2019
Том 71
№ 7

All Issues

Sharko V. V.

Articles: 19
Article (English)

Functions and Vector Fields on $C(ℂP^N)$-Singular Manifolds

Libardi Alice Kimie Miwa, Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 3. - pp. 311–315

Let $M^{2n+1}$ be a $C(ℂP^N)$ -singular manifold. We study functions and vector fields with isolated singularities on $M^{2n+1}$. A $C(ℂP^N)$ -singular manifold is obtained from a smooth manifold $M^{2n+1}$ with boundary in the form of a disjoint union of complex projective spaces $ℂP^n ∪ ℂP^n ∪ . . . ∪ ℂP^n$ with subsequent capture of a cone over each component of the boundary. Let $M^{2n+1}$ be a compact $C(ℂP^N)$ -singular manifold with k singular points. The Euler characteristic of $M^{2n+1}$ is equal to $X\left({M}^{2n+1}\right)=\frac{k\left(1-n\right)}{2}$. Let $M^{2n+1}$ be a $C(ℂP^n)$-singular manifold with singular points $m_1 , ... ,m_k$. Suppose that, on $M^{2n+1}$, there exists an almost smooth vector field $V(x)$ with finite number of zeros $m_1 , ... ,m_k , x_1 , ... ,x_l$. Then $X(M 2n + 1) = ∑_{i = 1}^l ind(x_i ) + ∑_{i = 1}^k ind(m_i )$.

Anniversaries (Ukrainian)

Yurii Stephanovych Samoilenko (on his 70th birthday)

Berezansky Yu. M., Boichuk О. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Nikitin A. G., Nizhnik L. P., Samoilenko A. M., Sharko V. V., Sharkovsky O. M., Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1408-1409

Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 75th birthday)

Berezansky Yu. M., Boichuk О. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Nikitin A. G., Perestyuk N. A., Portenko N. I., Samoilenko Yu. S., Sharko V. V., Sharkovsky O. M., Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 3 - 6

Article (English)

$S^1$-bott functions on manifolds

Repovš D., Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1685-1698

We study $S^1$$ -Bott functions on compact smooth manifolds. In particular, we investigate $S_1$-invariant Bott functions on manifolds with circle action.

Anniversaries (Ukrainian)

Oleksandr Ivanovych Stepanets’ (on the 70 th anniversary of his birthday)

Gorbachuk M. L., Lukovsky I. O., Makarov V. L., Motornyi V. P., Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Sharko V. V., Zaderei P. V.

Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 579-581

Anniversaries (Ukrainian)

Yurii Ivanovych Samoilenko (on the 80th anniversary of his birthday)

Bakhtin A. K., Gerasimenko V. I., Plaksa S. A., Samoilenko A. M., Sharko V. V., Trohimchuk Yu. Yu, Yacenko V. O., Zelinskii Yu. B.

Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 574-576

Article (English)

Morse Functions on Cobordisms

Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 1. - pp. 119-129

We study the homotopy invariants of crossed and Hilbert complexes. These invariants are applied to the calculation of exact values of Morse numbers of smooth cobordisms.

Anniversaries (Ukrainian)

Yuri Yurievich Trokhimchuk (on his 80th birthday)

Berezansky Yu. M., Bojarski B., Gorbachuk M. L., Kopilov A. P., Korolyuk V. S., Lukovsky I. O., Mitropolskiy Yu. A., Portenko N. I., Reshetnyak Yu. G., Samoilenko A. M., Sharko V. V., Shevchuk I. A., Skorokhod A. V., Tamrazov P. M., Zelinskii Yu. B.

Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 701 – 703

Anniversaries (Ukrainian)

Fifty years devoted to science (on the 70th birthday of Anatolii Mykhailovych Samoilenko)

Berezansky Yu. M., Dorogovtsev A. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Mitropolskiy Yu. A., Perestyuk N. A., Rebenko A. L., Ronto A. M., Ronto M. I., Samoilenko Yu. S., Sharko V. V., Sharkovsky O. M.

Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 3–7

Article (English)

L2 -invariants and Morse - Smale flows on manifolds

Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 522-533

We study the homotopy invariants of free cochain and Hilbert complexes. These L2 -invariants are applied to the calculations of exact values of minimal numbers of closed orbits of some indexes of nonsingular Morse - Smale flows on manifolds of large dimensions.

Anniversaries (Ukrainian)

Evgen Yakovich Khruslov (on his 75 th birthday)

Berezansky Yu. M., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Marchenko V. O., Mitropolskiy Yu. A., Nizhnik L. P., Pastur L. A., Samoilenko A. M., Sharko V. V.

Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 549-550

Anniversaries (Ukrainian)

On the 90th birthday of Yurii Alekseevich Mitropol’skii

Berezansky Yu. M., Gorbachuk M. L., Korolyuk V. S., Koshlyakov V. N., Lukovsky I. O., Makarov V. L., Perestyuk N. A., Samoilenko A. M., Samoilenko Yu. I., Sharko V. V., Sharkovsky O. M., Stepanets O. I., Tamrazov P. M., Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 147–151

Obituaries (Ukrainian)

Andrei Reuter (1937-2006)

Bondarenko V. M., Drozd Yu. A., Kirichenko V. V., Mitropolskiy Yu. A., Samoilenko A. M., Samoilenko Yu. S., Sharko V. V., Stepanets O. I.

Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1584-1585

Article (Russian)

Additive Functions and Chain Complexes of Projective Modules

Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 2. - pp. 239-246

We study additive functions given on a category of finitely generated projective modules. Using these functions, we define p-minimal epimorphisms and give a necessary and sufficient condition for their existence. We prove results concerning the structure of p-minimal chains of projective modules.

Article (Russian)

Smooth and Topological Equivalence of Functions on Surfaces

Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 687-700

We obtain conditions under which the Morse functions defined on surfaces are smooth equivalent and functions with isolated critical (singular) points are topologically equivalent.

Article (Ukrainian)

Topological aspects of dynamical systems on manifolds

Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 876–878

Necessary and sufficient conditions are presented for the existence of dynamical systems on manifolds, for which the set of nonwandering points consists of a disconnected union of 2-dimensional tori with a hyperbolic structure.

Article (Ukrainian)

Exact round morse functions, Morse-type inequalities and integrals of Hamiltonian systems

Fomenko A. T., Sharko V. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 723–732

Article (Ukrainian)

Morse numbers and minimal morse functions on nonsimply connected manifolds

Sharko V. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 130–131

Article (Ukrainian)

Stable algebra and Morse theory

Sharko V. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 5. - pp. 711–713