2019
Том 71
№ 6

All Issues

Stegantseva P. G.

Articles: 2
Article (Russian)

On the existence of a surface in the pseudo-Euclidean space with given Grassman image

Grechneva M. A., Stegantseva P. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 10. - pp. 1320=1329

We study the properties of submanifolds of the Grassmanian manifold of the four-dimensional pseudo-Euclidean space and also the Grassman image of a surface in this space. The theorem on the existence of a surface in the pseudo-Euclidean space with the given Grassman image is formulated and proved.

Brief Communications (Russian)

Example of a function of two variables that cannot be an $R$-function

Stegantseva P. G., Velichko I. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 270–274

We note that the definition of R-functions depends on the choice of a certain surjection and pose the problem of the construction of a function of two variables that is not an R-function for any choice of a surjective mapping. It is shown that the function $x_1 x_2 − 1$ possesses this property. We prove a theorem according to which, in the case of finite sets, every mapping is an $R$-mapping for a proper choice of a surjection.