Multiplicities of interpoint distances in finite planar sets

What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted.     

Future contributions toJournal of Chemical Crystallography

Future contributions toJournal of Chemical Crystallography     

The force on a lattice defect in an elastic body

It is shown that the force on a lattice defect in an elastic body is, like the force on a disclination in a nematic liquid crystal, a real force which, for equilibrium, must be balanced by an external force applied to the closed surface enclosing the defect.     

Influence of poly(aminoquinone) on corrosion inhibition of iron in acid media

The inhibitor performance of chemically synthesized water soluble poly(aminoquinone) (PAQ) on iron corrosion in 0.5 M sulphuric acid was studied in relation to inhibitor concentration using potentiodynamic polarization and electrochemical impedance spectroscopy measurements. On comparing the inhibition performance of PAQ with that of the monomer o-phenylenediamine (OPD), the OPD gave an efficiency of 80% for 1000 ppm while it was 90% for 100 ppm of PAQ. PAQ was found to be a mixed inhibitor. Besides, PAQ was able to improve the passivation tendency of iron in 0.5 M H₂SO₄ markedly.     

Magnetic force microscopy studies of domain walls in nickel and cobalt films

A magnetic force microscopy is used to examine the domain walls in nickel and cobalt films deposited by argon ion sputtering. Thin nickel films deposited at high substrate temperatures exhibit coexistent Bloch and Neel walls. Films grown at room temperature display alternative Bloch lines with cap switches. These films agglomerate to form grains after annealed at high temperatures. The film composed of larger grains behaves better nucleation implying magnetic domains of closure, while the film composed of smaller grains exhibits more defects implying alternative Bloch lines. We have also observed domain displacements and cap switches, which occur due to precipitation of particles in small grain size films. Stripe domains are observed for film thicknesses larger than 100 nm. They become zigzag cells when an external field of 1.5 T is applied perpendicular to the surface of the films. This experiment indicates that the domain sizes in thin films and the strip widths for thick films both depend on the square-root of the film thickness, which varies from 5 to 45 nm and from 100 to 450 nm, respectively.     

Profile empirical likelihood for parametric and semiparametric models

This paper introduces a profile empirical likelihood and a profile conditionally empirical likelihood to estimate the parameter of interest in the presence of nuisance parameters respectively for the parametric and semiparametric models. It is proven that these methods propose some efficient estimators of parameters of interest in the sense of least-favorable efficiency. Particularly, for the decomposable semiparametric models, an explicit representation for the estimator of parameter of interest is derived from the proposed nonparametric method. These new estimations are different from and more efficient than the existing estimations. Some examples and simulation studies are given to illustrate the theoretical results. The first author is supported by NNSF projects (10371059 and 10171051) of China. The second author is supported by a grant from The Research Grants Council of the Hong Kong Special Administrative Region, China (#HKU7060/04P). The third author is supported by the University Research Committee of the University of Hong Kong and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU7323/01M).     

Analysis of triallate residues in cereals and soil by gas chromatography with ion-trap detection.

Triallate residues in barley seedlings and soil samples were determined by gas chromatography with ion-trap detection. Soil was extracted with methanol on a mechanical shaker, and plants were extracted with acetonitrile in a Sorvall homogenizer. After evaporation of the organic solvents, the residue was dissolved in hexane, and plants extracts were cleaned-up on an alumina column. Gas chromatographic analysis was carried out using a BP-1 fused-silica capillary column with helium as carrier gas. To quantitate residues the total-ion chromatogram was obtained and then the selected-ion monitoring chromatograms were displayed at m/z 86 for triallate and at m/z 154 for the internal standard, methyl-(4-amino-2-chloro)-benzoate. The average recovery through the method from barley and soil samples was always higher than 80%. The limit of detection in the selected-ion mode was 0.01 mg/kg. Barley and soil samples treated with triallate were also analysed. A good agreement was observed between results obtained by this method and by gas chromatography with nitrogen-phosphorus detection.