We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions for log-balancedness are given for the case when the sequence satisfies a two- (or more-) term linear recurrence. It is shown that many combinatorially interesting sequences belong to this class, and, as a consequence, that the above-mentioned double inequalities are valid for all of them.

A three-component system and the crystallization of selected salts from this system were investigated in this study. The studied system was a NaCl-Na2SO4-H2O three-component solution. A methodology for selective crystallization by various elementary pathways was developed, followed by a mathematical model of the complex process of selective crystallization. The developed mathematical model and algorithm of the process enabled the simulation of selective salt crystallization from the multicomponent system NaCl-Na2SO4-H2O.