Soliton concept in general relativity

Soliton physics has made considerable progress in solving nonlinear problems. This paper is meant to relate the soliten concept to the stationary axisymmetric vacuum fields in general relativity. We present a functional transformation which, working as a nonlinear creation operator, generates gravitational fields of isolated sources. When applied to flat space-time (gravitational vacuum) this operation leads to a nonlinear superposition of an arbitrary number of Kerr particles. This superposition also includes the Tomimatsu-Sato fields. The functional transformations form an infinite-parameter group which contains the Kinnersley-Geroch group as a subgroup.This essay received the second award from the Gravity Research Foundation for the year 1980.-Ed.     

Heterocyclische und carbocyclische 12-π- and 14-π-Molekülsysteme, 47. Mitteilung. Herstellung von 7, 9-Dimethyl-4, 5-dihydro-3 H-benz [cd]- azulen-3-on and 7,9-Dimethyl-3H-benz [cd]azulen-3-on. Eine einfache Synthese eines Azulenopseudophenalenons

Heterocyclic and Carbocyclic 12-π-and 14-π-Systems, 47th Commnunication¹. Synthesis of 7,9-Dimethyl-4,5-dihydro-3H-benz[cd]azualene-3-one and 7,9-Dimethyl-3H-benz[cd]azulene-3-one. A Simple Synthesis of Azulenopseudophenalenons 4, 6, 8-Trimethylazulene ( 3 ) reacts after metalation with lithiumdiisopropyl-amide in ether with bromoacetic acid to the 6, 8-dimethylaltulene-4-propionic acid ( 4 ), which undergoes cyclization to the 7, 9-dimethyl-4, 5-dihydro-3H-benz [cd]-azulene-3-one ( 5 ) in the presence of p-toluenesulfonic acid; oxidation of 5 with 2, 3-dichloro-5, 6-dicyanobenzoquinone yields 7, 9-dimethyl-3H-benz [cd]azulene-3--one ( 1b ). Alkylation of 1b with triethyloxonium tetrafluoroborate in CH₂C1₂ gives the 3-ethoxy [cd]benzazulenium tetrafluoroborate ( 6 ).     

Four-jet production in e+e−-annihilation

We investigate the four-jet production processes $e^{+}{e}^{?}\to q\overline{q}ggand{e}^{+}{e}^{?}\to q\overline{q}q\overline{q}$ in lowest order QCD perturbation theory. We estimate that four-jet events should be detectable at a rate of about 5% at the highest PETRA energy. The acoplanarity distribution is calculated and compared to nonperturbative effects.     

Convergence of m-bonacci ‘golden ratios’

This paper proves that the ratios of consecutive terms of the m-bonacci sequence converge to a limit φ_m < 2 and, as m → ∞, these φ_m converge to 2. Further, it is shown that the generating functions for the m-bonacci sequences converge pointwise to the geometric series.     

Alkali metal and ammonium cation–arene interactions with tetraphenylborate anion

Sodium, potassium, rubidium, caesium, ammonium and tetramethylammonium tetraphenylborates were studied by both positive and negative ion electrospray mass spectrometry. An affinity order of Cs⁺ > Rb⁺ > K⁺ ～ Na⁺ was obtained. The results obtained were compared with both calculations and solid-state structures, where available. The previously reported high affinity of caesium for tetraphenylborate concluded from NMR experiments was confirmed for the gas phase. The affinity does not appear to result from steric effects and a cation–pi interaction seems likely. In the positive ion mode, a unique acetonitrile complex of NaBPh₄ was observed.