Über das lineare Maß von Punktmengen

Ohne ZusammenfassungVorliegende Arbeit war vom Verfasser kurz vor seinem am 22. Oktober 1918 erfolgten Tode der Redaktion überreicht, aber nochmals zurückerbeten worden, weil an dem in den Nummern 11 bis 18 behandelten Beispiel einige Änderungen angebracht werden sollten. Der Herausgeber hat sich daher darauf beschränkt, unter Beibehaltung der Grundgedanken an dem erwähnten Beispiele einige Änderungen in der Beweisführung vorzunehmen, die diese offenbar in der Umarbeitung stecken gebliebenen Partien klären und leichter verständlich machen sollen. Eine Lücke konnte der Herausgeber leider nicht ausfüllen, worauf an den betreffenden Stellen verwiesen ist. In den übrigen Teilen beschränkte sich die Tätigkeit des Herausgebers auf die Verbesserung offensichtlicher Schreibfehler.     

Real sol-gel synthesis of catalytically active aluminium fluoride

Abstract Amorphous AlF₃ prepared via an anhydrous sol-gel synthesis route exhibits high surface area and Lewis acidity far beyond those known for crystalline AlF₃ phases. Its catalytic properties are comparable to those of SbF₅. Basis of its unusual properties is a sol-gel fluorination with anhydrous HF in organic solvents yielding first a wet Al-F-sol-gel, which can be dried and eventually post-fluorinated. All parts of the synthesis route were thoroughly investigated. The results of these investigations together with detailed analysis of the Al-F-materials obtained are reported and discussed.     

Breakup temperature of target spectators in 197Au + 197Au collisions at E/A = 1000 MeV

Breakup temperatures were deduced from double ratios of isotope yields for target spectators produced in the reaction ¹⁹⁷Au + ¹⁹⁷Au at 1000 MeV per nucleon. Pairs of ^3,4He and ^6,7Li isotopes and pairs of ^3,4He and H isotopes (p, d and d, t) yield consistent temperatures after feeding corrections, based on the quantum statistical model, are applied. The temperatures rise with decreasing impact parameter from 4 MeV for peripheral to about 10 MeV for the most central collisions. The good agreement with the breakup temperatures measured previously for projectile spectators at an incident energy of 600 MeV per nucleon confirms the universality established for the spectator decayat relativistic bombarding energies. The measured temperatures also agree with the breakup temperatures predicted by the statistical multifragmentation model. For these calculations a relation between the initial excitation energy and mass was derived which gives good simultaneous agreement for the fragment charge correlations. The energy spectra of light charged particles, measured at τ_lab = 150°, exhibit Maxwellian shapes with inverse slope parameters much higher than the breakup temperatures. The statistical multifragmentation model, because Coulomb repulsion and sequential decay processes are included, yields light-particle spectra with inverse slope parameters higher than the breakup temperatures but considerably below the measured values. The systematic behavior of the differences suggests that they are caused by light-charged-particle emission prior to the final breakup stage.