We discuss the problem of well-posedness of the Euler-Poisson system arising, for example, in the mathematical theory of semi-conductors, models of plasma and gaseous stars in astrophysics. We introduce the concept of dissipative weak solution satisfying, in addition to the standard system of integral identities replacing the original system of partial differential equations, the balance of tot...

With the help of the Diffusion Entropy technique we show the non-Poisson statistics of the distances between consecutive Omori’s swarms of earthquakes. We give an analytical proof of the numerical results of an earlier paper [Mega et al., Phys. Rev. Lett. 90 (2003) 188501].

We prove the nonlinear stability in L p , with 1 p 2, of particular steady solutions of the Vlasov-Poisson system for charged particles in the whole space IR 6. Our main tool is a functional related to the relative entropy or Casimir-energy functional.

We prove the nonlinear stability in L p , with 1 p 2, of particular steady solutions of the Vlasov-Poisson system for charged particles in the whole space IR 6. Our main tool is a functional associated to the relative entropy or Casimir-energy functional.

We study systems of classical point particles in d-dimensional Eu-clidean space. Using a result of O. Kallenberg we prove that probability measures , which (i) are translation-invariant, (ii) are stationary under the ideal gas dynamics, (iii) have a nite number of particles, energy, and entropy per unit volume, are in fact a convex combination of Poisson measures.

Based on the minimization of the Lagrange formula, which is composed of two kinds of information measure, the maximum entropy method (MEM) is derived for diffractive imaging contaminated by quantum noise. This gives a suitable object corresponding to the maximum entropy principle with an iterative procedure. The MEM-based iterative phase retrieval algorithm with the initial process of the hybri...

We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse ...

In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without boundary. L2 and almost surely consistency of this estimator as well as its asymptotic normality are investigated.

A version of the law of small numbers is analyzed in information-theoretic terms. Specifically, let f = {fi, i = 0, 1, . . .} be a probability mass function (pmf) on nonnegative integers with mean λ < ∞. Denote the nth convolution of f by f and denote the α-thinning of f by Tα(f). Then, as n → ∞, the entropy H(T1/n(f )) tends to H(po(λ)), where po(λ) denotes the pmf of the Poisson distribution ...