Schrodinger and Dirac operators with the Aharonov-Bohm and magnetic-solenoid fields

We construct all self-adjoint Schrodinger and Dirac operators (Hamiltonians) with both the pure Aharonov-Bohm (AB) field and the so-called magnetic-solenoid field (a collinear superposition of the AB field and a constant magnetic field). We perform a spectral analysis for these operators, which includes finding spectra and spectral decompositions, or inversion formulae. In constructing the Hamiltonians and performing their spectral analysis, we follow, respectively, the von Neumann theory of self-adjoint extensions of symmetric operators and the Krein method of guiding functionals.

Disintegration on heating of a Brazilian manganese lump ore

This pioneering study characterized the chemical, physical and mineralogical aspects of the Urucum Standard manganese ore typology, and evaluated some of its metallurgical characteristics, such as the main mineral heat decompositions, and the particle disintegration at room temperature and under continuous heating. A one-ton sample of ore was received, homogenized and quartered. Representative samples were collected and characterized with the aid of techniques, such as ICP-AES, XRD, SEM-EDS, BET and OM. Representative samples with particle sizes between 9.5 mm and 15.9 mm were separated to perform tumbling tests at room temperature, and thermogravimetry tests for both air and nitrogen constant flow at different temperatures. After each heating cycle, the mechanical strength of the orewas evaluated by means of screening and tumbling procedures. The Urucum Standard typology was classified as an oxidized anhydrous ore, with a high manganese content (~47%). This typology ismainly composed of cryptomelane and pyrolusite; however there is a significantamount of hematite. The Urucum Standard particles presented low susceptibility to disintegration at room temperature, but as temperature increased, susceptibility increased. No significant differences were observed between the tests done with the air or nitrogen injections.