Context. While Jupiter’s massive gas envelope consists mainly of hydrogen and helium, the key to understanding formation evolution lies in distribution remaining (heavy) elements. Before Juno mission, lack high-precision gravity harmonics precluded use statistical analyses a robust determination heavy-element envelope. Aims. In this paper, we assemble most comprehensive diverse collection Jupit...

A propagation scheme for time-dependent inhomogeneous Schrödinger equations is presented. Such equations occur in time dependent optimal control theory and in reactive scattering. A formal solution based on a polynomial expansion of the inhomogeneous term is derived. It is subjected to an approximation in terms of Chebychev polynomials. Different variants for the inhomogeneous propagator are de...

We consider a cosmology in which a spherically symmetric large scale inhomogeneous enhancement or a void are described by an inhomogeneous metric and Einstein’s gravitational equations. For a flat matter dominated universe the inhomogeneous equations lead to luminosity distance and Hubble constant formulas that depend on the location of the observer. For a general inhomogeneous solution, it is ...

A Legendre polynomial expansion of electromagnetic fields for analysis of layers with an inhomogeneous refractive index profile is reported. The solution of Maxwell’s equations subject to boundary conditions is sought in a complete space spanned by Legendre polynomials. Also, the permittivity profile is interpolated by polynomials. Different cases including computation of reflection–transmissio...

Medium vibration properties to characterize interface layers and quality of bonding can be examined by an ordinary approach using homogeneous waves or by a more general inhomogeneous ~or complex harmonic! wave scattering technique. It is known that only particular inhomogeneous plane waves can stimulate eigenvibrations of a given structure, and not the homogeneous wave. The reflection and trans...

We study time-inhomogeneous Markov chains with finite state spaces using Nash and Logarithmic-Sobolev inequalities, and the notion of cstability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.

This paper investigates Bayesian estimation for Gaussian Markov random elds. In particular, a new class of inhomogeneous model is proposed. This inhomogeneous model uses a Markov random eld to describe spatial variation of the smoothing parameter in a second random eld which describes the spatial variation in the observed intensity image. The coupled Markov random elds will be used as prior dis...

Abstract: Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of R. Pyke and R. Schaufele (1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example in finance and insurance. Unfortunately, no limit theorems have been ...