An Expansion Formula for Fractional Derivatives and its Application

An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type.

On the Generalized Confluent Hypergeometric Function and Its Application

2000 Mathematics Subject Classification: 26A33, 33C20

A Method for Classification of Doubly Resolvable Designs and Its Application

This article presents the principal results of the Ph.D. thesis Investigation and classification of doubly resolvable designs by Stela Zhelezova (Institute of Mathematics and Informatics, BAS), successfully defended at the Specialized Academic Council for Informatics and Mathematical Modeling on 22 February 2010.

Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

PC Points and their Application to Vector Optimization

AMS subject classification: 90C29, 90C48

Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.

Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast

2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.

Digital Libraries and Portals Saving National Cultural Heritage (IMI–BAS Experience)

The current research activities of the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences (IMI—BAS) include the study and application of knowledge-based methods for the creation, integration and development of multimedia digital libraries with applications in cultural heritage. This report presents IMI-BAS’s developments at the digital library management systems and portals, i.e. the Bulgarian Iconographical Digital Library, the Bulgarian Folklore Digital Library and the Bulgarian Folklore Artery, etc. developed during the several national and international projects: - "Digital Libraries with Multimedia Content and its Application in Bulgarian Cultural Heritage" (contract 8/21.07.2005 between the IMI–BAS, and the State Agency for Information Technologies and Communications; - FP6/IST/P-027451 PROJECT LOGOS "Knowledge-on-Demand for Ubiquitous Learning", EU FP6, IST, Priority 2.4.13 "Strengthening the Integration of the ICT research effort in an Enlarged Europe" - NSF project D-002-189 SINUS "Semantic Technologies for Web Services and Technology Enhanced Learning". - NSF project IO-03-03/2006 ―Development of Digital Libraries and Information Portal with Virtual Exposition "Bulgarian Folklore Heritage". The presented prototypes aims to provide flexible and effective access to the multimedia presentation of the cultural heritage artefacts and collections, maintaining different forms and format of the digitized information content and rich functionality for interaction. The developments are a result of long- standing interests and work in the technological developments in information systems, knowledge processing and content management systems. The current research activities aims at creating innovative solutions for assembling multimedia digital libraries for collaborative use in specific cultural heritage context, maintaining their semantic interoperability and creating new services for dynamic aggregation of their resources, access improvement, personification, intelligent curation of content, and content protection. The investigations are directed towards the development of distributed tools for aggregating heterogeneous content and ensuring semantic compatibility with the European digital library EUROPEANA, thus providing possibilities for pan- European access to rich digitalised collections of Bulgarian cultural heritage.

3D Laser Scanning for Digital Preservation and Dissemination of Cultural Heritage Main scanned objects - Four Temples of Different Religions in Sofia

The project demonstrates the use of modern technologies for preservation and presentation of the cultural and historical heritage. The idea is a database of cultural and historical heritage sites to be created applying three dimensional laser scanning technology and a combination of geodetic and photogrammetric methods and shooting techniques. For the purposes of carrying out this project, we have focused on some heritage sites in the central part of Sofia. We decided to include these particular buildings because of the fact that there is hardly another city in the world where within a radius of 400 m are located four temples of different religions - Jewish, Muslim, Orthodox and Catholic. In the recent years, preservation of cultural heritage has been increasingly linked to objectives of sustainable development. Today, it has become clear that cultural heritage is also an economic resource that should be used for further economic development (through compulsory preservation of its authentic cultural values). There has been a more active public debate on the role of cultural heritage, regarding the following topics: improving the quality of life through development of cultural tourism, leading to an increase of the employment rate, constantly improving the business climate, etc. Cultural heritage preservation is becoming one of the priority objectives of the urban development policy. The focus has been shifted to new ways of preservation, mainly combinations of sophisticated technological solutions and their application for the purposes of preservation and dissemination of the cultural heritage.