http://dspace.nbuv.gov.ua:80/handle/123456789/140887 2026-04-16T21:38:45Z http://dspace.nbuv.gov.ua:80/handle/123456789/140903 О моногенных отображениях кватернионной переменной Шпаковский, В.С.; Кузьменко, Т.С. В работе [1] рассмотрен класс, так называемых, G-моногенных (дифференцируемых по Гато) кватернионных отображений. В этой работе введены кватернионные H-моногенные (дифференцируемые по Хаусдорфу) отображения и установлена связь между G-моногенными и H-моногенными отображениями. Доказана эквивалентность разных определений G-моногенного отображения.; In the last paper we consider a new class of quaternionic mappings, so-called, G-monogenic (differentiable in the sense of Gateaux) mappings. In the present paper the quaternionic H-monogenic (differentiable in the sense of Hausdorff) mappings are introduced and the relation between G-monogenic and H-monogenic mappings is established. The equivalence of different definitions of G-monogenic mapping is proved. 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/140902 Spectral and pseudospectral functions of various dimensions for symmetric systems Mogilevskii, V.I. The main object of the paper is a symmetric system Jy′ − B(t)y = λ∆(t)y defined on an interval I = [a, b) with the regular endpoint a. 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/140901 Збіжність косих броунівських рухів з локальними часами в кількох точках, які стягуються в одну Крикун, І.Г. Отримано умови збiжностi в середньому процесiв косого броунiвського руху з локальними часами в кiлькох точках, якi стягуються в одну граничну точку. Доведено, що граничним процесом також є косий броунiвський рух з локальним часом в граничнiй точцi. Знайдено формулу для обчислення коефiцiєнту при локальному часi граничного процесу.; Conditions of convergence in mean of skew Brownian motions with local times in several points, which are contracted in a limiting point, are obtained. It is proved that the limiting process is also skew Brownian motion with the local time in the limiting point. We found a formula to calculate the coefficient of local time of limiting process. 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/140900 On recent advances in boundary value problems in the plane Gutlyanskii, V.Y.; Ryazanov, V.I. The survey is devoted to recent advances in nonclassical solutions of the main boundary value problems such as the well–known Dirichlet, Hilbert, Neumann, Poincare and Riemann problems in the plane. Such solutions are essentially different from the variational solutions of the classical mathematical physics and based on the nonstandard point of view of the geometrical function theory with a clear visual sense. The traditional approach of the latter is the meaning of the boundary values of functions in the sense of the so–called angular limits or limits along certain classes of curves terminated at the boundary. This become necessary if we start to consider boundary data that are only measurable, and it is turned out to be useful under the study of problems in the field of mathematical physics, too. Thus, we essentially widen the notion of solutions and, furthermore, obtain spaces of solutions of the infinite dimension for all the given boundary value problems. The latter concerns to the Laplace equation as well as to its counterparts in the potential theory for inhomogeneous and anisotropic media. 2016-01-01T00:00:00Z