Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games

In Pang and Fukushima (Comput Manage Sci 2:21–56, 2005), a sequential penalty approach was presented for a quasi-variational inequality (QVI) with particular application to the generalized Nash game. To test the computational performance of the penalty method, numerical results were reported with an example from a multi-leader-follower game in an electric power market. However, due to an inverted sign in the penalty term in the example and some missing terms in the derivatives of the firms’ Lagrangian functions, the reported numerical results in Pang and Fukushima (Comput Manage Sci 2:21–56, 2005) are incorrect. Since the numerical examples of this kind are scarce in the literature and this particular example may be useful in the future research, we report the corrected results. The online version of the original article can be found under doi:.     

Effect of melt viscosity and surface tension of polymers on the percolation threshold of conductive-particle-filled polymeric composites

The electrical conductivities of carbon-black-filled low-density polyethylene (LDPE), poly(methyl methacrylate) (PMMA), and poly(vinyl chloride)-vinyl acetate (PVC/ VAc) copolymer were measured as functions of carbon content and melt viscosity of the matrix at the temperatures at which the composites were prepared. Sharp breaks in the relationship between the carbon filler content and the conductivity of composites were observed in all specimens at some content of the carbon filler. The conductivity jumps as much as 10 orders of magnitude at the break point. This phenomenon has been known as the “percolation threshold”. The critical carbon content corresponding to the break point     

Manganese(III)-Catalysed Oxidation of Sulphides with Sodium Chlorite in an Aprotic Solvent in the Presence of Alumina

A wide variety of sulphides can be readily converted to the corresponding sulphoxides in good to excellent yields by treatment with a combination of sodium chlorite, (salen)manganese(III) complex, and chromatographic alumina in dichloromethane under mild and neutral conditions.     

A practical synthesis of L-ribose

L-Ribose was synthesized by a simple four-step method with overall yield of 76.3% from a protected L-arabinose derivative, which is a compatible intermediate for the synthesis of L-deoxyribose. The key step of this strategy is the Swern oxidation and subsequent stereoselective reduction accompanied by inversion of the 2-hydroxy group of protected L-arabinose.     

Palladium-catalyzed multiple arylation of thiophenes

Secondary 2-thiophenecarboxamides efficiently undergo unique triarylation accompanied by formal decarbamoylation under palladium catalysis. 3-Substituted thiophenes, especially having an electron-withdrawing group, can also be triarylated.