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Simulation of dose distribution irradiation
Večeřa, Petr ; Hlaváč, Martin (referee) ; Kolářová, Jana (advisor)
This project deals with the issue of simulation of dose irradiation. This principle is used in a radiotherapeutic device known as a Leksell Gamma Knife for the treatment of intracranial tumours. With regard to the theoretical observations obtained by studying this device, the project suggests the use of analytical geometry for the creation of a mathematical model for calculation of the intensity in the rayed area. A demonstration program Leksell_xvecer08 has been created for this model in a MatLab software background, which enables the user to change various input arguments and simulate a picture of the dosage spread in the target scanned areas.
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Building Model Generator for Open Street Maps
Galacz, Roman ; Poulíček, Zbyněk (referee) ; Polok, Lukáš (advisor)
This work concerns obtaining data from the maps provided by the project OpenStreetMap. The data are converted from the format of geographical latitude and longitude to the Cartesian coordinate system. This work also concerns building type recognition in build-up area which are situated on the downloaded map. Part of the work is a demonstration application which is able to model 3D geometry of the buildings, based on the results of the recognition algorithms and also creates a terrain in which these buildings are situated. Generated model is displayed using the OpenGL graphics library.
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Safety of a Commercial Aircraft after Damage to Airframe due to Terrorist Attack
Lošťák, Miroslav ; Salga, Jaroslav (referee) ; Kusák,, Jan (referee) ; Petrásek, Miloslav (advisor)
Modern-day terrorist attacks present a considerable danger for commercial aircrafts. This thesis analyzes potential methods of such attacks with a critical analysis of the most dangerous type: an attack from the outside of the aircraft via a fragmentation missile warhead. Such missiles cause damage to the airframe of the aircraft through fragments created by the explosion. In this thesis, analytical geometry is used to determine the area of the aircraft affected by the fragmentation. The aircraft’s geometry and the fragments’ dispersion are calculated by analytical functions, and the effect of the damage is analyzed. A shooting experiment was also carried out, in which fragments were shot at a reinforced skin panel that was manufactured according to the real design of commercial aircraft. The results of the experiment revealed that only directly hit sections of the structure are damaged. Data obtained by the experiment was then used for the creation and improvement of the model used in the simulation by means of the finite element method. This model is used for the numerical calculation of the damage sustained. Further included in the thesis is an analysis of the change in the load-bearing capacity after such an attack. The relationship between the size of the damage and its effect on the load-bearing capacity of the component as well as the entire structure is defined. First, the effect of component damage is analyzed via the FMEA/FMECA methods. This analysis is then extended using fuzzy logic. Fuzzy logic analysis is based on the determination of the size of the damaged component area and the component’s importance on the structure’s carry loads. Application of the defined approach is described for several parts of an aircraft’s life cycle, including development, operation after the terrorist attack, and assessment of causes after a crash caused by a fragmentation missile warhead.
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Angles, areas, volumes: dot product and determinant
Ondič, Milan ; Beran, Filip (advisor) ; Zamboj, Michal (referee)
This bachelor thesis deals with the introduction of scalar product and determinant, which are important tools of analytic geometry. The purpose of the thesis is to provide a parallel interpretation of these two key concepts of advanced algebra - the dot product and the determinant - primarily from a geometric, not an algebraic, point of view. The aim of the thesis is to show how both representations can be derived just by solving geometric problems in two-dimensional space and then how to transfer them to three-dimensional space. The first part of the work is devoted to finding the angle between two vectors in the plane and to calculating the area of a triangle. Both of problems are solved in several ways and then the scalar product and determinant are derived. The second part of the work is devoted to three-dimensional space, in particular the angle between two vectors, lines and planes and the volume of a tetrahedron and parallelogram. This is then supplemented by the introduction of some notions of linear algebra, an investigation of the algebraic properties of the dot product and determinant, and a generalization of the notions to the n-dimensional space. The last part of the thesis is devoted to the analysis of selected czech high school mathematics textbooks in terms of the occurrence and...
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Elementary mathematics of imaging methods for radiology assistants
JELÍNKOVÁ, Barbora
The topic of the bachelor's thesis responded to the finding that there is currently no suitable educational text containing mathematical foundations for the education of radiological assistants and other related fields. The bachelor thesis contains selected areas of mathematics that are necessary to know to understand the physical foundations of imaging methods. The formulation of these areas is appropriate to the needs of future graduates of these fields of study. The goals of the bachelor thesis were the following: G1 Creation of an educational text and examples containing elementary mathematics that are essential to fully understand physical principles of imaging methods. G2 Compilation of a test that will be used to verify the knowledge of mathematics of radiological assistance field students and its graduates, followed by a statistical expression of knowledge level. Based on the goals, the following hypotheses were made: H1 By application of a curricular process a structure of elementary mathematics of imaging methods for radiological assistants can be described. H2a By comparing mathematical structures with components of a radiological assistant´s profile, individual structural levels of elementary mathematics for radiological assistants can be described. H2b According to needs and abilities of radiological assistants, examples of functions, differentiation, integration, and vectors can be chosen. H3 Knowledge of respondents in radiology mathematics will be distributed close to a normal distribution. With regard to the curricular process, a teaching text was compiled together with example illustrations. This step led to the fulfillment of goal G1. Then, a single-choice test of 20 questions was compiled to determine the level of mathematics knowledge across the field of radiological assistance. This step led to the achievement of goal G2. This test was subsequently extended using an online form among radiological assistants and students in this field. Given the above objectives, hypotheses H1, H2a and H2b could be confirmed. The test results were statistically expressed in the practical part of the bachelor thesis. It was confirmed that the empirical distribution of test responses is close to the normal distribution. Hypothesis H3 was also confirmed by this step. The benefits of the bachelor's thesis can be seen in the practical level (construction of an educational text verified by a test survey) and in the theoretical level (verification of the application of the theory of the curricular process).
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A Collection of Solved Problems in Analytical Geometry
Kvapilová, Babeta ; Hromadová, Jana (advisor) ; Surynková, Petra (referee)
This thesis is intended for teachers and students of high schools and universities. It consists collection of solved problems from plane analytical geometry including various solutions and their comparison. The thesis aims to increase the student knowledge of the topic and to provide different approaches to problems and working materials for lessons for teachers. Pictures for better understanding are added for more difficult problems. The practical part focusing on common mistakes and their elimination is included.
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Practical didactic tests for preparation for the math matriculation examination
PIVOŇKA, Jiří
This bachelor thesis deals with the practical didactic tests for the math matriculation examination. It is divided into two parts. The first part is divided into 7 chapters. Each chapter deals with a specific thematic subjects for the math matriculation examination. The second part includes 3 didactic tests. For each didactic test is assigned solution. The aim of this bachelor thesis is to help students perform math matriculation examination.
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