Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
Archives

Shadow problem and related questions

##plugins.themes.bootstrap3.article.sidebar##

PDF (Русский)
Published Apr 25, 2017
DOI https://doi.org/10.15673/tmgc.v9i3-4.319

##plugins.themes.bootstrap3.article.main##

Yuri Zelinskii
Institute of mathematics NAS Ukraine
http://orcid.org/0000-0001-5648-0785
Irina Vygovskaya
Institute of mathematics NAS Ukraine
Hayjaa Kudhair Dakhil
Taras Shevchenko National University of Kyiv

Abstract

In work we give review of results related to problem shade, got in study for the last one and a half year. There are discussed unsolved problems and are given estimations of necessary and sufficient conditions.

Keywords:
Euclidean space, sphere, ball, convexity, generalized convexity

##plugins.themes.bootstrap3.article.details##

How to Cite
Zelinskii, Y., Vygovskaya, I., & Dakhil, H. (2017). Shadow problem and related questions. Proceedings of the International Geometry Center, 9(3-4). https://doi.org/10.15673/tmgc.v9i3-4.319
Issue
Vol 9 No 3-4 (2016)
Section
Papers

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgment of the work’s authorship and initial publication in this journal.

Provided they are the owners of the copyright to their work, authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository, in a journal or publish it in a book), with an acknowledgment of its initial publication in this journal.

Authors are permitted and encouraged to post their work online (e.g., in institutional repositories, disciplinary repositories, or on their website) prior to and during the submission process.

Author Biographies

Yuri Zelinskii, Institute of mathematics NAS Ukraine

Head of department of complex analysis and potential theory

Irina Vygovskaya, Institute of mathematics NAS Ukraine

Junior research worker department of complex analysis and potential theory

Hayjaa Kudhair Dakhil, Taras Shevchenko National University of Kyiv

Phd student chair of mathematical analysis

References

1. Солтан В. П. Введение в аксиоматическую теорию выпуклости, Кишинев: Штиинца, 1984.

2. Зелинский Ю.Б., Выговская И.Ю., Стефанчук М.В. Обобщённо выпуклые множества и задача о тени// Український математичний журнал т. 67, №12, 2015. — C.1659-1666.

3. Худайберганов Г. Об однородно-полиномиально выпуклой оболочке объединения шаров // Рукопись деп. в ВИНИТИ 21.02.1982 г. № 1772 — 85 Деп.

4. Зелинский Ю.Б. Многозначные отображения в анализе. — Kиев: Наукова думка, 1993.- 264 с..

5.Зелинский Ю.Б. Выпуклость. Избранные главы. — Праці Інституту математики НАНУ, Київ: Інститут математики НАНУ.- 2012.- т.92.- 280 с.

6. Зелинский Ю.Б. Задача о тени для семейства множеств// Збірник праць Інституту математики НАНУ, 2015, т.12, №4. – C.197-204.

7. Ткачук М.В., Осипчук Т.М. Задача о тени для эллипсоида вращения// Збірник праць Інституту математики НАНУ, 2015, т.12, №3. – C.243-250.

8. Зелінський Ю.Б., Стефанчук М.В. Узагальнення задачі про тінь // Український математичний журнал т. 68, №6, 2016. — C.657-662

9. Zelinskii Yu. B. Generalized Convex Envelopes of Sets and the Problem of Shadow // Journal of Mathematical Sciences, (2015), 211, No.5, – P. 710–717.

10. Zelinskii Yu. B. Problem of shadow (complex case) // Advances in Mathematics: Scientific Journal, (2016), 5, No.1, – P. 1–5.

11. Zelinskii Yu. B. The problem of the shadows // Bulletin de la societ´e des sci. et letters de L´od´z, (2016), 66, No.1, – P.34-42.

12. Zelinskii Yu.B. Problem of shadow for tangent bundle of straight line on sphere //Proceedings of 7th International Conference on Complex Analysis & Dynamical Systems (in print).

13. http://ru.wikipedia.org/wiki/ Икосаэдр.

14. http://ru.wikipedia.org/wiki/ Додекаэдр.

15. http://ru.wikipedia.org/wiki/ Правильный пятиугольник.