A composite functional equation from algebraic aspect

In this paper we discuss the composite functional equation f(x+2f(y))=f(x)+y+f(y) on an Abelian group. This equation originates from Problem 10854 of the American Mathematical Monthly. We give an algebraic description of the solutions on uniquely 3-divisible Abelian groups, and then we construct all solutions f of this equation on finite Abelian groups without elements of order 3 and on divisible Abelian groups without elements of order 3 including the additive group of real numbers

Slow Water Diffusion in Micellar Solutions

Slowly diffusing water molecules were found by quasi-elastic neutron scattering (QENS) in a sodium dodecyl sulfate (SDS) micellar solution, and both their diffusion coefficient (4.33 x 10(-6) cm2 x s(-1)) and mole fraction (0.057) were determined. After successfully checking the mean slowing down of solvent molecules by the gradient compensated stimulated spin-echo (GCSTE) pulse sequence NMR method, a similar effect was observed with this technique in the solvent phase of dodecyl trimethylammonium bromide (DTAB) and differing chain length (X = 12, 20, 30, and 40) ethoxylated nonyl phenol (9NX) micellar systems. Following the literature, the experimental results are qualitatively explained by assuming that, apart from ionic hydration, H-bonds may form between the solvent molecules and the O or N atoms present in the hydrophilic (head)groups of the micelle-forming monomers