Ukraine

2021, Mathematics, Ukraine / 20.07.2021

Seymour’s Second Neighborhood Conjecture states that every simple digraph without loops or two-cycles contains a vertex whose second neighborhood is at least as large as its first. In this project we show that from existence of a counterexample to Second Neighborhood Conjecture it follows that there exist strongly-connected counterexamples with both low and high density (dense and sparse graph). We...

2021, Physics, Ukraine / 20.07.2021

Optical inhomogeneity plays an essential role in the observation of various objects. For example, it underlies phenomena such as astronomical refraction and mirages occurrence. It is also used in optical devices: for instance, in the Luneburg lens, which is used in the radar reflector and microwave antenna. The research aim is to construct and examine the trajectory of light in...

2020, Physics, Ukraine / 19.07.2021

Magnetic springs have a lot of advantages in comparison with regular steel ones: they are more durable, they save almost all of their properties and serve well for dozens of years. That means that a replacement of mechanical springs and bearings with magnetic ones will lower the consumption sufficiently, due to the larger lifespan. Consequently, it acts very positively for...