Одержані достатні умови існування i єдиностi неперервно диференцiйовного N-перiодичного (N -цiле додатне число) розв'язку систем диференцiально-рiзницевих рівнянь нейтрального типу i дослiдженi його властивості.
We consider functions on compact 3-manifolds with boundary without critical points and with less than 4 critical points of its restrictions on the boundary. Their topological classification is obtained.
This paper studies smooth functions with isolated critical points. They are considered to within fiber equivalence. The fd-graph, which specifies the f-atom, is constructed. The necessary and sufficient condition for fiber ...
Приведена классификация многообразий Римана-Картана. Изучены геометрические свойства некоторых из выделенных классов многообразий Римана-Картана. Получены условия, которые препятствуют существованию псевдокиллинговых и ...
Классическими методами математического анализа с использованием инфинитезимальных гармонических преобразований изучаются солитоны Риччи на некомпактных и компактных многообразиях.
In this paper we study representations of semigroups (over a field k) generated by idempotents with partial null multiplication in the case when the corresponding quiver has not oriented cycles.
We obrain that any 2-form and any smooth function on a given 2-manifold with boundary can be realized as the curvature form and the gaussian curvature function of some Riemmanian metric, respectively.
LetM be a smooth manifold, F be a smooth vector field on M, and (Ft) be the local flow of F. Denote by Sh(F) the subset of C^∞(M,M) consisting of maps h : M → M of the following form:
h(x) = Fα(x)(x), where _ runs over ...
We prove the following theorem. Let U be a pseudo-harmonic function on a surface M². For a real valued continuous function V : M² → R to be a conjugate pseudo-harmonic function of U on M² it is necessary and sufficient ...
Let W²ⁿ be a closed manifold of dimension ≥ 6 with semi-free circle having finitely many fixed points. We study S¹-invariant Morse-Bott functions on W²ⁿ. The aim of this paper is to obtain exact values of minimal numbers ...
The generalized left Bol 3-web Bl(p,q,q) on a smooth manifold M, dimM = p+q, defined by a local smooth Bol quasigroup is considered. The symmetric space structure connected with the web Bl(p,q,q)is studied.
Trokhimchuk inner mappings are continuous open isolated endomorphisms. The paper consider the Trokhimchuk inner mappings with infinite number of preimages from a dynamical systems view. Examples given that shows an essential ...
Let S¹ = {(x,y) belongs R² : x² + y² = 1} be a circle, S¹ v S¹ = (S¹ II.S¹)/~, x0 ~ y0 a topological space with a fix point and f : S¹ v S¹ → R a continuous function with a finite number oflocal extrema. We will consider ...