Algebraic independence results for the values of certain Mahler functions and their application to infinite products

In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a linear recurrence sequence, an entire function defined by an infinite product such that its values as well as its all successive derivatives at algebraic points other than its zeroes are algebraically independent. Zeroes of such an entire function form a subsequence of the linear recurrence sequence. We prove the algebraic independency by reducing those values at algebraic points to those of Mahler functions.     

Okamurallene,a novel halogenated C15 metabolite from the red alga laurencia okamuhai yamada

Okamurallene ($\text{1}$), a novel nonterpenoid C₁₅ bromoallene containing cyclopropane ring, has been isolated from the red alga Laurencia okamurai Yamada and its structure was determined by the spectral evidence.     

Round-efficient perfectly secure message transmission scheme against general adversary

In the model of Perfectly Secure Message Transmission Schemes (PSMTs), there are n channels between a sender and a receiver, and they share no key. An infinitely powerful adversary A can corrupt   (observe and forge) the messages sent through some subset of n channels. For non-threshold adversaries called Q ², Kumar et al. showed a many round PSMT (Ashwin Kumar et al. On perfectly secure communication over arbitrary networks. PODC 2002, pp. 193–202, 2002). In this paper, we show round efficient PSMTs against Q ²-adevrsaries. We first give a 3-round PSMT which runs in polynomial time in the size of the underlying linear secret sharing scheme. We next present a 2-round PSMT which is inefficient in general. (However, it is efficient for some special case.)     

Crystal base andq-vertex operators

Theq-deformed vertex operators of Frenkel and Reshetikhin are studied in the framework of Kashiwara's crystal base theory. It is shown that the vertex operators preserve the crystal structure, and are naturally labeled by the global crystal base. As an application the one point functions are calculated for the associated elliptic RSOS models, following the scheme of Kang et al. developed for the trigonometric vertex models.Dedicated to Huzihiro Araki     

Electron transfer of conjugated polymeric ferrocenes

This paper describes three topics on the π‐conjugated ferrocene oligomers and polymers; the first is the dependence of intervalence‐transfer bands for mixed‐valence oligo(1,1'‐dihexylferrocenylene)s on the oxidation number and the number of ferrocene units, the second is synthesis of azo‐bridged ferrocene oligomers and a polymer and electrochemical and optical analysis of internuclear electronic interactions in their mixed‐valence states and the third is synthesis, redox behaviors and electrodeposition of oligoferrocenylene‐modified gold clusters.