2018
Том 70
№ 9

All Issues

Trohimchuk Yu. Yu

Articles: 20
Article (Russian)

Total differential

Trohimchuk Yu. Yu

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1250-1256

We present necessary and sufficient conditions for a continuous differential form to be the total differential.

Anniversaries (Ukrainian)

Volodymyr Leonidovych Makarov (on his 75th birthday)

Korolyuk V. S., Lukovsky I. O., Nesterenko B. B., Nikitin A. G., Perestyuk N. A., Samoilenko A. M., Solodkii S. G., Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1715-1717

Brief Communications (Russian)

Jacobian and the Darboux Property

Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 10. - pp. 1439-1440

We present a simple proof of the Darboux property for the Jacobian of a differentiable mapping.

Article (Russian)

Two Theorems of Complex Analysis

Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 973-980

We prove two fundamental theorems of multidimensional complex analysis by the methods of this analysis without using the theory of subharmonic functions. As a single violation, we can mention the use of Green’s formula.

Anniversaries (Ukrainian)

Yurii Stephanovych Samoilenko (on his 70th birthday)

Berezansky Yu. M., Boichuk A. 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

Article (Russian)

Mean-Value Theorem

Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 9. - pp. 1276–1282

We propose a new approach to the classical mean-value theorem in which two mean values are used instead of one. This approach is of especial importance for complex functions because there are no available theorems of this kind for these functions.

Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 75th birthday)

Berezansky Yu. M., Boichuk A. 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

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 (Russian)

Modules of continuity and analytic functions

Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1106–1113

For a function analytic in a compact domain and continuous in its closure, it is shown that the modules of continuity on the boundary of the domain and in its closure coincide.

Brief Communications (Ukrainian)

Denjoy problems

Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 718–720

We solve Denjoy problems concerning the elimination of singularities of analytic functions of measure zero.

Article (Russian)

On one criterion for analyticity of functions

Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 10. - pp. 1410–1418

We prove a generalization of the well-known Dzyadyk theorem that gives an interesting geometric criterion for the analyticity of functions.

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

Article (Russian)

On one criterion of constancy of a complex function

Safonov V. M., Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1096–1104

A new criterion of constancy of complex functions is proved.

Article (Ukrainian)

Differential properties of real and complex functions

Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 4. - pp. 

Article (Ukrainian)

Differential properties of functions

Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 3. - pp. 289–294

Article (Ukrainian)

Investigations in function theory in the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, during the Soviet regime

Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 6. - pp. 65–72

Article (Russian)

On derivatives with respect to direction of functions of many variables

Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 6. - pp. 67-79

Article (Russian)

On continuous mappings of plane regions

Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 1. - pp. 89-94

Article (Russian)

On continuous mappings of regions in a Euclidian space

Trohimchuk Yu. Yu

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 196-211

The basic assertion of this paper is that a set of branch points in space $R^n$ with $n \geq 3$ cannot be zero-dimensional. The proof is based on applying the very important theorem on continuity, which is also presented in the article.

Brief Communications (Russian)

On one example of a point set

Trohimchuk Yu. Yu

Full text (.pdf)

Ukr. Mat. Zh. - 1961. - 13, № 1. - pp. 117-118