The modified Randić index of a graph G is a graph invariant closely related to the classical Randić index, defined as

A few facile synthetic pathways for bicyclic aminopyridinol antioxidants are presented. Attachment of a long alkyl chain to the bicyclic pyridinol scaffold was established using ester linkage. Non-substituted pyrrolopyridinols and 1,3-oxazine-fused pyridinols were also synthesized as novel antioxidant scaffolds. Antioxidant activities were measured by a radical clock method and new compounds pr...

The molybdenum-mediated cleavage reactions of isoxazoline rings fused in bicyclic frameworks were investigated. A tandem N-O bond cleavage-retro aldol reaction of an isoxazoline ring fused in a bicyclic framework led to the cleavage of the bicyclic framework. These reactions provide a novel stereoselective synthesis of substituted cyclopentene rings, cyclopentane rings, and attached-ring system...

Bicyclic peptides are promising scaffolds for the development of inhibitors of biological targets that proved intractable by typical small molecules. So far, access to bioactive bicyclic peptide architectures is limited due to a lack of appropriate orthogonal ring-closing reactions. Here, we report chemically orthogonal ring-closing olefin (RCM) and alkyne metathesis (RCAM), which enable an eff...

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If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...

A domino reaction has been developed for the synthesis of oxygen bridged bicyclic ethers through the coupling of 4-(2-hydroxyethyl)cyclohex-3-enols with aldehydes in the presence of 10 mol% of molecular iodine in dichloromethane at 25 °C. This method is highly diastereoselective affording the corresponding bicyclic ethers, i.e. octahydro-4a,7-epoxyisochromenes in good yields with high selectivi...

The fragmentation reaction of differently functionalized [2.2.2]- and [2.2.1]bicyclic systems that leads to substituted five membered heterocycles and five/six membered carbocycles is broadly studied. This reaction is carried out through a retro-Dieckmann-type condensation on strained [2.2.1]bicyclic β-ketosulfones and their counterparts β-ketoesters under very mild catalytic acid or basic cond...