one of the main steps within the geoid computation methodology without applying the stokes formula is downward continuation of the harmonic residual observables from the surface of the earth down to the surface of the reference ellipsoid. this downward continuation is done via the abel-poisson integral and its derivatives. this integral in which the unknowns, i.e. harmonic residual potential va...

It is shown that in the complex trajectory representation of quantum mechanics, the Born’s Ψ⋆Ψ probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this probability axiom to the complex plane, we first attempt to find a probability density by solving an appropriate conservation equation. The characteristic curves of this cons...

We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit calculation of the second-order terms which are shown to agree with the results obtained from the hydrodynamical description of the system. Then, we explain that thi...

Let us assume that (S,S) is a metric space with Borel σ algebra S and η̃ is a time homogeneous compensated Poisson random measure defined on a filtered probability space (Ω;F ; (Ft)0≤t<∞;P) with intensity measure ν on S, to be specified later. Let us assume that 1 < p ≤ 2, E is a Banach space of martingale type p, see e.g. the Appendix of [7] for a definition. We consider in the following the It...

In this paper, we establish oracle inequalities for penalized projection estimators of the intensity of an inhomogeneous Poisson process. We study consequently the adaptive properties of penalized projection estimators. At first we provide lower bounds for the minimax risk over various sets of smoothness for the intensity and then we prove that our estimators achieve these lower bounds up to so...