In this work we deal with conversion of 3D triagonal polygonal meshes to the 3D spline patches using spectral analysis. The converted mesh is divided into quadrilaterals using eigenvectors of Laplacian operator. These quadrilaterals will be converted into spline patches. We will present some interesting results of this method. The assets and imperfections of this method will be briefly discussed.

This diploma thesis deals with computing of edit influences on assigned stiff body from the flow of inviscid liquid. There are derived equations for computation of the influences during translational or torsional wobble and follow-up calculation of the units of their tensors.

Classical operators of harmonic analysis in Orlicz spaces V'ıt Musil We deal with classical operators of harmonic analysis in Orlicz spaces such as the Hardy-Littlewood maximal operator, the Hardy-type integral operators, the maximal operator of fractional order, the Riesz potential, the Laplace transform, and also with Sobolev-type embeddings on open subsets of Rn or with respect to Frostman measures and, in particular, trace embeddings on the boundary. For each operator (in case of embeddings we consider the identity operator) we investigate the question of its boundedness from an Orlicz space into another. Particular attention is paid to the sharpness of the results. We further study the question of the existence of optimal Orlicz domain and target spaces and their description. The work consists of author's published and unpublished results compiled together with material appearing in the literature.

Hlavním zájmem diplomové práce je studium zobecněné nabla Laplaceové transformace na časových škálach a její jednoznačnosti, včetně důkazu jednoznačnosti a aplikace jednoznačnosti v zlomkovém kalkulu na časových škálach.

The thesis deals with flexible shaft couplings especially with new category of flexible couplings on the principle of fluid. Mathematical model of gas spring and rotor system with two degrees of freedom are derivated in this work. Last part of the work deals with design modification of flexible coupling with gas springs.

The aim of this thesis is to determine the size of overshoot produced at the output of a linear continuous second order system controlled by pulse width modulation depending on the period and duty cycle of the modulation and system parameters. This thesis contains analytic calculation of the size of overshoot produced at the output of the second order system with damping ratio > 0, except the damping ratio equals to 1 (i.e. both underdamped and damped system) depending on period and duty cycle of the modulation. This thesis also includes a comparison of partial analytic results to numerical simulation in Matlab program and also with measurement at second order system model.

It the thesis, we study retarded functional differential equations. As a result of the Banach fixed point theorem, it is easy to show that there exists a unique solution to such problems. Alas, this theorem gives us no information on the form of the solution. Therefore, we are particularly interested in expressing it. We achieve that by applying Laplace transform to both sides of the equation, we get a solution to this modified problem and subsequently claim that we can apply the inverse Laplace transform to express the solution of the former problem. At the end of the thesis, we formulate and prove the exponential estimate of the solution. 1

In this manuscript we study the action of one-dimensional integral operators on rearrangement-invariant Banach function spaces. Our principal goal is to characterize optimal target and optimal domain spaces corresponding to given spaces within the category of rearrangement-invariant Banach function spaces as well as to establish pointwise estimates of the non-increasing rearrangement of a given operator applied on a given function. We apply these general results to proving optimality relations between special rearrangement-invariant spaces. We pay special attention to the Laplace transform, which is a pivotal example of the operators in question. Powered by TCPDF (www.tcpdf.org)

Dizertační práce se zabývá konstrukcí obecného řešení slabě zpožděných systémů lineárních diskrétních rovnic v ${\mathbb R}^3$ tvaru \begin{equation*} x(k+1)=Ax(k)+Bx(k-m), \end{equation*} kde $m>0$ je kladné celé číslo, $x\colon \bZ_{-m}^{\infty}\to\bR^3$, $\bZ_{-m}^{\infty} := \{-m, -m+1, \dots, \infty\}$, $k\in\bZ_0^{\infty}$, $A=(a_{ij})$ a $B=(b_{ij})$ jsou konstantní $3\times 3$ matice. Charakteristické rovnice těchto systémů jsou identické s charakteristickými rovnicemi systému, který neobsahuje zpožděné členy. Jsou získána kriteria garantující, že daný systém je slabě zpožděný a následně jsou tato kritéria specifikována pro všechny možné případy Jordanova tvaru matice $A$. Systém je vyřešen pomocí metody, která ho transformuje na systém vyšší dimenze, ale bez zpoždění \begin{equation*} y(k+1)=\mathcal{A}y(k), \end{equation*} kde ${\mathrm{dim}}\ y = 3(m+1)$. Pomocí metod lineární algebry je možné najít Jordanovy formy matice $\mathcal{A}$ v závislosti na vlastních číslech matic $A$ and $B$. Tudíž lze nalézt obecné řešení nového systému a v důsledku toho pak odvodit obecné řešení počátečního systému.

Kontrola řízení vozidla se stala významným problémem v automatizačních aplikacích v automobilovém průmyslu. Ta se stala reálnou díky zavedení různých "by-wire" subsystémů, jako je např. "steer-by-wire," "break-by-wire," atd. Tyto subsystémy reprezentují elektronické ekvivalenty již existujících mechanických a hydraulických subsystémů. Především pak může být zavedeno číslicové řízení, určené na základě vzorkování dynamiky vozidla. Výhodou periodického snímání vstupních veličin je vyvarování se určitých poruch spojitého řízení.