Weights computation for simplicial Whitney forms of degree one

We investigate some simple techniques of computation of the weights (‘moments’) of simplicial Whitney p-forms of first polynomial degree. The classical metric-dependent computation of weights is shown to be equivalent to an affine one, more suitable in the context of differential forms. To cite this article: F. Rapetti, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

On the role of major, minor and trace elements in provenancing ceramic material. A case study: Roman terra sigillata from Augusta Praetoria

Summary Forty-five sherds of Roman terra sigillata were analysed for seven major and minor elements by inductively coupled plasma emission spectroscopy and for thirty trace elements by instrumental neutron activation analysis. Autoscaling, cluster analysis and principal component analysis were performed on the analytical data to obtain separate classifications of the sherds by accounting for major and minor elements, on the one side, and for trace elements, on the other. The ability of each element in discriminating between the obtained groups was determined by accounting for either Fisher weights or mutual correlations. The results obtained indicated that some major and minor elements display a greater discriminating capability than trace elements, and that the latter allow recognition of a greater number of compositional groups just because they greatly outnumber major and minor elements.     

Generalization of Backward Differentiation Formulas for Parallel Computers

We analyze an extension of backward differentiation formulas, used as boundary value methods, that generates a class of methods with nice stability and convergence properties. These methods are obtained starting from the boundary value GBDFs class, and are in the class of EBDF-type methods. We discuss different ways of using these linear multistep formulas in order to have efficient parallel implementations. Numerical experiments show their effectiveness.     

Real and virtual photon contributions to inelasticep scattering

We investigate direct and resolved photon contributions to hardep scattering at high energies. Some terms of the direct contribution are already included in the resolved photon one, described in terms of the photon structure functions. A suitable subtraction mechanism has to be found in order to avoid double counting. Inelasticep scattering requires the knowledge of photon structure functions over a wide range in photon virtuality, in particular from approximately zero up to almost 10⁵ GeV² at HERA. We analyse the real and virtual photon structure function and we comment on the structure of the photon in the intermediate region of low virtuality. We finally describe howep cross sections can be obtained as functions of the virtuality of the exchanged photon.     

Nonlinear eigenvalue Neumann problems with discontinuities

In this paper we study nonlinear eigenvalue problems with Neumann boundary conditions and discontinuous terms. First we consider a nonlinear problem involving the p-Laplacian and we prove the existence of a solution for the multivalued approximation of it, then we pass to semilinear problems and we prove the existence of multiple solutions. The approach is based on the critical point theory for nonsmooth locally Lipschitz functionals.