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Methods for topology optimization of mechanically loaded structures and their application on trusses
Pánek, Ondřej ; Lošák, Petr (referee) ; Ševeček, Oldřich (advisor)
This bachelor thesis deals with a topology optimization of truss structures. In the first part of this thesis an overview of individual methods of the structural optimization and brief description of their principle based on recherche of available literature is given. The second part of the thesis deals with an application of selected methods to the topology optimization of truss structures, employing the computational codes programmed in the MATLAB software. In the first step, a code for computation of stresses in individual trusses and displacements in nodes of the truss structure by the finite element method was programmed. This code was later used in individual topology optimization codes for computation of parameters mentioned above. Selected topology optimization methods and their computational codes were then used for optimization of two model tasks – bridge and cantilever beam subjected to isolated forces, in order to reduce their weight while maintaining safety to the limit states of elasticity and buckling stability. At the end of the thesis, gained results were compared to results available in literature (nevertheless optimized as a continuum structure) and it can be concluded, that both these results are in a very good agreement.
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Thought intersections of philosophy and mathematics
Hlavešová, Ilona ; Hogenová, Anna (advisor) ; Blažková, Miloslava (referee)
The submitted thesis addresses the ideas that are at the intersections of philosophy and mathematics. These intersections have been in the course of the history as follows: Numerical ratios, the concept of infinity, continuum partition, space specification, determinism versus randomness and exploring of the mathematics foundations with an overlap into philosophy. The results herewith presented have been achieved on the basis of the HTF lectures and seminars, available literature, my own knowledge and reasoning. The thesis documents processes of how mathematics stimulated certain philosophical principles and vice versa how mathematics was influenced by philosophical views. Last but not least, there are presented comparisons between philosophic propositions and the current mathematics and physics knowledge in the mentioned intersections.
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Big families of incomparable continua
Doležalová, Anna ; Vejnar, Benjamin (advisor) ; Kurka, Ondřej (referee)
The goal of the thesis is to define the basic concepts of continuum theory and explore properties of some special continuous mappings between them. These are used for the construction of infinite families of continua which are incomparable by homeomorphic, open or monotone mappings. Special concern is given to families of dendrites. In particular, we describe an uncountable family of homeomorphically incomparable dendrites, an uncountable family of open incomparable dendrites and a countable family of monotone incomparable local dendrites. Existence of an uncountable family of monotone incomparable dendrites is open problem, in this thesis we describe a family of such dendrites of arbitrary finite cardinality. Powered by TCPDF (www.tcpdf.org)
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Homeomorphisms in topological structures
Vejnar, Benjamin ; Pyrih, Pavel (advisor) ; Charatonik, Włodzimierz (referee) ; Illanes, Alejandro (referee)
In this thesis, we present solutions to several problems concerning one-dimensi- onal continua. We give an inductive description of graphs with a given disconnec- tion number, this answers a question of S. B. Nadler. Further, we state a topo- logical characterization of the Sierpi'nski triangle. In the study of shore sets in dendroids and λ-dendroids we obtain several positive results and we also provide some counterexamples. By doing this, we continue in the recent work of several authors. We are also dealing with the notion of 1 2 -homogeneity and we prove that up to homeomorphism there are only two 1 2 -homogeneous chainable continua with just two end points. We present also a new elegant proof of a classical theorem of Waraszkiewicz. 1
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Thomas Bradwardine. Life and Work
Školoud, Barnabáš ; Bečvář, Jindřich (advisor) ; Halas, Zdeněk (referee)
This thesis deals with the life and work of an english scholar Thomas Bradwardine who lived in the first half of the 14th century. The first chapter of the work summarizes information about his life and puts it into historical context (the Hundred Years' War, the Black Death in Europe, the philosophy of that period). The second chapter deals with Bradwardine's works on theology, logic, natural philosophy and mathematics. The treatises De proportionibus, in which Bradwardine presented his new dynamic law, and De continuo, in which he refused the indivisibilist positions on the composition of the continuum and defended Aristotelic conception, are analyzed in more detail. Furthermore, the second chapter includes the description of the scientific movement in the 13th and 14th centuries.
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What is a curve?
Koudela, Libor ; Veselý, Jiří (advisor) ; Pyrih, Pavel (referee) ; Bobok, Jozef (referee)
The notion of a curve played important role in the history of mathematical thought. This dissertation is focused on the conception of a curve in analysis, point set theory and topology. The rectification of curves and the notion of arc length are considered in connection with the history of analysis from antiquity to the beginning of the 20th century. "Measurement of curves" is also discussed from the measure-theoretic viewpoint and various definitions of linear measure and fractional dimension are described. Historically, there are two main approaches to understanding curves. Jordan defined a curve as a continuous image of a closed interval. However, his definition appeared to be too wide, since it was met by objects such as the Peano curve. In the point set theory, a curve is considered to be a one-dimensional continuum. The development of the dimension theory and the continuum theory, starting with the pioneering work of Bolzano, was motivated by the search for rigorous topological definition of a curve, a surface etc. Among "pathological" curves, that were often introduced as counterexamples in the development of modern analysis, we can find early examples of fractals. The fractal theory motivated further study of mathematical properties of these curves in the late 20th century, such as self-similarity and...
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Postmodernism in British and American comics : postmodernist overtones in the works of Alan Moore and Grant Morrison
Holub, Martin ; Ženíšek, Jakub (advisor) ; Chalupský, Petr (referee)
The aim of this thesis is the examination and analysis of postmodernist overtones in the medium of comics. It is concerned both with the postmodernist content in comics, and comics' possibilities and attributes as a postmodernist medium. The first part of the thesis elaborates on sequential art in general and the essential elements of postmodernism, such as deconstruction, metafiction, and intertextuality, within its context. The second part of the thesis is concerned with selected postmodernist works of prominent comicbook authors: Alan Moore and Grant Morrison. Key words Comics, comicbook, graphic novel, postmodernism, metafiction, intertextuality, continuum, narration, binary oppositions, deconstruction, superhero, author, creation, Watchmen, Animal Man
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