Über Umlagerungen bei der Cyclialkylierung von Arylpentanolen zu 2,3‐Dihydro‐1H‐inden‐Derivaten, 5. Mitteilung

On Rearrangements by Cyclialkylations of Arylpentanols to 2,3‐Dihydro‐1 H ‐indene Derivatives. Part 5. The Acid‐Catalyzed Cyclialkylation of 2‐(2‐Chlorophenyl)‐2,4‐dimethylpentan‐3‐ol The mechanism proposed in [1] to explain the surprising result of the cyclialkylation of 4‐(2‐chlorophenyl)‐2,4‐dimethylpentan‐2‐ol ( 3 , R=Me), which gives not only the ‘normal' product, i.e., the 4‐chloro‐2,3‐dihydro‐1,1,3,3‐tetramethyl‐ ( 4 ), but also the isomer trans‐4‐chloro‐2,3‐dihydro‐1,1,2,3‐tetramethyl‐1H‐inden ( 5 ), could be differentiated in two sections (cf. Scheme 2): the first from 3 to the intermediary ion IIa ⇌ IIb , and the second from the latter ions to the final product 5 . For the first section, a sufficiently satisfactory explanation has been given in [1]; the second section has received important support from the mechanisms of the cyclialkylation of 2,4‐dimethyl‐2‐phenylpentan‐3‐ol ( 6 ), the precursor of II′a , the ion IIa without the o‐Cl substituent (cf. Schemes 2, 3 and 5 and [4]). The present communication gives an explanation of the influence of the o‐Cl substituent: a mechanism is proposed for the very complex cyclialkylation of 2‐(2‐chlorophenyl)‐2,4‐dimethylpentan‐3‐ol ( 11 ; cf. Scheme 9). Both mechanism may be considered as definitive. It is very surprising that, by the cyclialkylation of the compounds 1, 3, 8, 11, 15 , and 17 , only compound 1 gives the ‘normal' product; the cyclialkylation of all other phenylpentanols follows complex pathways including Et, i‐Pr, and Ph migrations, which could not be expected. In addition, it has been established that the transformation of 21 to 22 (cf. Scheme 12) and that of 23 to 24 (cf. Scheme 13) occur through two consecutive 1,2‐ and not through a single 1,3‐hydride migration or through an elimination‐addition process (cf. Scheme 13). It can be assumed that the transformation of ion IV (the 2‐(2‐chlorophenyl)‐3,4‐dimethylpent‐2‐ylium ion) to the ion V (the 4‐(2‐chlorophenyl)‐3,4‐dimethylpent‐2‐ylium ion (both shown in Scheme 9 as D‐isomers) occurs through the same pathway.     

Cryptography in Hierarchical Coded Caching: System Model and Cost Analysis

The idea behind network caching is to reduce network traffic during peak hours via transmitting frequently-requested content items to end users during off-peak hours. However, due to limited cache sizes and unpredictable access patterns, this might not totally eliminate the need for data transmission during peak hours. Coded caching was introduced to further reduce the peak hour traffic. The idea of coded caching is based on sending coded content which can be decoded in different ways by different users. This allows the server to service multiple requests by transmitting a single content item. Research works regarding coded caching traditionally adopt a simple network topology consisting of a single server, a single hub, a shared link connecting the server to the hub, and private links which connect the users to the hub. Building on the results of Sengupta et al. (IEEE Trans. Inf. Forensics Secur., 2015), we propose and evaluate a yet more complex system model that takes into consideration both throughput and security via combining the mentioned ideas. It is demonstrated that the achievable rates in the proposed model are within a constant multiplicative and additive gap with the minimum secure rates.