Glazunov Nikolai Mihailovich
Doctor of Physical and Mathematical Sciences, Senior Researcher
Leading research associate
Biography
Graduated from Lviv State University. I. Franko (1969) and postgraduate studies at the Institute of Cybernetics of the USSR Academy of Sciences (1972); defended his dissertation (1973); defended his doctoral dissertation (2005)
1969 - 2006, 2020 Engineer, graduate student , junior researcher, group leader, senior researcher, leading researcher of the Institute of Cybernetics of the USSR Academy of Sciences (VM Glushkov Institute of Cybernetics of NASU), Kyiv.
2006 - 2020 Professor of the Department of Electronics, Robotics and Technology of Monitoring and the Internet of Things; Head of the Department of Applied Informatics; Head of the Department of Computer Multimedia Technologies. National Aviation University, Kyiv.
Research interests
- Theory of formal schemes, formal groups, their generalizations and applications. < li style = "text-align: justify;"> Li groups and algebraic groups.
- Characters, L-functions, distribution and density functions, applications.
- < span style = "font-size: 18px;"> Geometry of numbers.
- Optimization on varieties.
- Undifferentiated optimization
- Dynamic systems on manifolds and mirror symmetry.
- Computer algebra and (interval) computational methods.
-
Semantic Web and (categorical) models of artificial intelligence.
The main results
Теорія формальних схем, формальних груп, їхні узагальнення і застосування
- Глазунов М.М. Про «нормені підгрупи» одновимірних формальних груп, визначених над кільцем цілих локального поля. Доповіді Академії Наук УРСР. 1973. Серія А. № 11. С.965-968.
- Глазунов Н.М. Замечания об n-мерных коммутативных формальных группах над кольцом целых поля ρ-адических чисел. Укр. Мат. Журнал, т. 3, 1973, 352-354.
- Glazunov N.M. On norm maps and "universal norms" of formal groups over integer rings of local fields. Continuous and Distributed Systems. Theory and Applications. Berlin Heidelberg: Springer, 2014. P. 73 – 80.
Групи Лі і алгебраїчні групи
- Glazunov N.M., Karpinsky F., Kornyak V. Solving some problems of Algebra, Analysis and Mathematical Physics on Computer Algebra Systems. Cybernetics. 1991, No. 2, p.23-29.
- Glazunov N.M. Duality in abelian varieties and formal groups over local fields. I. Chebyshevskii Sbornik 19:1, 2018, P. 44–56.
Характери, L-функції, функції розподілу і щільності, застосування
- Glazunov N.M. On Equidistribution of Values of Kloosterman Sums. Doklady Acad. Nauk Ukr. SSR, ser. A, 1983, N 2. P.9-12.
- Glazunov N.M. On moduli spaces, equidistribution, bounds and rational points of algebraic curves. Ukrainian Math. Journal, no.9, 2001, pp.1174-1183.
- Glazunov N.M, Arithmetic Statistics, Probabilities and Langlands correspondence, “Analytical and computational methods in probability theory and its applications - ACMPT-2017”, Proc. of Int. Conf. on Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017), Lomonosov Moscow state University, Russia, 2017, pp.220-225.
Геометрія чисел
Доведена (в співавторстві) гіпотеза Г. Мінковського про критичний визначник області , p > 1;
- Глазунов Н.М., Голованов А.С., Малышев А.В. Доказательство гипотезы Минковского о критическом определителе области // Исследования по теории чисел. 9. Записки научных семинаров ЛОМИ. – 1986. – 151.- С.40-53.
- Glazunov N.M. Minkowski's Conjecture on Critical Lattices and the Quantifier Elimination. Algoritmic algebra and logic. Proc. of the A3L 2005, Passau, Germany, pp. 111-114.
- Glazunov N.M. On A. V. Malyshev's approach to Minkowski's conjecture concerning the critical determinant of the region |x| ^p +|y|^ p <1 for p>1 // Chebyshevskii Sbornik 17:4, 2016. P. 185–193.
Оптимізація на многовидах
- Глазунов Н.М. Разработка методов обоснования гипотез формальных теорий. Lambert Acad. Publ., ISBN 978-3-659-58011-6. 2014. 289 p.
- Glazunov N.M. Nondifferentiated optimization and forms of elastic bodies with standing the maximum load. Proceedings of the 4th international conference "Mathematical modeling, optimization and information technologies", 2014. Chisinau, Evrica, pp. 109-116.
Недифференційована оптимізація
- Глазунов Н.М., Постникова Л.П., Шор Н.З. Арифметическое моделирование случайных процессов и эргодическая теория // Кибернетика и системный анализ. - 2004.- № 4 . - С.73-86.
- Glazunov N.M. 2012. Arithmetic minima problems and methods for their investigation // Proceedings of the 3th international conference "Mathematical modeling, optimization and information technologies", Chisinau, Evrica, 2012, pp. 286-290.
- Glazunov N.M. 2012. Arithmetic modeling of random processes and r-algorithms, Cybernetics and Systems Analysis: Volume 48, Issue 1, 2012, Page 17-25.
Динамічні системи на многовидах і дзеркальна симетрія
- Glazunov N.M. On algebraic geometric and computer algebra aspects of mirror symmetry // Proc. of the Int. Conf. "Computer Algebra and its Applications to Physics." Dubna-2001. Joint Institute of Nuclear Research, Dubna, 2002, pp. 104-113.
- Glazunov N.M. Mirror Symmetry: Algebraic Geometric and Special Lagrangian Fibrations Aspects. Proc. of the Int. Conf. "Symmetry-2001", Part 2 of Volume 43 of Proceedings of Institute of Mathematics of NAS of Ukraine. Kiev-2002, pp.623-628.
- Glazunov N.M., Kryvonos Yu.G., Kharchenko V.P. Differential-algebraic equations and dynamical systems on manifolds // Cybernetics and Systems Analysis: Volume 52, Issue 3 (2016), Page 408-418.
Комп’ютерна алгебра та (інтервальні) обчислювальні методи
- Glazunov N.M. Integration of Computer Algebra Systems and Interval Computations, and Applications // Programming (Programmirovanie). 1992, no. 5, pp.51-57.
- Glazunov N.M. On Validated Numerics, Category Theory and Computer Algebra Framework for Simulation and Computation in Theoretical Physics // Nuclear Instruments & Methods in Physics Research, Section A, vol.502, Nos.2-3, 2003, pp. 654-656.
- Glazunov N.M. Interval computations and their Categorification // Numerical Algorithms, 37, 159-164, 2004.
Семантичний Web та (категорні) моделі штучного інтелекту
- Glazunov N.M., Kalughnin L.A., Stogny A.A., Sushchansky V.I. Problems Concerned with Development of Algebraic Computer Aided Research // Cybernetics (Kibernetika, Kiev), 1983, no. 2, pp.1-10.
- Glazunov N.M. Categorification of Fourier Transforms, Efficient Computation and Computing Intelligence // Nuclear Instruments & Methods in Physics Research, Section A, vol.534, 2004, pp. 324-328.
- Glazunov N.M. ‘Object-oriented knowledge base system for judgments about OWL ontology’ (in Ukraine), Scientific report on scientific and technical work. I, II stages. 2006-2007. The state registration number is 0106U009460. National Academy of Sciences of Ukraine - State Committee of Communications of the Cabinet of Ministers of Ukraine. 60 p.