Abstract:
We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength -1. In this case, the Hamiltonian is conserved by the symmetry which exchanges the positive vortices with the negative vortices. We prove the existence of some fixed and relative equilibria, and then study their stability with the ``Energy Momentum Method''. Most of the results obtained are nonlinear stability results. To end, some bifurcations are described.

Abstract:
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortices systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method permits also to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.

Abstract:
We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of latitudinal rings of identical vortices for the non-rotating sphere persists to be a relative equilibrium when the sphere rotates. We study the nonlinear stability of a polygon of planar point vortices on a rotating plane in order to approximate the corresponding relative equilibrium on the rotating sphere when the ring is close to the pole. We then perform the same study for geostrophic vortices. To end, we compare our results to the observations on the southern hemisphere atmospheric circulation.

Abstract:
We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two polar vortices. Such configurations have dihedral symmetry, and the symmetry is used to block diagonalize the relevant matrices, to distinguish the subspaces on which their eigenvalues need to be calculated, and also to describe the bifurcations that occur as eigenvalues pass through zero.

Abstract:
In this paper, we investigate the topology of a class of non-K\"ahler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in $\Bbb C^n$ which are invariant with respect to the natural action of the real torus $(\Bbb S^1)^n$ onto $\Bbb C^n$. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-crossing problem by introducing holomorphic equivariant elementary surgeries related to some transformations of the simple convex polytope. Finally, as a nice consequence, we obtain that affine non K\"ahler compact complex manifolds can have arbitrary amount of torsion in their homology groups, contrasting with the K\"ahler situation.

Abstract:
Bounds consistency is usually enforced on continuous constraints by first decomposing them into binary and ternary primitives. This decomposition has long been shown to drastically slow down the computation of solutions. To tackle this, Benhamou et al. have introduced an algorithm that avoids formally decomposing constraints. Its better efficiency compared to the former method has already been experimentally demonstrated. It is shown here that their algorithm implements a strategy to enforce on a continuous constraint a consistency akin to Directional Bounds Consistency as introduced by Dechter and Pearl for discrete problems. The algorithm is analyzed in this framework, and compared with algorithms that enforce bounds consistency. These theoretical results are eventually contrasted with new experimental results on standard benchmarks from the interval constraint community.

Abstract:
We report an innovative high pressure method combining the diamond anvil cell device with the technique of picosecond ultrasonics. Such an approach allows to accurately measure sound velocity and attenuation of solids and liquids under pressure of tens of GPa, overcoming all the drawbacks of traditional techniques. The power of this new experimental technique is demonstrated in studies of lattice dynamics, stability domain and relaxation process in a metallic sample, a perfect single-grain AlPdMn quasicrystal, and rare gas, neon and argon. Application to the study of defect-induced lattice stability in AlPdMn up to 30 GPa is proposed. The present work has potential for application in areas ranging from fundamental problems in physics of solid and liquid state, which in turn could be beneficial for various other scientific fields as Earth and planetary science or material research.

Abstract:
We prove that two disjoint graphs must always be drawn separately on the Klein bottle, in order to minimize the crossing number of the whole drawing.

Abstract:
The two essays included here are parts of a longer study of temporality, and the genesis of the “religious.” The first part, “Multiple Nows,” depicts a universe in which a present to past relation is establishable from any and every point in consciousness. The resulting perspective differs from that offered by the linear timeline of chronological history. Remembering where I put my glasses is an historicizing act, as fully as is remembering when the Battle of Zama was fought or who won there. On this alternate view of temporality the genesis of the historical perspective is the historicizing subject. The second essay, “The History of a House,” places the observer before an historical structure, then asks where the historicity in the structure is. We discover that the historicity is put there by the observer/subject. This discovery resembles our earlier discovery that historicity is generated by an infinite sequence of nows. The two essays converge on a description of historical cognition as subject-generated.