Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method of uniformization: We assign to the nonlocal problem a pseudodifferential operator with the same index, acting in sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah-Singer index theorem.Comment: 16 pages, no figure

DIGITAL TRANSFORMATION STRATEGY: ASSESSMENT OF DIGITAL MATURITY OF THE RUSSIAN ELECTRIC POWER INDUSTRY

Based on the analysis of domestic and foreign experience of digital transformation and the conducted expert survey, the authors conclude that Russia, in comparison with other countries, does not have a leading position in the implementation of digital technologies. At the same time, the electric power industry being the basic sector of the economy which is responsible for its safe and sustainable development, in terms of digitalization is on the sidelines, yielding to retail, the banking industry, telecommunications and the manufacturing industry. At the same time, digitalisation is a promising direction and can have a significant positive impact on the electric power industry. The purpose of the study is to assess the current level of digital maturity of the electric power industry in Russia, identify the main barriers to digital transformation and develop proposals in order to overcome them.The article uses generalisation, comparative analysis, analyses empirical data of digitalisation in Russia and abroad, conducts a survey of experts in the electric power industry about its digital maturity

Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.Comment: 14 pages, corrected typos, references and comments adde

RISK OF RENEWABLE ENERGY SOURCES DEVELOPMENT IN THE OIL AND GAS INDUSTRY IN THE CONTEXT OF COVID-19

The global climate problem of climate warming has led to the active development of renewable energy almost all over the world. Many European countries and international corporations are already striving for carbon neutrality.This article analyzes the current trends in the development of the renewable energy sources industry in the world and in Russia, assesses the applicability of renewable energy sources in the oil and gas industry and the impact of the coronavirus crisis on the perspectives for renewable energy. The analysis of the indicators of the volumes of commissioning of generating capacities for 2020 is given, the obstacles encountered in the development of the industry due to the unstable global situation are considered.The article also discusses investment in renewable energy by oil and gas companies and their transformation under the influence of the renewable energy sector, as well as the participation of Russian companies in this transformation and their long-term prospects in relation to renewable energy

DEVELOPING MICROGENERATION BASED ON RES AS A DRIVER OF DECARBONISATION AND ECONOMIC GROWTH IN RUSSIA

Having analysed the domestic and foreign experience of developing the market of microgeneration based on renewable energy sources (RES) the authors conclude that a smart industrial policy can ensure an expedited transition to zero-carbon economy and stimulate economic growth. Research background – Russia’s commitment to achieve carbon neutrality by 2060. Research purpose – assessing the prospects and barriers in the development of microgeneration based on RES. Methods – generalising, comparing, analysing empirical evidence of microgeneration market development in Russia and abroad, calculating the levelized cost of electricity (LCOE) of a solar plant and comparing it with current low voltage tariffs for small and medium-sized businesses. Results and novelty – the authors have determined the most effective industrial policy tools for developing the market of microgeneration based on RES

Comparative physical-tribological properties of anti-friction ion-plasma Ti-C-Mo-S coating on VT6 alloy or 20X13 and 40X steels

Results of comparative tests mechanical and tribological properties of solid antifriction Ti-C-Mo-S coating, deposited by magnetron-plasma combined sputtering method on substrates of VT6 titanium alloy, 40X and 20X13 hardened steels are provided. Coating is sputtered using the same conditions and technological regimes on substrates of different materials. However, the friction tests results showed significant difference in tribological characteristics of coating depending on type of material used for substrate, first of all by wear-resistance ability. Authors suppose that this is due to difference between physical properties such as composition and structure of substrate materials that determines hardness and coating adhesion to surface

РИСКИ РАЗВИТИЯ ВИЭ В НЕФТЕГАЗОВОЙ ОТРАСЛИ В УСЛОВИЯХ COVID-19

The global climate problem of climate warming has led to the active development of renewable energy almost all over the world. Many European countries and international corporations are already striving for carbon neutrality.This article analyzes the current trends in the development of the renewable energy sources industry in the world and in Russia, assesses the applicability of renewable energy sources in the oil and gas industry and the impact of the coronavirus crisis on the perspectives for renewable energy. The analysis of the indicators of the volumes of commissioning of generating capacities for 2020 is given, the obstacles encountered in the development of the industry due to the unstable global situation are considered.The article also discusses investment in renewable energy by oil and gas companies and their transformation under the influence of the renewable energy sector, as well as the participation of Russian companies in this transformation and their long-term prospects in relation to renewable energy.Глобальная проблема изменения климата привела к активному развитию возобновляемой энергетики практически по всему миру. Множество европейских стран и международных корпораций уже сегодня стремятся к углеродной нейтральности.В настоящей статье проанализированы сложившиеся тенденции развития отрасли возобновляемых источников энергии в мире и в России, оценены применимость ВИЭ в нефтегазовой отрасли и влияние коронакризиса на перспективы возобновляемой энергетики. Приведен анализ показателей объемов ввода генерирующих мощностей за 2020 год, описаны возникшие препятствия в развитии отрасли в связи с нестабильным характером мировой ситуации.Также в статье рассмотрены особенности инвестирования в ВИЭ со стороны нефтегазовых компаний и их трансформация под влиянием сектора возобновляемых источников энергии, а также участие российских компаний в этой трансформации