New Lie symmetry classification of the known class of reaction-diffusion-convection equations is presented. The classification method is based on combining the standard group classification method and the form-preserving transformation approach.

No abstract

A class of generalized nonlinear Kolmogorov equations is investigated. We present the group classification of Lie symmetries of the class with respect to the group of equivalence transformations. We find a number of exact solutions of nonlinear Kolmogorov equations which has the maximal symmetry properties.

Introduction. The article examines the peculiarities of implementing Web 2.0 technology into the educational process, covers the advantages of certain web-services and electronic resources. It is noted that in the conditions of the information society there is a rapid development of software and hardware. Using services and electronic resources that support Web 2.0 technology, allows to diversify the educational process, make it more qualitative and interactive. The purpose of the article is to reveal specific features and benefits of online services and Web 2.0 electronic resources for organizing the educational process of a higher school. Results. It has been found that capabilities of Web 2.0 make it possible to create a modern educational environment, provide mixed and distance learning, and ensure creative application of acquired knowledge. This can be achieved thanks to various online services and electronic resources, which can be divided into several groups. It has been exposed that Web 2.0 technology is considered to be more a social innovation than a technological one. This is due to the possibility of creating thematic communities. It has also been revealed that virtual social networks, Google Classroom, Internet-blog, webinars, etc. are used to organize educational activities and communication between students and the teacher. It has been discovered that today's youth often stay in the virtual space of social networks, communicate, do educational tasks, etc. With that in view, there have been established the conditions that affect the effectiveness of the application of Web 2.0 technology in the educational process. Originality. The possibilities of virtual social networks, Google Classroom, Internet-blog, webinars and other services to organize the educational process in higher education have been identified. Conclusion. The implementation of Web 2.0 online resources and services allows to diversify the educational process, make it more interactive and interesting. The possibilities of Web 2.0 allow users to learn, exchange multimedia, increase social and informational competences. Working with Web 2.0 technology does not require special computer skills. The authors consider the usage of Web 3.0 technology in the educational process to be a promising direction of research.

No abstract