Degree-based topological indices of hexagonal nanotubes

There are several papers that determine one or a few chosen degree-based topological indices for hexagonal nanotubes. We present formulas, which can be used to compute any degree-based topological index for those nanotubes. Then we give exact values of the best-known degree-based indices for hexagonal nanotubes.     

Theoretical analysis of discrete contact problems with Coulomb friction

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction F depending on the spatial variable is analysed. It is shown that a solution exists for any F and is globally unique if F is sufficiently small. The Lipschitz continuity of this unique solution as a function of F as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary F > 0 is studied. The question of existence of locally Lipschitz-continuous branches of solutions with respect to the coefficient F is converted to the question of existence of locally Lipschitz-continuous branches of solutions with respect to the load vector f. A condition guaranteeing the existence of locally Lipschitz-continuous branches of solutions in the latter case and results for determining their directional derivatives are given. Finally, the general approach is illustrated on an elementary example, whose solutions are calculated exactly.