We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relying on geometric ideas reminiscent of the reflection principle, we give an explicit formula for the density in such cases.

We prove statistical limit laws for Hölder observations of the Lorenz attractor, and more generally for geometric Lorenz attractors. In particular, we prove the almost sure invariance principle (approximation by Brownian motion). Standard consequences of this result include the central limit theorem, the law of the iterated logarithm, and the functional versions of these results.

in this paper the effect of using various models for conductivity and viscosity considering brownian motion of nanoparticles is investigated. this study is numerically conducted inside a cavity full of water-al2o3 nanofluid at the case of mixed convection heat transfer. the effect of some parameters such as the nanoparticle volume fraction, rayleigh, richardson and reynolds numbers has been exa...

Recent ezperimental results [I] on human &ion show that low fractal dimension lines are highly capable to evocate namable objects. In other t e r n , regular lines are recognized by human vision as object edges. In this paper, a regularity measure of discrete lines geometry is presented. This quantitative measure based on a ratio between lines lengths at different scale is analyzed in the frame...