Bridgeland’s Hall algebras and Heisenberg doubles

Let [Formula: see text] be a finite-dimensional hereditary algebra over a finite field, and let [Formula: see text] be a fixed integer such that [Formula: see text] or [Formula: see text]. In the present paper, we first define an algebra [Formula: see text] associated to [Formula: see text], called the [Formula: see text]-periodic lattice algebra of [Formula: see text], and then prove that it is isomorphic to Bridgeland’s Hall algebra [Formula: see text] of [Formula: see text]-cyclic complexes over projective [Formula: see text]-modules. Moreover, we show that there is an embedding of the Heisenberg double Hall algebra of [Formula: see text] into [Formula: see text].

Less stable tautomers form stronger hydrogen bonds: the case of water complexes

Hydrogen bonding in cyclic complexes of water with tautomeric pairs of molecules M0 and M1 is calculated to be stronger by more than 25% for the less stable tautomer M1 in all cases where the energy gap between the two tautomers is large (ΔE(M0 − M1) > 10 kcal mol−1).

Hydrogen bonding in cyclic complexes of carboxylic acid–sulfuric acid and their atmospheric implications

Carboxylic acids form cyclic ring structures with sulfuric acid and they could potentially be important in new particle formation.

Electrochemical sensing using boronic acids

Boronic acids can bind with 1,2- or 1,3-diols to form five or six-membered cyclic complexes and also can interact with Lewis bases to generate boronate anions, making them suitable for the electrochemical sensing of these species