Problems and Theorems in the Theory of Multiplier Sequences

The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent definitions, cited references and related results, and in several instances, elucidated the problems by examples.

DML and RusDML – Virtual Library Initiatives for Covering All Mathematics Electronically

With the rapidly growing activities in electronic publishing ideas came up to install global repositories which deal with three mainstreams in this enterprise: storing the electronic material currently available, pursuing projects to solve the archiving problem for this material with the ambition to preserve the content in readable form for future generations, and to capture the printed literature in digital versions providing good access and search facilities for the readers. Long-term availability of published research articles in mathematics and easy access to them is a strong need for researchers working with mathematics. Hence in this domain some pioneering projects have been established addressing the above mentioned problems.

Computer Processing of Medieval Slavic Sources in the Institute of Literature at BAS Repertorium Project (1994–2004)

Mixed-content miscellanies (very frequent in the Byzantine and mediaeval Slavic written heritage) are usually defined as collections of works with non-occupational, non-liturgical application, and texts in them are selected and arranged according to no identifiable principle. It is a “readable” type of miscellanies which were compiled mainly on the basis of the cognitive interests of compilers and readers. Just like the occupational ones, they also appeared to satisfy public needs but were intended for individual usage. My textological comparison had shown that mixed- content miscellanies often showed evidence of a stable content – some of them include the same constituent works in the same order, regardless that the manuscripts had no obvious genetic relationship. These correspondences were sufficiently numerous and distinctive that they could not be merely fortuitous, and the only sensible interpretation was that even when the operative organizational principle was not based on independently identifiable criteria, such as the church calendar, liturgical function, or thematic considerations, mixed-content miscellanies (or, at least, portions of their contents) nonetheless fell into types. In this respect, the apparent free selection and arrangement of texts in mixed-content miscellanies turns out to be illusory. The problem was – as the corpus of manuscripts that I and my colleagues needed to examine grew – our ability to keep track of the structure of each one, and to identify structural correspondences among manuscripts within the corpus, diminished. So, at the end of 1993 I addressed a letter to Prof. David Birnbaum (University of Pittsburgh, PA) with a request to help me to solve the problem. He and my colleague Andrey Boyadzhiev (Sofia University) pointed out to me that computers are well suited to recording, processing, and analyzing large amounts of data, and to identifying patterns within the data, and their proposal was that we try to develop a computer system for description of manuscripts, for their analysis and of course, for searching the data. Our collaboration in this project is now ten years old, and our talk today presents an overview of that collaboration.

Digital Collections in Regional Public Library “P. R. Slaveikov” – Veliko Tarnovo in the Context of the National Program for Preservation and Promotion of Literary Heritage

Nowadays the great public libraries in Bulgaria are gaining the appearance of digital centers which provide new informational resources and services in the digital space. The digital conversion as a way of preservation is one of the important priorities of Regional Public Library in Veliko Tarnovo. In the last few years we persistently search for possible ways of financing by national and foreign programs in this direction. In the beginning the strategy was oriented to digitalization of the funds with most urgent conversion – these of the local studies periodicals from 1878 till 1944 year. The digitalization of funds will create conditions of laying the basement of full text database of Bulgarian periodical publications. The technology that is offered gives opportunities for including other libraries in the Unified index, which can develop it into a National Unified index of periodical publications. The integrated informational environment that is created is an attractive, comfortable and useful place for work in home or at work for researchers, historians, art experts, bibliographers. The library readers use very actively all informational services of the library internet page and work competently with the on-line indexes provided there, they find the necessary title, which can be demanded later for usage in home or in the library, using electronic means again.