Action variables for Toda Lattices

This Letter contains constructions of complex action variables for both the full Kostant-Toda Lattice in sl(n, 22866047/xxlarge8450.gif" alt="Copf" align="BASELINE" BORDER="0">) and the generalized nonperiodic tridiagonal Toda lattice associated to an arbitrary complex semisimple Lie algebra g. The main tool is the explicit factorization solution for certain Hamiltonian flows. The Letter also contains a generalization of the standard factorization solution theorem necessary for the analysis of the full Kostant-Toda lattice.     

On a bosonic-parafermionic realization ofU_q (\widehat{sl(2)})

We realize the current algebra at an arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that the operator product expansions of these parafermionic fields involve an infinite number of simple poles and simple zeros, which then condensate to form a branch cut in the classical limitq1. Our realization coincides with those of Frenkel-Jing and Bernard when the levelk takes the values 1 and 2, respectively.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

Enantioselective synthesis of hydroxy-substituted α-methyl-α-amino acids using Al and Mn derivatives of cyclo-(L-Ala-L-AIa) bis-Iactim ethers

Aluminum and manganese derivatives of lithiated bis-lactim ethers of cyclo-(L-Ala-L-Ala) were used for the enantioselective synthesis of 22hh/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-hydroxy and polyhydroxy 22hh/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-amino acids of the 2-methyIserine series. A new variant of the synthesis of these acids via 3-acyl-2, 5-dialkoxy-3, 6-dimethyl-3, 6-dihydropyrazines is proposed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 590–595, March, 1993.     

Semistable measures and limit theorems on real andp-adic groups

For any locally compact groupG, we show that any locally tight homomorphism from a real directed semigroup intoM ¹ (G) (semigroup of probability measures onG) has a shift which extends to a continuous one-parameter semigroup. IfG is ap-adic algebraic group then the above holds even iff is not locally tight. These results are applied to give sufficient conditions for embeddability of some translate of limits of sequences of the form {v _n ^kn } and M ¹ (G) such that ()= ^M , for somek>1 and AutG (cf. Theorems 2.1, 2.4, 3.7).     

Macrocycle opening in crown ethers

Macrocycle opening in derivatives of benzocrown ethers under the action of amines is affected by the nature of the heteroatoms in the macrocycle, the nature of the functional group in the benzene ring of the crown ether, and the length, branching, and number of hydrocarbon radicals at the amine nitrogen atom. A distinguishing feature of this reaction is the template effect of MeNH₃ ⁺, Me₂NH₂ ⁺, Na⁺, and K⁺ ions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 687–692, March, 1996.For Part I see Ref. 1.     

Comparison of 6Mo/MCM-22 and 6Mo/ZSM-5 in the MDA process

A comparison of methane dehydroaromatization (MDA) on 6Mo/MCM-22 and 6Mo/ZSM-5 was carried out using a gas mixture of 90%CH₄, 2%CO₂ and 8%Ar as the feed. The results indicate that the stability of 6Mo/MCM-22 is better than that of 6Mo/ZSM-5. A detailed study reveals that the ability for coke accommodation and the retention of the shape selectivity for aromatics formation is responsible for the stability of a MDA catalyst. This revised version was published online in August 2006 with corrections to the Cover Date.     

1H NMR Detection of σ-Adducts in S NH Reactions of Nitroquinolines with Chloromethyl Phenyl Sulfone

The intermediate 22h85258h146j7/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">-adducts of chloromethyl phenyl sulfone with 3-nitro-, 5-nitro-, 6-nitro-, 7-nitro- and 8-nitroquinoline are detected by ¹H NMR spectroscopy.