An Artificial Neural Network (ANN) was used to analyse the capillary rise in porous media. Wetting experiments were performed with fifteen liquids and fifteen different powders. The liquids covered a wide range  of  surface  tension ( 15.45-71.99  mJ/m2 )  and  viscosity (0.25-21 mPa.s). The powders also provided an acceptable range of particle size (0.012-45 μm) and surface free...

We shall denote the set of all regularly varying functions by R. We shall also denote by L the set of slowly slowly varying (or slowly oscillating) functions, namely those functions in R for which the index ρ = 0. It is easy to show that if h ∈ R, then there exists L ∈ L such that h(x) = xL(x), with ρ being the index of h. Slowly varying functions arise naturally in many branches of number theo...

We prove a vertex-isoperimetric inequality for [n], the set of all r-element subsets of {1, 2, . . . , n}, where x, y ∈ [n] are adjacent if |x∆y| = 2. Namely, if A ⊂ [n] with |A| = α ( n r ) , then its vertex-boundary b(A) satisfies |b(A)| ≥ c √ n r(n− r)α(1− α) ( n r )

Aut(H) = PGL2(R) = PSL2(R) = SL2(R)/{±I2}, where the plus sign denotes matrices with positive determinant. A fundamental result of Riemann states that every simply connected connected Riemann surface is isomorphic to C,P1(C) or H. In fact, any punctured Riemann surface, R (namely R ⊆ R with R a compact Riemann surface and R−R a finite set of points), which is hyperbolic, that is, 2− 2 · genus(R...