We report a systematic study of the optical conductivity of twisted bilayer graphene (tBLG) across a large energy range (1.2-5.6 eV) for various twist angles, combined with first-principles calculations. At previously unexplored high energies, our data show signatures of multiple van Hove singularities (vHSs) in the tBLG bands as well as the nonlinearity of the single layer graphene bands and t...

Bertrand’s paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand’s paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover,...

A number of nutrient media have been described by Goodman (1954), Katagiri (1954), Niedercorn (1952), Petty et al. (1953), Van Dyke and De Somer (1952), and others that allow Streptomyces aureofaciens Duggar to grow in aerated, liquid culture and to accumulate substantial quantities of 7-chlorotetracycline.' The concentrations of 7-chlorotetracycline accumulated on these different media vary fr...