|
|
Optimality of function spaces for integral operators
Takáč, Jakub ; Pick, Luboš (advisor) ; Honzík, Petr (referee)
In this work, we study the behaviour of linear kernel operators on rearrange- ment-invariant (r.i.) spaces. In particular we focus on the boundedness of such operators between various function spaces. Given an operator and a domain r.i. space Y, our goal is to find an r.i. space Z such that the operator is bounded from Y into Z, and, whenever possible, to show that the target space is optimal (that is, the smallest such space). We concentrate on a particular class of kernel operators denoted by Sa, which have important applications and whose pivotal instance is the Laplace transform. In order to deal properly with these fairly general operators we use advanced techniques from the theory of rearrangement- invariant spaces and theory of interpolation. It turns out that the problem of finding the optimal space for Sa can, to a certain degree, be translated into the problem of finding a "sufficiently small" space X such that a, the kernel of Sa, lies in X. 1
|
|
|
Measures of non-compactness of Sobolev embeddings
Bouchala, Ondřej ; Hencl, Stanislav (advisor) ; Honzík, Petr (referee)
The measure of non-compactness is defined for any continuous mapping T : X Y between two Banach spaces X and Y as β(T) := inf { r > 0: T(BX) can be covered by finitely many open balls with radius r } . It can easily be shown that 0 ≤ β(T) ≤ ∥T∥ and that β(T) = 0, if and only if the mapping T is compact. My supervisor prof. Stanislav Hencl has proved in his paper that the measure of non-compactness of the known embedding W k,p 0 (Ω) → Lp∗ (Ω), where kp is smaller than the dimension, is equal to its norm. In this thesis we prove that the measure of non-compactness of the embedding between function spaces is under certain general assumptions equal to the norm of that embedding. We apply this theorem to the case of Lorentz spaces to obtain that the measure of non-compactness of the embedding Wk 0 Lp,q (Ω) → Lp∗,q (Ω) is for suitable p and q equal to its norm. 1
|
|
|
Competitions in Artificial Intelligence
Šafář, Pavel ; Hynčica, Tomáš (referee) ; Honzík, Petr (advisor)
My thesis is focused on the field of artificial intelligence and especially on the competitions in the areas of robotics, computer vision, communication, time series forecasting and game playing programmes. Furthermore I devoted myself to the research of the use of neural network as a tool to solve the Gomoku game problems. The neural network processes the game situations and sets up the output values based on the pre-set models.
|
|
|
Character recognition in the soundtrack with SOM
Malásek, Jan ; Honzík, Petr (referee) ; Honzík, Petr (referee) ; Pohl, Jan (advisor)
This bachelor´s thesis describes a history of neural networks evolution and their using in speech recognition systems and shows problems with working and learning neural networks. It presents three chosen systems for speech recognition including their evaluation in experiments, their advantages and disadvantages. It is also about human speech characteristics and systems of its recognition. The last part is focused on frequency spectrums of different types of vowels and gives instructions for programming neural networks using MATLAB.
|
|
|
Modelování spotových cen elektrické energie
Šmíd, Vítězslav ; Honzík, Petr (advisor) ; Hencl, Stanislav (referee)
We describe a single-period vector autoregressive model with parameter restrictions and find a consistent estimator of the parameters. We apply several restricted models to electricity prices in two markets. The datasets are comprised of the settlement prices of day-ahead auctions in which market participants bid on next day's electricity deliveries in 24 separate hourly blocks. We therefore model the data as a time series in R^24. To avoid overfitting we crossvalidate all models using sliding windows of training and testing data. We find that simple models perform better because they are more resilient in volatile periods than more comprehensive models. We suggest that model performance could be improved by incorporating exogenous data, such as weather conditions. Powered by TCPDF (www.tcpdf.org)
|
|
|
Liability for damage of the employee caused to the employer
Honzík, Petr ; Štangová, Věra (advisor) ; Brádlerová, Libuše (referee)
Thesis is engaged in labour-law issues of the legal relation between employee and employer in the field of the liability for damage. The thesis is divided in four chapters: the first chapter is engaged in theoretical questions of the labour-law relation and its Czech as well as Euro- pean specificities. The following chapter describes the theory of the labour-law liability and the third chapter is engaged in liability for damage itself. The last chapter develops detailed the topic of the thesis: the liability for damage of the employee caused to the employer in the light of the actual judgments of Czech labour-law courts of justice. The thesis is also engaged in theoretical issues related to the essential principles of labour-law liability as an important element of the labour-law relation de lege lata as well as de lege fer- enda. KEYWORDS employee, employer, liability for damage
|
|
|
Relations of a function and its graph
Drahovský, Matej ; Zajíček, Luděk (advisor) ; Honzík, Petr (referee)
In presented work we study relation between a real function, or a map between two metric spaces, and its graph, a subset of Cartesian product of two metric spaces. Mainly, we will focus on real function of one real variable, but if possible theorems will be concerning maps between other metric spaces. In first chapter we study functions with closed graph. First we characterize these functions by their limit points and then, under some additional conditions, we characterize set of points of discontinuity of a function with closed graph. In second chapter, we introduce Hausdorff distance of subsets of metric space and we will show relations between different types of convergence of functions and convergence of Hausdorff distance of their graphs to zero. In the last chapter, we define Gibbs phenomenon from the theory of Fourier series as convergence of Hausdorff distance of graphs of partial sums of Fourier series from modified graph of approximated function to zero. 1
|
|
|
Sobolev embedding theorem on domains without Lipschitz boundary
Roskovec, Tomáš ; Hencl, Stanislav (advisor) ; Honzík, Petr (referee)
We study the Sobolev embeddings theorem and formulate modified theorems on domains with nonlipschitz boundary. The Sobolev embeddings the- orem on a domain with Lipschitz boundary claims f ∈ W1,p ⇒ f ∈ Lp∗ (p) , kde p∗ (p) = np n − p . The function p∗ (p) is continuous and even smooth. We construct a domain with nonlipschitz boundary and function of the optimal embedding i.e. analogy of p∗ (p) is not continous. In the first part, according to [1], we construct the domain with the point of discontinuity for p = n = 2. Though we used known construction of domain, we prove this by using more simple and elegant methods. In the second part of thesis we suggest the way how to generalize this model domain and shift the point of discontinuity to other point than p = n = 2.
|
|
|
Control of linear systems
Cesneková, Ivana ; Milota, Jaroslav (advisor) ; Honzík, Petr (referee)
The aim of this work is to look into the theory of linear systems via population model represented by partial differential equations with boundary and initial condition. Special attention is devoted to the strongly continuous semig- roups on a complex Banach space. For this purpose, the notion of a homogeneous and inhomogeneous Cauchy problem is introduced and we solve our model in this abstract formulation. The system behaviour is based on properties of the resolvent set and spectrum. Controllability question limits to solve the uniformly exponen- tially stability and the exponentially stabilizability. The point of this problem is in the case of the unstability to show exponencially stability of the system by using feedback. Keywords: control, differential equations, stability, controllability 1
|
|
|
Differentiability of the inverse mapping
Konopecký, František ; Hencl, Stanislav (advisor) ; Honzík, Petr (referee)
Primary objective of the thesis is proof of the statement that if for ∈ ℕ a ≥ 1 a bilipschitz mapping belongs to +1, loc ∩ ,∞ loc then also its inverse −1 belongs to +1, loc . We prove a similar statement also for spaces loc . For this purpose we construct a new ordering of -th partial derivatives to generalized Jacobian matrix. Thanks to this matrix we are able to differentiate matrices in an applicable way. Generalized Jacobian matrix is projected so that there still holds the Chain rule and, in some way, also rules for matrices product differentiation. 1
|
guest ::
