Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

Cataloguing the Slavonic Manuscript Collection of the Plovdiv Public Library – Problems and MARC 21* Solutions

MARC 21 (‘Machine-Readable Cataloguing’) is a US library standard established worldwide and recently translated also in Bulgarian (those parts used most by librarians in their everyday work). The Bulgarian translations are freely available on the NALIS website (http://www.nalis.bg/) under the Library Standards Section, where also an Online Multilingual Dictionary of MARC 21 Terms can be found. All these works are approved by the US Library of Congress and published on its MARC 21 website under Translations (http://www.loc.gov/marc/translations.html#bulgarian).