Given a finite set A and a distinguished function f : A −→ A , we study the set of all functions g : A −→ A that are continuous for all topologies for which f is continuous. The main result is a characterization of the functions f such that this set is trivial, that is, contains only the constant functions and the iterates of f . Introduction The Problem. Let A be a set and f : A → A be a fixed...

Semivalues like the Shapley value and the Banzhaf value may assign the same payoff vector to different games. It is even possible that two games attain the same outcome for all semivalues. Due to the linearity of the semivalues, this exactly occurs in case the difference of the two games is an element of the kernel of each semivalue. The intersection of these kernels is called the shared kernel...

cobalt hydrogensulfate is an efficient catalyst for the condensation of β-naphthol, aromatic aldehydes and 5,5-dimethyl-1,3-cyclohexanedione at 120 °c to afford 9,9-dimethyl-12-phenyl-8,10,11,12-tetrahydro-9-h-benzo[a]xanthen-11-one derivatives in high yields. also, polycondensation reactions of phenols with phthalic anhydride were carried out in the presence of cobalt hydrogensulphate under so...