A lower bound for the equilateral number of normed spaces

We show that if the Banach-Mazur distance between an -dimensional normed space and is at most , then there exist equidistant points in . By a well-known result of Alon and Milman, this implies that an arbitrary -dimensional normed space admits at least equidistant points, where is an absolute constant. We also show that there exist equidistant points in spaces sufficiently close to , .

     

The microscopic investigation of structures of moving flux lines by neutron and muon techniques

We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux lines in low T _c type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbor FLL direction. This tends to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo technique to observe the energy change of neutrons diffracted by moving flux lines. The muon spin rotation (μSR) technique gives the distribution of values of magnetic field within the FLL. We have recently succeeded in performing μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors.     

Lattice and ion dynamics in gel electrolytes based on poly(acrylonitrile) by6Li-7Li NMR

Two composite gel electrolytes prepared from mixtures of poly(acrylonitrile) (PAN), propylene carbonate (PC), ethylene carbonate (EC) and LiClO₄ have been studied with differential scanning calorimetry (DSC) and⁷Li-⁶Li NMR. The data allow estimation of ionic conductivities, local (short range) diffusivities, and lattice dynamics. Furthermore, they point to an unexpected behavior of the Li-rich sample that hints to a complex LiClO₄-PAN phase diagram. Paper presented at the 1st Euroconference on Solid State Ionics, Zakynthos, Greece, September 11–18,1994     

Monitoring by two-dimensional electrophoresis somatic embryogenesis in leaf and petiole explants from Vitis.

A two-dimensional electrophoretic analysis of the total proteins was carried out in Vitis rupestris as model system in order to characterize the different developmental stages--from callus to plantlets--of somatic embryogenesis events in the grapevine. The patterns of callus, embryogenetic callus, somatic embryos and plantlets derived from leaf and petiole explants were compared. Each differentiation step was characterized by specific peptide spots.     

GRASP and path relinking for project scheduling under partially renewable resources

Recently, in the field of project scheduling problems the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labor scheduling. In this paper, we develop some preprocessing techniques and several heuristic algorithms for the problem. Preprocessing significantly reduces the dimension of the problems, therefore improving the efficiency of solution procedures. Heuristic algorithms based on GRASP and Path relinking are then developed and tested on existing test instances, obtaining excellent results.     

Galois module structure of Tate modules

Dedicated to Professor Peter Roquette Received 1 February 1996; in final form 26 April 1996     

Addition of methoxy radicals to olefins

The addition of methoxy radicals to several olefins has been studied by a competitive method at 127°C in gas phase. The thermal decomposition of dimethyl peroxide was used as methoxy radical source. The rate of addition to the double bond was measured relative to the oxidation of carbon monoxide. For the addition to ethylene it was obtained that This rate constant is similar to the one shown by methyl radicals under similar conditions. From the relative rate of addition to several chlorinated and fluorinated olefins it can be concluded that methoxy radicals show very little “electrophilic” character.     

Nuclear interaction of 300 GeV negative poins in emulsion

Experimental data are presented on charged particle multiplicities production in interactions of 300 GeV/c negative poins with emulsion nuclei. Correlations were established and the obtained parameters of multiplicity distributions compared with those obtained from proton-nucleus interaction data at 300 GeV/c.     

Reactivity of β-aluminas with water

The reactivity with air moisture of finely divided crystals of Na β and Li⁺-containing β-aluminas is analyzed with thermogravimetric and X-ray techniques. For Na β-alumina two distinct water intake processes are evident: 1) a fast one, controlled by the elastic interactions among water molecules near the crystal boundaries; 2) a slow one, driven by water diffusion away from the boundaries. For finely divided crystals of Li β-alumina the two processes cannot be distinguished but the slow one is observable in crystals of macroscopic dimensions. The water intake is generally accompanied by an expansion of the c-axis. However, the relationship between water content and c-parameter is highly non-linear and the c-axis length at room temperature depends upon the thermal history of the sample. Our results confirm previous reports suggesting that β-aluminas absorb about one water molecule per cation of the conducting plane.