A refinement of Stone duality to skew Boolean algebras

We establish two theorems that refine the classical Stone duality between generalized Boolean algebras and locally compact Boolean spaces. In the first theorem, we prove that the category of left-handed skew Boolean algebras whose morphisms are proper skew Boolean algebra homomorphisms is equivalent to the category of étale spaces over locally compact Boolean spaces whose morphisms are étale space cohomomorphisms over continuous proper maps. In the second theorem, we prove that the category of left-handed skew Boolean -algebras whose morphisms are proper skew Boolean -algebra homomorphisms is equivalent to the category of étale spaces with compact clopen equalizers over locally compact Boolean spaces whose morphisms are injective étale space cohomomorphisms over continuous proper maps.     

Front Cover: In Celebration of the International Year of the Periodic Table 2019 (Chem. Eur. J. 1/2019)

The cover of this issue is directly from the Editorial Team at Chemistry – A European Journal . The image depicts a journal vision for an international Chemistree Journalis , a rare and unique species of elemental value, designed in celebration of the International Year of the Periodic Table. Find out more information in the Editorial by H. Ross 10.1002/chem.201806058 .     

Reactivity of 2-diethylaminomethylphenol and its copper(II) complex in the reaction with 4-nitrophenylbis(chloromethyl)-phosphinate

The kinetics of reactions of 2-diethylaminomethylphenol (I) and its Cu²⁺ complex (with a metal: ligand composition of 12) (II) with 4-nitrophenylbis(chloromethyl)-phosphinate have been studied in aqueous-ethanolic media (10–70 vol. % ethanol); bimolecular rate constants have been calculated for the reactions of different forms of compound (I) and complex (II). It was shown that compound (I) in aqueous-ethanolic media is a nucleophilic catalyst for hydrolysis of 4-nitrophenylbis (chloromethyl)-phosphinate. The reactivity of complex (II) is an order of magnitude greater than that of the zwitterion form of the ligand which exists in the same range of pH 7–9.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 555–560, March, 1991.     

Reaction of 2-alkylaminomethylphenols with 4-nitrophenyl-bis(chloromethyl)phosphinate in toluene micellar solutions of polyethylene glycol-600 monolaurate

The effect of polyethylene glycol-600 monolaurate (PEG-ML) reversed micelles on the reaction of 2-alkylaminomethylphenols (AMP) with 4-nitrophenyl-bis(chloromethyl) phosphinate in toluene has been investigated. PEG-ML increases the observed rate constant of the reaction by more than one order of magnitude. AMP concentration in solution affects the position of the maximum on the concentration dependence of the micellar-catalyzed-reaction rate constants. The reaction rate constant in the micellar phase and the binding constant of the substrate with micelles depend on the alkyl chain length and AMP concentration. Inhibition of the reaction studied is observed in the presence of high PEG-ML concentrations and low AMP concentrations.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2134–2138, December, 1994.     

Synthesis and Antibacterial Activity of 9-Oxo-9,10-dihydroacridinecarboxylic Acids Esters Bearing a Triazole Fragment

An effective method for the synthesis of new acridine-9(10H)-one (acridone) derivatives containing 1,2,3-triazole fragment was developed. A number of new triazole-containing compounds were synthesized from propargyl acridone acetate and their antimicrobial activity was studied.