Technetium-99 in Fucusand seawater samples in the Finnish coastal area of the Baltic Sea, 1999

Liquid discharges of ⁹⁹Tc from the Sellafield nuclear facilities increased largely in the mid 90"s. These releases are transported to the Nordic sea areas by the ocean currents. Results of the ⁹⁹Tc activities along the Norwegian coastal areas and in the North Sea have been reported but then again, the spreading of ⁹⁹Tc into Baltic Sea has not been studied thoroughly. Fucus vesiculosus and seawater samples were collected in the summer 1999 from the Finnish coastal areas for measuring ⁹⁹Tc in the Baltic Sea area. A modified analytical method for measuring ⁹⁹Tc in the environmental samples was developed at that time. The method based on extraction chromatography and liquid scintillation measurement of ⁹⁹Tc. The ⁹⁹Tc concentration in the Fucus vesiculosus in the Finnish coast of the Baltic Sea varied from 1.6 to 11.6 Bq/kg (dry weight) being highest at the most northern sampling sites. These values were considerable lower than those in the Danish and Norwegian coasts. The variation in the concentrations observed are probably due to biological factors. The ⁹⁹Tc concentration in the Baltic Sea water studied was below 0.2 Bq/m³.     

Packing chromatic number, $$\mathbf (1, 1, 2, 2) $$ ( 1 , 1 , 2 , 2 ) -colorings,and characterizing the Petersen graph

The packing chromatic number $$\chi _{\rho }(G)$$     

The mathematical technique in Fermat's deduction of the law of refraction

This article attempts to explain Fermat's not quite obvious calculations connected with his deduction of the law of refraction in Analysis ad refractiones (1662), and to describe the development which led to these calculations. In 1657 Fermat tried to deduce a law of refraction based on the principle that light follows the quickest path between two given points. He did not succeed because he found that the calculations were too long and tedious. The calculations are indeed complicated, but if Fermat, in 1657, had been willing to accept Descartes' law of refraction he would probably also have seen that it solved his problem. However, Fermat was of the opinion that Descartes' law was wrong and, therefore, he did not expect that solution. Only in 1662, when he succeeded in reducing the calculations substantially, did he realize that they led to the sine law of Descartes.     

Restrictions of relatively Tauberian operators

For operators T with the property which in addition satisfy a spectral condition we consider conditions under which the restriction of T to a closed invariant subspace also satisfies the same inclusion on the subspace.     

Hillock formation on ion-irradiated graphite surfaces

Abstract

Scanning probe microscopy experiments show that ion irradiation of (0001) graphite results in the formation of isolated defects comprising of a few tens of atoms. We use molecular dynamics simulations and density-functional theory calculations to study the formation probabilities of these defects. We identify different defect structures which correspond to experimentally observed hillocks on graphite surfaces. We find that the predominant source of defects are vacancies and interlayer interstitials, and identify a three-atom carbon ring defect on the graphite surface.     

A boundary condition for arbitrary shaped inlets in lattice–Boltzmann simulations

We introduce a mass‐flux‐based inlet boundary condition for the lattice‐Boltzmann method. The proposed boundary condition requires minimal amount of boundary data, it produces a steady‐state velocity field which is accurate close to the inlet even for arbitrary inlet geometries, and yet it is simple to implement. We demonstrate its capability for both simple and complex inlet geometries by numerical experiments. For simple inlet geometries, we show that the boundary condition provides very accurate inlet velocities when Re?1. Even with moderate Reynolds number, the inlet velocities are accurate for practical purposes. Furthermore, the potential of our boundary condition to produce inlet velocities which convincingly adapt to complex inlet geometries is highlighted with two specific examples. Copyright © 2009 John Wiley & Sons, Ltd.