Reference : D’Accolti, L.; Dinoi, A.; Fusco, C.; Russo, A.; Curci, R. J. Org. Chem. 2003, 68, 7806−7810. 
D’Accolti, Dinoi, Fusco, Russo, and Curci discuss the mechanisms of dioxiranes in the article cited above in Journal of Organic Chemistry. In the paper, they assert that dioxiranes, or three-membered cyclic peroxides, can oxidize unactivated carbon-hydrogen bonds under mild conditions. It is important to note that a dioxirane was chosen in particular to oxidize the double bond in Molecule 48. TFDO in particular is assessed in the article by D’Accolti, et al. as an oxidizing agent which can act under particularly mild conditions with selectivity and higher conversion yield. Therefore, TFDO is often used when a specific stereoisomer is desired and others are not.
Reference : Gonzalez-Nunez, M.; Royo, J.; Mello, R.; Baguena, M.; Martinez Ferrer, J.; Ramirez de Arellano, C.; Asensio, G.; Prakash, G. ChemInform 2005, 36, 7919-7924.
Gonzalez-Nunez et. al reported that a concerted electrophilic O-atom insertion was observed for all substituents that were tested on 2-substituted adamantanes.
In the epoxidation of olefins, the reagent TFDO can be used as a powerful oxidizing reagent for strongly electron-deficient or electron rich olefins under neutral conditions. Compared to our paper, this paper is similar, because it also references hydrocarbons containing cyclopropyl moieties.
Reference: Grabovskiy, S. A.; Antipin, A. V.; Ivanova, E. V.; Dokichev, V. A.; Tomilov, Y. V.; Kabal’nova, N. N. Org. Biomol. Chem. 2007, 5, 2302-2310.
TFDO is used here in the stereoselective oxyfunctionalization of an unactivated carbon hydrogen bond.
Reference: D’Accolti, L.; Fusco, C.; Annese, C.; Rella, M. R.; Turtletaub, J. S.; Williard, P. G.; Curci, R. J. Org. Chem. 2004, 69, 8510-8513.
In this paper, there is a similar electron-withdrawing effect in molecule 49 due to the oxygen on the oxirane on the electron density at proximal C--H bonds. The oxiranyl ring produces a deactivating effect on proximal alpha--CH2 in dioxirane oxidations.
Conventionally, oxyfunctionalization by TFDO takes place at the “less activated” or more substituted and stable C-H bond. However, the reaction rate and stereoselectivity decrease as the electron-withdrawing effect by distant substituent increases.
Reference: Curci, R.; D’Accolti, L.; Fusco, C.; Acc. Chem. Res. 2006, 39, 1-9.
This article citing the original article describes the selective oxyfunctionalization of unactivated C-H bonds by dioxiranes, TFDO in particular, similarly in mild conditions, with high yield, and low reaction time.
This paper is similar to the reference paper, because it provides the data that the dioxirane oxidation of simple hydrocarbons obtaining cyclopropyl moieties entails that alkane C--H bonds in the alpha position to a cyclopropane ring might become activated toward dioxirane O-insertion.
Without compromising regioselectivity, electron deficiency reduces the stereoselectivity for the less sterically hindered C-H bond during TFDO epoxidation. Regarding to the double bond in molecule 48, instead of following the conventional insertion of an O atom to the less substituted carbon, oxidation also happen at the more substituted but more electron rich carbon to afford a diastereomeric mixture of epoxides 49 and 50.
Reference: Annese, C.; D’Accolti, L.; Fusco, C.; Gandolfi, R.; Eaton, P. E.; Curci, R. J. Org. Lett. 2009, 11, 3574-3577.
This article cites the article by D’Accolti, et al. and assesses the activity of TFDO in the direct mono- and bis-hydroxylation of cubane in addition to its oxidizing activity. It is noted that it is hydroxylated by TFDO under mild conditions, giving a high yield.