The wavelet transform of a function f(t) is deened by the formula: Wf(t; a) = W a f(t) = 1 p a Z f(s)g(t ? s a) ds where g(t) is a xed function, t 2 R and a 2 R +. This transform yields a joint timescale representation the original input function that has been of great recent interest. (See for example D1] D2] and HW]). In a recent correspondence, Flandrin F] proposed the use of the wavelet tra...

the effect of a transverse magnetic field on the boundary layer flow and heat transfer of anisothermal stretching cylinder is analyzed. the governing partial differential equations for themagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a setof ordinary differential equations using similarity transformations. the obtained ordinarydifferential equations ar...

the falling and settling of solid particles in gases and liquids is a natural phenomenon happens in many industrial processes. this phenomenon has altered pure forced convection to a combination of heat conduction and heat convection in a flow over a plate. in this paper, the coupling of conduction (inside the plate) and forced convection of a non-homogeneous nanofluid flow (over a flat plate) ...

We study the small deviation problem logP(supt∈[0,1] |Xt| 6 ε), as ε → 0, for general Lévy processes X . The techniques enable us to determine the asymptotic rate for general real-valued Lévy processes, which we demonstrate with many examples. As a particular consequence, we show that a Lévy process with non-vanishing Gaussian component has the same (strong) asymptotic small deviation rate as t...

 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 present functional versions of recent results on the univariate distributions of the process Vx ,u = x +Wuτ(x), 0 ≤ u ≤ 1, where W• is the standard Brownian motion process, x > 0 and τ(x) = inf{t > 0 : Wt =−x}. Let {Wt}t≥0 be the standard univariate Brownian motion process and, for x > 0, Wx ,t := x +Wt , t ≥ 0, τ(x) := inf{t > 0 : Wx ,t = 0}. As is well known, τ(x) is a proper random variab...

We consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure. Uniqueness of the Gibbs measure for two cases is shown. Also the typical path behaviour and some further properties are derived. We use cluster expansion in the small coupling parameter.