Nonsolvable Groups Satisfying the One-prime Hypothesis

Recall that a finite group G satisfies the one-prime hypothesis if the greatest common divisor for any pair of distinct degrees in cd(G) is either 1 or a prime. In this paper, we classify the nonsolvable groups that satisfy the one-prime hypothesis. As a consequence of our classification, we show that if G is a nonsolvable group satisfying the one-prime hypothesis, then |cd(G)| ≤ 8, and hence, if G is any group satisfying the one-prime hypothesis, then |cd(G)| ≤ 9. Presented by Don Passman.     

Values of the Pukánszky invariant in McDuff factors

In 1960 Pukánszky introduced an invariant associating to every masa in a separable II₁ factor a non-empty subset of N∪{∞}. This invariant examines the multiplicity structure of the von Neumann algebra generated by the left-right action of the masa. In this paper it is shown that any non-empty subset of N∪{∞} arises as the Pukánszky invariant of some masa in a separable McDuff II₁ factor containing a masa with Pukánszky invariant {1}. In particular the hyperfinite II₁ factor and all separable McDuff II₁ factors with a Cartan masa satisfy this hypothesis. In a general separable McDuff II₁ factor we show that every subset of N∪{∞} containing ∞ is obtained as a Pukánszky invariant of some masa.     

Second-kind integral formulations of the capacitance problem

The standard approach to calculating electrostatic forces and capacitances involves solving a surface integral equation of the first kind. However, discretizations of this problem lead to ill-conditioned linear systems and second-kind integral equations usually solve for the dipole density, which can not be directly related to electrostatic forces. This paper describes a second-kind equation for the monopole or charge density and investigates different discretization schemes for this integral formulation. Numerical experiments, using multipole accelerated matrix–vector multiplications, demonstrate the efficiency and accuracy of the new approach. This revised version was published online in June 2006 with corrections to the Cover Date.     

Sulfuration and reversion reactions of brominated poly(isobutylene‐co‐isoprene)

The sulfuration and reversion products of brominated poly(isobutylene‐co‐isoprene) (BIIR) were characterized through the use of a model compound, brominated 2,2,4,8,8‐pentamethyl‐4‐nonene (BPMN). The reaction of BPMN with S₈ produced bisallylic polysulfides of various ranks, yielding sulfur bromide intermediates that likely contributed to the rapid oxidation of allylic sulfides into thiophenes. Reductive cure reversion to pentamethylnonene was also observed in the latter stages of vulcanization. The reaction of 2,2′‐dithiobisbenzothiazole with BIIR and BPMN produced a stable adduct that reduced the concentration of allylic bromide available for vulcanization. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1915–1926, 2003     

Comparison of carbon-silicon hyperconjugation at the 2- and 4-positions of the N-methylpyridinium cation

[structure: see text] N-Methyl-2-trialkylsilylmethylpyridinium cations 6a-c and 4-trialkylsilylmethylpyridinium cations 5a-c were prepared and investigated using (29)Si and (13)C NMR and single-crystal X-ray crystallography. Systematic differences in the (29)Si chemical shifts and (29)Si-(13)C one-bond coupling constants for these cations suggested that the Si-CH(2) bond interacts more strongly at the 2-position of the electron-deficient pyridinium ring than at the 4-position. This result is supported by the X-ray structures of the pyridinium cations 5b and 6b.