The Fiftieth Anniversary of the Institute of Mathematics and Informatics

In October 1997 we celebrate the fiftieth anniversary of the founding of the Institute for Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS).

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.

Digitization of Old Mathematical Periodicals Published by the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

The digitization practice for retro-converting of the mathematical periodicals, published by the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (IMI-BAS) and the followed benefits for long-term preserving and assuring open access to these materials is discussed in the article.

Modeling Optical Response of Thin Films: Choice of the Refractive Index Dispersion Law

Determination of the so-called optical constants (complex refractive index N, which is usually a function of the wavelength, and physical thickness D) of thin films from experimental data is a typical inverse non-linear problem. It is still a challenge to the scientific community because of the complexity of the problem and its basic and technological significance in optics. Usually, solutions are looked for models with 3-10 parameters. Best estimates of these parameters are obtained by minimization procedures. Herein, we discuss the choice of orthogonal polynomials for the dispersion law of the thin film refractive index. We show the advantage of their use, compared to the Selmeier, Lorentz or Cauchy models.

Tail Inference for a Law in a Max-Semistable Domain of Attraction

2000 Mathematics Subject Classification: 62G32, 62G05.