We present a new covering theorem for a nonlinear mapping on a convex cone, under the assumptions weaker than the classical Robinson’s regularity condition. When the latter is violated, one cannot expect to cover the entire neighborhood of zero in the image space. Nevertheless, our covering theorem gives rise to natural conditions guaranteeing stability of a solution of a cone-constrained equation subject to wide classes of perturbations, and allowing for nonisolated solutions, and for systems with the same number of equations and variables. These features make these results applicable to various classes of variational problems, like nonlinear complementarity problems. We also consider the related stability issues for generalized Nash equilibrium problems.

The report implements the initiative round table on the theme "Convergence of professional, scientific and educational network communities and prerequisites for its implementation: a collaboration of intellectual processes and investigations of advanced technology precursors". The target setting corresponds to a new project focused on a comprehensive discussion of issues of formation of digital socio-economic environments and assessment of the quality of life of the Russian population on the basis of conceptual models of integration, collective expertise, and convergence of professional, scientific and educational network communities. The aim of the new project is to ensure interdisciplinary interaction of groups of researchers in the interrelated fields of sociohumanitarian and natural sciences. The thematic area of the project is "Theoretical and methodological aspects of the formation of digital socio-economic environments based on conceptual models of integration, collective expertise, and convergence of professional, scientific and educational network communities in the conditions of the digital economy of Russia and the evolutionary self-organization of the information landscape". The main content of the project is the development of an original digital platform. In this regard, interdisciplinary research and development in its fundamental basis are directly aimed at the implementation of effective management of the socio-economic environment of professional, scientific and educational network communities (professional social network of research teams) in the transition to digital, intelligent 110 production technologies, new materials, by creating original tools for search, collection, storage and processing of pertinent information resources in modern conditions of rapid development of bioinspired technologies. At the same time, the complex studies (in the presented problematic issues of the initiated project) are determined by the internal logic of the development of socio-humanitarian and natural sciences. This work described by the context of the problem of ensuring the humanity readiness for big challenges, taking into account the interaction of man and technology, social institutions at the present stage of global development.

Modern information and telecommunication technologies allow not only to provide information required for training students in electronic form, they promote changes in educational process. The electronic information educational environment provides the necessary mechanism for implementing student’s individual trajectories of training. Depending on his or her learning progress the process can vary from basic to intensive, with changes in volumes of information provided. One of the approaches to developing an adaptive electronic educational course is described in this paper. The tree of concepts mastered by students is considered as a basis for knowledge component organization. The tree of concepts will allow not only to organize theoretical material of the course in the form of the separate blocks of educational information intended for studying but also to determine a necessary and sufficient set of questions for testing students.