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Information × Registration Number 0216U005309, 0111U001026 , R & D reports Title Algebraic-analytical and topological methods of complex analysis popup.stage_title Head Zelinskii Yuri Borisovich, Registration Date 21-01-2016 Organization Institute of mathematics NAS of Ukraine popup.description2 The object of the investigation is problems of complex analysis, potential theory and the theory of mappings. The purpose is to conduct research on a wide range of problems of complex analysis, potential theory and the theory of mappings, that is, the theory of analytical, monogenic functions, extreme and marginal problems of multidimensional analysis. A complete solution of the problem of shadow is obtained. This problem is equivalent to finding the conditions of the membership of a point to generalized convex hull of the family of compact sets. It is also investigated a number of problems that are naturally associated with this problem and their solutions are obtained. The criterions, which by some external characteristics of domain or the boundary of compact of the Euclidean space, give the conclusion about their convexity or generalized convexity, are received. There are obtained the criterions of the convexity and strong linear convexity of the priori acyclic compacts in the real and complex Euclidean spaces which use only the intersection of compacts with their support planes and generalize results of Aumanna G. It is established the criterion of linear convexity of bounded Hartogs domains with a smooth boundary of two-dimensional quaternion space. The theorems about fixed point for multivalued mappings, including explosive, whose restriction to some subset of the closure of a domain of the Euclidean space satisfy the "angle condition" or the "strict angle condition", are obtained. The problem of Mizel-Zamfiresku is solved. The conditions of the existence of continuous involution on the manifold are obtained. It is proved the general mean value theorem for an arbitrary continuous function of a real variable, and new mean value theorems for complex functions. There are obtained the generalizations and improves of some classical results of the theory of extreme decompositions of the Riemann sphere due to the developed method of "control" functionals. This method yielded to obtain a new type estimates with "floating" majorants which takes into account deviations of an arbitrary element of the set from extreme one. Thus, it is obtained the solution of the known VM Dubinin's problem about the description of extreme configurations that maximize the product of internal radii non-overlapping domains and given degree of the inner radius (relative to zero) of region which non-overlap them. For classes of space mappings that some modular estimates, there are obtained a number of theorems on local and marginal behavior. In particular, it is proved Goering analog of known theorem about the local lipshyts property and it is received the analogue of Lemma Icom-Schwartz. For all results, there are proposed applications to Sobolev-Orlicz classes. The constructive methods of building of the spatial solutions of the Laplace equation and the biharmonic equation in the form of monogenic functions components with values in commutative Banach algebra, are developed. There are proved analogues of classical theorems of complex analysis (Cauchy theorem, Morera, Taylor, Laurent, Cauchy's integral formula) for these functions. It is established that every function continuous in multidimensional Euclidean domain and subharmonic in the complement to the set of its zeros is subharmonic in the domain, if this function has total differential in each of its zero. The results will be used in function theory, potential theory, the theory of mappings in the theory of boundary problems for equations of mathematical physics, which in turn are used in hydrodynamics, dynamics of gas, thermal physics, mechanics, theoretical physics, tomography and other applied disciplines. Product Description popup.authors Бахтін Олександр Костянтинович В'юн Вікторія Володимирівна Виговська Ірина Юріївна Грибович Людмила Іванівна Грищук Сергій Вікторович Денега Ірина Володимирівна Заболотний Ярослав Володимирович Зелінський Юрій Борисович Кліщук Богдан Анатолійович Осіпчук Тетяна Михайлівна Плакса Сергій Анатолійович Покровський Андрій Володимирович Пухтаєвич Роман Петрович Салімов Руслан Радікович Ткачук Максим Володимирович Трохимчук Юрій Юрійович Шпаківський Віталій Степанович popup.nrat_date 2020-04-02 Close