Optimal transport and dynamics of expanding circle maps acting on measures

Using optimal transport we study some dynamical properties of expanding circle maps acting on measures by push-forward. Using the definition of the tangent space to the space of measures introduced by Gigli, their derivative at the unique absolutely continuous invariant measure is computed. In particular it is shown that 1 is an eigenvalue of infinite multiplicity, so that the invariant measure admits many deformations into nearly invariant ones. As a consequence, we obtain counter-examples to an infinitesimal version of Furstenberg's conjecture. We also prove that this action has positive metric mean dimension with respect to the Wasserstein metric.Comment: 35 pages; v4 includes a corrigendum (Lemma 4.2 statement and proofs are corrected without influence on the main results) and an addendum (application to an infinitesimal version of Furstenberg Conjecture, Theorem 1.7 and Corollary 1.8

Rozliczać? Tak, ale…

To answer the following question, one has to give some general reasons for the compensation. On the other hand, one has to examine them on the basis of some relevant variables modifying their use. Jacek Filek’s axiological theory of “demanding by values (a given response)” rooted in thinking of Roman Ingarden, Max Scheler and Nicolai Hartmann contains the best suggestion of such reasons. It has to be referred to important moments such as: who?, whom?, for what?, when?, how long?, etc. It is necessary to avoid a change of this concept into revenge

Instrumentalization as a sin of untruth

The reconstructions, analyses and discussions concerning various broadly understood instrumentalized objects available in the subject literature allow one to distinguish and identify at least two interrelated forms of instrumentalization - a weak and a strong form. The former consists of using a particular object for fulfilling an aim in its unspecific functions. Thus, it can be treated as opposite to the phenomenon of functional fixation. The essence of the latter is a change in the position of the instrumentalized object, both in the ontological and axiological order - one which is a degrading change. It is this form of instrumentalization which allows the possibility of its reinterpretation in the categories of a sin of untruth. Such reinterpretation makes use of the multitude of forms of truth and their interrelationships, as well as of the distinction between a "great and small truth." Thus, the heuristic value of the rhetoric of sin used here enables one to emphasise some important factual aspects. Firstly, referring to many possible dimensions in which instrumentalization can be subjected to evaluation, sin will be treated here metaphorically (due to taking into account all dimensions together) and literally (in order to highlight in consequence its moral, conscious and intended character). Secondly, this rhetoric can reflect the complex structure of instrumentalization, expressed in the categories of a sin committed "in thought, word, deed and omission," of a light or heavy nature, with violation carried out on the nature of the instrumentalized object as its extreme form. Thirdly, rhetoric allows one to understand the perpetrator of instrumentalization's activation of disguising, justifying or even absolving his activities. Fourthly, this results in seeking out the psychological mechanism of "being led into temptation." Its complex character can be clearly seen in many cases, especially in the case of political instrumentalization of religion, where, on the one hand, the profanation of religion takes place, while on the other, the legitimisation, ennoblement or even sacralisation of politics occurs

Segregation in noninteracting binary mixture

Process of stripe formation is analyzed numerically in a binary mixture. The system consists of particles of two sizes, without any direct mutual interactions. Overlapping of large particles, surrounded by a dense system of smaller particles induces indirect entropy driven interactions between large particles. Under an influence of an external driving force the system orders and stripes are formed. Mean width of stripes grows logarithmically with time, in contrast to a typical power law temporal increase observed for driven interacting lattice gas systems. We describe the mechanism responsible for this behavior and attribute the logarithmic growth to a random walk of large particles in a random potential due to the small ones.Comment: 5 pages, 4 figure

Double step structure and meandering due to the many body interaction at GaN(0001) surface in N-rich conditions

Growth of gallium nitride on GaN(0001) surface is modeled by Monte Carlo method. Simulated growth is conducted in N-rich conditions, hence it is controlled by Ga atoms surface diffusion. It is shown that dominating four-body interactions of Ga atoms can cause step flow anisotropy. Kinetic Monte Carlo simulations show that parallel steps with periodic boundary conditions form double terrace structures, whereas initially V -shaped parallel step train initially bends and then every second step moves forward, building regular, stationary ordering as observed during MOVPE or HVPE growth of GaN layers. These two phenomena recover surface meandered pair step pattern observed, since 1953, on many semiconductor surfaces, such as SiC, Si or GaN. Change of terrace width or step orientation particle diffusion jump barriers leads either to step meandering or surface roughening. Additionally it is shown that step behavior changes with the Schwoebel barrier height. Furthermore, simulations under conditions corresponding to very high external particle flux result in triangular islands grown at the terraces. All structures, emerging in the simulations, have their corresponding cases in the experimental results.Comment: 25 pages, 8 figure

Glosa do wyroku Sądu Ochrony Konkurencji i Konsumentów sygn. akt XVII Amo 1/21 z dnia 7 czerwca 2021 roku, dotyczącego decyzji Prezesa Urzędu Ochrony Konkurencji i Konsumentów nr DKK-34/2021 z 5 lutego 2021 roku

Glosa dotyczy wyroku Sądu Ochrony Konkurencji i Konsumentów wydanego w sprawie Orlen/Polska Press. Omówiono w niej również wydane w ww. sprawie decyzje Prezesa Urzędu Ochrony Konkurencji i Konsumentów, a także odwołanie od decyzji Rzecznika Praw Obywatelskich. Glosa obejmuje głównie zagadnienia dotyczące możliwości uwzględnienia przesłanek pozaekonomicznych w ramach oceny planowanej koncentracji

Życie rodzin wojskowych podczas powstania listopadowego

The article deals with the life of soldiers’ families during the November Uprising.With the beginning of the uprising their lives had changed in many areas. The Capital, which was constantly overcrowded, was not able to provide lodging even for militaries. During the war the amount of payment was decreasing. Despite the bad financial situation of the Polish Kingdom, the authorities tried to pay salaries and pensions regularly. Meanwhile the families tried to communicate. One of the chance were visits in the camps.W artykule poruszono kwestię życia rodzin wojskowych podczas powstania listopadowego. Wraz z wybuchem powstania zmieniło się wiele sfer ich życia. W stolicy, która była nieustannie przeludniona, brakowało kwater nawet dla wojskowych. Stopniowemu pomniejszeniu ulegały również stawki żołdu wojskowych. Mimo złej sytuacji finansowej Królestwa Polskiego, władze starały się regularnie wypłacać pensje oraz emerytury. Tymczasem rodziny starały się wzajemnie kontaktować. Jedną z form były odwiedziny w obozach