Preparation of Halodifluoromethanesulfonic Acid Derivatives

Classical and Quantum Dilogarithm Identities

“…Let us rewrite the identity (3.14) with genuine 'nontropical', or universal, quantum y-variables Y kt (t). This generalizes the new variation of the pentagon relation (3.21) recently found by [63] and its generalization to any simply laced finite type [62]. To be more precise, the pentagon relation of [63] is expressed by the initial variables of the Y-system, while our version is expressed by the initial y-variables, so that they have different expressions.…”

“…2) Identities in universal form for Ψ q (x). This is the form presented by [63,62], and it looks as follows…”

“…In general, they are obtained from the identities in tropical form (1.7) by the 'shuffle method' due to A.Yu. Volkov [62].…”

“…A.Yu. Volkov explained us how to derive his pentagon relation and its generalization to any simply laced finite type from the tropical one using the 'shuffle method' in the Y-system setting [62]. Below we apply his shuffle method adapted in our cluster algebraic setting.…”

Preparation of α,α-difluoroalkanesulfonic acids

“…Chlorodifluoromethanesufonic acid (ClCF 2 SO 3 H, 1) can be considered as a superacidic analog of triflic acid. The first preparation of ClCF 2 SO 3 H was reported by Yagupol'skii and co-workers [8] via a tedious pathway. Sweeney et al [9] also reported the preparation of 1 by the reaction of Cl 2 CHSH with HOF over CuCl 2 -KCl in low yield.…”