Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.

Global classical solutions near Maxwellians are constructed for the Boltzmann and Landau equations with soft potentials in the whole space. The construction of global solutions is based on refined energy analysis. Our results generalize the classical results in Ukai and Asano (Publ. Res. Inst. Math. Sci. 18 (1982), 477–519) to the very soft potentials for the Boltzmann equation and also extend ...

Rocks ranging in composition from trondhjemite to diorite (plagiogranites) have been recovered from ocean ridges and are common constituents of ophiolites. Velocities and densities of diorite and trondhjemite from the MidAtlantic Ridge are shown to differ significantly from similar properties of metadolerite and gabbro. Compressional (V p) and shear (V s.>velocities of plagiogranites are relati...

The problem of the derivation of hydrodynamics from the Boltzmann equation and related dissipative systems is formulated as the problem of a slow invariant manifold in the space of distributions. We review a few instances where such hydrodynamic manifolds were found analytically both as the result of summation of the Chapman–Enskog asymptotic expansion and by the direct solution of the invarian...

We give a necessary and sufficient condition for the global existence of the classical solution to the Cauchy problem of the compressible Euler-Poisson equations with radial symmetry. We introduce a new quantity which describes the balance between the initial velocity of the flow and the strength of the force governed by Poisson equation.

The configurational entropy of nanoscale solutions is discussed in this paper. As follows from the comparison of the exact equation of Boltzmann and its Stirling approximation (widely used for both macroscale and nanoscale solutions today), the latter significantly over-estimates the former for nano-phases and surface regions. On the other hand, the exact Boltzmann equation cannot be used for p...

The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented. Introducing the conditional probability satisfying the requirement of the background not larger than the observed events to construct the Bayesian credible interval is also discussed. A Fortran routine, BPOCI, h...

We show that the Boltzmann factor has a geometrical origin. Its derivation follows from the microcanonical picture. The Maxwell-Boltzmann distribution or the wealth distribution in human society are some direct applications of this new interpretation.

We study the production and the equilibration of a non-Abelian q ¯ q plasma in an external chromoelectric field, by solving the Boltzmann equation with the non-Abelian features explicitly incorporated. We consider the gauge group SU (2) and show that the colour degree of freedom has a major and dominant role in the dynamics of the system. It is seen that the assumption of the so called Abelian ...

A Poisson process is one in which events are randomly distributed in time, space or some other variable with the number of events in any non-overlapping intervals statistically independent. For example, naturally occurring gamma rays detected in a scintillation detector are randomly distributed in time, or chocolate chips in a cookie dough are randomly distributed in volume. For simplicity, we ...