Elements of fractional calculus. Fractional integrals

The paper is devoted to the basic properties of fractional integrals. It is a survey of the well-known properties of fractional integrals, however, the authors tried to present the known information about fractional integrals as short and transparently as possible. We introduce fractional integrals on the compact interval and on the semi-axes, consider the famous Hardy-Littlewood theorem and other properties of integrability of fractional integrals. Among other basic properties, we consider Holder continuity and establish to what extent fractional integration increases the smoothness of the integrand. Also, we establish continuity of fractional integrals according to the index of fractional integration, both at strictly positive value and at zero. Then we consider properties of restrictions of fractional integrals from semi-axes on the compact interval. Generalized Minkowsky inequality is applied as one of the important tools. Some examples of calculating fractional integrals are provided. Pages of the article in the issue: 11 - 19 Language of the article: Ukrainia

Probing photo-ionization: Experiments on positive streamers in pure gasses and mixtures

Positive streamers are thought to propagate by photo-ionization whose parameters depend on the nitrogen:oxygen ratio. Therefore we study streamers in nitrogen with 20%, 0.2% and 0.01% oxygen and in pure nitrogen, as well as in pure oxygen and argon. Our new experimental set-up guarantees contamination of the pure gases to be well below 1 ppm. Streamers in oxygen are difficult to measure as they emit considerably less light in the sensitivity range of our fast ICCD camera than the other gasses. Streamers in pure nitrogen and in all nitrogen/oxygen mixtures look generally similar, but become somewhat thinner and branch more with decreasing oxygen content. In pure nitrogen the streamers can branch so much that they resemble feathers. This feature is even more pronounced in pure argon, with approximately 10^2 hair tips/cm^3 in the feathers at 200 mbar; this density could be interpreted as the free electron density creating avalanches towards the streamer stem. It is remarkable that the streamer velocity is essentially the same for similar voltage and pressure in all nitrogen/oxygen mixtures as well as in pure nitrogen, while the oxygen concentration and therefore the photo-ionization lengths vary by more than five orders of magnitude. Streamers in argon have essentially the same velocity as well. The physical similarity of streamers at different pressures is confirmed in all gases; the minimal diameters are smaller than in earlier measurements.Comment: 28 pages, 14 figures. Major differences with v1: - appendix and spectra removed - subsection regarding effects of repetition frequency added - many more smaller change

"Енциклопедія Сучасної України": регіональний аспект

The article is devoted to the actual issues of the preparation of the Encyclopedia of Modern Ukraine (EMU) and the participation of representatives of different regions in its creation. The potential of interaction of the centre and periphery in the implementation of the nationwide encyclopedic project is revealed on the example of this encyclopedia. In particular, it is traced how the national encyclopedia influences the development of regional encyclopedic book sphere as well as studies of regional encyclopedias, and vice versa, how regional encyclopedists contribute to the formation of the encyclopedic knowledge of the nationwide scale. The tasks for the editors of the EMU are formulated, which are updated in the regional context: a) use of the resource of the EMU at the lessons in secondary schools, in particular in history, law, etc.; b) the attraction of EMU materials to numerous state websites for the purpose of operating reliableinformation (nowadays information of geographical, historical, jurisprudential nature is often produced by the administrations of districts, regions, cities, towns, villages); c) creation of encyclopedic content in English, which will provide access to the international level.Статтю присвячено актуальним питанням підготовки "Енциклопедії Сучасної України" (ЕСУ) та участі науковців із регіонів України в її створенні.Обґрунтовано ЕСУ як пріоритетний напрям діяльності НАН України. Стверджено її значення в розвитку знань про історію, сьогодення, культуру України, українців у світі. Аргументовано наявність в Україні низки енциклопедичних видань, що в різні періоди її історії репрезентували розвиток національної енциклопедистики. Зроблено історичні порівняння в розвитку ЕСУ як продовження "Енциклопедії українознавства" й ВУЕ якправонаступника "Української радянської енциклопедії" та паралель з єдиним виданням "Енциклопедія Брокгауз" Німеччини. Виокремлено ключове завдання ЕСУ для створення образу України в географічному, політичному, науковому, культурному, мистецькому, спортивному вимірах. Стверджено наявність на першу половину 2019 року за сприяння потужної української діаспори 20-ти видрукуваних томів ЕСУ. Проаналізовано першопричини створення ЕСУ в контексті стратегії залучення до роботи над корпусом статей авторів з різних регіонів України, взаємодії при редакції ЕСУ інституту координаторів зі столичними, регіональними закладами вищої освіти, науковими інститутами НАНУ, науково-дослідними інститутами різних профілів, творчими спілками. Виокремлено як засіб реалізації енциклопедичних проектів діяльність мобільних опорних груп фахівців, які добре володіють інформацією про коло науковців, мистецтвознавців, краєзнавців для підготовки відповідних статей енциклопедичного стилю. На прикладі названого видання розкрито потенціал взаємодії центру й периферії в реалізації загальнонаціонального енциклопедичного проєкту. Простежено, як створення національної енциклопедії впливає на розвиток регіональної енциклопедистики, і як натомість регіональні енциклопедисти сприяють формуванню корпусу енциклопедичних знань загально-національного масштабу

Prepare Innovative integrated tools and platforms for radiological emergency preparedness and post-accident response in europe

International audienceThe PREPARE project that started in February 2013 and will end at the beginning of 2016 aims to close gaps that have been identified in nuclear and radiological preparedness in Europe following the first evaluation of the Fukushima disaster. Among others, the project will address the review of existing operational procedures for dealing with long-lasting releases and crossborder problems in radiation monitoring and food safety and further develop missing functionalities in decision support systems (DSS) ranging from improved source-term estimation and dispersion modelling to the inclusion of hydrological pathways for European water bodies. In addition, a so-called Analytical Platform will be developed exploring the scientific and operational means to improve information collection, information exchange and the evaluation of such types of disasters. The tools developed within the project will be partly integrated into the two DSS ARGOS and RODOS. © The Author 2014

Guided ionization waves: The physics of repeatability

Free to read on publisher website Guided ionization waves, or plasma streamers, are increasingly important for many applications in spanning materials processing and biomedicine. The highly reproducible, repeatable behavior of the most puzzling kind of the streamers–plasma bullets is highly attractive as it promises a high degree of control in many applications. However, despite a dozen years since the discovery of this phenomenon, the exact reasons for such behavior still remain essentially unclear. To understand the dynamics of the guided ionization wave (plasma bullet), a large number of works have been carried out and many interesting results have been reported. Here, we critically examine the available results and generalize the physical mechanisms of the guided ionization waves, which are of particular interest to practical applications of atmospheric-pressure plasma discharges, in general. The critical examination of the fundamental principles will show that, in order to propagate in a repeatable-mode, the plasma bullet must propagate in a channel with a high seed electron density (HSED), which is on the order of 109 cm−3. This review concludes that to distinguish guided ionization waves from traditional positive streamer discharges, it is most appropriate to describe an atmospheric-pressure discharge featuring a plasma bullet behavior as an HSED discharge. When the HSED condition is met, the dynamics of a plasma plume appears to be repeatable. On the contrary, it propagates in an unrepeatable mode and emerges more like a positive streamer discharge when the HSED condition is not satisfied. According to this theory, the transition of the propagation mode of the plasma bullet between the repeatable mode and the stochastic mode can be well explained. Besides by controlling the seed electron density around the transition region between the HSED discharge and the traditional positive streamer, this knowledge will help in better understanding of the positive streamer discharges in air, in cases relevant to practical applications of such plasma discharges in materials processing technologies, industrial chemistry, nanotechnology, and health care

Nuclear and radiological preparedness: The achievements of the European research project prepare

International audienceThe PREPARE project aimed closing gaps identified in nuclear and radiological preparedness in Europe following the first evaluation of the Fukushima disaster. With 46 partners from Europe and Japan, it collected the key players in the area of emergency management and rehabilitation preparedness. Starting from February 2013, the project ended in January 2016. Among others, the project reviewed existing operational procedures for long-lasting releases, cross-border problems in radiation monitoring and food safety and further developed missing functionalities in decision support systems ranging from improved source term estimation and dispersion modelling to the inclusion of hydrological pathways for European water bodies. In addition, a so-called Analytical Platform has been developed to explore the scientific and operational means to improve information collection, information exchange and the evaluation of such types of disasters. The tools developed within the project will be partly integrated into the decision support systems ARGOS and JRODOS