ensures the increase of the efficiency of the heating unit. For usage in the areas without electric power, the power supply is secured by thermoelectric generator. The system has to function on the basis of autonomous system which turns itself on only when necessary. In the introductory part of the paper there is a recherché of thermoelectric generators for general usage. Next it mentions the basic findings in from the field of DC/DC converters for low power applications. In this part attention is given to MPPT algorithm. Furthermore basic knowledge from the field of heat transmission together with its most used elements is described. Subsequently existing applications that increase the effectiveness of heating are mentioned. Their disadvantage however is that they depend on the external source of power supply. The practical part to a large extent covers the analysis of the suitability of the chosen thermoelectric module. For securing of the heat gradient of the generator there was a model created meeting the figures in the manual and there are several simulations in the MATLAB program. Furthermore several measurements of the thermoelectric module took place in order to secure realistic figures. Subsequently a DC/DC converter was chosen. Finally the testing was made on the real composition. In conclusion there is an overall evaluation including the real usage and the economical aspect of the project. The outcomes of the work enable to avoid common mistakes that are part of many specialized articles. The created system is to be used after the adjustment of the cooling to the required aim. At the same time it becomes very effective.
|
|
|
Design of transport mechanism for the stationary robot
Kříž, Pavel ; Vejlupek, Josef (referee) ; Ripel, Tomáš (advisor)
This bachelor's thesis describes design of the transport mechanism for the autonomous robot. The main aim is modification of the chassis and design of the control mechanism. The designed concept comes out of requirements assigned by external company. It also includes the list and description of various considered concepts. The final construction variant is divided into several construction sections described in the thesis. The check calculation of potentially critical part is specified in the final part. The result is design of the transport mechanism for the stationary robot which serves as multifunctional kiosk.
|
|
|
Stochastic models of production planning
Kříž, Pavel ; Fiala, Petr (advisor) ; Pelikán, Jan (referee)
Při plánování produkce se často můžeme setkat s nejistotou ohledně velikosti budoucí poptávky. Potom nezbývá než modelovat poptávku jako náhodnou veličinu, čímž se však modely plánování produkce stávají úlohami stochastického programování. Cílem této práce je pak prostudovat jednotlivé koncepty stochastického programování a aplikovat je na modely plánování produkce. Pozornost bude přitom věnována jak rozhodováním za rizika, kdy přesně známe rozdělení pravděpodobnosti náhodných parametrů, tak také rozhodováním za neurčitosti, kdy máme o těchto rozděleních jen částečnou informaci. Na závěr budou jednotlivé postupy demonstrovány na numerickém příkladu.
|
guest ::
