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 ex...

We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions the geometric Brownian motion with delay. The are written terms parameters explicit case decay. For decay, they easily resolvable numerically. analytical method is based on construction a Lyapunov functional (asymptotic decay) forward-backward estimate (exponential decay).

In this paper, we describe a class of Wiener functionals that are ‘indeterminate by their moments’, that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on...

the problem of steady magnetohydrodynamic boundary layer flow of an electrically conducting nanofluid due to an exponentially permeable stretching sheet with heat source/sink in presence of thermal radiation is numerically investigated. the effect of transverse brownian motion and thermophoresis on heat transfer and nano particle volume fraction considered. the governing partial differential eq...

Assume that the surplus of an insurer follows a jump­diffusion process and the insurer would invest its surplus in a risky asset, whose prices are modelled by a geometric Brow­ nian motion. The resulting surplus for the insurer is called as a jump­diffusion surplus process compounded by the geometric Brownian motion. In this resulting surplus process, ruin may be caused by a claim or by oscilla...