Carleman estimate for a stationary isotropic Lamé system and the applications

For the isotropic stationary Lamé system with variable coefficients equipped with the Dirichlet or surface stress boundary condition, we obtain a Carleman estimate such that (i) the right hand side is estimated in a weighted L ²-space and (ii) the estimate includes nonhomogeneous surface displacement or surface stress. Using this estimate we establish the conditional stability in Sobolev's norm of the displacement by means of measurements in an arbitrary subdomain or measurements of surface displacement and stress on an arbitrary subboundary. Finally by the Carleman estimate, we prove the uniqueness and conditional stability for an inverse problem of determining a source term by a single interior measurement.     

Incipient plasticity during nano-scratch in Ni3Al

The subsequent sliding behaviour of the initially elastic, submicron contacts between a diamond tip and bulk polycrystalline Ni₃Al was investigated by nano-scratch tests. Scratches are made under constant normal loads otherwise too low to trigger crystal plasticity in uniaxial nanoindentation experiments. Three types of behaviour are observed: (i) the entire scratch is purely elastic with a sliding coefficient of friction (μ) of about 0.086; (ii) a sudden strain burst in the normal direction, commonly known as pop-in, occurs at the onset of sliding and the subsequent sliding is plastic with μ typically a few times larger than 0.086; and (iii) an intermediate case in which the scratch is initially elastic followed by a pop-in beyond which the sliding becomes plastic. The intermediate case occurs rather randomly. The μ for elastic sliding is found to be load- or size-independent, but that for plastic sliding exhibits a strong size effect, i.e. it is small at small loads, but increases towards a steady value at larger loads.     

Mathematics,Science of Possibility ‐‐ A Critical Review

This paper supports the view that search for the applicative standpoint in mathematical education has yet to be sufficiently exploited. Mathematical propositions are considered to have both an ‘internal’ and ‘external’ role and thus a system of ‘potential models’ is evolved. Despite the stress on the applicative nature of the subject it is argued in conclusion that the position in the body of the paper is compatible with the synthetic apriority of mathematics.

     

Antibacterial Behavior of Pyridinecarboxylatesilver(I) Complexes

FT‐IR spectroscopy of carboxylic groups and viability tests were useful to understand the antibacterial properties of six highly efficient silver(I) pyridinecarboxylate (nicotinic, picolinic and isonicotinic acids) and bipiridinecarboxylate (pyridine‐2,3‐dicarboxylic, pyridine‐2,4‐dicarboxylic and pyridine‐2,5‐dicarboxylic acids) complexes with Ag? O and Ag? N bonds against E. coli (ATCC 25922) and Streptococcus agalactiae (ISP 329‐09). The results show a tendency between the nature of Ag? X (X=oxygen and nitrogen) bonds and the rate or efficiency of antibacterial behavior.     

Discrete May–Leonard Competition Models I

The local dynamics of two discrete-time models applicable to three competing plant species are shown to have properties similar to the May–Leonard (M-L) differential equation model. The dynamics of the two discrete models are shown to be similar. However, they are not dynamically consistent with the continuous M-L model. Unlike the continuous M-L model, the Hopf bifurcations of the discrete M-L models are not degenerate. The continuous M-L model is the limiting case of the discrete models.