Caps and codes

The packing problem in the theory of caps is that of finding, or at least bounding, the size m(r, q) of an ovaloid (cap of largest size) in the projective space S_r,q of dimension r over a field of q elements. This problem and that of constructing and classifying ovaloids are approached by consideration of certain codes associated with caps. Improved general upper bounds on m(r, q) are found, which give m(5, 3)?56 as a particular case. A 56-cap in S_5,3 is constructed via its code and its uniqueness as an ovaloid is demonstrated.     

Gelation and the production of surface grown polyethylene fibres

Summary In the course of examining the limiting conditions for growth of polyethylene fibres by the surface growth method (1, 2) an unexpected gelation effect was observed. Accordingly a solution, after having been stirred at such elevated temperatures where no visible crystallization can take place, is found to set as a gel after cooling under quiescent conditions. It is established that the ability to form this gel is a necessary condition for fibre production byPennings andZwijnenburg's surface growth method which by the new findings essentially should consist of the stretching of such gels. We verified that material indeed accumulates at the surface of the rotor used in the surface growth method as was originally envisaged, but we now infer that this material consists of gel particles formed during the preceding treatments. This adhesion of the gel to a rotating surface enables it to be readily stretched by an externally introduced fibre as done in the surface growth method. The gel precursor is of interest in its own right. We find that it is a transient structure but with long, up to several hours, persistence time during which the solution `remembers' that it has been stirred. The structure itself is presumably an incipient network forming crystallization induced by localised chain stretching, where the crystal junctions are likely to provide the nuclei for the more permanent fibrous crystals which arise on cooling causing the gel to set. Electron microscopy indeed identified smooth fibres in the gel which could develop into shish-kebabs on appropriate treatment, while the bulk of the gel consists of large single crystal platelets which arise within the network on final cooling to room temperature. Finally we suggest, that many, if not all, shishkebab structures conventionally observed on stirring arise by the stretching of the gel network formed at a preceding stage of the preparation procedure.     

Transition metal-stabilized arenium cations: protonation of arenes dihapto-coordinated to pi-basic metal fragments

A series of metal complexes was synthesized in which arenes were dihapto-coordinated to pi-basic metal fragments having the general form [TpM(pi-acid)(L)], where Tp = hydridotris(pyrazolyl)borate, M = rhenium, molybdenum, or tungsten, pi-acid = CO or NO(+), and L = 1-methylimidazole, 1-butylimidazole, pyridine, or trimethylphosphine. The arene complexes were shown to be significantly more basic than the analogous pentaammineosmium(II) arene complexes and were protonated by moderate acids to give remarkably stable eta(2) and eta(3) arenium cation complexes. A crystal structure of [TpRe(CO)(MeIm)(5,6-eta(2)-2H-anisolium)](OTf) confirmed the eta(2) coordination of the anisolium ligand, but suggests a weak long-range interaction between the metal and C1 of the anisolium.     

Do light colored scalars exist?

The general question of the properties of light, neutral colored spin-zero particles in QCD is examined. Models with spontaneous breaking of QCD at very large distances, such as that of DeRújula, Giles, and Jaffe and the SO(3) scheme of Slansky, Goldman, and Shaw, require such light colored Higgs scalars. These scalars will form color-singlet hadronic bound states at short distances and estimates are given of bound state masses, decay widths, and production rates in processes such as ψ → γ + X within the MIT bag model. The resulting states are expected in the mass neighborhood ～1.5 GeV and should resemble glueballs.     

Investigation of the fermi edge in sodium tungsten bronzes by photoelectron spectroscopy

High-resolution photoelectron spectra of sodium tungsten bronzes Na _xWO₃ (0.26<x< 0.76) reveal a linear variation in the density of states at the Fermi energy as a function of sodium content. This behaviour does not appear to arise from filling of a rigid conduction band. Magnetic susceptibilities calculated from photoemission data using a simple independent-electron model agree with measured values.