Radiation and the structure of space-time

The classical bremsstrahlung problem is discussed with respect to the global structure of space-time. Various physical phenomena (such as the Hawking effect, etc.) connected with the large-scale structure of space-time are mentioned.This work was supported by the Deutsche Forschungsgemeinschaft (DFG).     

Circle and divisor problems,and double series of Bessel functions

In approximately 1915, Ramanujan recorded two identities involving doubly infinite series of Bessel functions. The identities were brought to the mathematical public for the first time when his lost notebook was published in 1988, and are connected with the classical, long-standing circle and divisor problems, respectively. We provide a proof of the first identity for the first time by analytically continuing a new kind of Dirichlet series. Delicate estimates of exponential sums are needed, and the new methods we introduce may be of independent interest.     

TRANSESTERIFICATION OF TRIS(p-NITROPHENYL) PHOSPHATE WITH SODIUM ALKOXIDES: BIS(p-NITROPHENYL) METHYL PHOSPHATE,BIS(p-NITROPHENYL) BENZYL PHOSPHATE,BIS(p-NITROPHENYL) n-BUTYL PHOSPHATE

Abstract

Transesterification of tris(p-nitrophenyl) phosphate by sodium alkoxides, in dichloromethane at 0°, provides a convenient synthetic route to diaryl alkyl phosphates which are produced in a high state of purity and in moderate to high yields. The procedure is used to prepare bis(p-nitrophenyl) methyl phosphate, bis(p-nitrophenyl) benzyl phosphate and bis(p-nitrophenyl) n-butyl phosphate.     

Graphene on Ru(0001): contact formation and chemical reactivity on the atomic scale

Graphene on Ru(0001) is contacted with Au tips of a cryogenic scanning tunneling microscope. The formation and conductance of single-atom contacts vary within the moiré unit cell. Density functional calculations reveal that elastic distortions of the graphene lattice occur at contact due to a selectively enhanced chemical reactivity of C atoms at hollow sites of Ru(0001). Concomitant quantum transport calculations indicate that the graphene-Ru distance determines the conductance variations.