The Chemistry of Stable Carbenes. Part 2. Benzoin-type condensations of formaldehyde catalyzed by stable carbenes

Stable carbenes derived from thiazole, 1H-imidazole, and 4H-1,2,4-triazole are efficient catalysts for benzointype condensations of formaldehyde. Catalysts derived from N-substituted thiazolium salts trimerize formaldehyde to dihydroxyacetone ( II ). Catalysts based on 1,4-disubstituted 4H-1,2,4-triazol-1-ium salts give glycolaldehyde ( I ) as the main product and no II , whereas N,N′-disubstituted 1H-imidazol-3-ium salts yield mixtures of both products. The isolation of several intermediates in the catalytic cycle provide a better insight into the reaction mechanism.     

Rapid high-performance liquid chromatographic method for the determination of peroxyacetic acid

The selective oxidation of methyl p-tolyl sulfide (MTS) to the corresponding sulfoxide (MTSO) by peroxyacetic acid and the subsequent rapid separation of the sulfide and sulfoxide are the basis for a fast and reliable HPLC method for the determination of this oxidizing agent in the presence of hydrogen peroxide. The time required for chromatographic separation was reduced to less than 1 min. To improve the long-term stability of the sulfoxide solution, hydrogen peroxide was decomposed catalytically by manganese dioxide. Even in the presence of a tenfold molar excess of hydrogen peroxide, a storability of at least 20 h without a significant increase in MTSO concentration was achieved. External calibration can be performed using the stable and commercially available MTSO. Real samples from a brewery cleaning-in-place disinfection process were analysed and the results were compared with those of the classical two-step titration.     

A Lattice-Geometric Proof of Wedderburn’s Theorem

This note presents a proof of Wedderburn’s theorem concerning the classification of semisimple rings within the conceptual frame of projective lattice geometry.     

Acetylenic chemistry. Part 24. N-vinylation of N-H acid heterocycles

The vinylation of 9H-carbazole ( 1 ), 1H-indole ( 3a ), and 1H-pyrrolo[2,3-b]pyridine ( 3b ) with propiolic acid ethyl ester resulting in N-acrylic esters is reported here.     

Symmetric transition probabilities in convex model of quantum mechanics

The relation between the geometry and the statistics of the quantum theory is most explicit in the convex models of quantum mechanics. A class of models is investigated where the manifold S of all states is a convex set with a smooth boundary. It is shown that for these models the simple assumption about symmetry of the transition probability implies an ellipsoidal shape of S, thus leading to the “spherical” geometries described in [7].     

Completeness properties of perturbed sequences

If S is an arbitrary sequence of positive integers, let P(S) be the set of all integers which are representable as a sum of distinct terms of S. Call S complete if P(S) contains all large integers, and subcomplete if P(S) contains an infinite arithmetic progression. It is shown that any sequence can be perturbed in a rather moderate way into a sequence which is not subcomplete. On the other hand, it is shown that if S is any sequence satisfying a mild growth condition, then a surprisingly gentle perturbation suffices to make S complete in a strong sense. Various related questions are also considered.