Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the 2-sphere (whose holonomy is seen to be responsible for the geometric phase). We also give an approximate geometric interpretation of the geometric phase for motions starting close to an unstable equilibrium point. Introduc...

The fast increasing size of datasets in scientific computing, mechanical engineering, or virtual medicine is quickly exceeding the graphics capabilities of modern computers. Toolkits for the large model visualization address this problem by combining efficient geometric techniques, such as occlusion and visibility culling, mesh reduction, and efficient rendering. OpenSG PLUS is such a toolkit w...

The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set Ω ⊂ R with given volume A that minimizes the sum of its surface area and its Coulomb self energy. A ball minimizes the former and maximizes the latter, but the conjecture is that a ball is always a minimizer – when there is a minimizer. Even the exis...

This paper deals with the extraction of the hedgerow and copse network from hyperspectral images acquired with the Compact Airborne Spectrographic Imager (CASI). The strategy of segmentation integrates several levels of data fusion allowing a decision to be taken concerning the membership of each pixel to the hedgerow and copse network from the large set of original data. The first level leads ...