Том 16 № 1

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https://card-file.ontu.edu.ua/handle/123456789/24977

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  • Документ
    Monogenic functions and harmonic vectors
    (2023) Sergiy Plaksa
    We consider special topological vector spaces with a commutative multiplication for some of elements of the spaces and monogenic functions taking values in these spaces.Monogenic functions are understood as continuous and differentiable in the sense of G^ateaux functions.We describe relations between the mentioned monogenic functions and harmonic vectors in the three-dimensional real space and establish sufficient conditions for infinite monogeneity of functions. Unlike the classical complex analysis, it is done in the case where the validity of the Cauchy integral formula for monogenic functions remains an open problem.
  • Документ
    σ-monogenic functions in commutative algebras
    (2023) Vitalii Shpakivskyi
    In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.
  • Документ
    A.K. Bakhtin. Scientific legacy
    (2023) Iryna Denega, Yaroslav Zabolotnyi
    In the paper we give a brief overview of the O. Bakhtin' scientific results
  • Документ
    On weakly 1-convex sets in the plane
    (2023) Тетяна Осіпчук, Максим Володимирович Ткачук
    The present work considers the properties of generally convex sets in the plane known as weakly 1-convex. An open set is called weakly 1-convex if for any boundary point of the set there exists a straight line passing through this point and not intersecting the given set. A closed set is called weakly 1-convex if it is approximated from the outside by a family of open weakly 1-convex sets. A point of the complement of a set to the whole plane is called a 1-nonconvexity point of the set if any straight passing through the point intersects the set. It is proved that if an open, weakly 1-convex set has a non-empty set of 1-nonconvexity points, then the latter set is also open. It is also shown that the non-empty interior of a closed, weakly 1-convex set in the plane is weakly 1-convex.
  • Документ
    On the asymptotic behavior at infinity of one mapping class
    (2023) Bogdan Klishchuk, Ruslan Salimov, Mariia Stefanchuk
    We study the asymptotic behavior at infinity of ring Q-homeomorphisms with respect to p-modulus for p>n