MAGNETIC FLOW AND ITS QUANTIZATION

It is noted that the elementary electric charge is equal to e , from which fact the well-known principle of quantization of the electric charge definitely follows, namely, the electric charge is quantized and a quantum is the charge of the electron e (or positron). Or any change in the charge is equal to an integer number of electrons (or positrons). The formally identical transformation of the principle of quantization of the electric charge allows formulating the principle of quantization of the magnetic flux, namely, the quantity inverse to the magnetic flux is quantized and a quantum is the inverse of the quantum of the F. London magnetic flux. Or any change in the reciprocal of the magnetic flux is equal to an integer number of quantities inverse to the quantum of the F. London magnetic flux. The reciprocal of the magnetic flux quantum is equal to the sum of two quantities inverse to the quantum of the F. London magnetic flux. The validity of the principle of quantization of the magnetic flux with respect to the hydrogen atom is illustrated by Theorem 1: quantization of the energy of the hydrogen atom is a consequence of the principle of quantization of the magnetic flux. Theorem 2 is proved: the magnetic flux of a hydrogen atom in the ground state is equal to the quantum of the F. London magnetic flux. Theorem 3 is proved: the quantum of the magnetic flux is not the minimum possible for a nonzero magnetic flux. It is established that the quantum of the magnetic flux is not a quantum in the sense of a portion (like the F. London quantum). A quantum is the inverse of the quantum of the F. London magnetic flux. It is established that the magnitude of the magnetic flux quantum is not the minimum possible for a nonzero magnetic flux. It is established that the magnetic flux of a hydrogen atom in the ground state is equal to the quantum of the F. London magnetic flux. A discrete set of energies of the hydrogen atom is noted to be a consequence of the solution of the Schrödinger equation, which, in turn, is phenomenological. The reverse discourse used in the proof of Theorem 1 can show that the Schrödinger equation is a consequence of the principle of quantization of the magnetic flux.

A journey as a strategy of gaining the knowledge of the Jewish world in fiction of the end of the 19th — first decades of the 20th century

The article analyzes imagological parameters of the Jewish ethnoimage presented through the dimension of travel in the fiction of the late 19th and early 20th centuries. Due to the intensification of national imagology in the past decades, the study of the Others’s existence is an actual scholarly issue. The representation of Jewry is traced by the example of three texts of different aesthetics and genres with the commonality of travel discourse: Istoriia odniieii podorozhi [The Story of One Journey] (1890) by Ahatanhel Krymskyi, Modest Levytskyi’s Porozhnim hodom [In Vain] (1918) and Shchastia Peisakha Leidermana [The Happiness of Peisakh Leiderman] (1918), and Mike Yohansen’s essay Podorozh liudyny pid kepom (Ievreiski kolonii) [The Journey of a Man in a Cap (Jewish Colonies)] (1927). According to the paper, the geopoetic component, that is the movement in space, seems to be a way of cultural, identical transformation, a shift in the experience of the characters and the reader: moving “inside” of the Jewish culture and the Jewish world in real and symbolically, everyone cognizes better the other culture, and simulthaneously His own. In Krymskyi’s story, the journey of Itsko the Jew and Skalskis the Ukrainians is denoted by the imagological inversion of ethnostereotypes: the figures of Ukrainians are depicted in a negative mode, while a Jewish image is positive. This confirms the dynamics of gradual decline from the stereotypical interpretation of the Others by writers. In the end, we get the image of Jew built-in a realistic axiological paradigm, whose personal tragedy is tangled by social prejudices. The “Doctor's Stories” by Modest Levitskyi against the backdrop of heavy Jewish life appeal to the universal context of human suffering. Penetrating into the other culture, the protagonist gradually undergoes a personal transformation and recognizes the Others more deeply. Mike Yohansen’s alter ego’s observation of colonial Jews’ life in the Southern Ukrainian regions reveal the spiritual and social proximity of the Ukrainian and Jewish peoples, their comfortable coexistence in a common geographical, linguistic, and economic space. The research originality lies in the fact that valuable in the imagological light texts of Ahatanhel Krymskyi, Modest Levytskyi and Mike Yohansen are considered as representing the Jewish ethnoimage from the position of homo viator. The perspective of the development of the topic is multidimensional study of the Jewish ethno-form in the unexplored segments of the national literary space.

MATHEMATICAL FORMALIZATION OF INSTITUTIONS

The article proposes the way of mathematical formalization of institutions in the framework of game-theory approach. The rules are represented by transpositions of payoffs in payment matrix. Such the transitions call the change the structure of game equilibriums. This approach allows separation of coordination and distribution aspects of institutions, division institutions into classes and distinguishing aggregateс of institutions, which produce identical transformation. Through evolutionary game theory formalism it is shown that such parametric management influences the structure of steady states, what allows investigation of institutions’ influence on self-organization, in particular, through transformation of topology of phase portrait of the system. In accordance with the fact that dynamic with multiple steady states is typical for coordination problem as a whole, an approach suggested of the rules formalization appears to have rather broad application.

The Abelian Case of Solitar's Conjecture on Infinite Nielsen Transformations

The paper proves that the group of infinite bounded Nielsen transformations is generated by elementary simultaneous Nielsen transformations modulo the subgroup of those transformations which are equivalent to the identical transformation while acting in a free abelian group. This can be formulated somewhat differently: the group of bounded automorphisms of a free abelian group of countably infinite rank is generated by the elementary simultaneous automorphisms. This proves D. Solitar's conjecture for the abelian case.