Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Static and Dynamic Integrated Expert Systems: State of the Art, Problems and Trends

Systemized analysis of trends towards integration and hybridization in contemporary expert systems is conducted, and a particular class of applied expert systems, integrated expert systems, is considered. For this purpose, terminology, classification, and models, proposed by the author, are employed. As examples of integrated expert systems, Russian systems designed in this field and available to the majority of specialists are analyzed.

Digital Preservation and Access to Cultural and Scientific Heritage: Presentation of the KT-DigiCult-BG Project

The fast development and wide application of digital methods, combined with broadened access to the Internet and falling computing costs, have created intense interest in electronic presentation and access to cultural and scientific heritage resources. Information technologies have offered cultural institutions new opportunities for the presentation of their holdings, which are now made accessible not only to the specialists, but also to the citizens and interested parties worldwide. The paper presents an overview of the Bulgarian experience in the field of digital preservation and access and on-going work on the project “Knowledge Transfer for the Digitisation of Scientific and Cultural Heritage to Bulgaria” (MTKD-CT-2004-509754) supported by the Marie Curie programme of the FP6 of the EC.

3D Reconstruction and Digital Visualization of the South of the Royal Palace in Great Preslav

The report presents the film 10th century. The South of the Royal Palace in Great Preslav. It consists of two parts – 10th century. The Royal Palace in Great Prelsav. The Square with the Pinnacle and The Ruler’s Lodgings. 3D and virtual reconstructions of an architectural ensemble – part of the Preslav Royal Court unearthed during archaeological researches are used in the film. 3D documentaries have already gained popularity around the world and are well received by both scholars and the public at large. One of the distinguished tourist destinations in Bulgaria is Great Preslav – capital of the mediaeval Bulgarian state and a significant cultural center of the European Southeast in 9th–10th centuries, too. The first part of the film is created with the financial support of America for Bulgaria Foundation and the second – with the funding of Bulgarian National Science Fund at the Ministry of Education, Youth and Science. A team of almost 20 members worked on the film, including computer specialists, professional actors, and translators in the four main European languages – English, German, French and Russian, Trima Sound Recording Studio. In the first part of the 3D film are shown a segment of the Royal Palace, the square with the water pinnacle and the adjacent buildings – an important structural element of the town-planning of the Preslav Court center in the 10th century. In the second part the accent is the southern part of the Royal Palace in Great Preslav, where the personal residence of the Preslav ruler’s dynasty is situated. The work on the virtual reconstruction was done by Virtual Archaeology club at the Mathematical School, Shumen. Due to the efforts of its members it is now clear how the square in front of the southern gate looked like.