Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions

It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical invariants then define topological conserved quantities. Underlying evolution equations are shown to be associated with a triad of linear equations. Our examples include Ishimori equation and Myrzakulov equations which are shown to be geometrically equivalent to Davey-Stewartson and Zakharov -Strachan (2+1) dimensional nonlinear Schr\"odinger equations respectively.Comment: 13 pages, RevTeX, to appear in J. Math. Phy

IMPROVING THE EFFICIENCY OF LIGHTING LAMPS AND ENERGY-SAVING TECHNOLOGIES

In this article, their energy efficiency was determined by comparing lamps. Currently, led lamps are leading. Instead of traditional sources, energy-saving led lighting can be approximately 93% compared to incandescent lamps; compared to halogen lamps, efficiency is 90% and 66% compared to fluorescent lamps. Led lamp keeps brightness even after using more than 50,000 hours. The average lampshade is 1,000 hours (1,500 hours) and the fluorescent clock is approximately 6,000 hours. If you use led bulbs almost every 8 hours, you need to replace them for 16-17 years. Compared with fluore-scent lamps, energy-saving led lamps do not contain toxic substances or harmful gases. In addition, they do not cause ultraviolet radiation, and cause harm to humans for a long time. The absence of ultraviolet radiation leads to another advantage - they do not attract many types of insecticides that are sensitive to ultraviolet radiation

Radiation-Stimulated Adsorption Processes on the Surface of Beryllium Oxide

Received: 19.11.2021. Revised: 18.01.2022. Accepted: 27.01.2022. Available online: 28.01.2022.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.The paper presents the study results of photo and gamma radiation effect on the beryllium oxide (BeO) surface properties. Photoadsorption studies of О2 on BeO by the methods of infrared (IR) spectroscopy and manometry with a change in the temperature of preliminary annealing from 473 to 1073 K show that samples subjected to preliminary training at 473 K are most active. The maximum of adsorption activity on -irradiated beryllium oxide is observed on the samples annealed at 673 K before the irradiation. The maximum of paramagnetic centers (PMCs) is also observed on samples annealed at this temperature. Comparison of electron paramagnetic resonance (EPR) and adsorption studies shows that absorption of H2 and O2 leads to the destruction of paramagnetic centers. It is assumed that, upon irradiation, adsorption centers with electron and hole modes are formed on the surface of BeO