Evgeny Lipachev

OntoMath PRO Ontology: A Linked Data Hub for Mathematics

In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.

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.

Boundary-Value Problems for the Helmholtz Equation for a Half-Plane with a Lipschitz Inclusion

I consider the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. Boundary value problems, modeling the process of wave diffraction, are constructed in the form of Helmholtz equations and boundary conditions on the boundary, formulated in terms of traces, as well as the radiation conditions at infinity. I carry out research on these problems in generalized Sobolev spaces. I proved the solvability of the boundary value problems of Dirichlet and Neumann. I have obtained solutions of boundary value problems in the form of functions that by their properties are analogs of the classical potentials of single and double layers. Boundary problems are reduced to integral equations of the second kind.

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.