A Statistical Convergence Aplication for the Hopfield Networks

When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ξ^1,ξ^2,...,ξ^p as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented

Fuzzy Set Theory Approach as the Basis of Analysis of Financial Flows in the Economical Security System

The problems of formalization of the process of matching different management subjects’ functioning characteristics obtained on the financial flows analysis basis is considered. Formal generalizations for gaining economical security system knowledge bases elements are presented. One of feedback directions establishment between knowledge base of the system of economical security and financial flows database analysis is substantiated.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

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The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research.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.

Analysis and Coordination of Expert Statements in the Problems of Intellectual Information Search

* This work was financially supported by RFBF-04-01-00858.

On the Mastering of Knowledge and Skills for Solving Mathematical Problems in the Context of the Relationship "Reflection–Synergy"

On the basis of topical investigations on the reflection in the mathematics education, in this article there are presented some contemporary ideas about refining the methodology of mastering knowledge and skills for solving mathematical problems. The thesis is developed that for the general logical and for some particular mathematical methods to become means of solving mathematical problems, first they need to be a purpose of the education.

Some Aspects of the Theme "Information Platform" in the Training of Students in Economic Majors

Information Platform has a major impact on the core activities and development of businesses. In this connection it is necessary for students of economics (the future leaders of such entities) to submit any problems related to the Information Platform, the risks they may pose, and exemplary approach to solve part or all of the problems and minimizing risks. The current issue examines the adaptation of the above problems when presenting them to students in economic majors. To the students are presented generalizations based on long observation of the occurrence and development of Information Platforms to the businesses in Bulgaria in a growing market economy.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Problems Connected with the Realisation of State E-governance in the Republic of Bulgaria

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Digitization of Literary Heritage in the Bulgarian Libraries: Facing Problems and Challenges

Paper deals with the current issues and challenges before digitization of literary heritage in the Bulgarian libraries. Main problems are outlined. Socialization of digitized heritage is commented.

Discover the Thracians - An Approach for Use of 2D and 3D Technologies for Digitization of Cultural Heritage in the Field of E-learning

Information and communication technologies (ICT) offer an easier access to and a multi-perspective view of cultural heritage artifacts and may also enrich and improve cultural heritage education through the adoption of innovative learning/teaching methods. This paper examines the different practices and opportunities for digitization of cultural artifacts with historical significance and describes the work on a pilot project concerning the development of e-learning materials in the Thracian cultural and historical heritage. The proposed method presents an approach based on a combination of 2D and 3D technologies to facilitate the overall process of digitization of individual objects. This approach not only provides greater opportunities for presenting the Thracian heritage but also new perspectives for studying it - students, scientists, PhD students will have the opportunity to work with the materials without having access to them.

Achievements and Problems in the In-service Teacher Education in Inquiry Based Style

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

Cyber Threats Identification in the Evolving Digital Reality

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

An Approach for a more Objective Evaluation of Practical Projects, Used in the Training Process

Well–prepared, adaptive and sustainably developing specialists are an important competitive advantage, but also one of the main challenges for businesses. One option of the education system for creation and development of staff adequate to the needs is the development of pro jects with topics from real economy ("Practical Projects"). The objective assessment is an essential driver and motivator, and is based on a system of well-chosen, well-defined and specific criteria and indicators. An approach to a more objective evaluation of practical projects is finding more objective weights of the criteria. A natural and reasonable approach is the accumulation of opinions of proven experts and subsequent bringing out the weights from the accumulated data. The preparation and conduction of a survey among recognized experts in the field of project-based learning in mathematics, informatics and information technologies is described. The processing of the data accumulated by applying AHP, allowed us to objectively determine weights of evaluation criteria and hence to achieve the desired objectiveness. ACM Computing Classification System (1998): K.3.2.