New radiocarbon accelerator dates on artefacts from the early Mesolithic site of Star Carr, North Yorkshire

For the well-known early Mesolithic site of Star Carr, dating of organic artefacts by accelerator mass spectrometry (AMS) has been hampered by treatment of bone and antler recovered during the original excavations with preservatives. Some, untreated, artefacts were, however, collected after Clark's excavation in 1950. Four of these artefacts were AMS dated in 1995, but two of the dates were significantly younger than the others, and were questionable due to their low collagen yields. These suspect samples have now been re-analysed, demonstrating that all four artefacts are of similar date. The significance of these dates for the chronology of Star Carr is discussed.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

The problem of two fixed centers: bifurcation diagram for positive energies

We give a comprehensive analysis of the Euler-Jacobi problem of motion in the field of two fixed centers with arbitrary relative strength and for positive values of the energy. These systems represent nontrivial examples of integrable dynamics and are analysed from the point of view of the energy-momentum mapping from the phase space to the space of the integration constants. In this setting, we describe the structure of the scattering trajectories in phase space and derive an explicit description of the bifurcation diagram, i.e., the set of critical value of the energy-momentum map.