Static spherically symmetric solutions of the Einstein-Yang-Mills equations

We study the global behaviour of static, spherically symmetric solutions of the Einstein-Yang-Mills equations with gauge groupSU(2). Our analysis results in three disjoint classes of solutions with a regular origin or a horizon. The 3-spaces (t=const.) of the first, generic class are compact and singular. The second class consists of an infinite family of globally regular, resp. black hole solutions. The third type is an oscillating solution, which although regular is not asymptotically flat.This article was processed by the author using the Springer-Verlag TEX CoMaPhy macro package 1991.     

A new method for designing optical resolutions and for determination of relative configurations

A new method has been elaborated for designing optical resolutions via diastereoisomeric salt formation, based upon the principle of three point interaction. In our method the favourite resolving agent to a given racemate and suitable resolution method can be found, and it can be predicted which enantiomer is expected in excess in the crystallized diastereoisomeric salt.     

Transmethylation of trimethylbenzenes and toluene on H- and Ni/H-mordenites

Under pressure in the presence of hydrogen the calculated transmethylation equilibrium composition was approached on synthetic H-mordenite at 350°C, on natural H-mordenites at 450–500°C. The high activity of H-mordenite is maintained without deactivation by using the reduced Ni, H-form of synthetic mordenite with a nickel content of 2.4 mass %.

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- 350°C - 450–500°C. - , Ni, - 2,4 . %

     

Primitive permutation groups of simple diagonal type

LetG be a finite primitive group such that there is only one minimal normal subgroupM inG, thisM is nonabelian and nonsimple, and a maximal normal subgroup ofM is regular. Further, letH be a point stabilizer inG. ThenH∩M is a (nonabelian simple) common complement inM to all the maximal normal subgroups ofM, and there is a natural identification ofM with a direct powerT ^m of a nonabelian simple groupT in whichH∩M becomes the “diagonal” subgroup ofT ^m: this is the origin of the title. It is proved here that two abstractly isomorphic primitive groups of this type are permutationally isomorphic if (and obviously only if) their point stabilizers are abstractly isomorphic. GivenT ^m, consider first the set of all permutational isomorphism classes of those primitive groups of this type whose minimal normal subgroups are abstractly isomorphic toT ^m. Secondly, form the direct productS _m×OutT of the symmetric group of degreem and the outer automorphism group ofT (so OutT=AutT/InnT), and consider the set of the conjugacy classes of those subgroups inS _m×OutT whose projections inS _m are primitive. The second result of the paper is that there is a bijection between these two sets. The third issue discussed concerns the number of distinct permutational isomorphism classes of groups of this type, which can fall into a single abstract isomorphism class.