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

This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz equations and boundary conditions Dirichlet or Neumann on the boundary, as well as the radiation conditions at infinity. We carry out research on these problems in generalized Sobolev spaces. We use the operators of potential type, that by their properties are analogs of the classical potentials of single and double layers. We proved the solvability of the boundary value problems of Dirichlet and Neumann. We have obtained solutions of boundary value problems in the form of operators of potential type. Boundary problems are reduced to integral equations of the second kind

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

© 2018, Pleiades Publishing, Ltd. 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

Diffraction of electromagnetic waves by gratings with piecewise smooth boundaries

We consider a boundary value problem for the Helmholtz equation that arises in the mathematical modeling of the scattering of a plane electromagnetic wave by infinite perfectly conducting gratings with an arbitrary piecewise-smooth profile of finite size. In the Hilbert space of the square-integrable functions we find the solution of this problem as a potential whose density represents a solution of a weakly singular integral equation

Lobachevskii DML: Towards a semantic digital mathematical library of Kazan University

The digital mathematical library Lobachevskii DML is one of the national initiatives that have emerged in the past decade in different countries of the world. During this time, the formed technical and organizational conditions allowed making mathematicians' dreams of a global World Digital Mathematical Library (WDML) a reality. Following the vision approved by the International Mathematical Union, we started the Lobachevskii DML project in 2017 - the year of the 225-th anniversary of the birth of the brilliant mathematician Nikolai Ivanovich Lobachevskii, the founder of non-Euclidean geometry, the rector of the Kazan University. The main task of Lobachevskii DML project is the development of tools for managing mathematical content, which take into account not only the specifics of mathematical texts, but also the features of processing Russian-language texts. A particular task of creating this digital library is the integration of mathematical resources of Kazan University. Therefore, the original goal of the project was to build up a sound basis for a digital archive comprising the relevant mathematical literature published for 213 years of the existence of Kazan University and stored in the libraries of the University and Kazan. According to our assumption, the digital library Lobachevskii DML should be endowed with all conceivable necessary functions and services, making it a comprehensive and up-to-date live DML, generally respected and used by the local as well as the global mathematical community. From the very beginning, we had in mind that the Lobachevskii DML should constitute a building block for the envisioned global WDML. In this paper, the results of the implementation of the digital mathematical library Lobachevsky-DML are presented. We describe the purpose of creating this digital library, methods of managing mathematical content based on semantic technologies. The following show how Lobachevskii DML interacts with the information systems of scientific journals. We also present a system of services to support the life cycle of a mathematical document and highlight technologies for supporting new forms of scientific publications and providing integration services with other digital mathematical archives and libraries

Mathematical content semantic markup methods and open scientific E-journals management systems

© Springer International Publishing Switzerland 2014. 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

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. © 2014 Allerton Press, Inc

Digital mathematical libraries: Overview of implementations and content management services

The paper gives a review of existing projects of implementation of digital mathematical libraries. An analysis of existing information systems of digital mathematical libraries is performed using the evaluation criteria embedded in the DELOS DLRM model, emphasis is placed to the methods of managing mathematical content on the basis of semantic technologies. All projects are in different degrees of completeness, the range of services provided is different. We found that most of digital mathematical libraries are concentrated on the transfer of the resources to the electronic form and their preservation, rather than on the development of semantic services

Mathematical knowledge management: Ontological models and digital technology

This paper is discussed basic ideas, approaches and the results obtained in the research project the objective of which is to develop mathematical knowledge management technologies based on ontologies. We are developing the digital ecosystem OntoMath for mathematical knowledge management, which includes a set of specialized ontologies, text analytics tools and applications for managing mathematical knowledge. The results obtained are close to main problems declared in the World Digital Math Library (WDML) project. The main purpose of WDML is to build a global system of linked repositories for saving all digital mathematical documents, including contemporary and historic sources. This paper is devoted to decisions of some problems in this global initiative. In particular, we developed the program services for processing large collections of mathematical papers

OntoMath^PRO ontology: A linked data hub for mathematics

© Springer International Publishing Switzerland 2014. 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

Digital ecosystem ontomath: Mathematical knowledge analytics and management

© Springer International Publishing AG 2017.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