https://card-file.onaft.edu.ua/handle/123456789/6193 Fri, 04 Mar 2022 09:05:59 GMT 2022-03-04T09:05:59Z https://card-file.onaft.edu.ua/handle/123456789/6208 Title: Нескiнченно малi перетворення у просторах сталої скалярно кривини та iнварiантнiсть певних геометричних об'єктiв Authors: О. Є. Чепурна Abstract: Розглянуто iнфiнiтезимальнi перетворення рiманових просторiв з умовою iнварiантностi тензору Ейнштейна. Визначено умови iнварiантностi цього тензору. Також, знайденi iншi тензорнi iнварiнти перетворень. Також, розглянутi перетворення у просторах сталоЁ скалярноЁ кривини. Sun, 01 Jan 2017 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/6208 2017-01-01T00:00:00Z https://card-file.onaft.edu.ua/handle/123456789/6207 Title: Голоморфно-проективнi перетворення та конформно-келеровi многовиди Authors: Є. В. Черевко Abstract: Розглянуто голоморфно-проективнi вiдображення та можливiсть Ёх iснування на локально конформно-келерових многовидах. Отримана система рiвнянь типу Коши, що є визачальною для групи конформно голоморфно-проективних iнфiнiтезимальних перетворень. Sun, 01 Jan 2017 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/6207 2017-01-01T00:00:00Z https://card-file.onaft.edu.ua/handle/123456789/6204 Title: K-theory and phase transitions at high energies Authors: T. V. Obikhod Abstract: The duality between E8xE8 heteritic string on manifold K3xT2 and Type IIA string compactified on a Calabi-Yau manifold induces a correspondence between vector bundles on K3xT2 and Calabi-Yau manifolds. Vector bundles over compact base space K3xT2 form the set of isomorphism classes, which is a semi-ring under the operation of Whitney sum and tensor product. The construction of semi-ring V ect X of isomorphism classes of complex vector bundles over X leads to the ring KX = K(V ect X), called Grothendieck group. As K3 has no isometries and no non-trivial one-cycles, so vector bundle winding modes arise from the T2 compactification. Since we have focused on supergravity in d = 11, there exist solutions in d = 10 for which space-time is Minkowski space and extra dimensions are K3xT2. The complete set of soliton solutions of supergravity theory is characterized by RR charges, identified by K-theory. Toric presentation of Calabi-Yau through Batyrev's toric approximation enables us to connect transitions between Calabi-Yau manifolds, classified by enhanced symmetry group, with K-theory classification. Sun, 01 Jan 2017 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/6204 2017-01-01T00:00:00Z https://card-file.onaft.edu.ua/handle/123456789/6206 Title: Geometry of a Chaos: Advanced computational ap- proach to treating chaotic dynamics of environ- mental radioactivity systems II Authors: A. V. Glushkov, O. Yu. Khetselius, V. V. Buyadzhi Abstract: In the paper we go on our work on application of a chaos geometry tools and non-linear analysis technique to studying chaotic features of different nature systems. Here there are presented the results of using an advanced chaos-geometric approach to treating chaotic dynamics of environmental radioactivity systems. A usually, an approach combines together application of the advanced mutual information scheme, Grrasberger-Procachi algorythm, Lyapunov exponent's analysis etc. Sun, 01 Jan 2017 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/6206 2017-01-01T00:00:00Z