The use of conformal transformation as a method for generating solutions of Einstein's equations has been mainly studied in the cases where the original spacetime is vacuum. The generated spacetimes then frequently belong to the class of pp-waves. In the present work, the electrovacuum spacetimes are stud- ied, i.e the solutions of coupled Einstein's and Maxwell's equations. By using the conformal transformation, it is possible to circumvent solving the later equa- tions. This method is concretely studied for null Einstein-Maxwell fields and it turns out that the admissible spacetimes are pp-waves again. However, if the method is generalized, it is possible to enlarge the class of conformal null Einstein-Maxwell fields to a wider family of Kundt spacetimes. 1

The main objective of the thesis is to verify the hydraulic inducer designs and to determine its effect on the cavitation characteristics of the pump. To increase the suction capability and cavitation resistance, the inducer is placed in front of the impeller centrifugal pump. Its role is to protect the impeller against the cavitation. The literary part of the thesis analyzes the issue of cavitation, its origin, development and termination of the cavitation bubble with so-called implosion. Special attention is devoted to describtion of cavitation effect occuring at the hydrodynamic pumps. In the theoretical part, the author is then dealing with the general principles and so far used approaches to the inducer design. The practical part of the thesis describes the process and the derivation of own designs of cylindrical inducer. The aim of the used, unconventional approaches to the inducer design is to achieve a constant pressure field and specific energy of the inducer design output. Partial variants of inducer blades design geometry are tested by the controlled calculation with CFD.

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1 Title Helical symmetry and the non-existence of asymptotically flat periodic solutions in general relativity Author Martin Scholtz Department Institute of theoretical physics Faculty of Mathematics and Physics Charles University in Prague Supervisor Prof. RNDr. Jiří Bičák, DrSc., dr. h.c. Abstract. No exact helically symmetric solution in general relativity is known today. There are reasons, however, to expect that such solutions, if they exist, cannot be asymptotically flat. In the thesis presented we investigate a more general question whether there exist periodic asymptotically flat solutions of Einstein's equations. We follow the work of Gibbons and Stewart [3] who have shown that there are no periodic vacuum asymptotically flat solutions an- alytic near null infinity I. We discuss necessary corrections of Gibbons and Stewart proof and generalize their results for the system of Einstein-Maxwell, Einstein-Klein-Gordon and Einstein-conformal-scalar field equations. Thus, we show that there are no asymptotically flat periodic space-times analytic near I if as the source of gravity we take electromagnetic, Klein-Gordon or conformally invariant scalar field. The auxilliary results consist of corresponding confor- mal field equations, the Bondi mass and the Bondi massloss formula for scalar fields. We also...

The aim of this diploma thesis is to describe mechanisms involved in a lubricant film formation in textured conformal contacts. For exploring of the lubricant film formation, the method of optical interferometry is implemented on a pin-on-disc tribometer. That allows to study an influence of a texture on lubricant film thickness and coefficient of friction of textured samples. These samples have different parameters of a texture. On the basis of these effects and the visual image of the contact, the flow of lubricant in the contact area is described. Shallow dimples lead to larger film thickness in elasto-hydrodynamic lubrication regime. They act like a lubricant reservoir. Deep dimples positively affect film thickness in hydrodynamic lubrication regime, where the effect of shallow dimples descend. During experiments, the formation of a cavitation is observed. The cavitation causes a starvation of dimples in many cases. This leads to reducing of the lubricant film thickness. This effect can be eliminated by appropriate parameters of texture in operational conditions of elements.

The aim of this diploma thesis is to experimentally elucidate the connection between the friction of the specimen with the textured surface and the optical observation of the sliding contact surface. The thesis focuses on the configuration of the journal bearing. This configuration is achieved by replacing the block with a circular sapphire section on a block-on-ring tribometer. For exploring of the lubricant film formation, the method of optical interferometry and fluorescence is implemented on the block-on-ring tribometer. These adjustments allow examination of the effect of the textured surface on the friction coefficient and the thickness of the lubricant film. In a mixed mode, the textures cause a significant increase in friction values and reduce the thickness of the lubricant film. The negative influence of dimples increases with the increasing radial load size. In the hydrodynamic mode, the textures have a lower negative effect on the resulting values than in the mixed mode. The changes are dependent on the size of the radial load and the viscosity of the lubricant. In the hydrodynamic mode, cavitation was not observed, and the effect of the textured surface does not correspond to theoretical prerequisites, which is reflected by lower lubricant thickness and higher friction.

Conformal geometric algebra is defined in the thesis. Representations of geometric objects and possibilities of their geometric transformations are presented. Conformal geometric algebra is applied to the calculation of forward kinematics of a robotic manipulator UR10 from Universal Robots. It is also applied to determine the position of the machine based on the location and rotation of two cameras. Then it is used in an inverse task, where based on records from the two cameras, dimensions of the UR10 manipulator and possibilities of its movement, the mutual position of these cameras is determined. And consequently the possibilities of their location in space. Finally, the derived procedures are implemented in a custom program created in the CluCalc environment, using which a sample example verifying the correctness of these procedures is calculated.

his diploma thesis deals with hydraulic design of vane wheel impeller of wide range Francis turbine; in addition to hydraulic calculation it consists overview of used theory, modelling in SolidWorks and computing in Fluent.

Tato diplomová práce má za cíl seznámit čtenáře se stále ještě relativně novou a neznámou oblastí matematiky, s geometrickou algebrou. Nejdříve jsou uvedeny základní definice a poté jsou studovány vlastnosti obecné geometrické algebry. Další velká část textu se věnuje Konformní geometrické algebře, která je v současnosti jedna z nejvíce zkoumaných a aplikovaných geometrických algeber. Jsou popsány její algebraické a geometrické vlastnosti, konkrétně schopnost reprezentovat určité geometrické objekty jako vektory. Taktéž umožňuje počítat jejich průniky a konformní transformace. Další část textu je zaměřena na aplikace Konformní geometrické algebry, nejdříve k popisu kinematiky robotické ruky a poté v binokulárním viděni.

This thesis focuses on robotic 3D vision for application in Bin Picking. The new method based on Conformal Geometric Algebra (CGA) is proposed and tested for identification of spheres in Pointclouds created with 3D scanner. The speed, precision and scalability of this method is compared to traditional descriptors based method. It is proved that CGA maintains the same precision as the traditional method in much shorter time. The CGA based approach seems promising for the use in the future of robotic 3D vision for identification and localization of spheres.