New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

Measurement of UV light emission of the nighttime Earth by Mini-EUSO for space-based UHECR observations

The JEM-EUSO (Joint Experiment Missions for Extreme Universe Space Observatory) program aims at the realization of the ultra-high energy cosmic ray (UHECR) observation using wide field of view fluorescence detectors in orbit. Ultra-violet (UV) light emission from the atmosphere such as airglow and anthropogenic light on the Earth's surface are the main background for the space-based UHECR observations. The Mini-EUSO mission has been operated on the International Space Station (ISS) since 2019 which is the first space-based experiment for the program. The Mini-EUSO instrument consists of a 25 cm refractive optics and the photo-detector module with the 2304-pixel array of the multi-anode photomultiplier tubes. On the nadir-looking window of the ISS, the instrument is capable of continuously monitoring a ~300 km x 300 km area. In the present work, we report the preliminary result of the measurement of the UV light in the nighttime Earth using the Mini-EUSO data downlinked to the ground. We mapped UV light distribution both locally and globally below the ISS obit. Simulations were also made to characterize the instrument response to diffuse background light. We discuss the impact of such light on space-based UHECR observations and the Mini-EUSO science objectives.Comment: 11 pages, 5 figures, presented in 37th International Cosmic Ray Conference (Berlin