KNOTTED SURFACES AND EQUIVALENCIES OF THEIR DIAGRAMS WITHOUT TRIPLE POINTS

The singularity set of a generic standard projection to the three space of a closed surface linked in four space, consists of at most three types: double points, triple points or branch points. We say that this generic projection image is p-diagram if it does not contain any triple point. Two p-diagrams of equivalent surface links are called p-equivalent if there exist a finite sequence of local moves, such that each of them is one of the four moves taken from the seven on the well known Roseman list, that connects only p-diagrams. It is natural to ask that whether any of two p-diagrams of equivalent surface links always p-equivalent? We introduce an invariant of p-equivalent diagrams and an example of linked surfaces that answers our question negatively.

Une méthode de pénalité-projection pour les écoulements dilatables

We present in this paper a novel pressure correction method for dilatable flows. Named "penalty-projection method", this scheme differs from the usual projection method by the addition in the prediction step of a penalty term, built to enforce the mass balance. This term is proportional to a penalty parameter r. Numerical experiments show that the accuracy of the scheme is drastically improved. The splitting error, dominant at large time steps, may be reduced down to zero by choosing larger and larger values for r; note, however, that a too large value degrades the conditioning of the operator associated to the prediction step. In addition, the loss of convergence observed with the standard projection method in case of open boundary conditions is not observed anymore, as soon as r is nonzero.

Determination of a convex body from the average of projections and stability results

Analysis of projections of a convex body is a familiar topic in tomography. However, instead of considering standard projection bodies, this work investigates a convex body introduced by Schneider [8] which is a Minkowski average of projections. The question addressed here is similar to that posed by Goodey and Weil [4] with respect to Minkowski averages of sections, as opposed to projections, that is, can the shape of a convex body be determined from random sections? Their main result shows that a body K is determined by the average of its two-dimensional sections, but not by the average of its one-dimensional sections. The goal of this study is to uncover the extent to which a convex body is determined by the average of its projections.

PERIODIC AND QUASI-PERIODIC LAGUERRE TILINGS

The Laguerre construction extends and unifies the notions of Voronoi (or Dirichlet) and Delaunay complex. It is shown how the standard projection formalism for the generation of quasi-periodic tilings from higher-dimensional periodic “oblique” (or “klotz”) tilings associated to periodic Voronoi and Delaunay complexes also applies more generally to Laguerre complexes. It turns out that all quasi-periodic tilings obtained this way are Laguerre tilings themselves.

A Method for Obtaining Parametrized Bands of Rutile VO2

With the metallic phase of VO2 in view, a method of obtaining parametrized bands, originally due to Slater and Koster, is developed for rutile structures in general. Thirty-four unsymmetrized Bloch states arising from localized 3d, 4s, 4p vanadium orbitals and 2s, 2p oxygen orbitals are projected into symmetric states—by the standard projection operator technique—at various points of symmetry of the BZ. The secular determinant with respect to these symmetric states is then reduced, the degree of reduction depending on the point of symmetry. Typical results are quoted. The paper concludes with some preliminary remarks concerning the connection of the present work with the phenomenological approach of Goodenough based on crystal field theory. In particular the π-like hybrid levels which feature prominently in this latter work are tentatively identified.