Trace and extension operators for fractional Sobolev spaces with variable exponent

We show that, under certain regularity assumptions, there exists a linear extension operator

Density properties for fractional Sobolev spaces with variable exponents

International audienceIn this article we show some density properties of smooth and compactly supported functions in fractional Sobolev spaces with variable exponents. The additional difficulty in this nonlocal setting is caused by the fact that the variable exponent Lebesgue spaces are not translation-invariant

THEORY OF CAPACITIES IN FRACTIONAL SOBOLEV SPACES WITH VARIABLE EXPONENTS

In this paper we develop a capacities theory connected with the fractional Sobolev spaces with variable exponents. Two kinds of capacities are studied: Sobolev capacity and relative capacity. Basic properties of capacities, including monotonicity, outer capacity and several results, are studies. We prove that both capacities is a Choquet capacity and all borel sets are capacitable. Mathematics Subject Classification: Primary 31B15, 46E35

On the Continuous embeddings between the fractional Haj{\l}asz-Orlicz-Sobolev spaces

Let $G$ be an Orlicz function and let $\alpha, \beta, s$ be positive real numbers. Under certain conditions on the Orlicz function $G$, we establish some continuous embeddings results between the fractional order Orlicz-Sobolev spaces defined on metric-measure spaces $W_s^{\alpha, G}(X, d, \mu)$ and the fractional Haj{\l}asz-Orlicz-Sobolev spaces $M^{\beta, G}(X,d,\mu)$

أهمية المقاربة الحضارية في تفعيل التراث: مداخل توجيهية = Significance of civilisational approach in activating heritage: key guidelines = Kepentingan pendekatan tamadun dalam mengaktifkan warisan: garis panduan utama

This paper addresses the importance of the civilizational approach in activating and renewing Islamic heritage. This vision of heritage is comprehensive, taking into account the various dimensions and factors that affect our understanding of heritage and dealing with it in an organised and authentic way that reflects its spirit and values. The paper clarifies the necessity to develop integrated approaches to dealing with heritage in view of understanding, analysis, criticism, evaluation and utilization provided that it adheres to the supreme reference of revelation and its general purposes. There have appeared readings that deal with various heritage issues, including rejection, acceptance and the integrated moderate. The paper provides major keys of the civilizational approach to heritage. It concluded that the heritage cannot be activated only through unfounded criticism, but with a systematic vision that takes into account its nature and characteristics. The paper suggests the need to work on completing the components of the civilizational approach and its applications and to work on disseminating and teaching them as courses or programs in universities and relevant institutions. Keywords: Civilisational approach, Heritage, Tawhidic Reference, Epistemology Theorisation

Machine Learning for Photovoltaic Systems Condition Monitoring:A Review

Condition Monitoring of photovoltaic systems plays an important role in maintenance interventions due to its ability to solve problems of loss of energy production revenue. Nowadays, machine learning-based failure diagnosis is becoming increasingly growing as an alternative to various difficult physical-based interpretations and the main pile foundation for condition monitoring. As a result, several methods with different learning paradigms (e.g. deep learning, transfer learning, reinforcement learning, ensemble learning, etc.) have been used to address different condition monitoring issues. Therefore, the aim of this paper is at least, to shed light on the most relevant work that has been done so far in the field of photovoltaic systems machine learning-based condition monitoring

Machine Learning-Based Condition Monitoring for PV Systems: State of the Art and Future Prospects

From MDPI via Jisc Publications RouterHistory: accepted 2021-09-30, pub-electronic 2021-10-03Publication status: PublishedTo ensure the continuity of electric power generation for photovoltaic systems, condition monitoring frameworks are subject to major enhancements. The continuous uniform delivery of electric power depends entirely on a well-designed condition maintenance program. A just-in-time task to deal with several naturally occurring faults can be correctly undertaken via the cooperation of effective detection, diagnosis, and prognostic analyses. Therefore, the present review first outlines different failure modes to which all photovoltaic systems are subjected, in addition to the essential integrated detection methods and technologies. Then, data-driven paradigms, and their contribution to solving this prediction problem, are also explored. Accordingly, this review primarily investigates the different learning architectures used (i.e., ordinary, hybrid, and ensemble) in relation to their learning frameworks (i.e., traditional and deep learning). It also discusses the extension of machine learning to knowledge-driven approaches, including generative models such as adversarial networks and transfer learning. Finally, this review provides insights into different works to highlight various operating conditions and different numbers and types of failures, and provides links to some publicly available datasets in the field. The clear organization of the abundant information on this subject may result in rigorous guidelines for the trends adopted in the future