After OR: An Agenda for Postmodernism and Poststructuralism in OR

Postmodernism and poststructuralism have only been mentioned in passing within this journal. There is much more to be said, and this paper aims to open up the debate, to begin to explore the vast terrain and to present one/some agenda/s for the future, introducing some of the ideas that have inspired O(u)R practice. The paper is in four episodes. We begin by exploring the differences between modernism and postmodernism and introducing some of our sources (episode 1), moving on to the study of language through structuralism and into poststructuralism (episode 2). This section introduces some key concepts and approaches which we illustrate in a short case study (episode 3) of the language of OR. The final section (episode 4) sketches in the outlines of our future agenda. A warning is in order for people unfamiliar with postmodernism: the terminologies and style may seem unusual and untraditional for the journal.     

NMR imaging in solids

The use of NMR imaging for the study of solids is demonstrated. A modified version of the convolution algorithm is used to construct the images. The modification removes the NMR linebroadening as the image is formed. Examples are presented using the mixed ionic conductor (Na_1?x, K_x) β-alumina.     

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