Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Integrable semiclassical deformations of general algebraic curves and associated conservation laws

Based on the Lenard relations, we completely classify integrable deformations of general algebraic curves. We construct the general solution of the Lenard relation from the invariance condition with respect to an element of the Galois group of the curve. We give some examples and also some associated conservation laws. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 458–469, June, 2007.     

Crossing of shears bands in196Pb

High-spin states in¹⁹⁶Pb have been populated using the reaction¹⁷⁰Er(³⁰Si,4n). The previously observed shears bands in this nucleus have been extended and some of their transitions have been reordered. They now form regular bands with band crossings. One of the bands splits into two pathways at high spin.     

New classes of 2-weight cyclic codes

We introduce new classes of 2-weight cyclic codes which are direct sums of 1-weight irreducible cyclic codes      

Novel antibiotics: second generation macrocyclic peptides designed to trap Holliday junctions

Described are the syntheses of 15 macrocyclic peptides designed to trap Holliday junctions (HJs) in bacteria during site-specific and homologous recombination. This leads to inhibiting bacterial growth. These second generation macrocycles were based on the C-2 symmetrical HJ. They were synthesized using a strategy that permits elucidation of the amino acid role in binding HJs. The syntheses of these macrocycles are an important step in the development of a new class of antibiotics.     

On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001