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.     

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     

Nonlinear optical studies of the transient coherence in the Quantum Hall system

We review recent investigations of the femtosecond nonlinear optical response of the two-dimensional electron gas (2DEG) in a strong magnetic field. We probe the Quantum Hall (QH) regime for filling factors ν∼1. Our focus is on the transient coherence induced via optical excitation and on its time evolution during early femtosecond timescales. We simultaneously study the interband and intraband coherence in this system by using a nonlinear spectroscopic technique, transient three-pulse four wave mixing optical spectroscopy, and a many-body theory. We observe striking differences in the temporal and spectral profile of the nonlinear optical signal between a modulation doped quantum well system (with the 2DEG) and a similar undoped quantum well (without a 2DEG). We attribute these qualitative differences to Coulomb correlations between the photoexcited electron-hole pairs and the 2DEG. We show, in particular, that intraband many-particle coherences assisted by the inter-Landau-level magnetoplasmon excitations of the 2DEG dominate the femtosecond nonlinear optical response. The most striking effect of these exciton-magnetoplasmon coherences is a large off-resonant four-wave-mixing signal in the case of very low photoexcited carrier densities, not observed in the undoped system, with strong temporal oscillations and unusually symmetric temporal profile.     

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.     

An IR study of poly-1,4-phenylenevinylene (PPV), the 2,5-dimethoxy derivative [(MeO)2-PPV], and their corresponding xanthate precursor polymers and monomers

A detailed comparison of the infrared (IR) spectra of poly-1,4-phenylenevinylene (PPV), its xanthate precursor polymer, and its bis-xanthate precursor monomer along with the corresponding 2,5-dimethoxy derivatives has provided a clearer basis for characterizing these species with regard to both structure and purity. All the xanthate precursor monomers and polymers exhibit characteristic intense absorptions typical of the xanthate group near 1220, 1110, and 1050 cm(-1). Upon complete conversion of the precursor polymer to the vinylene linked final product, the intense IR peaks of the xanthate group have disappeared and new bands resulting from the vinylene linkages are found. The latter include a moderately strong band near 965 cm(-1) due to the out-of-plane -CHCH- deformation of the trans-vinylene conjugated with and linking the phenyl rings into an optoelectronic polymer. Unfortunately, the corresponding C-H stretching vibration of this same group of atoms expected to appear near 3020 cm(-1) falls in the same region of the spectrum as the aromatic C-H stretches of the phenyl rings. Similarly, for the 2,5-dimethoxy polymer derivative, [(MeO)(2)-PPV], the C-H stretching vibration near 3055 cm(-1) contains contributions from both aromatic and vinylene C-H. Density functional theory (DFT) calculations on the monomers were instrumental in assigning the infrared spectra of these materials. This study provides a systemic means for verifying that the precursor monomer has been polymerized into the precursor polymer and that thermal conversion to the conjugated polymer is complete.     

Competitive Multi-period Pricing for Perishable Products: A Robust Optimization Approach

We study a multi-period oligopolistic market for a single perishable product with fixed inventory. Our goal is to address the competitive aspect of the problem together with demand uncertainty using ideas from robust optimization and variational inequalities. The demand function for each seller has some associated uncertainty and we assume that the sellers would like to adopt a policy that is robust to adverse uncertain circumstances. We believe this is the first paper that uses robust optimization for dynamic pricing under competition. In particular, starting with a given fixed inventory, each seller competes over a multi-period time horizon in the market by setting prices and protection levels for each period at the beginning of the time horizon. Any unsold inventory at the end of the horizon is worthless. The sellers do not have the option of periodically reviewing and replenishing their inventory. We study non-cooperative Nash equilibrium policies for sellers under such a model. This kind of a setup can be used to model pricing of air fares, hotel reservations, bandwidth in communication networks, etc. In this paper we demonstrate our results through some numerical examples.