Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach

We derive weak turbulence and quasilinear models for relativistic charged particle dynamics in pitch-angle and energy space, due to interactions with electromagnetic waves propagating (anti-)parallel to a uniform background magnetic field. We use a Markovian approach that starts from the consideration of single particle motion in a prescribed electromagnetic field. This Markovian approach has a number of benefits, including: 1) the evident self-consistent relationship between a more general weak turbulence theory and the standard resonant diffusion quasilinear theory (as is commonly used in e.g. radiation belt and solar wind modeling); 2) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; 3) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales. The quasilinear diffusion coefficients that we derive are not new in and of themselves, but this concise derivation and discussion of the weak turbulence and quasilinear theories using the Markovian framework is physically very instructive. The results presented herein form fundamental groundwork for future studies that consider phenomena for which some of the assumptions made in this manuscript may be relaxed.

Thermodynamic description of metastable fcc/liquid phase equilibria and solidification kinetics in Al-Cu alloys

The thermodynamic description of the fcc phase in the Al-Cu system has been revised, allowing for the prediction of metastable fcc/liquid phase equilibria to undercoolings of Δ T = 421 K below the eutectic temperature. Hypoeutectic Al-Cu alloys that are prone to pronounced microsegregation were solidified containerlessly in electromagnetic levitation. Solidus and liquidus concentrations were experimentally determined from highly undercooled samples employing energy-dispersive X-ray analysis. Solid concentrations at a rapidly propagating solid/liquid interface were additionally calculated using a sharp interface model that considers all undercoolings and is based on solvability theory. Modelling results (front velocity versus undercooling) were also corroborated by in situ observation with a high-speed camera. A newly established thermodynamic description of the fcc phase in Al-Cu is compatible with existing CALPHAD-type databases. Inconsistencies of previous descriptions such as a miscibility gap between Al-fcc and Cu-fcc on the Al-rich side, an unrealistic curvature of the solidus line in the same composition range or an azeotropic point near the melting point of Cu, are amended in the new description. The procedure to establish the description of phase equilibria at high undercoolings can be transferred to other alloy systems and is of a general nature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Fractional calculus pertaining to multivariable Aleph-function

In this paper we study a pair of unied and extended fractional integral operator involving the multivariable Aleph-function, Aleph-function and general class of polynomials. During this study, we establish ve theorems pertaining to Mellin transforms of these operators. Furthers, some properties of these operators have also been investigated. On account of the general nature of the functions involved herein, a large number of (known and new) fractional integral operators involved simpler functions can also be obtained . We will quote the particular case concerning the multivariable I-function dened by Sharma and Ahmad [20] and the I-function of one variable dened by Saxena [13].

Introduction: Black Swans and Sinatra Inferences

Public mismanagement as a threat to life and limb is a rare and highly improbable phenomenon—the proverbial Black Swan. Bridges and buildings collapse, claiming the lives of people who had every reason to believe that governmental agencies protect their physical integrity through public oversight and maintenance. Properly analyzed, however, these unlikely events reveal causal mechanisms of a general nature, strong enough to trigger fateful mismanagement even under the restrictive conditions of professional bureaucracies and democratic government. Hence the “Sinatra Inference”: When a mechanism is powerful enough ‘to make it there’—i.e., where causal leverage is supposedly low—it is likely to ‘make it everywhere’ as soon as leverage is enlarged by weaker accountability structures, lower professional standards and lesser values than human safety.

Vitality Analysis Algorithm in the Study of Plant Individuals and Populations

Background: The article presents an algorithm of the vitality analysis of plant individuals in the populations that enables the assessment of the prospects for the existence of species within certain phytocenoses and provides important information on the conditions of their growth. There are three basic stages of the algorithm: the first stage is the selection of qualitative characters, which characterize the viability of individuals; the second stage is the assessment of the vitality of specific plant individuals included in the sampling; the third stage is an integral assessment of the population vitality structure. Objective: The goal of the study is to develop the basic algorithm for vitality analysis of populations based on the assessment of the vitality of plant individuals, as well as the authors’ algorithms for vitality analysis, considering the characteristic features of species, in particular, their different life strategies (C-type and R-type). The algorithm of the vitality analysis is demonstrated on the example of populations of the annual weed Persicaria scabra Moench (Polygonaceae), which grows in the pea crop planting (Sumy Region, Ukraine). Methods: The algorithm of vitality analysis is based on the method of Yu. A. Zlobin, which includes 3 main stages. The vitality analysis of populations is carried out on the basis of the assessment of the vitality of certain individuals. The assessment of the vitality structure of populations is the third stage of vitality analysis, where the population belonging to the prosperous, equilibrium, or depressive types is determined depending on the ratio of individuals of different vitality classes (a, b, c). The calculation of the vitality analysis provides for the transformation of absolute values into unit fractions. It ensures the equivalence of the contribution of each of the features used in the assessment of the vitality of individuals and populations as a whole. Results: The article presents a basic algorithm for vitality analysis of plant populations. It also shows the algorithm for vitality analysis considering some biological and ecological characters of the studied species, which may be used in special and relatively rare cases. Some examples of analyses with a well-defined primary strategy ‒ competitors (C-type) or explerents (R-type) have been presented in the article. To calculate the morphoparameters of plant individuals and populations, the most convenient is the statistical package “Statistics”, which provides for the possibility of calculation automation via the command line. The division of populations into three types according to vitality is of general nature. The method of assessing the population vitality is inherently comparative, and this feature is considered to be its advantage. Conclusion: Vitality analysis is useful in assessing the populations of rare plant species, meadow grasses, chemical contamination on the population of plants, identifying any changes in the status populations of forest herbs in the change of forest growth conditions, as well as a number of species of forest-forming tree species. The proposed variants of the algorithm to calculate the vitality of plant species and local populations are characterized by the high biological informative value and flexibility. The incorporated information on the vitality structure of populations in quantitative PVA models to predict their dynamics will significantly increase the reliability of forecasts regarding the prospects for the existence of phytopopulations of species in various plant communities.

Combined system of extreme control of mineralized water dilution in river basins

The theory of combined systems of extreme control, which is used in technical systems, was developed and adapted in socio-ecological-economic systems. For example, river basins are such systems. A combined extreme control system has been formalized to control the dilution of mineralized mine waters in river sections. A mathematical model of the distribution of water masses and pollution in river beds from point and diffuse sources is proposed on the basis of a system of difference balance equations under the influence of stochastic uncontrolled disturbances. With regard to such conditions as adequate instrumentation, a combined control system has been developed that uses decision-making according to environmental and economic criteria based on the analysis of input and output data simultaneously, identification and tracking of the optimum in conditions of displacement under the influence of the disturbances of extreme characteristics of the system. The structural and functional diagram is represented by the open-loop diagram, the identification of which is carried out on the basis of modeling the process of water dilution in various situations at a specific object. A closed part with a recognition system as a corrector provides feedback. Formalized mathematical models of the dynamics of water masses and pollution from point and diffuse sources are of a general nature and can be used for the basins of other rivers. The extreme control system can adapt to the hydrological conditions and water quality parameters of a particular river. A mathematical model has been formalized for the combined extreme control of mine water dilution in the section of the Ingulets river. The water for dilution comes from a storage pond in the Svystunov gully. Regulatory actions that maintain water quality without exceeding the normative values ​​of maximum permissible discharge are determined. At the same time, water consumption for dilution is minimized. The scenario analysis of the options showed a saving of up to 30% of water resources, namely 17.5 million m3, compared to the dilution carried out in February-March 2021 according to the existing individual regulations.

Independence of Regulatory Authorities in the Energy Market. Comment to the Judgement of EU Court of Justice in C-378/19 Prezident Slovenskej republiky

In its judgement C-378/19, the Court of Justice of the European Union responded to the question for a preliminary ruling referred by the Slovak Constitutional Court. The ECJ found in this judgement that Directive 2009/72/EC must be interpreted as not precluding withdrawal of the competence of the President of a Member State to appoint and dismiss the chairperson of the national regulatory authority, and conferral of the same power to the Member State’s government. Similarly, allowing the participation of the Ministers of the Environment and of the Economy in certain price-setting procedures does not violate the decision-making independence of the national regulatory authority. In his commentary, the author cites the line of argument in the judgement and presents the political context in Slovakia that led to the preliminary question. The author then comments approvingly on the judgement, noting that the Court rightly refrained from assessing the political situation in Slovakia, instead opting to focus on the law. At the end of the commentary, the author makes remarks of a general nature relating to the independence of national regulatory authorities.

Painting as a continuous script. Protocols for an idea

Every knowledge, every understanding or attempt to arrange the world usually carries within it a certain degree of change, of recreation. Given the general nature of reality, the artist’s accumulated subjective experience is the only possible guide, landmark, or main source of knowledge. An idea is the notion of some thing initself. The ideas and thinking of the world in metaphors make the connection between art and reality, between the integral and the multiple, but also between the real and the imaginary. The artistic effort is reduced to the search for ways to translate, to draw, to express things through forms, giving them both universal validity and individuality. The text protocols a subjective/author’s project from the idea to the realization.

TIME LIMITS FOR STORAGE OF PERSONAL DATA PROCESSED IN THE MINISTRY OF INTERIOR IN CONNECTION WITH CONDUCTING CRIMINAL PROCEEDINGS UNDER THE PENAL PROCEDURE CODE AND WITH CHECKS FOR THE EXISTENCE OF DATA OF CRIMES OF A GENERAL NATURE

The report discusses the compliance of the regulation establishing the time limits for storage of personal data processed by the Ministry of Interior in connection with criminal proceedings and inspections for data of crimes of a general nature with the requirements of the Personal Data Protection Act and EU law.

Vliv organizace státní správy na (místní) příslušnost soudů ve správním soudnictví

This paper deals with changes that have taken place in the organisation of state administration from the perspective of administrative justice and its local jurisdiction. In order to do so, the paper answers the basic question of whether the organisation of state administration (in terms of the local jurisdiction of administrative authorities) and the organisation of administrative courts (also in terms of their local jurisdiction) are related or not. In this context, it is worth considering whether the organisation of administrative justice should follow the organisation of the public/state administration as such and its trends, or even the opposite, and whether the two phenomena should not be independent of each other. The paper summarises the issue of the criteria for determining the local jurisdiction of administrative courts, the legal regulation of which has undergone certain developments, similar to the development of the legal regulation of the organisation of the state administration. The question is whether any common indicators can be traced. The issue under examination is not only of a purely practical nature, such as the criteria for determining the local jurisdiction of an administrative court. It is related to the overall state of both the state administration and the administrative justice and their organization, and it offers a number of questions of a more general nature, such as the formal and informal impact of “its” regional court on the administrative authorities within its jurisdiction, the influence of their case law on “local administrative law”, the question of the availability of administrative courts, or access to them, as well as their caseload. Overall, the paper discusses whether it is possible to find any relationship, or rather consequences, arising from the local jurisdiction of administrative authorities, resulting of course from the form of the organisation of the state administration, and the (non)corresponding local jurisdiction of the administrative justice. Possible de lege ferenda considerations in terms of the organisation and local jurisdiction of the administrative justice are also mentioned.