National Repository of Grey Literature 7 records found  Search took 0.00 seconds. 
Non-standard analysis and its applications
Hýlová, Lenka ; Pražák, Dalibor (advisor) ; Slavík, Jakub (referee)
The aim of this thesis is to apply methods of nonstandard analysis on the topic of strong derivative. First of all, we sum up basic knowlegde of nonstan- dard analysis, we introduce some nonstandard definitons (such as continuity, derivative, . . . ) and we prove the equivalence of standard and nonstandard definitions. In the second chapter we introduce the notion of strong derivative (in both standard and nonstandard way) and we prove rules for its computing and some basic properties. For example, if a function has strong derivative at some point, then it satisfies a Lipschitz condition in a neighbourhood of this point. In the final part of the thesis we define strong partial differentiability and we prove the theorem which claims that the existence of partial derivatives of a function from R2 to R with respect to both factors, one of them strong, implies the existence of a total derivative. 1
Evolutionary differential equations in unbounded domains
Slavík, Jakub ; Pražák, Dalibor (advisor) ; Miranville, Alain (referee) ; Skalák, Zdeněk (referee)
We study asymptotic properties of evolution partial differential equations posed in unbounded spatial domain in the context of locally uniform spaces. This context allows the use of non-integrable data and carries an inherent non-compactness and non-separability. We establish the existence of a lo- cally compact attractor for non-local parabolic equation and weakly damped semilinear wave equation and provide an upper bound on the Kolmogorov's ε-entropy of these attractors and the attractor of strongly damped wave equation in the subcritical case using the method of trajectories. Finally we also investigate infinite dimensional exponential attractors of nonlinear reaction-diffusion equation in its natural energy setting. 1
Online Comparators in Insurance Business
Slavík, Jakub ; Ducháčková, Eva (advisor) ; Cibulka, Jakub (referee)
This bachelor thesis deals with problems of on-line insurance comparators. The theoretical part is devoted to the importance of insurance products, the pricing of insurance products, distribution channels of insurance products, on-line comparators and insurance products that can be arranged on them. Practical part deals with depth analysis of clients' awareness, behaviour and needs on the market of on-line comparators and the experience of clients with comparators, evaluates priorities, why they arrange insurance in this way and maps benefits to clients. The results of the questionnaire survey are formulated in the hypothesis evaluation. The conclusion summarizes its own findings and evaluation.
Analysis of the SIR model
Kociánová, Barbora ; Pražák, Dalibor (advisor) ; Slavík, Jakub (referee)
The thesis deals with stability of delay epidemiological models. For this pur- pose we formulate the basic theory of delay differential equations and the fun- damental theorems about Ljapunov functions and stability, that we state with detailed proofs. We briefly comment on the meaning of each equation and con- stants used in three epidemiological models: SIR with constant population size, SIR with varying population size and SEIR model. It is a system of two, three and four delay differential equations, respectively. By combining different procedures from source articles we find appropriate Ljapunov functions and with the help of them we prove global asymptotic stability of the disease free equilibrium and local asymptotic stability of the endemic equilibrium for each of the models.
Nestandardní analýza dynamických systémů
Slavík, Jakub ; Pražák, Dalibor (advisor) ; Růžička, Pavel (referee)
In the presented thesis, we study an application of nonstandard analysis to dynamical systems, in particular to ω-limit set, stability and global attractor. We recall the definition and properties of elementary embedding, in detail ex- plore the introduction of infinitesimals to the real line and study metric spaces using nonstandard methods, in particular continuity and compactness which are closely related to the theory of dynamical systems. Last we attend to dynamical systems and present nonstandard characterizations of some of its properties such as asymptotic compactness and dissipativity and using these characterizations we prove one of the basic results of this theory - existence of a global attractor. 1
Habitat selection game
Slavík, Jakub ; Pražák, Dalibor (advisor) ; John, Oldřich (referee)
In the presented work we study an application of evolutionary game theory in behavioral ecology, specifically the habitat selection game, which describes the distribution of population into a finite number of patches. We also show the existence, uniqueness and evolutionary stability of the ideal free distribution (IFD) observed in natural environments. To describe the process of the distri- bution we specify the dynamics of the habitat selection game using dispersion dynamics, and we show the stability of the IFD for different types of dispersion dynamics using the classical theory of ordinary differential equations and the theory of ordinary differential equations with discontinuous righthand sides. 1

See also: similar author names
10 SLAVÍK, Jiří
1 Slavík, J.
48 Slavík, Jan
1 Slavík, Jaroslav
10 Slavík, Jiří
2 Slavík, Josef
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