On a Multivalued Version of the Sharkovskii Theorem and its Application to Differential Inclusions

Motivated by the applications to differential equations without uniqueness conditions, we separately prove multivalued versions of the celebrated Sharkovskii and Li–Yorke theorems. These are then applied, via multivalued Poincaré operators, to Carathéodory differential inclusions. Thus, besides another, infinitely many subharmonics of all integer orders can be obtained. Unlike in the single-valued case, for example, period three brings serious obstructions. Three counter-examples, related to these complications, are therefore presented as well. In a multivalued setting, new phenomena are so exhibited.     

Copper-mediated difluoromethylation of aryl and vinyl iodides

Selectively fluorinated molecules are important as materials, pharmaceuticals, and agrochemicals, but their synthesis by simple, mild, laboratory methods is challenging. We report a straightforward method for the cross-coupling of aryl and vinyl iodides with a difluoromethyl group generated from readily available reagents to form difluoromethylarenes and difluoromethyl-substituted alkenes. The reaction of electron-neutral, electron-rich, and sterically hindered aryl and vinyl iodides with the combination of CuI, CsF and TMSCF(2)H leads to the formation of difluoromethyl-substituted products in high yield with good functional group compatibility. This transformation is surprising, in part, because of the prior observation of the instability of CuCF(2)H.     

Electrical conductivity of silicate glasses with tetravalent cations substituting Si

The effects of substituting Si by M^4 + cations in soda-lime silica glasses were analyzed by impedance spectroscopy in the frequency range of 1 Hz–1 MHz. The glass composition was (mol%) 22Na₂O·8CaO·65SiO₂·5MO₂, M = Si, Ti, Ge, Zr, Sn, and Ce. Although the Na⁺ concentration in the glasses is constant, the Zr-containing glass exhibits the highest dc conductivity and the lowest activation energy, while the Ce-containing glass exhibits the lowest conductivity. The activation energies obtained experimentally agree with those obtained by a theoretical equation proposed by Anderson and Stuart. The differences in electrical conductivity presented by the several M-containing glasses are attributed to the effect that the M^4 + ion has on the mobility of the diffusing Na⁺ ion.     

Copper-mediated fluorination of aryl iodides

The synthesis of aryl fluorides has been studied intensively because of the importance of aryl fluorides in pharmaceuticals, agrochemicals, and materials. The stability, reactivity, and biological properties of aryl fluorides can be distinct from those of the corresponding arenes. Methods for the synthesis of aryl fluorides, however, are limited. We report the conversion of a diverse set of aryl iodides to the corresponding aryl fluorides. This reaction occurs with a cationic copper reagent and silver fluoride. Preliminary results suggest this reaction is enabled by a facile reductive elimination from a cationic arylcopper(III) fluoride.     

Late-Stage 18O Labeling of Primary Sulfonamides via a Degradation–Reconstruction Pathway

A late-stage ¹⁸O labeling approach of sulfonamides that employs the corresponding unlabeled molecule as the starting material was developed. Upon deamination of the sulfonamide, a sulfinate intermediate was isotopically enriched using eco-friendly reagents H₂¹⁸O and ¹⁵NH₃(aq) to afford a M+5 isotopologue of the parent compound. This degradation–reconstruction approach afforded isolated yields of up to 96 % for the stable isotope labeled (SIL) sulfonamides, and was compatible with multiple marketed therapeutics, including celecoxib, on a gram scale. The SIL products also exhibited no ¹⁸O/¹⁶O back exchange under extreme conditions, further validating the utility of this green strategy for drug labeling for both in vitro and in vivo use. This procedure was also adapted to include pharmaceutically relevant methyl sulfones by using ¹³CH₃, affording M+5 isotopic enrichment, thereby illustrating the broad utility of this methodology.     

A general strategy for the perfluoroalkylation of arenes and arylbromides by using arylboronate esters and [(phen)CuR(F)

A versatile method for the synthesis of aryl perfluoroalkanes from arenes and aryl bromides is described. Substituted arenes or aryl bromides are converted in situ to an aryl boronate ester that readily undergoes perfluoroalkylation in air with [(phen)CuR(F)]. A broad range of aryl bromide substrates were perfluoroalkylated in good yield for the first time. [(phen)CuCF(3)] is now commercially available and has been prepared on 20?g scale.