Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Software and Services − Research and Education in Bulgaria

Доклад по покана, поместен в сборника на Националната конференция "Образованието в информационното общество", Пловдив, май, 2010 г.

Project Proposals Development – Entrepreneurship and Reflection in Teaching Information Technology

This work presents a model for development of project proposals by students as an approach to teaching information technology while promoting entrepreneurship and reflection. In teams of 3 to 5 participants, students elaborate a project proposal on a topic they have negotiated with each other and with the teacher. The project domain is related to the practical application of state-of-theart information technology in areas of substantial public interest or of immediate interest to the participants. This gives them ample opportunities for reflection not only on technical but also on social, economic, environmental and other dimensions of information technology. This approach has long been used with students of different years and programs of study at the Faculty of Mathematics and Informatics, Plovdiv University “Paisiy Hilendarski”. It has been found to develop all eight key competences for lifelong learning set forth in the Reference Framework and procedural skills required in real life.

Construction and evaluation of achievement tests In English

Доклад, поместен в сборника на Националната конференция "Образованието в информационното общество", Пловдив, май, 2011 г.

High-Order Control Variations and Small-Time Local Controllability

The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is studied and a new sufficient STLC condition is proved.

An Analysis and Forecast of Software and Services Research in Bulgaria

In the last 40 years much has been achieved in Software Engineering research and still more is to be done. Although significant progress is being made on several fronts in Service-Oriented Architecture (SOA), there is still no set of clear, central themes to focus research activity on. A task within the EU FP7 Sister project aimed at defining research priorities for the Faculty of Mathematics and Informatics (Sofia University) in the area of Software and Services. A dedicated methodology was proposed and developed, based on various sources of information. The information accumulated was systematised and processed according to this methodology. The final results obtained are described and discussed here.

Technology-Enhanced Learning: Review and Prospects

This paper is a reflection on the history and future of technology-enhanced learning. Over the last century various new technologies were introduced in education. Often, educational revolutions were proclaimed. Unfortunately, most of these new technologies failed to meet the high expectations. This paper reviews the rise and fall of various "revolutionary" learning technologies and analyses what went wrong. Three main driving factors are identified that influence the educational system: 1) educational practice, 2) educational research, and 3) educational technology. The role and position of these factors is elaborated and critically reviewed. Today, again many promising new technologies are being put in place for learning: gaming, social web, and mobile technologies, for example. Inevitably, these are once again proclaimed by its supporters to revolutionise teaching and learning. The paper concludes with identifying a number of relevant factors that substantiate a favourable future outlook of technology-enhanced learning.

The Global Campus - ICT and the Future of Universities

This paper analyses the changes which the ICT causes on a global scale. The globalization of higher education triggered by e-Learning, the emergence of e-infrastructure for e-science, the Open Educational Resources movement, e-libraries and the tendency of building global educational alliances are analysed as well. Special emphasis is put on several wellknown university models, e.g. Research University, Open University and Entrepreneurial University, as well as on some emerging university models for the Knowledge Society, such as: Global University and Innovation University. The paper puts in focus the influence of the ICTs and the new organizational and business models they bring, such as Virtual University, eCampus, Enterprise 2.0, University 2.0. A new university model is defined—the Global Campus Model. Some arguments that the ultimate result of the ICTs driven transformations could turn the whole world into a Global Campus in the next few decades.

Services for Content Creation and Presentation in an Iconographical Digital Library

Content creation and presentation are key activities in a multimedia digital library (MDL). The proper design and intelligent implementation of these services provide a stable base for overall MDL functionality. This paper presents the framework and the implementation of these services in the latest version of the “Virtual Encyclopaedia of Bulgarian Iconography” multimedia digital library. For the semantic description of the iconographical objects a tree-based annotation template is implemented. It provides options for autocompletion, reuse of values, bilingual entering of data, automated media watermarking, resizing and conversing. The paper describes in detail the algorithm for automated appearance of dependent values for different characteristics of an iconographical object. An algorithm for avoiding duplicate image objects is also included. The service for automated appearance of new objects in a collection after their entering is included as an important part of the content presentation. The paper also presents the overall service-based architecture of the library, covering its main service panels, repositories and their relationships. The presented vision is based on a long-term observation of the users’ preferences, cognitive goals, and needs, aiming to find an optimal functionality solution for the end users.

Two-Language, Two-Paradigm Introductory Computing Curriculum Model and its Implementation

This paper analyzes difficulties with the introduction of object-oriented concepts in introductory computing education and then proposes a two-language, two-paradigm curriculum model that alleviates such difficulties. Our two-language, two-paradigm curriculum model begins with teaching imperative programming using Python programming language, continues with teaching object-oriented computing using Java, and concludes with teaching object-oriented data structures with Java.

Processing of Byzantine Neume Notation in Ancient Historical Manuscripts

This article presents the principal results of the doctoral thesis “Recognition of neume notation in historical documents” by Lasko Laskov (Institute of Mathematics and Informatics at Bulgarian Academy of Sciences), successfully defended before the Specialized Academic Council for Informatics and Mathematical Modelling on 07 June 2010.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

Series in Mittag-Leffler Functions: Inequalities and Convergent Theorems

MSC 2010: 30A10, 30B10, 30B30, 30B50, 30D15, 33E12