The Head of the Department

Nickolay D. KOPACHEVSKY, Professor, Doctor of Physical and Mathematical Sciences
Phone: +38 0652 23-02-80
E-mail: kopachevsky@tnu.crimea.ua

History

It is the oldest department at the University, established in 1963. In different times it was directed by the astronomer and physicist E.F.Skvortsov, Assistant Professors B.A.Manson, Sh.Sh.Sutyusheva and V.D.Andronov.

Faculty Members

Nickolay D.Kopachevskiy, Honoured Worker of Science and Technology of Ukraine, Doctor of Physical and Mathematical Sciences Professor
Courses Taught:

• Applied Functional Analysis (lectures);
• Operational Methods of Mathematical Physics (lectures);
• Operational Methods of Hydromechanics (lectures and practice);
• Special Course on Spectral Theory of Operator Sheaves and its Applications;
• Special Course on Calculus of Variations and Its Applications;
• Special Course on Differential Equations in Banach Spaces and Their Applications;
• Special Course on Operational Methods in Mathematical Physics;
• Special Course on Operational Methods in Linear Hydrodynamics;
• Special Course on Volterra Integral and Differential Equation in Banach Space;
• Scientific Seminars.

Mustafa A.Muratov, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Mathematical Analysis (lectures and practice);
• Function Theory of Complex Variable (lectures);
• Operational Calculus (lectures);
• Mathematics for Economists (lectures);
• Special Course on Elements of Spectral Theory of Linear Operators;
• Special Course on Spectral Theory of Bounded Operators in Hilbert Space;
• Special Course on Elements of Spectral Theory of Self-adjoint Operator (lectures and practice).

Alexander I..Kovalenko, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Mathematical Analysis (lectures);
• Additional Chapters of Mathematical Analysis (lectures and practice);
• Probability Theory and Mathematical Statistics (lectures and practice);
• Theory of Waiting Lines (lectures);
• Special Course on Elements of the Mathematical Theory of Reliability (lectures).

Boris D.Marianin, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Higher Mathematics (lectures and practice);
• Bases of Higher Mathematics (lectures and practice);
• Probability Theory (lectures and practice);
• Probability Theory and Mathematical Statistics (lectures);
• Random Processes (lectures and practice);
• Theory of Waiting Lines (lectures);
• Social Statistics (lectures and practice);
• Special Course on Differential Forms;
• Special Course on Differential Calculus in Infinite-dimensional Spaces;
• Special Course on Elements of Random Processes Theory (lectures).

Alexey S.Tikhonov, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Mathematical Analysis and Additional Chapters of Mathematical Analysis (lectures and practice);
• Probability Theory (lectures and practice);
• Probability Theory and Mathematical Statistics (lectures and practice);
• Theory of Complex Variable Functions (lectures and practice);
• Special Course on Selected Issues of Elementary and Higher Mathematics;
• Special Course on Selected Issues of the Group Theory;
• Special Course on Riemann Surfaces.

Vladimir P.Smolich, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Mathematical Analysis (lectures and practice);
• Theory of Complex Variable Functions (lectures);
• Probability Theory and Mathematical Statistics (lectures and practice);
• Theory of Waiting Lines (lectures);
• Special Course on Linear Operators Theory;
• Special Course on Linear Operators in Hilbert Space;
• Special Course on Operational Calculus (lectures and practice).

Svetlana I.Smirnova, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Mathematical Analysis (lectures and practice);
• Probability Theory and Mathematical Statistics (lectures and practice).

Yulia S.Pashkova, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Mathematical Analysis (lectures and practice);
• Probability Theory and Mathematical Statistics (lectures);
• Theory of Complex Variable Functions (lectures and practice);
• Complex Analysis (lectures and practice).

Dmitriy A.Zakora, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Operational Methods in Mathematical Physics (lectures and practice);
• Mathematical Analysis (lectures and practice);
• Differential Equation in Banach Space (lectures and practice);
• Operational Methods of Hydromechanics (lectures);
• Probability Theory and Mathematical Statistics (practice);
• Special Course on Differential Equation in Banach Space and Their Applications (lectures).

Pavel A.Starkov, Candidate of Physical and Mathematical Sciences, Assistant Professor
Courses Taught:

• Mathematical Analysis (practice);
• Probability Theory and Mathematical Statistics (lectures and practice);
• Computer Theories in Mathematics (practice);
• Special Course on Introduction to Asymptotic Methods (lectures).

Denis O. Tsvetkov, Candidate of Physical and Mathematical Sciences, Assistant
Courses Taught:

• Mathematical Analysis (practice);
• Probability Theory and Mathematical Statistics (practice);
• Complex Analysis (practice);
• Theory of Complex Variable Functions (practice);
• Random Processes (practice).

Lidia V.Koreneva, Senior Lecturer
Courses Taught:

• Mathematical Analysis (lectures and practice);
• Higher Mathematics (practice);
• Special Course on Problem Tasks of Elementary Mathematics (practice).

Galina I.Kushnereva, Senior Lecturer
Courses Taught:

• Mathematical Analysis (practice);
• Probability Theory and Mathematical Statistics (practice);
• Theory of Complex Variable Functions (practice).

A.A.Bespaltsev, Assistant
Courses Taught:

• Mathematical Analysis (practice);
• Probability Theory and Mathematical Statistics (practice);
• Theory of Complex Variable Functions (practice);
• Mathematical Statistics and Random Processes (practice);
• Higher Mathematics (practice).

Boris M.Vronskiy, Assistant
Courses Taught:

• Mathematical Analysis (practice);
• Additional Chapters of Mathematical Analysis (practice);
• Probability Theory and Mathematical Statistics (practice);
• Theory of Complex Variable Functions (practice);
• Complex Analysis (practice);
• Higher Mathematics (practice).

Scientific Work

Researches of the theory of operator submatrixes with unlimited operator factors and its applications in the continuum mechanics , and problems of interface. Extensive scientific researches - theoretical, and applied - are carried out. They are devoted to the differential and integral-differential equations in Hilbert space, to differential calculus in topological vector spaces and, in applied aspect, to researches of wave processes in the confined reservoirs.
Scientific seminars work at the department. For 16 years the department has been organizing the International Crimean Autumn Mathematical School-Symposium on Spectral and Evolutionary Problems in the settlement of Batiliman in Crimea. In 2005 more than 220 scientists from 14 countries of the world took part in its work, among them more than 80 doctors of sciences and 9 full members and member-correspondents of national Academies of Sciences of Ukraine, Russia, Poland, Armenia and Georgia. Works of School-Symposium annually are issued in publishing house of TNU. The faculty is engaged in research of modern problems of the mathematical and functional analysis, application of methods of the theory of linear operators in problems of mechanics of continuous environments. Results of researches are reflected in numerous articles and monographies.
5 candidate dissertations and one thesis for a doctor's degree have been defended recently.
Beside individual scientific activity, the collective of the department conducts work on following scientific subjects: "Mathematical Analysis and Its Applications", the leader - Professor N.D. Kopachevskiy, "Development of Operational Methods in Functional Spaces and Their Applications in Mechanics of Continuous Environments", the leader - Professor N.D. Kopachevskiy.

Publications (in original languages)

1. В.Г.Бабский, H.Д.Копачевский, А.Д.Мышкис, Л.А.Слобожанин, А.Д.Тюпцов. Гидромеханика невесомости. - М.: Hаука, 1974, 504 с.
2. A.D.Myshkis, V.G.Babskii, N.D. Kopachevskii, L.A.Slobozhanin, A.D.Tyuptsov. Low-Gravity Fluid Mechanics. - Springer Verlag, Berlin, Heidelbery, New York, London, Paris, Tokio, 1987, 583 p.
3. Н.Д. Копачевский, С.Г. Крейн, Нго Зуй Кан. Операторные методы в линейной гидродинамике: Эволюционные и спектральные задачи. - М: Наука, 1989, 416 с.
4. А.Д.Мышкис, В.Г.Бабский, М.Ф.Жуков, Н.Д.Копачевский, Л.А.Слобожанин, А.Д.Тюпцов. Методы решения задач гидромеханики для условий невесомости (под ред. А.Д. Мышкиса). - Киев: Наукова думка, 1992, 592 с.
5. N.D.Kopachevskii, S.G.Krein. Operator Approach in Linear Problems of Hudrodynamics. Vol. 1: Self-Adjoint Problems for Ideal Fluid; Vol. 2: Not Self-Adjoint Problems for Viscous Fluid. - Birkhauser Vertlad, Basel, Boston, Berlin, 1999 (to appear).
6. Kopachevsky N.D., Mennicken R., Pashkova Yu.S. Complete second order linear differential operator equations in Hilbert space and applications in hydrodynamics. //Transactions of the AMS, (2004), N 3, p. 341-346.
7. Копачевский Н.Д. Абстрактная формула Грина и задача Стокса. //Изв.ВУЗов. Северокавк. регион. Ест. науки. Математика и механика сплошной среды. Ростов-на-Дону, 2004, с. 137-141.
8. Копачевский Н.Д., Крейн С.Г. Абстрактная формула Грина для тройки гильбертовых пространств, абстрактные краевые и спектральные задачи. //Украинский матем. вестник, т. 1 (2004), 1, с. 69-97.
9. Копачевский Н.Д. Об абстрактной формуле Грина для тройки гильбертовых пространств и её приложениях к задаче Стокса. //Таврический вестник информатики и математики, 2004, 2, с. 52-80.
10. Kopachevsky N.D. On abstract Green's Formula for a triple of Hilbert spales and applications. //Internat.Conf. Diff.Equations and Related Topics , Book of abstracts, Moscow, May 16-22, 2004, p. 111.
11. Закора Д.А., Копачевский Н.Д. Задачи и указания к их решению по курсу "Операторные методы математической физики". //ТНУ, 2004, учебное пособие, 87 с.
12. Закора Д.А., Копачевский Н.Д. Задачи и указания к их решению по курсу "Прикладной функциональный анализ". //ТНУ, 2004, учебное пособие, 48 с.
13. Starkov P. А. The problem on small movements of an ideal fluid in a vessel with a solid wall and a hole. //Spectral and Evolutionary problems: Proceedings of the 9-th Crimean Autumn Mathematical School-Symposium, Simferopol - 1999. - p. 128-133. (in English)
14. Kopachevsky N., Starkov P. Operator approach to transmission problems for Helmholtz equation. //UMC-2001, Nonlinear partial Differential equations: Book of abstracts, Donetsk, - 2001. - p. 68. (in English)
15. Старков П. А. Операторный подход к задачам сопряжения. //Ученые записки Таврического национального университета. Математика. Механика. Информатика и Кибернетика. - 2002. - т. 15 (54), N 1. - с. 58 - 62.
16. Старков П.А. Случай общего положения для операторного пучка, возникающего при исследовании задач сопряжения. //Ученые записки Таврического национального университета. Математика. Механика. Информатика и Кибернетика. - 2002 - т. 15 (54), N 2. - с. 82 - 88.
17. Kopachevsky N., Starkov P. Abstract Green's formula and transmission problems. //International conference on functional analysis and its applications: Book of abstracts, Lviv, LNU - 2002. - p. 112-113. (in English)
18. Старков П.А. Исследование задач сопряжения при исключительных значениях фиксированного параметра. //Ученые записки Таврического национального университета. Математика. Механика. Информатика и Кибернетика. - 2003. - т. 16 (55), N 2. - с. 81-89.
19. Старков П.А. О базисности системы собственных элементов в задачах сопряжения. //Таврический вестник информатики и математики. - 2003. - Вып. 1. - с. 118 - 131.
20. Старков П.А. О начально-краевой задаче, порождающей внутреннюю задачу сопряжения. //Таврический вестник информатики и математики. - 2003. - Вып. 2. - с. 112 - 118.
21. Starkov P.A. Abstract Transmission Problems. //1-ая летняя школа по топологической алгебре и функциональному анализу, Львовский национальный университет им.И.Франко, Львов. - 2003. - с. 37-38. (in English)
22. Старков П.А. Задачи сопряжения для уравнения Гельмгольца и их абстрактные аналоги. //Сборник тезисов межд. конф. "Дифференциальные уравнения и смежные вопросы" посвященной 103-летию со дня рождения И.Г. Петровского, Москва. - 2004. - с. 220.
23. Tsvetkov D.O. On normal oscillations of a viscous stratified fluid. //Ученые записки Таврического национального университета. Математика. Механика. Информатика и Кибернетика. - 2002. - т. 15 (54), N 1. - с. 100 - 104.
24. Цветков Д.О. Малые движения стратифицированной жидкости. //Ученые записки Таврического национального университета. Математика. Механика. Информатика и Кибернетика. - 2002. - т. 15 (54), N 2. - с. 99 - 104.
25. Цветков Д.О. Нормальные колебания частично диссипативной гидросистемы. //Ученые записки Таврического национального университета. Математика. Механика. Информатика и Кибернетика. - 2003. - т. 16 (55), N 2. - с. 99 - 108.
26. Цветков Д.О. О малых движениях частично диссипативной гидросистемы, состоящей из стратифицированных жидкостей. //Межведомственный научный сборник "Динамические системы". - 2004. - Вып. 18. - с. 119 - 124.
27. Цветков Д.О. Малые движения идеальной стратифицированной жидкости в сосуде //Таврический вестник информатики и математики. - 2002. - Вып.1. - с. 98 - 103.
28. Цветков Д.О. Малые движения стратифицированной жидкости во вращающемся сосуде //Таврический вестник информатики и математики. - 2003. - Вып. 1 - с. 140 - 149.
29. Tsvetkov D.O. On small motions of a partially dissipative hydrosystems consisting of stratified fluids. //International Conference on Functional Analysis and its Applications. Book of Abstracts. - Lvov (Ukraine). - 2002. - р. 200 - 201.
30. Цветков Д.О. Математические проблемы теории колебания стратифицированной жидкости. //XXVI Конференция молодых ученных механико-математического факультета МГУ им. М.В. Ломоносова. Тезисы докладов. - Москва - 2004. - 134 - 136.
31. Tikhonov A.S. Boundary values of operator-valued functions and trace class perturbations. Rom. J. of Pure and Appl. Math., 47 (2002), N 5-6, 761-767.
32. Tikhonov A.S. Functions of system and their perturbations, Proceedings CD of the Fifteenth International Symposium of Mathematical Theory of Networks and Systems(MTNS 2002), South Bend, USA, 2002.
33. Tikhonov A.S. "Curved" conservative systems and their applications. Uchenye zapiski TNU, ser. Math.,Mach. and CS, 2002, N 2, 89-94. (in Russian)
34. Tikhonov A.S. Functional model and duality of spectral components for operators with continuous spectrum on a curve. Algebra i Analiz, 14 (2002), N 4, 58-195; English transl., St. Petersburg Math. J. 14 (2003), N 4, 169-184.
35. Tikhonov A.S. Extreme factorizations of J-contractive-valued functipons. Uchenye zapiski TNU, ser. Math.,Mach. and CS, 2003, N 2, 80-94. (in Russian)
36. Tikhonov A.S. Spectral Components of Operators with Spectrum on a Curve. Funktsional'nyi Analiz i Ego Prilozheniya, 37 (2003), N 2, 90-91; English transl., Functional Analysis and Its Applications, 37 (2003), N 2.
37. Tikhonov A.S. Property of maximality for spectral components (case of multiply connected domains). Uchenye zapiski TNU, ser. Math., Mach. and CS, 2004, N 2, 123-126. (in Russian)
38. Tikhonov A.S. Property of maximality for spectral components in Mathematical studies Vol.197, Functional Analysis and its Applications, Elsevier, 2004.
39. Tikhonov A.S. Transfer functions for "curved" conservative systems. Operator Theory: Adv. and Appl., Birkhauser, Basel-Boston, Vol. 153 (2004), 255-264.
40. Tikhonov A.S. Free functional model related to simply-connected domains. Operator Theory: Adv. and Appl., Birkhauser, Basel-Boston, Vol. 154 (2004), 405-415.
41. Вронский Б.М. "О малых движениях системы "жидкость-газ" в ограниченной области". //Ученые записки Таврического национального университета им. В.И. Вернадского, N 1, 2004.
42. Муратов М.А., Чилин В.И. Сходимости в *-алгебрах локально измеримых операторов. //Таврический вестник информатики и математики. - 2004. - N 2. - C.
43. Марянин Б.Д., Смирнова С.И., Калинюк И.В. Методические указания и контрольные задания по курсу "Теория вероятностей и математическая статистика" (тема "Линейная регрессия") //Симферополь: ТНУ, 2003. - 16 с.
44. Копачевский Н.Д., Орлов И.В., Смирнова С.И. К пятнадцатилетию Крымской осенней математической школы (КРОМШ). //Таврический вестник информатики и математики. - 2004. - N 2. - c. 7-39.
45. Орлов И.В., Смирнова С.И. Крымские Осенние Математические Школы 2003 г. и 2004 г. //Интегральные преобразования и специальные функции. - 2005. - т. 5, N 1 - с. 66-84.