We study in details the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko [10] for a large class of densities on Rd. We then use the work of Bickel and Breiman [2] to prove a central limit theorem in dimensions 1 and 2. In higher dimensions, we provide a development of the bias in terms of powers of N−2/d. This allows us to use a Richardson extrapolation to build, i...

Let a(t) ∼ A+ ’(t)∑∞i=0 it as t → 0+, where a(t) and ’(t) are known for 0¡t6c for some c¿ 0, but A and the i are not known. The generalized Richardson extrapolation process GREP is used in obtaining good approximations to A, the limit or antilimit of a(t) as t → 0+. The convergence and stability properties of GREP for the case in which ’(t) ∼ t as t → 0+; 6= 0;−1;−2; : : : ; have been studied t...

Let σ , θ be commuting involutions of the connected semisimple algebraic group G where σ , θ and G are defined over an algebraically closed field k, char k = 0. Let H := Gσ and K := Gθ be the fixed point groups. We have an action (H × K )×G → G, where ((h, k), g) 7→ hgk−1, h ∈ H , k ∈ K , g ∈ G. Let G/ (H × K ) denote the categorical quotient SpecO(G)H×K . We determine when this quotient is smo...

Experiments have been performed to assess the efficiency of mechanical mixers in destratifying water bodies. The effects of Reynolds number, physical scale, and Richardson number were all considered. The results demonstrated that the variation of mixing efficiency with Richardson number was well described by two different power-law regimes. At low Richardson numbers, the efficiency increased wi...

Dropsondes from the NOAA G-IV aircraft were used to examine the presence of low bulk Richardson numbers RB in tropical cyclones. At least one 400-m layer above z 5 7.5 km exhibited RB , 1 in 96% of the sondes andRB# 0.25 in 35%of the sondes. The latter represent almost certain turbulence. Sondes frommajor Hurricane Ivan (2004) were examined in detail. Turbulent layers fell into three broad grou...

In this paper, mixed convection of Al2O3-EG-Water nanofluid in a square lid-driven enclosure is investigated numerically. The focus of this study is on the effects of variable thermophysical properties of the nanofluid on the heat transfer characteristics. The top moving and the bottom stationary horizontal walls are insulated, while the vertical walls are kept at different constant temperature...

This study investigates the effect of lid motion on the optimal characteristics a thin rectangular fin attached on the hot wall of a square lid-driven cavity with active vertical walls. The optimal fin position is studied for Richardson numbers of 0.1-10. The effect of mounting a rectangular fin with a thermal conductivity of 1 and 1000 on minimization and maximization of heat transfer through ...