Alexander Elizarov

Mathematical knowledge representation: semantic models and formalisms

The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering wide range of fields of mathematics. We demonstrate applications of this representation in mathematical formula search, and learning.

Digital Ecosystem OntoMath: Mathematical Knowledge Analytics and Management

A mathematical knowledge management technology is discussed, its basic ideas, approaches and results are based on targeted ontologies in the field of mathematics. The solution forms the basis of the specialized digital ecosystem OntoMath which consists of a set of ontologies, text analytics tools and applications for managing mathematical knowledge. The studies are in line with the project aimed to create a World Digital Mathematical Library whose objective is to design a distributed system of interconnected repositories of digitized versions of mathematical documents.

Methods for analyzing semantic data of electronic collections in mathematics

A survey of the key approaches to the semantic processing of mathematical texts is presented. A software platform prototype for the electronic storage of mathematical documents, which is based on the linked open-data (LOD) model and uses semantic information for data management, including formula-fragment searching, is proposed. The analysis of mathematical documents and the extraction of semantic information from the latter are carried out based on the electronic collection of the Izv. Vyssh. Uchebn. Zaved., Mat. (1995–2009) using special-purpose ontologies, metadata representation in the RDF (Resource Description Framework) format, and integration with existing LOD sets.

Electronic scientific journal-management systems

In this article, the authors present modern information systems for the automatization of the full cycle of electronic scientific journal creation and publishing. The advantages of using open-access journal systems are shown. The choice of the Open Journal System (OJS) as the platform for creating an electronic base of scientific journals is substantiated. The authors present the structure of an electronic scientific journal-management system and describe the features of its implementation within the framework of the pilot system of the e-Government of the Republic of Tatarstan.

Mathematical Content Semantic Markup Methods and Open Scientific E-Journals Management Systems

The paper discusses the approach to automate the processing of electronic mathematical documents and their transformation into semantic documents. Structuring electronic storage of periodical issues in mathematics and multi-volume works conferences was performed.

Strict superharmonicity of Mityuk’s function for countably connected domains of simple structure

Strict superharmonicity of generalized reduced module as a function of a point (we call it Mityuk’s function) is established for the subclass of countably connected domains with unique limit point boundary component. The function just mentioned was first studied in detail by I.P. Mityuk and plays now an important role in the research of the exterior inverse boundary value problems of the theory of analytic functions in the multiply connected domains. At the heart of such a research one can see the fact that the critical points of Mityuk’s function are only maxima, saddles or semisaddles of corresponding surface. This fact is followed from the above strict superharmonicity.

Generalized Reduced Module of a Domain Over the Unit Disc with Circular and Radial Slits

For (n + 1)-ly connected planar domain D with analytic boundary we construct the function F(w,w0) = (w − w0)f(w,w0) which maps D conformally onto the unit disk with circular and radial slits. We show that if n ≥ 2, then Mityuk’s function, M(w) = −(2π)−1 ln |f(w,w)|, representing the generalized reduced module of the domain D has at least one stationary point in D.

Informetrics in the World System of Higher Education

Consideration is given of the modern state of education in informetrics (bibliometrics and scientometrics) at higher-educational institutions in Russia and abroad. A database is presented of the courses on informetrics taught at various universities worldwide. The distribution of the courses is analyzed by country, by university, by academic major, and by degree level (bachelor’s, master’s, or postgraduate program).

Scientific documents ontologies for semantic representation of digital libraries

We present a system of services for the automatic processing of collections of scientific documents that are part of digital libraries. These services are based on ontologies for scientific documents representation, as well as on methods for semantic analysis of mathematical documents. The developed tools automatically check validity of documents for compliance with manuscript guidelines, convert these documents into required formats and generate their metadata.

Semantic formula search in digital mathematical libraries

We are presenting semantic methods of search for mathematical objects in scientific publications. In particular, methods of search for mathematical formulas, as well as methods based on the logical structure of mathematical documents, are being discussed here. Based on the digital mathematical library Lobachevskii DML, created at Kazan Federal University in 2017, declared as Lobachevsky Year, we developed and tested new methods of search in digital collections of mathematical documents.