The motion of stars in galaxies and the gravitational time dilatation

This article deals with the problem of the motion of stars in galaxies. By using the Newton's theory combined with a gravitational time dilatation for the weak gravitational field, it is possible to give a solution without using the dark matter

Time-dependent cosmological interpretation of quantum mechanics

The aim of this article is to define a time-dependent cosmological interpretation of quantum mechanics in the context of an infinite open FLRW universe. A time-dependent quantum state is defined for observers in similar observable universes by using the particle horizon. Then, we prove that the wave function collapse of this quantum state is avoided.Comment: 8 page

Homology of algebras of families of pseudodifferential operators

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology degenerates at $E^2$ and converges to Hochschild homology. As a byproduct, we deduce an identification of the space of residue traces on fibrations by manifolds with corners. In the process, we prove several general results about algebras of complete symbols on manifolds with corners.Comment: 29 pages, LaTe