It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity , which is usually smaller than the channel capacity . In order to remove the loss , we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each massage. Several bounds of achievable multiplex coding rate region are derived for general wiretap channels in the sense of information-spectral methods, by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels. Furthermore, the exact region for deterministic coding is determined for stationary memoryless full-rank wiretap channels.

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Dual intermolecular hydrophosphination of conjugated diynes with two equivalents of diphenylphosphine was catalyzed by ytterbium complexes, Yb(η 2-Ph 2 CNPh)(hmpa) 3 (1) and Yb[N(SiMe 3) 2 ] 3 (hmpa) 2 (2), to give the corresponding 1,4-bis(diphenylphosphinyl)buta-1,3-dienes in high yields after oxidative work-up. Distribution of the four possible stereoisomers sharply depended on substituents of the substrates. (Z,Z)-Isomers were predominantly obtained from the disubstituted 2 diynes, together with minor (Z,E)-isomers. On the other hand, the reaction of the terminal diynes provided major (E,Z) and minor (E,E)-butadienes. 1,4-Di-tert-butylbuta-1,3-diyne was exclusively converted to an allenic compound. Moreover, the dual hydrophosphination using phenyphosphine was also performed with 1 and 2. Thus, the reaction of two equivalents of aromatic alkynes with PhPH 2 and subsequent oxidation gave bis(alkenyl)phosphine oxides in preference of the (Z,Z)-stereoisomers.

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