Lie superalgebras graded by the root system B(<Emphasis Type="Italic">m,n</Emphasis>)

We determine the Lie superalgebras that are graded by the root system B(m,n) of the orthosymplectic Lie superalgebra osp(2m + 1,2n). Mathematics Subject Classification (2000) Primary 17B70, Secondary 17A70     

Crystal bases for the quantum superalgebra

A crystal base theory is introduced for the quantized enveloping algebra of the general linear Lie superalgebra , and an explicit realization of the crystal base is given in terms of semistandard tableaux.     

Dielectric breakdown and avalanches at nonequilibrium metal-insulator transitions

Motivated by recent experiments on the finite temperature Mott transition in VO(2) films, we propose a classical coarse-grained dielectric breakdown model where each degree of freedom represents a nanograin which transitions from insulator to metal with increasing temperature and voltage at random thresholds due to quenched disorder. We describe the properties of the resulting nonequilibrium metal-insulator transition and explain the universal characteristics of the resistance jump distribution. We predict that by tuning voltage, another critical point is approached, which separates a phase of boltlike avalanches from percolationlike ones.     

The effect of supplier capacity on the supply chain profit

In this paper, we study the role of capacity on the efficiency of a two-tier supply chain with two suppliers (leaders, first tier) and one retailer (follower, second tier). The suppliers compete via pricing (Bertrand competition) and, as one would expect in practice, are faced with production capacity. We consider a model with differentiated substitutable products where the suppliers are symmetric differing only by their production capacity. We characterize the prices, production amounts and profits in three cases: (1) the suppliers compete in a decentralized Nash equilibrium game, (2) the suppliers “cooperate” to optimize the total suppliers’ profit, and (3) the two tiers of the supply chain are centrally coordinated. We show that in a decentralized setting, the supplier with a lower capacity may benefit from restricting her capacity even when additional capacity is available at no cost. We also show that the loss of total profit due to decentralization cannot exceed 25 % of the centralized chain profits. Nevertheless, the loss of total profit is not a monotonic function of the “degree of asymmetry” of the suppliers’ capacities. Furthermore, we provide an upper bound on the supplier profit loss at equilibrium (compared with the cooperation setting) that depends on the “market power” of the suppliers as well as their market size. We show that there is less supplier profit loss as the asymmetry (in terms of their capacities) increases between the two suppliers. The worst case arises when the two suppliers are completely symmetric.     

On the formality of equivariant classifying spaces

Partially supported by NSF MCS 7701623     

Cascade intramolecular N-arylation/intermolecular carboamination reactions for the construction of tricyclic heterocycles

A new method for the stereoselective synthesis of tetrahydropyrroloindoles and hexahydropyrroloquinolines of general structure 8 is described. These products are formed through cascade Pd-catalyzed coupling reactions between aryl chlorides and unsaturated amine substrates 5. A single catalyst effects an intramolecular N-arylation reaction followed by an intermolecular alkene carboamination reaction to generate two rings, three bonds, and one stereocenter with good chemoselectivity, diastereoselectivity, and chemical yield.