The main aim of my thesis on the topic of "Euler's number in mathematical analysis" is to create an overview of the Euler numbers in calculus. This essay in the first part deals with the rise of the number e, in other parts of the current use of calculus. Purpose of this work is the insight students of secondary schools and universities to problems Euler numbers and to better understand the importance of e not only in mathematics.

Nowadays, the near-horizon regions of black holes have enjoyed great attention thanks to their role in the popular AdS/CFT correspondence and their specific geometry suitable for formulations of uniqueness theorems in higher dimensions. A strictly general-relativistic point of view reveals also many interesting phenomena taking place near black-hole horizons. Our aim was to investigate how horizon multiplicity affects near-horizon geometry, geodesical distance, radial motion of photons and massive, charged particles, and also the possibility of collision processes leading to unbound collision energies near the horizon. We chose the Reissner-Nordström-de Sitter metric, which, on the one hand, is simple thanks to being static and spherically symmetric but which, on the other hand, is rich enough to enable the existence of up to a doubly degenerate ultra-extreme horizon. After discussing the physical feasibility of the near-horizon limit, we applied it to single, double, and triple horizons, their near-horizon geometries, and local collision processes. We found continuous coordinate systems covering all types of horizons and analytic solutions for motion of radial photons and special or critical, massive, charged particles in their vicinity. We addressed particle collisions in the immediate vicinity of horizons...

This doctoral thesis focuses on noise generated during construction. It defines the legislative and physical aspects of this topic. It determines heavy machinery as noise source and categorizes them by their usage in construction technologies. It collects source data of the machinery noises which can be further used in prognostic models. It analyses the level of construction noise which can impact the nearby residential areas and offers methodology for modelling and designing the possible arrangements for the noise reduction. It defines partial effects of the construction site which are significant for the noise spreading. It establishes their role in the value of acoustic pressure level of the noise affecting the façade of the considered building. With the data collection and with case study verification it offers a prepared work tool which can be easily used to predict noise levels on construction sites and can be applied in the early constructions preparations. The structure of this thesis is planned for possible usage as university textbook or study support.