Analytical quasinormal modes of spherically symmetric black holes in the eikonal regime

Quasinormal modes in the high frequency (eikonal) regime can be obtained analytically as the Mashhoon-Will-Schiutz WKB formula is exact in this case. This regime is interesting because of the correspondence between eikonal quasinormal modes and null geodesics, as well as due to existence of potential eikonal instabilities in some theories of gravity. At the same time in a number of studies devoted to quasinormal modes of spherically symmetric black holes this opportunity was omitted. Here we find analytical quasinormal modes of black holes in various alternative and extended theories of gravity in the form of the Schwarzschld eikonal quasinormal modes and added corrections due to deviations from Einstein theory. We also deduce a generic formula for analytical calculations of the eikonal quasinormal modes for the class of asymptotically flat metrics in terms of small deviations from the Schwarzschild geometry.Comment: 5 pages, 1 figure, revtex, new material and references adde

Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line

In this paper we establish some new Kolmogorov type inequalities for the Marchaud and Hadamard fractional derivatives of functions defined on a real axis or semi-axis. Simultaneously we solve two related problems: the Stechkin problem on the best approximation of unbounded operators by bounded ones on a given class of elements and the problem of optimal recovery of operator on elements from some class given with prescribed error. Keywords: inequalities for derivatives, fractional derivatives, approx- imation of unbounded operators by bounded ones, optimal recovery of operators, ideal lattice.Comment: 3 figure

String loop vibration around Schwarzschild black hole

String loop vibrations in a central plane of a Schwarzschild black hole are investigated for various string equations of state. We discuss string loop stability and derive frequencies of vibrational modes. Using the vibrating string loop model we fit the quasi-periodic oscillation (QPO) observed in X-ray signal coming from some compact sources. We demonstrate how the string-loop parameters are related to the radial and vertical fundamental vibration modes, and how the vibrational instability can be related to the Q-factor characterizing the observed QPOs.Comment: 13 pages, 9 figure

Financial analysis in a selected business entity

Bakalářská práce je zaměřena na finanční analýzu ve vybraném podnikatelském subjektu a to konkrétně u společnosti JTEKT Automotive Czech Plzen s.r.o. Cílem této bakalářské práce je zhodnotit výkonnost vybraného podniku a navrhnout doporučení pro zlepšení ekonomické situace. V teoretické části je definována podstata finanční analýzy, její účel, uživatele a potřebné zdroje informací. Dále jsou popsány základní metody a ukazatele finanční analýzy, ke kterém patří absolutní, poměrové, rozdílové a souhrnné ukazatele. V praktické části je představena vybraná společnost a následně je provedena její finanční analýza pomocí elementárních metod. Zdrojem informací byly výkazy společnosti za roky 2017 až 2021 a statistické údaje Ministerstva průmyslu a obchodu České republiky. V poslední kapitole je shrnuta celková ekonomická situace společnosti a jsou navrženy doporučení pro její zlepšení.ObhájenoThe graduation work is focused on the financial analysis of the selected enteprenurial organization, namely the company JTEKT Automotive Czech Pilsen LLC. The purpose of this bacherol's thesis is to evaluate the effectiveness of the chosen enterprise and offer recommendations to improve the economic situation. The theoretical part defines the essence of financial analysis, its purpose, users and necessary sources of information. The following is a description of the basic methods and ratios of financial analysis, which include absolute, ratio, difference and summary ratios. In the practical part of the work the selected company is presented and then conducted its financial analysis with the help of elementary methods. The main sources of information were company reports for 2017-2021, as well as statistical data from the Ministry of Industry and Trade of the Czech Republic. The last chapter summarizes the overall economic situation of the company and proposes recommendations for its improvement