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Topological indices have played an important role in predicting physico-chemical properties of chemical compounds. Degree-based topological indices have been proved to have good correlation with boiling points, strain energy, entropy and a number of other properties of compounds.In this paper, we calculate some degree-based indices and conindices of titania nanotubes TiO2.

In this paper a Jessen's type inequality for normalized positive C 0 -semigroups is obtained. An adjoint of Jessen's type inequality has also been derived for the corresponding adjoint semigroup, which does not give the analogous results but the behavior is still interesting. Moreover, it is followed by some results regarding positive definiteness and exponential convexity of complex structures involving operators from a semigroup. MSC: 47D03; 46B42; 43A35; 43A17

In this paper the Jessen's type inequality for normalized positive C 0 -semigroups is obtained. An adjoint of Jessen's type inequality has also been derived for the corresponding adjoint-semigroup, which does not give the analogous results but the behavior is still interesting. Moreover, it is followed by some results regarding positive definiteness and exponential convexity of complex structures involving operators from a semigroup.