Arithmetic on Groups of Positive Rationals

In this paper we develop a theory of unique factorization for subgroups of the positive rationals. We show that this theory is strong enough to include arithmetic progressions and the theory of genera in algebraic number fields. We establish generalizations of both Dirichlet's theorem on primes in arithmetic progressions and the theory of genera for Abelian extensions of the rationals.     

S 1 actions and elliptic genera

A proof is given of Witten's conjectures for the rigidity of the index of the Dirac-Ramond operator on the loop space of a spin manifold which admits anS ¹ symmetry.Research supported in part by the National Science Foundation     

Minimal Bar Tableaux

Motivated by recent results of Stanley, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S_n vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s Q_λ symmetric functions in terms of the power sum symmetric functions. Received November 20, 2003     

The synthesis of 6-trifluoroethyl-l-lysine: a method to introduce functionality at C-6 of l-lysine

Described is a method of introducing trifluoroalkyl groups at C-6 of lysine. This chemistry has the potential to introduce a variety of functionality at C-6 of lysine.     

Spectroscopic studies of new model compounds for poly[N,N′-bis(phenoxyphenyl)pyromellitimide]

New model compounds for poly[N,N′-bis(phenoxyphenyl)pyromellitimide] have been synthesized in order to investigate the formation of imine bonds which are proposed to form during the curing process and lead to crosslinking in the bulk polymer. Raman studies show that terminal amines can react with imide carbonyls during curing to form C?N bonds. The Raman band due to C?N appears at 1656 cm^?1 and the band due to C?O closest to the imine bond is observed at 1742 cm^?1. These results are in agreement with previously published results on vapor deposited polyimide films.     

Succinic acid adsorption from fermentation broth and regeneration

More than 25 sorbents were tested for uptake of succinic acid from aqueous solutions. The best resins were then tested for successive loading and regeneration using hotwater. The key desired properties for an ideal sorbent are high capacity, complete stable regenerability, and specificity for the product. The best resins have a stable capacity of about 0.06 g of succinic acid/g of resin at moderate concentrations (1–5 g/L) of succinic acid. Several sorbents were tested more exhaustively for uptake of succinic acid and for successive loading and regeneration using hot water. One resin, XUS 40285, has a good stable isotherm capacity, prefers succinate over glucose, and has good capacities at both acidic and neutral pH. Succinic acid was removed from simulated media containing salts, succinic acid, acetic acid, and sugar using a packed column of sorbent resin, XUS 40285. The fermentation byproduct, acetate, was completely separated from succinate. A simple hot water regeneration successfully concentrated succinate from 10 g/L (inlet) to 40–110 g/L in the effluent. If successful, this would lower separation costs by reducing the need for chemicals for the initial purification step. Despie promising initial results of good capacity (0.06 g of succinic/g of sorbent), 70% recovery using hot water, and a recovered concentration of >100 g/L, this regeneration was not stable over 10 cycles in the column. Alternative regeneration schemes using acid and base were examined. Two (XUS 40285 and XFS-40422) showed both good stable capacities for succinic acid over 10 cycles and >95% recovery in a batch operation using a modified extraction procedure combining acid and hot water washes. These resins showed comparable results with actual broth.     

Multi-Wavelength Optical Packet Routing Technologies Based on Superstructured Fiber Bragg Gratings

A WDM compatible Edge-to-Edge Self-Routed optical packet switched network that simplifies the optical processing is proposed. The system employs all-optical packet label generation and recognition using coded superstructured Fiber Bragg gratings.