An experimental study of the phase inversion behavior of liquid-liquid dispersion has been conducted in a spray extraction column for systems of toluene / water, n-hexane/water, CCl4/water, toluene /water + glycerol (25 % wt), toluene + CCl4 (25 % wt) / water and toluene / acetic acid (5 % wt)/water. The effects of physical properties, mass transfer and column geometry...

Let Ω be a domain in Cn. An upper semicontinuous function u : Ω → [−∞,∞) is said to be plurisubharmonic if the restriction of u to each complex line is subharmonic (we allow the function identically −∞ to be plurisubharmonic). We say that u is strictly plurisubharmonic if for every z0 ∈ Ω there is a neigbourhood U of z0 and λ > 0 such that u(z) − λ|z|2 is plurisubharmonic on U . We write PSH(Ω)...

the optimum shape of balance weights is determined, using two different criteria. according to one, one of the balance weights should have minimum size. while the other requires that the mass moment of inertia about the axis of rotation should be minimum. in the second case, the calculus of variation is used to determine the optimum shape. graphs are presented to enable designers to find the di...

The aim of this research was to assess the effect of fat type and concentration as well as the continuous phase viscosity on the rheological properties of an oil-in-water (O/W) emulsion. Thus, sunflower oil and tallow fat were used as the dispersed phase of the emulsion both at 10 and 50% (w/v) and CMC solutions (at 0.1, 0.3 and 0.5% w/v) were acted as the continuous phase. CMC solutions and em...

Alexandroff T0-spaces have been studied as topological models of the supports of digital images and as discrete models of continuous spaces in theoretical physics. Recently, research has been focused on the dimension of such spaces. Here we study the small inductive dimension of the digital space X (W) constructed in [15] as a minimal open quotient of a fenestrationW ofRn . There are fenestrati...

Consider a balanced non triangular two-color Pólya-Eggenberger urn process, assumed to be large which means that the ratio σ of the replacement matrix eigenvalues satisfies 1/2 < σ < 1. The composition vector of both discrete time and continuous time models admits a drift which is carried by the principal direction of the replacement matrix. In the second principal direction, this random vector...

2073 The bound can also be adapted to continuous alphabets by replacing the probability distribution p(.) by a density, the cardinality lB,(p)l by a volume, and the entropy H (p) by the corresponding differential entropy. With these substitutions-and provided that a density p(.) of the form (3) and satisfying (4) exists-the nonasymptotic part of the first proof, and thus the bound (2), is still...

We analyze the set of continuous viscosity solutions of the infinity Laplace equation −∆∞w(x) = f(x), with generally sign-changing right-hand side in a bounded domain. The existence of a least and a greatest continuous viscosity solutions, up to the boundary, is proved through a Perron’s construction by means of a strict comparison principle. These extremal solutions are proved to be absolutely...

Weighted norm inequalities for singular integral operators appear naturally in many areas of analysis, probability, operator theory ect. The one-weight case is now pretty well understood, and the answers are given by the famous Helson–Szegö theorem and the Hunt–Muckenhoupt–Wheden Theorem. The fist one state that the Hilbert Transform H is bounded in the weighted space L(w) if and only if w can ...

Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space H. We show that if W and its inverse W−1 both satisfy a matrix reverse Hölder property introduced in [2], then the weighted Hilbert transform H : LW (R,H) → L 2 W (R,H) and also all weighted dyadic martingale transforms Tσ : LW (R,H)→ L 2 W (R,H) are bound...