A. Yurkov

collaborators

5 papers

math.CO2026

Nonlinear maps preserving the polynomial

Andrey Yurkov

Let $F$ be a field and $P \in F [x_{1}, \dots, x_{n}]$ be a homogeneous polynomial such that $∣ F ∣ > A^° (P)$ and $I ¨ , I ¨ : F^{n} \to F^{n}$ be two…

math.CO2026

Linear maps preserving the Cullis' determinant. II

Alexander Guterman, Andrey Yurkov

This paper is the second in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belongin…

math.CO2026

Linear varieties and matroids with applications to the Cullis' determinant

Alexander Guterman, Andrey Yurkov

Let $V$ be a vector space of rectangular $n \times k$ matrices annihilating the Cullis' determinant. We show that $dim (V) \leq (n - 1) k$ , extending Dieudonn{Ã©}'s result on the dimens…

math.CO2025

Linear maps preserving the Cullis' determinant. I

Alexander Guterman, Andrey Yurkov

This paper is the first in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belonging…

physics.class-ph2025

To the theory of helical waveguides

A. S. Yurkov

It makes sense to consider a helical waveguide with a fine pitch approximately, replacing the turns with anisotropic conductivity: infinite along the turns and zero across them. Th…