|
|
Delay Difference Equations and Their Applications
Jánský, Jiří ; Hilscher, Roman Šimon (oponent) ; Čermák, Libor (oponent) ; Čermák, Jan (vedoucí práce)
This thesis discusses the qualitative properties of some delay difference equations. These equations originate from the $\Theta$-method discretizations of the differential equations with a delayed argument. Our purpose is to analyse the asymptotic properties of these numerical solutions and formulate their upper bounds. We also discuss stability properties of the studied discretizations. Several illustrating examples and comparisons with the known results are presented as well.
|
|
|
Nonlinear differential equations in the framework of the Karamata theory
Bukotin, Denys ; Opluštil, Zdeněk (oponent) ; Řehák, Pavel (vedoucí práce)
The goal of the thesis is to unify and generalize known results from literature, to study asymptotic behaviour of positive regularly varying solutions to the certain type of non-linear differential equations (known as nearly-half-linear differential equations) using available tools. This work includes description of theory of regular variation, some information on non-linear differential equations of various types, detailed derivations of results related to asymptotic behaviour of the solutions and examples of application of obtained results.
|
|
|
Regulární variace a její aplikace
Ženatá, Kamila ; Opluštil, Zdeněk (oponent) ; Řehák, Pavel (vedoucí práce)
Bakalářská práce se zabývá pojmem regulární variace a jejími aplikacemi v různých oblastech matematiky. Práce poskytuje přehled základních vlastností regulárně měnících se funkcí, pojmů s nimi souvisejících a konkrétní aplikace poznatků v diferenciálních rovnicích a nekonečných řadách.
|
|
|
Vanishing solutions of a second-order discrete non-linear equation of Emden-Fowler type
Diblík, J. ; Korobko, E.
The paper discusses a discrete equation of an Emden-Fowler type Δ2v(k) = -k3 (Δv(k))3 where v is a dependent variable, k is an integer-valued independent variable, Δv and Δ2v are the first and second-order forward differences of v, respectively. The paper aims to prove the existence of a nontrivial and vanishing solution for k ! 1. The equation is transformed into a system of two first-order difference equations, which makes it possible to apply previously known results when investigating the system.
|
|
|
Nonlinear differential equations in the framework of the Karamata theory
Bukotin, Denys ; Opluštil, Zdeněk (oponent) ; Řehák, Pavel (vedoucí práce)
The goal of the thesis is to unify and generalize known results from literature, to study asymptotic behaviour of positive regularly varying solutions to the certain type of non-linear differential equations (known as nearly-half-linear differential equations) using available tools. This work includes description of theory of regular variation, some information on non-linear differential equations of various types, detailed derivations of results related to asymptotic behaviour of the solutions and examples of application of obtained results.
|
|
| |
|
|
Delay Difference Equations and Their Applications
Jánský, Jiří ; Hilscher, Roman Šimon (oponent) ; Čermák, Libor (oponent) ; Čermák, Jan (vedoucí práce)
This thesis discusses the qualitative properties of some delay difference equations. These equations originate from the $\Theta$-method discretizations of the differential equations with a delayed argument. Our purpose is to analyse the asymptotic properties of these numerical solutions and formulate their upper bounds. We also discuss stability properties of the studied discretizations. Several illustrating examples and comparisons with the known results are presented as well.
|
|
| |
|
|
Some remarks on the variance in Markov chains with rewards
Sladký, Karel ; Sitař, Milan
We consider a discrete time Markov reward process with finite state space and assume that the rewards associated with the transitions are random variables with known probability distributions and finite first and second moments. We are interested in properties of cumulative reward earned in the subsequent transitions of the Markov chain. Explicit formulas for expected values and variance of the cumulative (random) reward are obtained for finite and infinite horizon models.
|
host ::
RSS.