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Lineární algebraické modelování úloh s nepřesnými daty
Vasilík, Kamil ; Hnětynková, Iveta (advisor) ; Janovský, Vladimír (referee)
In this thesis we consider problems Ax b arising from the discretization of ill-posed problems, where the right-hand side b is polluted by (unknown) noise. It was shown in [29] that under some natural assumptions, using the Golub-Kahan iterative bidiagonalization the noise level in the data can be estimated at a negligible cost. Such information can be further used in solving ill-posed problems. Here we suggest criteria for detecting the noise revealing iteration in the Golub-Kahan iterative bidiagonalization. We discuss the presence of noise of different colors. We study how the loss of orthogonality affects the noise revealing property of the bidiagonalization.
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Descriptive and topological aspects of Banach space theory
Kurka, Ondřej
of doctoral thesis Descriptive and topological aspects in Banach space theory Deskriptivní a topologické aspekty v teorii Banachových prostorů Ondřej Kurka The thesis consists of three papers of the author. In the first paper, it is shown that the sets of Fréchet subdifferentiability of Lipschitz functions on a Banach space X are Borel if and only if X is reflexive. This answers a ques- tion of L. Zajíček. In the second paper, a problem of G. Debs, G. Godefroy and J. Saint Raymond is solved. On every separable non-reflexive Banach space, equivalent strictly convex norms with the set of norm-attaining func- tionals of arbitrarily high Borel class are constructed. In the last paper, binormality, a separation property of the norm and weak topologies of a Ba- nach space, is studied. A result of P. Holický is generalized. It is shown that every Banach space which belongs to a P-class is binormal. It is also shown that the asplundness of a Banach space is equivalent to a related separation property of its dual space. 1
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Numerical solution of the Navier-Stokes equations with a generalized state eqution
Ullrichová, Martina
Title: Numerical solution of the Navier-Stokes equations with a generalized state eqution Author: Martina Ullrichová Department: Department of numerical Mathematics Supervisor: doc. RNDr. Vít Dolejší, Ph.D., DSc. Supervisor's e-mail address: dolejsi@karlin.mff.cuni.cz Abstract: In the present work we study the simulation of viscous compressible flow. We consider a generalized model of gas described by a generalized state equation. We firstly summarize construction of this generalized equation and its consequences for the existence and uniquenes of the solution of the compressible flow problem. We suggest particular ways how define this generalized relations. Afterwards, we solve the Navier-Stokes problem by the discontinous Galerkin method. Considering the properties of the generalized model we choose explicit time discretization. Finally, we compare new generalized model with the standard model (ideal gas) for different flow regimes around the NACA0012 profil. Keywords: viscous compressible flow, Navier-Stokes equations, discontinous Ga- lerkin method, generalized state equation
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Risks in the Real Estate Business
Holub, Aladár ; Hromádka, Vít (referee) ; Vítková, Eva (advisor)
This master thesis is concerned with the risks associated with the process of selling and buying real estate. Lists of potential risks followed by a critical analysis which describes not only the risks but also will solve their minimization or complete removal. Risks will be monitored in terms owners and buyers of the properties.
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Numerical solution of the Navier-Stokes equations with a generalized state eqution
Ullrichová, Martina ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
Title: Numerical solution of the Navier-Stokes equations with a generalized state eqution Author: Martina Ullrichová Department: Department of numerical Mathematics Supervisor: doc. RNDr. Vít Dolejší, Ph.D., DSc. Supervisor's e-mail address: dolejsi@karlin.mff.cuni.cz Abstract: In the present work we study the simulation of viscous compressible flow. We consider a generalized model of gas described by a generalized state equation. We firstly summarize construction of this generalized equation and its consequences for the existence and uniquenes of the solution of the compressible flow problem. We suggest particular ways how define this generalized relations. Afterwards, we solve the Navier-Stokes problem by the discontinous Galerkin method. Considering the properties of the generalized model we choose explicit time discretization. Finally, we compare new generalized model with the standard model (ideal gas) for different flow regimes around the NACA0012 profil. Keywords: viscous compressible flow, Navier-Stokes equations, discontinous Ga- lerkin method, generalized state equation
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Mechanical properties of marine sediment near Koper and numerical modelling of a deep excavation
Tůma, Pavel ; Mašín, David (advisor) ; Miča, Lumír (referee)
Mechanical properties of marine sediment near Koper and numerical modelling of a deep excavation Engineering geological conditions near the port Koper in southwestern Slovenia forces geotechnical experts and civil engineers to solve problems in foundation various types of objects and purpose of the practice since the fifties of last century, when it began an intensive development of infrastructure of the port. The results of series of geological and geotechnical surveys, monitoring, and long experience with foundation in the local geology shows that it is almost always the 3rd geotechnical category, or foundation of complex structures in difficult geological conditions below the water table. The entire area belongs to Alpine-Dinaric tectonic area. The rock foundation is composed of complexes of flysch sediments Eocene age at which mounted files of recent marine sediments in the area widely submerged river valley fluvial sands and gravels. From the geotechnical point of view it is interesting site, where most buildings were based on a layer of soft marine sediments, where it is through the creation of special methods implemented in the establishment of deep-level endurable layers of gravel and sand of the river Rižana or at the level footingwall flysch. Set of marine sediments near the port Koper,...
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Evaluation of porosity in gravity - cast Al - alloy castings
Staňková, Markéta ; Nová, Iva (referee) ; Čech, Jaroslav (advisor)
Solving of this diploma thesis is evaluation porosity in sequence on mechanical properties from different Al alloys. Castings were made by gravity casting to the iron-mould or gravity casting to the sand. Measurements (mechanical properties, porosity, DAS - dendrite arm spacing, shape factors and sphericity) were statistically analysed and dependencies which were detected were processed to the graphs.
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Specific elemets of civil defence of the population regarding physically disabled people of the Slovak Republic.
HARMANOVÁ, Veronika
In Slovak Republic, fundamentals of protection of people, property and environment are established by the Constitution of Slovak Republic, the Security Strategy of Slovak Republic and by numerous Acts, Declarations or Regulations of Government which refer to Civilian Protection and Integrated Rescue System. Legislative standards with regards to protection of health or property does not take into account people with health disabilities despite the fact that the right for safety and timely warning of imminent danger is granted for every citizen on the territory of Slovak Republic. Objective of my diploma work is to investigate readiness of institutions participating on solutions of extraordinary events which struck people with health disabilities. Based on results of quantitative survey we would like to point out on deficiencies of the system and to propose a solution to improve procedures of the Integrated Rescue System and Civil Protection with regards to people with health disabilities. Further objective is to process a proposal of methodical tutorial which would contain basis gesticulation important for communication with the hearing impaired. Theoretical part of the diploma work consists of several chapters. The first part discusses basic families, classes and types of health impairment. Further on system of Civil Protection and its mission was processed. Last part is dedicated to the Integrated Rescue System. In that chapter we described fundamental and other rescue branches which by large participated on solutions of extraordinary events. The theory was processed by means of law legislation, sources of literature and internet websites. The empirical (practical) part of the thesis has been used qualitative research method. Because it is extremely difficult to collect such data were made through guided interview with experts of Civil Protection and managers of particular rescue branches (Fire fighting and Rescue Force, Rescue Health Service, Police Force) only in three selected counties of Presov region (Poprad, Stará Ľubovňa, Prešov). Results of the managed interview were evaluated by SWOT analysis which compares the internal and external environment. On the basis of empirical phenomenon a searching strategy (WO) was chosen whereby the focus was laid on utilizing opportunities and eliminating weaknesses. Based on results we concluded that issue of health disability isn?t incorporated into law legislation and plans to solve extraordinary events. There is no common education of managerial and executive rescue branches which would enable them to gather fundamental knowledge of classes and specifications of health disability, possibilities of communication and means of first-aid provision. For further qualitative and quantitative development of education there is a deficiency of material-didactic instruments which serve to accomplish the objective. We also concluded that when rescuing health-impaired people there are no special procedures and methods taken into account. At the same time for the hearing-impaired there is no system of timely warning and information of imminent danger and possibility to call rescue branches through the emergency phone line. With regards to existing deficiencies we proposed practical recommendations. To improve communication with hearing impaired people we created a proposal of a methodical instrument for rescue branches which contains basic signs. As a part of it there is also a one-hand and two-hand finger alphabet for refinement and visualisation of words.
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Design and development of an information system for the company Bistro na Formanské Cestě
Holub, Adam ; Pour, Jan (advisor) ; Šedivá, Zuzana (referee)
Aim of the thesis is to design and develop a small information system according to the needs of the specific customer. The customer is Bistro na Formanské Cestě, four-class restaurant. Developed system will record all business transactions in this company and will enable or facilitate some processes in this company. Part of this thesis is to analyze processes in this company and to identify its weaknesses and needs. Thesis is divided into three parts. In the first part, there are described processes and properties of above-mentioned company, followed by its main problems. Second part describes suggestions how to solve this problems by implementing information system into this company, and defines the functions that the system should contain. Third part contains description of all functions of the developed system, its database and use cases.
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Slabá řešení stochastických diferenciálních rovnic
Hofmanová, Martina ; Maslowski, Bohdan (referee) ; Seidler, Jan (advisor)
In the present work we study a stochastic di fferential equation with coefficients continuous in x having in this variable linear growth. As a main result we show that there exists a weak solution to this equation by a new, more elementary method. Standard methods are based either on the concept of the weak solution or equivalently on solving a martingale problem. However, both approaches employ the integral representation theorem for martingales, whose proof becomes rather complicated in dimension greater than one. By a simple modi cation of the usual procedure, one can identify the weak solution elementary, with no need to apply the above mentioned theorem. In the preliminaries we summarize some auxiliary results: namely, some properties of the space of continuous functions as the space of trajectories are established and an important theorem which allows us to approximate continuous function by functions Lipschitz continuous is proved.
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