Coincidence of Vietoris and Wijsman Topologies: A New Proof

Let (X, d) be a metric space and CL(X) the family of all nonempty closed subsets of X. We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric d forces X to be a compact space. In the literature only a more involved and indirect proof using the proximal topology is known. Here we do not need this intermediate step. Moreover we prove that (X, d) is boundedly compact if and only if the bounded Vietoris and Wijsman topologies on CL(X) coincide.

Technology for Ontological Engineering Lifecycle Support

The research is partially supported by Russian Foundation for Basic Research (grants 06-01-81005 and 07-01- 00053)

Ontological Multilevel Modeling Language

This paper presents ontological multilevel modeling language O2ML, aimed at using with metadata driven information systems. The first part of this paper briefly surveys existing modeling languages and approaches, while the last part proposes a new language to combine their benefits.

Ontological Approach to Domain Knowledge Representation for Information Retrieval in Multiagent Systems

An ontological representation of buyer interests’ knowledge in process of e-commerce is proposed to use. It makes it more efficient to make a search of the most appropriate sellers via multiagent systems. An algorithm of a comparison of buyer ontology with one of e-shops (the taxonomies) and an e-commerce multiagent system are realised using ontology of information retrieval in distributed environment.

The Initial Stage of Teaching Proof in Mathematics Course

This article discusses techniques for organization of propaedeutic stage of teaching proof in mathematics course. It identifies types of tasks that allow students of 5–6 classes to form the ability to carry out simple proofs. This article describes each type of tasks features, it gives some examples.

Ontological Presentation of East-Christian Iconographical Art Domain

In the recent years the East-Christian iconographical art works have been digitized providing a large volume of data. The need for effective classification, indexing and retrieval of iconography repositories was the motivation of the design and development of a systemized ontological structure for description of iconographical art objects. This paper presents the ontology of the East-Christian iconographical art, developed to provide content annotation in the Virtual encyclopedia of Bulgarian iconography multimedia digital library. The ontology’s main classes, relations, facts, rules, and problems appearing during the design and development are described. The paper also presents an application of the ontology for learning analysis on an iconography domain implemented during the SINUS project “Semantic Technologies for Web Services and Technology Enhanced Learning”.

Documenting Collections of Bulgarian Museums. Framing a CIDOC-based Ontological Presentation

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Zolotarev's proof of Gauss reciprocity and Jacobi symbols

2000 Mathematics Subject Classification: Primary 11A15.