Starting from literature about invariant mass, we will discuss the expression of the generalized additivity of masses in the special relativity for a system of particles. We will show the general formula of additivity in the framework of hyperbolic geometry too, showing it being invariant.
In previous discussions we have considered the Raman spectra of specific carbon-based materials, such as diamond, graphite, and the biochar resulting from pyrolysis of biomass. We have shown how spectra can be decomposed, according to the intended number of components and the proper line shapes. Here, we approach the Raman spectra of graphene and graphene oxide, to understand how many components are required to interpret the related fingerprints. Besides graphene and graphene oxides, here we also review some literature about the Raman spectroscopy of carbon nanotubes, focusing especially on the line shapes. As shown by literature, the Raman spectra are able of giving information on the nature of nanotubes (metallic or semiconducting) and if they are single- or multi-walled structures. We will find that the Raman spectroscopy is able of investigating even a single nanotube. It will be stressed the role of curvature in breaking the symmetry of carbon layers, to produce the observed Raman bands. In particular, the existence of Breit-Wigner-Fano lines will be investigated.
RRUFF database is proposing the Raman broad scans of glasses CaO-Al2O3-SiO2 with rare earth element (REE) oxides, that is of CaO-RE2O3-Al2O3-SiO2 glasses. Raman data are courtesy of E. Cairns, University of Edinburgh. Here we show how we can use the q-BWF functions to decompose these spectra. The q-BWF functions are generalizing the Breit-Wigner-Fano line shape in the framework of the q-exponential function proposed by Constantino Tsallis and his statistics. Besides asymmetry, the decompositions with q-BWF line shapes are stressing Gaussian and non-Gaussian behaviors of components. The data analysis of CaO-RE2O3-Al2O3-SiO2 glasses is highlighting the presence of photoluminescence regular patterns in the Raman broad scans. In another database, the Raman Open Database (ROD), we can find some spectra of rare-earth oxides. Therefore, it is possible to compare the available REO spectra with those of CaO-RE2O3-Al2O3-SiO2 glasses and study the broadening of the Raman bands.
According to Heinrich Nissen, in his Das Templum, 1869, the Roman town is a templum, an inaugurated space with its main axis, the decumanus, oriented towards the sunrise. The day on which the decumanus' direction was established, according to Nissen, was also the Dies Natalis of the town, and was associated with a festival in the Roman calendar. Nissen seems to have been the first to associate decumanus, sunrise, and festivals of the Roman calendar together. Nissen's Das Templum was used by Friedrich Nietzsche for his Der Gottesdienst der Griechen, which contains the lectures on the Greek cult that Nietzsche held between 1875 and 1878. Nietzsche endorsed Nissen's thesis regarding the decumanus. A totally different position is that of Isaac Valeton who, in his De Templis Romani (1983), shows that the town is not a templum and therefore does not require its decumanus ritually oriented to the sunrise. Valeton demonstrated that, according to Roman laws, the ground of the town is profane, and used by common people, subjected to the rule of the magistrate, not of àugurs. So Valeton criticizes Nissen's theory. We will also see in detail the discussion by Pierangelo Catalano, 1978, regarding the spatial aspects of the Roman juridical-religious system. In Catalano we find reiterated that the town is not a templum. Other scholar studies will be mentioned such as, for example, those by F. Castagnoli and J. Le Gall, which say the same. Regarding the centuriation, i.e. the subdivision of agricultural land, Castagnoli, Catalano and Le Gall stress that it is not a templum. Several scholars have therefore stressed that the town is not a templum, and the same for centuriation; this fact needs to be reiterated because archaeoastronomical approaches exist claiming to infer conclusions about the Roman world without considering Valeton, Catalano, Castagnoli, Le Gall and others' opinions about the templa.
