Approximation of surfaces with fault(s) and/or rapidly varying data, using a segmentation process, D m -splines and the finite element method

In many problems of geophysical interest, one has to deal with data that exhibit complex fault structures. This occurs, for instance, when describing the topography of seafloor surfaces, mountain ranges, volcanoes, islands, or the shape of geological entities, as well as when dealing with reservoir characterization and modelling. In all these circumstances, due to the presence of large and rapid variations in the data, attempting a fitting using conventional approximation methods necessarily leads to instability phenomena or undesirable oscillations which can locally and even globally hinder the approximation. As will be shown in this paper, the right approach to get a good approximant consists, in effect, in applying first a segmentation process to precisely define the locations of large variations and faults, and exploiting then a discrete approximation technique. To perform the segmentation step, we propose a quasi-automatic algorithm that uses a level set method to obtain from the given (gridded or scattered) Lagrange data several patches delimited by large gradients (or faults). Then, with the knowledge of the location of the discontinuities of the surface, we generate a triangular mesh (which takes into account the identified set of discontinuities) on which a D ^m -spline approximant is constructed. To show the efficiency of this technique, we will present the results obtained by its application to synthetic datasets as well as real gridded datasets in Oceanography and Geosciences.     

Systematic study for grey particles in relativistic nucleus + emulsion (Ag) interactions

The hadronic and string cascade model and the corresponding event generator LUCIAE are used to study systematically the production of the grey particles in (14.6, 60 and 200A GeV)0 + Em, (2004 GeV)Si + Em, (200A GeV)S + Em and (11.6A GeV)Au + Em reactions. The dependences of the mean multiplicity, the multiplicity distributions and the polar angular distributions of the grey particles on the incident energy, the projectile mass and the collision centrality observed in emulsion experiments, respectively, are all reproduced by LUCIAE calculations. In addition the effects of the rescattering on the grey particle production are also investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 19575071 and 19875019) and DFG of Germany.     

Synthesis of vulpinic acids from dimethyl tartrate

A series of vulpinic acids differing by the aryl or heteroaryl groups placed in the ester α-position were prepared by Suzuki-Miyaura cross-coupling involving a common iodide and the corresponding aryl boronates. The preparation of the iodide precursor from (+)-dimethyl l-tartrate required four steps: the esterification of one hydroxyl group, a Dieckmann cyclization allowing the construction of the tetronic acid moiety, a dehydration leading to the installation of the exocyclic double bond and lastly, an N-iodosuccinimide-mediated iodation of the alkene obtained.     

The n-order iterative schemes for a nonlinear Kirchhoff-Carrier wave equation associated with the mixed inhomogeneous conditions

In this paper, a high-order iterative scheme is established in order to get a convergent sequence at a rate of order N(N?1) to a local unique weak solution of a nonlinear Kirchhoff-Carrier wave equation associated with mixed nonhomogeneous conditions - the boundary conditions are Dirichlet in one part and Robin in other part of boundary. On the other hand, some numerical results were presented.     

Eigenvalue spectra and geometric transformation of polyhedra

Starting from one fullerene, the three geometric transformations, cap, face dual and edge dual produce series of carbon clusters and deltahedra. The geometric relation between these polyhedra implies that their topological matrices and eigenvalue spectra must be relative. We have developed a matrix algebra method to research some polyhedra with high symmetry and one kind, two or three kinds of equivalent vertices such as C₆₀(I_h), resolve their exact eigenvalues, and proved this point.     

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Four methods of construction of such confidence bands are proposed. The weird and conditional bootstrap methods are used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal-tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant. This research was partly supported by AGH grant No. 10.420.03.