Novel annulene dications from methylated [2.2]metacyclophane monoenes and [e]-ring benzannelated dimethyldihydropyrene

Tetramethyl- and hexamethyl-substituted [2.2]metacyclophane monoenes (10 and 11) are transformed into their corresponding trans-dimethyldihydroethanophenanthrenium dications (14(2+) and 15(2+)) in FSO(3)H x SbF(5) (4:1) and FSO(3)H x SbF(5) (1:1) with SO(2)ClF or SO(2) as the solvent; these 10 pi-dications are equivalent to the C-4/C-5 diprotonated dications of the 2,7-dimethyl derivative of trans-DMDHP, 3a. The trans-12c,12d-dimethyl-12c,12d-dihydrobenzo[e]pyrene (6) reacts with FSO(3)H/SO(2)ClF under surprisingly mild conditions to give initially a persistent diprotonated dication (6H(2)(2+)) and, subsequently, the oxidation dication (6(2+)); the 6(2+):6H(2)(2+) ratio reaches 4:1 after 1 week at low temperature. Protonation of the anti-metacyclophane (13) was also examined. Charge delocalization mode and tropicity in the resulting dications are gauged via detailed NMR studies at 500 MHz.     

THE MOLECULAR WEIGHT OF HAEMATOPORPHYRIN DERIVATIVE, ITS GEL COLUMN FRACTIONS and SOME OF ITS COMPONENTS IN AQUEOUS SOLUTION

Abstract— The average molecular weights of haematoporphyrin derivative (HPD), the fractions of HPD that can he obtained by gel chromatography and of purified haematoporphyrin and protoporphyrin in aqueous solution have been determined by ultracentrifugation. The results show that HPD contains polymeric material with the excluded fraction from the gel column (HPD aggregate) having an average molecular weight of greater than 20000. The two remaining gel column fractions of HPD have lower molecular weights and their similarity indicates that these fractions do not separate because of molecular weight differences. Purified haematoporphyrin has a comparatively low molecular weight in aqueous solution but the data is not capable of discriminating between monomer, dimer or slightly higher oligomer. In contrast, protoporphyrin sediments to the bottom of the centrifuge tube under the conditions of sedimentation equilibrium indicating that it has an average molecular weight considerably greater than that of HPD aggregate.     

Recent results from the TCV tokamak

During the first two years of operation, the TCV tokamak has produced a large variety of plasma shapes and magnetic configurations, with 1.0B _tor1.46T,I _p800kA,k2.05, –0.71. A new shape control algorithm, based on a finite element reconstruction of the plasma current in real time, has been implemented. Vertical growth rates up to 1000s^–1 have been stabilized using the external coil system. Ohmic H-modes with Troyon factors ( _tor aB/I _p) up to two and densities up to 2.25×10²⁰m^–3, corresponding to the Greenwald limit, have been obtained in diverted discharges. Limiter H-modes with line averaged electron densities up to 1.7×10²⁰m^–3 have been obtained in elongated D-shaped plasmas with 360 kAI _P600 kA.Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.This work was partly supported by the Fonds National Suisse de la Recherche Scientifique.     

Oriented local entropies for expansive actions by commuting automorphisms

Given an expansive action α of ?² by automorphisms of a compact connected metrizable abelian groupX, we show how the entropy of the action may be decomposed into local contributions, 1 $$h(\alpha ) = \sum\limits_{p \leqslant \infty } {h_p^{(a,b)} } (\alpha )$$ in which the summandh _p ^(a,b) (α) represents thep-adic entropy due to arithmetic or geometric hyperbolicity in the direction (a, b). We recognize thep-adic contribution as an integral over thep-adic unit circle, in analogy with the global counterpart. As (a, b) changes, the decomposition (1) changes only when the line through (a, b) passes through one of a finite collection of critical directions, which are explicitly identified.