Lagrangian formalism and Noether-type theorems for second-order delay ODEs

The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for DODEs of second order are presented. Algebraic construction of integrals for DODEs based on symmetries are demonstrated by examples

Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation

On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical completely conservative Samarsky-Popov schemes. In the case of finite conductivity, schemes are derived that admit all the symmetries and possess all the conservation laws of the original differential model, including previously unknown conservation laws. In the case of a frozen-in magnetic field (when the conductivity is infinite), various schemes are constructed that possess conservation laws, including those preserving entropy along trajectories of motion. The peculiarities of constructing schemes with an extended set of conservation laws for specific forms of entropy and magnetic fluxes are discussed.Comment: 29 pages; some minor fixes and generalizations + Appendix containing an additional numerical schem

Landslides in the Mailuu-Suu Valley, Kyrgyzstan—Hazards and Impacts

Mailuu-Suu is a former uranium mining area in Kyrgyzstan (Central Asia) at the northern border of the Fergana Basin. This region is particularly prone to landslide hazards and, during the last 50 years, has experienced severe landslide disasters in the vicinity of numerous nuclear waste tailing dams. Due to its critical situation, the Mailuu-Suu region was and still is the target area for several risk assessment projects. This paper provides a brief review of previous studies, past landslide events and a discussion on possible future risk scenarios. Various aspects of landslide hazard and related impacts in the Mailuu-Suu Valley are analyzed in detail: landslide susceptibility, historical evolution of landslide activity, size-frequency relationship, river damming and flooding as well as impacts on inhabited areas and nuclear waste storage zones. The study was carried out with standard remote sensing tools for the processing of satellite imagery and the construction of digital elevation models (DEMs). The processed inputs were combined on a GIS platform with digital landslide distribution maps of 1962, 1977, and 2003, digitized geological and geographic maps, and information from landslide monitoring and geophysical investigation. As a result, various types of landslide susceptibility maps based on conditional analysis (CA) are presented as well as predictions of future landslide activity and related damming potential and their possible impact on the population. For some risk scenarios, remediation and prevention measures are suggeste

The model of development of creative potential of students in the system of additional art education

In the article the model of development of creative potential of students in the Children's school of arts in the discipline "Computer graphics"В статье рассматривается модель развития творческого потенциала обучающихся в Детской школе искусств по дисциплине «Компьютерная графика