The tenacity of an incomplete connected graph G is defined as T (G) = min{ |S|+m(G−S) ω(G−S) : S ⊂ V (G), ω(G− S) > 1}, where ω(G− S) and m(G− S), respectively, denote the number of components and the order of a largest component inG−S. This is a reasonable parameter to measure the vulnerability of networks, as it takes into account both the amount of work done to damage the network and how bad...

Topoi are known to be categories with extra properties that make them much alike the category of Sets. In a Topoi it is possible to define adequate notions of membership, elements and subobjects, power ”sets”, and finally, every Topoi has an internal logic able to justify any reasoning carried inside it. Most of the cases, this logic is not Classical (Boolean). The general logic for the Topoi i...

Article history: Available online 25 March 2011 Submitted by J.J. Loiseau AMS classification: 15A80 15A39 15A03

A novel three-component reaction has been developed to assemble biologically and pharmaceutically important tetracyclic fused imidazo[1,2-a]pyridines in a one-pot fashion utilizing readily available 2-aminopyridines, isatins and isocyanides. The three-component coupling proceeds through the Groebke-Blackburn-Bienaymé reaction followed by a retro-aza-ene reaction and subsequent nucleophilic reac...

The first total synthesis of mycoleptodiscin A, a structurally unusual indolosesquiterpenoid possessing an ortho-benzoquinone motif, has been accomplished. A sulfone alkylation coupled two readily available fragments to give an aryl triene intermediate. The tetracyclic core of the molecule was assembled through a highly enantioselective iridium-catalyzed polyene cyclization. The benzylic homolo...

Here, we describe a new and simple synthetic strategy to various polycyclic sulfones via Diels-Alder reaction and ring-rearrangement metathesis (RRM) as the key steps. This approach delivers tri- and tetracyclic sulfones with six (n = 1), seven (n = 2) or eight-membered (n = 3) fused-ring systems containing trans-ring junctions unlike the conventional all cis-ring junctions generally obtained d...

Three triterpenes having the 6/6/5-fused tri- and 6/6/6/5-fused tetracyclic skeletons were isolated from an incubation mixture of the mutated F601A enzyme, these products being in accordance with a Markovnikov closure. Successful trapping of the tricyclic cationic intermediate by using the squalene analog having a highly nucleophilic hydroxyl group leads us to propose that the ring expansion pr...

dl-2-(7,11-Dimethyl-3,7,11 - trans,trans-dodecatrienyl)-3-methyl-cyclopent-2-enol was prepared by reduction of the corresponding ketone. This tetraenol, on treatment with trifluoroacetic acid, underwent stereoselective cyclization to give dl-3,17-dimethyl-A-nor-D-homoestra-3,16-diene. This tetracyclic material was readily converted, by oxidative cleavage to the bicyclic triketo aldehyde followe...

Swertia mileensis, known as Qing-Ye-Dan (QYD), has been documented in Chinese Pharmacopoeia to cure hepatitis. Interestingly, its announced main active component, swertiamarin, could not be detected the decoction, which indicated that efficacy of QYD might attributed heat-transformed products swertiamarin (HTPS). Further investigation on HTPS led isolation sweritranslactone D (1), a novel secoi...