Two classes of metric spaces

The class of metric spaces (X,d) known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.

Comparison of available measurements of the absolute air-fluorescence yield and determination of its global average value

Experimental results of the absolute air-fluorescence yield are given very often in different units (photons/MeV or photons/m) and for different wavelength intervals. In this work we present a comparison of available results normalized to its value in photons/MeV for the 337 nm band at 1013 hPa and 293 K. The conversion of photons/m to photons/MeV requires an accurate determination of the energy deposited by the electrons in the field of view of the experimental set-up. We have calculated the energy deposition for each experiment by means of a detailed Monte Carlo simulation and the results have been compared with those assumed or calculated by the authors. As a result, corrections to the reported fluorescence yields are proposed. These corrections improve the compatibility between measurements in such a way that a reliable average value with uncertainty at the level of 5% is obtained.