In this paper we consider the Aleksandrov equation f(L + x) = f(L) + f(x) where L is contained in Rn and f: L --> R and we describe the class of solutions bounded from below, with zeros and assuming on the boundary of the set of zeros only values multiple of a fixed a > 0. This class is the natural generalization of that described by Aleksandrov itself in the one-dimensional case.
A basic question in General Relativity from the point of view of the general field theory is to obtain the Einstein equations coupled with the stress-energy-momentum tensor of a dissipative fluid from a variational principle. We believe that this problem, whose solution for perfect fluids is well known, has not been faced in a systematic way, maybe by the thought of a possible nonsense, for the concept of dissipation is believed to be incompatible with the essentially conservative character of the...
We give a short account of some time-frequency methods which are relevant in the context of gravity waves detection. We focus on the case of wavelet analysis which we believe is particularly appropriate. We show how wavelet transforms can lead to efficient algorithms for detection and parameter estimation of binary coalescence signals. In addition, we give in an appendix some of the ingredients needed for the construction of discrete wavelet decompositions and corresponding fast algorithms.
We provide a geometric well-posedness theory for the Einstein equations within the class of weakly regular vacuum spacetimes with -symmetry, as defined in the present paper, and we investigate their global causal structure. Our assumptions allow us to give a meaning to the Einstein equations under weak regularity as well as to solve the initial value problem under the assumed symmetry. First, introducing a frame adapted to the symmetry and identifying certain cancellation properties taking place...
We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.
We provide an alternative algebraic and geometric approach to the results of [I. Bailleul, Probab. Theory Related Fields141 (2008) 283–329] describing the asymptotic behaviour of the relativistic diffusion.