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The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...
An equivalence relation on the tangent bundle of a manifold is defined in order to extend a structure (modulated or not) onto it. This extension affords a representation of a structure in any tangent space and that in another tangent space can easily be de ...
Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group o ...
Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only ...
This paper presents an application of the general sample-to-object approach to the problem of invariant image classification. The approach results in defining new SVM kernels based on tangent vectors that take into account prior information on known invari ...
A novel multiplexing three-axis spectrometer for thermal neutrons has been tested for single-crystal spectroscopy. Measuring the entire 2D dispersion manifold in the bc plane of the spin-Peierls compound CuGeO3, we demonstrate that the spectrometer fascili ...
We present a new descriptor and feature matching solution for omnidirectional images. The descriptor builds on the log-polar planar descriptors, but adapts to the specific geometry and non-uniform sampling density of spherical images. We further propose a ...
In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence ...
David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof assumes a certain degree of smoothness of t ...
In the framework of rockfall trajectory modelling, the bouncing phenomenon occurring when a rock block impacts with the slope surface is the most difficult to predict, owing to its complexity and its very limited understanding. Up to now, the rebound is co ...
