A snake (coil) is an induced path (cycle) in a hypercube. They are well known from the snake-in-the-box (coil-in-the-box) problem which asks for the longest snake (coil) in a hypercube. They have been generalized to k-snakes (k-coils) which preserve distances between their every two vertices at distance at most k − 1 in hypercube. We study them as a variant of Locke's hypothesis. It states that a balanced set F ⊆ V (Qn) of cardinality 2m can be avoided by a Hamiltonian cycle if n ≥ m + 2 and m ≥ 1. We show that if S is a k-snake (k-coil) in Qn for n ≥ k ≥ 6 (n ≥ k ≥ 7), then Qn − V (S) is Hamiltonian laceable. For a fixed k the number of vertices of a k-coil may even be exponential with n. We introduce a dragon, which is an induced tree in a hypercube, and its generalization a k-dragon which preserves distances between its every two vertices at distance at most k−1 in hypercube. By proving a specific lemma from my Bachelor thesis that was previously verified by a computer, we finish the proof of the theorem regarding Hamiltonian laceability of hypercubes without n-dragons.

Czech Republic has been always traditional industrial country and the importance of its industry will not diminish, even in spite of the growing share of services on GDP. The goal of this thesis is therefore to analyze strong and weak points of Czech manufacturing and its particular sectors. Measuring various indicators of macroeconomic competitiveness, the results for the Czech Republic have revealed relatively low labour costs, at least in comparison with the EU average, but this comparative advantage can be depleted over time. The challenge for the Czech manufacturing is thus to pass over to upper levels of production with higher margins and higher value added. The thesis is also dealing with different points of view on the topic of industrial policy and the role of government in this policy. The thesis introduces two strategical documents as well, Europe 2020 strategy published by the European Commission and Back on Top strategy published by Czech Ministry of Industry and Trade.

Title: Cloud-top morphology of convective storms as observed by meteorological satellites Author: Michaela Radová Department: Department of Atmospheric Physics Supervisor: RNDr. Martin Setvák, CSc., Czech Hydrometeorological Institute Abstract: This work focuses on study of features occurring at tops of convective storms, namely embedded warm areas, cold rings, cold-U/Vs and overshooting tops (OTs), mainly from the perspective of satellite observations. We have assembled a database of 104 subjectively detected cold rings and cold-U/Vs from the area of Europe. We discuss relationship between satellite- observed brightness temperature and cloud top height determined from radar measurements for storms with distinct cold-rings. Our results support the hypothesis that the warm area is a consequence of presence of central elevated dome reaching warmer lower stratosphere. Moreover, a storm with transformation of cold ring into cold-U is studied and an elevated plume above storm anvil in the warmer lower stratosphere is found to be a likely explanation of the warm area inside the cold-U. Both analyses confirm that thermal inversion above the tropopause is a necessary prerequisite for occurrence of cold rings and cold-U/Vs. We also propose a method for automated objective determination of spatial characteristics of...

Early adulthood is a period of peak bone mass formation, which is one of the basics in prevention of osteoporosis onset in older age. Milk and dairy products intake as a source of well-absorbed calcium is still very substantial at this age, as it was in the previous period of adolescence. However, it is also often a time of finding a person's own diet and a time of eliminating certain food groups from the diet, which is often due to succumbuing to widespread myths. Thus, milk is one of the most controversial foods for the public. The aim of the questionnaire research, which was part of the thesis, was to find out, how many young adults believe and succumb to these myths. Questions were asked about eating habits and respondents' views on the health benefits of milk. The survey shows that a significant percentage of them are misinformed by such myths and exclude milk from their diet, often for no reason. Although campaigns to promote milk consumption are still ongoing and have undoubtedly had a positive effect on public perception of the benefits of milk, it is certain that this activity needs to be continued and myths (not only) about milk still need to be debunked. keywords: milk, dairy products, early adulthood, myths, peak bone mass, calcium

Concepts from graph theory in primary school mathematic curriculum Ing. Tatiana Mutinová, 2014 Abstract This diploma thesis is focused on graph theory, especially on the concepts that are used in primary school mathematic curriculum. Furthermore it shows the reasons why it is necessary to include these graph concepts in young pupil's education. In the theoretical part, basic terms and definitions from chosen parts of graph theory are mentioned and few examples demonstrate how the applications of graph theory can help with solving real-life situations. The practical part summarized the current use of some graph theory concepts in primary school mathematic curriculum. This part also includes the demonstration of the graded series of problems and the sheets of exercises that could be usable in introducing and practising of some graph concepts. The experiment with mosaics, that was carried out within this diploma thesis, is an illustration how to connect mathematical and non-mathematical world and how to integrate research activities in young pupil's education. Key words: mathematics, graph theory, graph vertex, degree of graph vertex, edge of graph, problem of two colours, child of primary school

The diploma thesis is focused on an analysis of the first sentences of newspaper articles namely from an aspect of the topic-focus articulation, which is expressed in Czech primarily by word order. The word order depending on the increasing communicative dynamism of words in the sentence might be changed from an objective word order if new information follows known or before mentioned information into subjective word order resulting in a reverse order. E.g.: The CEZ group showed record profit of 52 milliard CZK last year, a reverse word order: (literal translation) Record profit (Obj) of 52 milliard CZK the CEZ group(Subj) showed last year. In our thesis, we describe the above mentioned changes and we determine sets of cases comprising the modifications and we attempt to specify kinds of rules and principles resulting in different word orders. The sentence in the case of the subjective word order begins with an object, an adverbial of time, place, or condition. Anyway, not always a sentence constituent at the beginning of the sentence indicates the subjective word order. A significant role in the analysis is played by head- lines, which affect considerably the result. We focus ou attention on sentences expressing a placement on the scene. These sentences are assessed in relation with the head-lines...

In computer graphics we can handle unstructured triangular 3D meshes which are not too usable for processing through their irregularity. In these situations it occurs need of conversion that 3D mesh to more suitable representation. Some kind of 3D spline surface can be proper alternative because it institutes regularity in the form of control points grid and that's why it is more suitable for next processing. During conversion, which is described in this thesis, quadrilateral 3D mesh is constructed at first. This mesh has regular structure but mainly the structure corresponds to structure of control points grid of resulting 3D spline surface. Created quadrilateral 3D mesh can be saved and consequently used in specific modeling applications for T-spline surface creation.

This Master Thesis deals with the drawing algorithms of graphs known from the mathematical theory. These algorithms deals with an appropriate distribution of the graph vertices in order to obtain the most clear and readable graphs for human readers. The main objective of this work was also to implement the drawing algorithm in the application that would allow to edit the graph. This work deals also with graphs representation in computers.