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Higher-order approximations in the finite element methods
Kolman, Karel ; Křížek, Michal (advisor) ; Feistauer, Miloslav (referee) ; Mlýnek, Jaroslav (referee)
A survey of existing nite element superconvergence theory is conducted. The Steklov postprocessing operator is presented and its properties are investigated, superconvergence bounds are proved. A two-level method for eigenvalue problems is generalized for application to a nonselfadjoint problem. Applications of superconvergence theory to variationally formulated eigenvalue problems are discussed. Numerical experiments documenting the methods are performed.
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Cosmology on Small Scales 2020: Excessive extrapolations and selected controversies in cosmology
Křížek, Michal ; Dumin, Y. V.
According to the modern cosmological paradigm, about 2/3 of the energy of the Universe is in dark form and about 5/6 of the matter is invisible. However, numerous recent independent attempts to detect dark-matter particles failed, and a number of other problems with the existence of dark energy and dark matter (such as the anomalous friction in the dark-matter halos of galaxies) become now more and more obvious. All these problems raise the question if the 'dark' substance is merely a result of the use of erroneous assumptions or incorrect models based e.g. on excessive extrapolations. Consequently, it is timely to gather specialists from various branches of astronomy and astrophysics to discuss these questions.
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A critical review of paradoxes in the special theory of relativity
Křížek, Michal
We show that the Doppler effect and aberration of light can produce more dominant and entirely opposite effects for relativistic speeds than those predicted by the Special Theory of Relativity, in particular, the clock paradox, time dilatation, and length contraction. For instance, an observer will measure a higher frequency of an approaching clock than the same clock has at rest. We also prove that under certain conditions an approaching bar on a photo may seem to have a larger length for a relativistic speed than at rest.
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Excessive extrapolations of Einstein's equations
Křížek, Michal ; Somer, L.
The standard cosmological model is surprisingly quite thoroughly investigated even though it possesses many paradoxes. We present several arguments indicating why excessive extrapolations of Einstein's equations to cosmological distances are questionable. First, we show how to express explicitly the first of Einstein's 10 partial differential equations to demonstrate their extremely large complexity. Therefore, it would be very difficult to find their solution for two or more bodies to model, e.g., the evolution of the Solar system. Further, we present some unexpected failures of the Schwarzschild and Friedmann solution of these equations. Then we explain why application of Einstein's equations to the whole universe represents incorrect extrapolations that lead to dark matter, dark energy, and several unrealistic situations. Finally, we give 10 further arguments showing why celebrated Einstein's equations do not describe reality well.
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Survey of the basic cosmological discoveries from years 1910-1930
Liška, Andrej ; Mészáros, Attila (advisor) ; Křížek, Michal (referee)
Between 1910 and 1930 a large number of astronomical discoveries took place. Henrietta Swan Leavitt revealed the relationship between the luminosity and the period of Cepheids, which then bacame the indicators for distance de- termination in the universe. Based on this relation in 1925 Edwin Powell Hubble calculated the distance to our neighboring Galaxy M31. Tireless exploration of the nebulae by Vesto Melvin Slipher brought a very important ratio between the red and blue shifts, where the red ones clearly dominated. In 1927 Georges Edouard Lemaître derived Hubble's law from Einstein's field equations, indepen- dently on Alexander Alexandrovich Friedmann. Two years later Hubble definitely demonstrated the linear behavior between the red shift and the distance. 1
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Cosmology on Small Scales 2018: Dark Matter Problem and Selected Controversies in Cosmology
Křížek, Michal ; Dumin, Y. V.
According to the standard cosmological model, our Universe needs a significant amount of dark matter, about six times more than that of the usual baryonic matter, besides an even larger amount of dark energy. But to date, both dark matter and dark energy have remained conceptually elusive, without concrete evidence based on direct physical measurements. Yet another subtle issue is that the Friedmann equation – the cornerstone of modern cosmology – was derived from the system of ten Einstein’s equations applied to a perfectly symmetric universe, which is homogeneous\nand isotropic for every fixed time instant. So, the question is whether one can perform such excessive extrapolations and, in particular, at which scale the effect of Hubble expansion is manifested.
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Neglected gravitational redshift in detections of gravitational waves
Křížek, Michal ; Somer, L.
In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the authors have not taken into account a large gravitational redshift of this binary system, which is a direct consequence of time dilation in a strong gravitational field. Thus the proposed masses are overestimated. In our paper we also give other arguments for this statement.
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Classification of distances in cosmology
Křížek, Michal ; Mészáros, A.
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single natural distance, since the universe is expanding, curved, and we look back in time. In this survey paper we will concentrate on geometrical interpretations of the above-mentioned distances.
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Trends in the field management of the education in dissertations of department
Křížek, Michal ; Trojan, Václav (advisor) ; Šafránková, Jana Marie (referee)
The Management of the education is the five years old filed of study of the Faculty of Education of Charles University in Prague. This dissertation is looks for some trends of this field, based on all dissertations of the department for the period 2012-2016. The dissertation also provides an overview that is good for understanding of important concepts such as management, school management, educational policy or management ef education. The main goal of this dissertation is to map the development of topics and contents that have appeared during the last five years in the dissertation of the department, to analyze the problems that were most often encountered and to find out which factors influenced the selection of themes and the whole process.
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