Prof. Alexander M. Krot
Affilation and Professional activity: Alexander M. Krot was born on the 5th of September in 1960 in Belarus. He graduated from the Belarusian State University, Department of Radiophysics in 1982. He received PhD degree at the age of 25 years in 1985, then he has completed his degree of Doctor of Sciences (DSc) at the age of 31 years in 1991 (by the decision of the Higher Attestation Commission of USSR in Moscow) and Professor degree in 1997 (by the decision of the Higher Attestation Committee of Republic of Belarus in Minsk). In 1993 Dr. A.M. Krot founded the Laboratory of Self-Organization System Modeling at the United Institute of Informatics Problems (the former Institute of Engineering Cybernetics) of the National Academy of Sciences of Belarus. He has been a Professor at the Department of Mathematical Physics of the Belarusian State University in Minsk since 2008 till 2016. Now Professor, DSc Alexander M. Krot is a Head of the Laboratory of Self-Organization System Modeling at the United Institute of Informatics Problems of the National Academy of Sciences of Belarus.
Scientific interest and projects: His current research interests are the analytical theory and computational modeling of self-organization processes and phenomena in complex systems (gas-dust protoplanetary media, aerohydrodynamic viscous flows, nervous fibres, neural network structures etc.), statistical theory of planetary (stellar) system forming, theory of nonlinear analysis of attractors of complex systems, digital signal processing etc.
Since 1997 till 2000 he was a Manager of B-95 ISTC project "Theory and methods of discrete dynamical systems in digital signal processing applications" (Collaborator of this project was Nobel Laureate, Professor I. Prigogine (Belguim/USA) and also Prof. M. Vetterly (Switzerland/USA), Prof. S. Holm (Norway), Prof. Duhamel (France)).
Publication activity: He has published 280 scientific works including 3 monographs: A.M. Krot "Discrete models of dynamical systems based on polynomial algebra": Minsk, Navuka i tekhnika, 1990, 312 pp., A.M. Krot, H.B. Minervina "Fast algorithms and programs for digital spectral processing of signals and images": Minsk, Navuka i tekhnika, 1995, 407 pp., A.M. Krot "Statistical theory of formation of gravitating cosmogonical bodies", Bel. Navuka, Minsk, 2012, 448 pp.) and more than 80 articles in refereed journals.
Membership in International society and journals: Prof. Krot was a member of American Mathematical Society (AMS) and International society of Optical Engineering (SPIE) (1994-2000), was a member of Program Committee of the SPIE’s “AeroSense” conference (Orlando, Florida, USA) and International Workshop on models and analysis of vocal emissions for biomedical applications (Florence, Italy).
He was a member of editorial boards of the following journals: “Achievement in Modern Radioelectronics”(Moscow, Russia), “Electromagnetic Waves and Electronic Systems”(Moscow, Russia), “Nonlinear Phenomena in Complex Systems”(Minsk, Belarus). He was a convener of scientific sessions PS15 “Models of Solar system forming” (2-7 April 2006, Vienna, Austria), PS7.1 “Extrasolar Planets and Planet Formation” (16-20 April 2007, Vienna, Austria), PS 9 “Extrasolar Planets and Planet Formation” (13-18 April 2008, Vienna, Austria), PS8 “Extrasolar planets and planet formation, exoplanetary magnetospheres and radio emissions” (19-24 April 2009, Vienna, Austria) General Assembly of European Geoscinces Union , ON1 “Planetary formation and the origin of the Solar System” (18-22 September 2006, Berlin, Germany), OG1 “Origin and Evolution” (14–18 September 2009, Potsdam, Germany) of European Planetary Science Congress.
Now he is member of editorial board of journals: «Chaotic Modeling and Simulation (CMSIM)» (Greece), «Fractal Geometry and Nonlinear Analysis in Medicine and Biology (FGNAMB)» (Italy) and «Informatics» (Belarus), he is member of Organizing Committee of «Satellite & Space Missions» (USA), Program Committee of «The Issues of Calculation Optimization» (Ukraine).
Honors: Recipient of Komsomol’s Republic awards in the area of science and engineering (1988 and 1990), A.S. Popov award of Radio-engineering Society (1991), award of National Academy of Sciences of Belarus (1993), grant of International Science Foundation (1993), grant of President of the Republic of Belarus (2007), award of Ministry of Industry of the Republic of Belarus (2010).
Since 1995 till now Professor Alexander M. Krot is a subject of biographical records in “Who is Who in the World” and “Who is Who in Science and Engineering”, New Providence, USA.
Monographs
1. Krot, A. M. Discrete models of dynamical systems based on polynomial algebra. Minsk: Navuka i tekhnika, 1990. – 312 pp. [in Russian];
2. Krot, A. M., Minervina, H. B. Fast algorithms and programs for digital spectral processing of signals and images. Minsk: Navuka i tekhnika, 1995. – 407 pp. [in Russian];
3. Krot, A. M. Statistical theory of formation of gravitating cosmogonical bodies. Minsk: Bel. Navuka, 2012. – 448 pp. [in Russian].
Selected articles
1. Krot, A. M. On a class of generalized shift operators in the theory of signals and systems / A. M. Krot // Soviet J. Comm. Tech. Electron. – 1986. – Vol. 31, no. 12. – P. 110-118. (translation of Radiotekhnika i Elektronika. – 1986. – Vol. 31, no. 8. – P. 1563-1570. (Scripta Technica, Inc., journal impact factor – 0,359)).
2. Krot, A. M. Synthesis of digital Fourier transformation algorithms for real sequences on the basis of polynomial algebra / A. M. Krot, H. B. Minervina // Soviet J. Comm. Tech. Electron. – 1987. – Vol. 32, no. 11. – P. 9-19. (translation of Radiotekhnika i Elektronika. – 1987. – No. 6. – P. 1217-1229. (Scripta Technica, Inc., journal impact factor – 0,359)).
3. Krot, A. M. Analysis of linear dynamic systems based on polynomial transformations of numerical sequences / A. M. Krot // Soviet J. Comm. Tech. Electron. – 1989. – Vol. 34, no. 1. – P. 6-13. (translation of Radiotekhnika i Elektronika. – 1988. – Vol. 33, no. 7. – P. 1458-1466. (Scripta Technica, Inc., journal impact factor – 0,359)).
4. Krot, A. M. Class of discrete random processes, nonstationary relative to a generalized shift operator. / A. M. Krot // Soviet J. Comm. Tech. Electron. – 1989. – Vol. 34, no. 8. – P. 23-31. (translation of Radiotekhnika i Elektronika. – 1988. – Ò. 33, ¹ 12. – Ñ. 2515-2523. (Scripta Technica, Inc., journal impact factor – 0,359)).
5. Krot, A. M. Spectral analysis of a class of nonstationary random processes in discrete biorthogonal bases / A. M. Krot // Soviet J. Comm. Tech. Electron. – 1989. – Vol. 34, no. 12. – P. 51-59. (translation of Radiotekhnika i Elektronika. – 1989. – Vol. 34, no. 1. – P. 59-68. (Scripta Technica, Inc., journal impact factor – 0,359)).
6. Krot, A. M. Fast Fourier transform algorithms for the real and Hermitian-symmetrical sequences / A. M. Krot, H. B. Minervina // Soviet J. Comm. Tech. Electron. – 1990. – Vol. 34, no. 12. – P. 122-129. (translation of Radiotekhnika i Elektronika. – 1989. – Vol. 34, no. 2. – P. 369-376. (Scripta Technica, Inc., journal impact factor – 0,359)).
7. Krot, A. M. The method of eigentransforms in differetnt fields for computing cyclic convolution and discrete Fourier transforms / A. M. Krot // Comput. Maths Math. Phys. – 1989. – Vol. 29, no. 3. – P. 23-34. (translation of Zh. Vychisl. Mat. i Mat. Fiz. – 1989. – Vol. 29, no. 5. – P. 675-692. (Pergamon Press, journal impact factor – 0,585)).
8. Krot, A. M. Synthesis of fast-Fourier-transform (FFT) split-radix algorithms for real-valued and Hermite-symmetrical series / A. M. Krot, H. B. Minervina // Radioelectronics and Communication Systems. – 1989. – Vol. 32, no. 12. – P. 10-15. (translation of Izvestiya VUZ. Radioelektronika. – 1989. – Vol. 32, no. 12. – P. 12-17. (Allerton Press, Inc., journal impact factor – 0,137)).
9. Krot, A. M. Synthesis of fast proper transformation algorithms for discrete convolution in rational and real fields / A. M. Krot // Soviet J. Comm. Tech. Electron. – 1990. – No. 15. – P. 16-25. (translation of Radiotekhnika i Elektronika. – 1990. – Vol. 34, no. 2. – P. 372-381. (Scripta Technica, Inc., journal impact factor – 0,359)).
10. Krot, A. M. A Unified approach to calculating convolutions and the discrete Fourier transform based on proper transforms in rational and real fields / A. M. Krot // Soviet J. Comm. Tech. Electron.: – 1991. – No. 2. – P. 26-34. (translation of Radiotekhnika i Elektronika. – 1990. – Vol. 35, no. 4. – P. 805-815. (Scripta Technica, Inc., journal impact factor – 0,359)).
11. Krot, A. M. On a class of discrete quasistationary linear dynamic systems / A. M. Krot // Sov. Phys. Dokl. – 1990. – Vol. 35, no. 8. – P. 711-713. (translation of Physics Section of Doklady Akad. Nauk SSSR. – 1990. – Vol. 313, no. 6. – P. 1376-1380. (Journal impact factor – 0, 473)).
12. Krot, A. M. On the multiplicative complexity of bilinear forms for which the Vandermonde transformation is an eigentransformation / A. M. Krot // Sov. Math. Dokl. – 1991. – Vol. 42, no. 2. – P. 646-650. (translation of Mathematics Section of Doklady Akad. Nauk SSSR. – 1990. – Vol. 314, no. 6. – P. 1312-1315. (Journal impact factor – 0, 307)).
13. Krot, A. M. Computational complexity of generalized KN-convolutions and the fast Vandermonde transform algorithm / A. M. Krot // Comput. Maths Math. Phys. – 1990. – Vol. 30, no. 6. – P. 17-26. (translation of Zh. Vychisl. Mat. i Mat. Fiz. – 1990. – Vol. 30, no. 11. – P. 1625-1637. (Pergamon Press, journal impact factor – 0, 585)).
14. Krot, A. M. Spectral representation of sequences on a field of a class of residues/ A. M. Krot, H. B. Minervina // Electronnoe modelirovanie. – 1991. – Vol. 13, No. 1. – P. 9-13.
15. Krot, A. M. Analysis and generation of information flows in problems of modeling of dynamic systems based on polynomial algebra: abstract diss. the doctor tehn. nauk / A. M. Krot; ITK AN BSSR. – Minsk, 1991. – 32 p.
16. Krot, A. M. Comment: Conjugate pair fast Fourier transform / A. M. Krot, H. B. Minervina // Electronics Letters: – 1992. – Vol. 28, No. 10. – P. 1143-1144. (IEE, journal impact factor – 1,152).
17. Krot, A. M. New fast algorithms for filtering and interpolating digital signals and images / A. M. Krot // Pattern Recognition and Image Analysis (Advances in Mathematical Theory and Applications). – 1993. – Vol. 3, No. 2. – P. 126-136. (Interperiodica Publ.).
18. Krot, A. M. A fast algorithm for calculating the inverse convolution for signal and image reconstruction / A. M. Krot, A. T. Kas¼ko, H. B. Minervina // Comput. Maths Math. Phys. – 1996. – Vol. 36, no. 2. – P. 269-277. (translation of Zh. Vychisl. Mat. i Mat. Fiz. – 1996. – Vol. 36, no. 2. – P. 164-175. (Pergamon Press, journal impact factor – 0,585)).
19. Krot, A. M. The local-topological method of determining the minimal embedding dimension of the chaotic attractor / A. M. Krot, V. F. Dailyudenko // Dolklady of the Academy of sciences of Belarus. – 1996. – Vol. 40, No. 3. – P. 70-75.
20. Krot, A. M. Theory and methods of dynamic systems for solving signal processing problems / A. M. Krot // Usp. Sovr. radioelectroniki. – 1996. – No. 6. – P. 3-18.
21. Krot, A. M. Synthesizing fast algorithms for optimal discrete control by the method of polynomial equations / A. M. Krot // Automation and Remote Control. – 1996. – Vol. 57, no. 8. – P. 1079-1090. (translation of Avtomatica i Telemekhanika. – 1996. – no. 8. – P. 22-35. (Plenum Publ. Co., journal impact facot – 0,265)).
22. Krot, A. M. The statistical model of the gravitational interactions of particles / A. M. Krot // Usp. Sovr. radioelectroniki. –1996. – No. 8. – P. 66-81.
23. Krot, A. M. An efficient procedure for restoration of signals and image on the basis of a fast algorithm of convolution inversion / A. M. Krot, H. B. Minervina // Pattern Recognition and Image Analysis. –1996. – Vol. 6, No. 3. – P. 582-591.
24. Krot, A. M. Coding of images based on finite algebraic structures and fast convolution algorithm / A. M. Krot, M. N. Dolgikh, N. A. Romanovskaya // Pattern Recognition and Image Analysis. – 1997. –Vol. 6, No. 3079. – P. 782-790.
25. Krot, A. M. Calculation of the minimal embedding dimension of a chaotic attractor on the basis of local topological analysis of phase trajectories / A. M. Krot, V. F. Dailydenko // Comput. Maths Math. Phys. – 1997. – Vol. 37, no. 3. – P. 311-319. (translation of Zh. Vychisl. Mat. i Mat. Fiz. – 1997. – Vol. 37, no. 3. – P. 315-324. (Pergamon Press, journal impact factor – 0,585)).
26. Krot, A. M. Methods and microelectronic facilities of the digital filtering of signals and images on the basis of number theoretic / A. M. Krot, V. F. Kravchenko // Usp. Sovr. Radioelectroniki. – 1997. – No. 6. – P. 3-31.
27. Krot, A. M. Algorithms and the multiplicative complexity of the reduction a modulo arbitrary polynomial, generalized KN-convolution and fast Vandermonde transform / A. M. Krot // Proc. of 13th Intern. Conf. on Digital Signal Proc. (DSP'97) / Greece — Santorini: 1997. — Vol. 2. — P. 893-897.
28. Krot, A. M. Algorithms and the multiplicative complexity of the reduction a modulo arbitrary polynomial, generalized KN-convolution and fast Vandermonde transform / A. M. Krot, N. N. Prokudina // Proc. of 13th Intern. Conf. on Digital Signal Proc. (DSP'97) / Greece — Santorini: –1997. – Vol. 2. – P. 587-590.
29. Krot, A. M. Algorithms and the multiplicative complexity of the modulo arbitrary polynomial reduction for the generalized KN-convolution and of the fast Vandermonde transform / A. M. Krot // Electromagnetic Waves &Electronic Systems. – 1998. – Vol. 3, No. 1. – P. 48-69.
30. Krot, A. M. Minimal multiplicative complexity and fast restoration algorithm of digital signals and images / A. M. Krot, H. B. Minervina // Proc. of SPIE 12th Annual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 13-17 Apr. / USA — Orlando, Florida: – 1998. – Vol. 3374. – P. 426-435.
31. Krot, A. M. Fast reduction a modulo polynomial and fast Vandermonde transform based on fast Fourier transform algorithms / A. M. Krot // Proc. of SPIE 12th Annual Intern. Symposium on Aero-space / Defense Sensing, Simulation, and Controls (AeroSense), 13-17 Apr. / USA — Orlando, Florida: – 1998. – Vol. 3374. – P. 505-514.
32. Krot, A. M. Fast algorithms for reduction a modulo polynomial and Vandermonde transform using FFT / A. M. Krot, H. B. Minervina // Proc. of IX European Signal Processing Conference, (EUSIPCO-98), 8-11 September / Greece —Rhodes: – 1998. – Vol. 1. – P. 173-176.
33. Krot, A. M. Identification of discrete input nonlinear systems for digital chaotic signal processing / A. M. Krot, M. A. Shcherbakov // in "Recent Advances in Information Science and Technology", World Scientific. – Singapore, New Jersey, London, Hong Kong: 1998. – P. 251-253.
34. Krot, A. M. Identification of discrete input nonlinear systems for digital chaotic signal processing / A. M. Krot, M. A. Shcherbakov // Proc. of 2nd IMACS/IEEE International Conference on: Circuits, Systems and Computers (IMACS-CSC'98). –1998. – Vol. 2. – P. 795-797.
35. Krot, A. M. An algorithm for fast polynomial reduction in digital signal processing problems / A. M. Krot, H. B. Minervina // in "Recent Advances in Information Science and Technology", World Scientific. – Singapore, New Jersey, London, Hong Kong: 1998. – P. 195-198.
36. Krot, A. M. An algorithm for fast polynomial reduction in digital signal processing problems / A. M. Krot, H. B. Minervina // Proc. of 2nd IMACS/IEEE International Conference on: Circuits, Systems and Computers (IMACS-CSC'98). – 1998. – Vol. 2. – P. 827-830.
37. Krot, A. M. The analysis of dynamics of a complicated system state on phase portraits in space of eigenvectors / A. M. Krot, A. A. Boriskevich, V. M. Demko, P. P. Tkachova // in "Recent Advances in Information Science and Technology", World Scientific. – Singapore, New Jersey, London, Hong Kong: 1998. – P. 191-194.
38. Krot, A. M. The analysis of dynamics of a complicated system state on phase portraits in space of eigenvectors / A. M. Krot, A. A. Boriskevich, V. M. Demko, P. P. Tkachova // Proc. of 2nd IMACS/IEEE International Conference on: Circuits, Systems and Computers (IMACS-CSC'98). –1998. –Vol. 2. – P. 874-877.
39. Krot, A. M. Eigen transforms over finite rings in filter bank structures / A. M. Krot, V. O. Kudryavtsev // Proc. of 6th IEEE Intern. Workshop on Intelligent Signal Processing and Communication Systems, 4-6 November / Australia – Melbourne: 1998. – P. 877-880.
40. Krot, A. M. Identification of Discrete 1-D and 2-D input nonlinear systems for digital signal and image processing / A. M. Krot, M. A. Shcherbakov // Proc. of 6th IEEE Intern. Workshop on Intelligent Signal Processing and Communication Systems, 4-6 November / Australia – Melbourne: 1998. – P. 881-885.
41. Krot, A. M. Minimal attractor embedding dimension for discrete dynamic system based on state-space methods / A. M. Krot, H. B. Minervina // Proc. of SPIE 13th Annual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 5-9 April / USA – Orlando, Florida: 1999. – Vol. 3720. – P. 416-422.
42. Krot, A. M. The variability problem solving in speech recognition based on nonlinear filtering / A. M. Krot, P. P. Tkachova // Proc. of SPIE 13th Annual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 5-9 April / USA – Orlando, Florida: 1999. – Vol. 3720. – P. 423-433.
43. Krot, A. M. Use of the statistical model of gravity for analysis of nonhomogeneity in earth surface / A. M. Krot // Proc. of SPIE 13th Annual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 5-9 April / USA – Orlando, Florida: 1999. – Vol. 3710, part 2. – P. 1248-1259.
44. Krot, A. M. The use of nonlinear signal decomposition into functional series for speech recognition / A. M. Krot, P. P. Tkachova // Proc. of the 3rd World Multiconference on: Circuits, Systems, Communications and Computers (IEEE/WSES/ IMACS) CSCC'99. –1999. – Vol. 1. – P. 2281-2286.
45. Krot, A. M. The use of nonlinear signal decomposition into functional series for speech recognition / A. M. Krot // Proc. of the 3rd World Multiconference on: Circuits, Systems, Communications and Computers (IEEE/WSES/ IMACS) CSCC'99. –1999. – Vol. 1. – P. 2291-2296.
46. Krot, A. M. The nonlinear signal decomposition in voice recognition system constructing / A. M. Krot, P. P. Tkachova // Proc. of the Intern. Workshop "Models and analysis of vocal emissions for biomedical applications", 1-3 Sept / Italy – Firenze: 1999. – P. 54-58.
47. Krot, A. M. Minimal attractor embedding dimension for discrete dynamic system using state-space method: theoretical ground / A. M. Krot, H. B. Minervina // Proc. of the 6th IEEE Int. Conf. on Electronics, Circuits and Systems, (ICECS'99), 5-8 Sept. / Cyprus – Pafos: 1999. – Vol. 2. – P. 941-944.
48. Krot, A. M. The development of fast procedures for optimal discrete control problems based on Diophantine equations / A. M. Krot // Proc. of the Artificial Neural Networks in Engineering Conference (ANNIE'99) "Smart engineering system design", 7-10 November / USA – St. Louis, Missouri, New York: ASME Press, 1999. – Vol. 9. – P. 645-651.
49. Krot, A. M. Nonlinear dynamics methods application to electrocardiosignal exploration / A. M. Krot, V. F. Dailyudenko, H. B. Minervina // Proc. of the 5th Intern. Symp. on Signal Processing and its Applications, August 22-25 / Australia. –1999. – Vol. 1. – P. 191-194.
50. Krot, A. M. The theory of filter bank analysis and synthesis and their application / A. M. Krot, V. O. Kudrjavtsev // Usp. Sovr. Radioelectroniki. – 1999. No. 2. – P. 3-17.
51. Krot, A. M. Statistical description of gravitational field: a new approach / A. M. Krot // Proc. of SPIE 14th Annual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 24-28 April / USA – Orlando, Florida: 2000. – Vol. 4038. – P. 1318-1329.
52. Krot, A. M. Biomedical signal processing based on spectral and chaotic dynamic methods // A. M. Krot, H. B. Minervina // Proc. of SPIE 14th Annual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 24-28 April / USA – Orlando, Florida: 2000. – Vol. 4052. – P. 353-361.
53. Krot, A. M. Speech recognition based on nonlinear signal decomposition / A. M. Krot, P. P. Tkachova // Proc. of SPIE 14th Annual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 24-28 April / USA – Orlando, Florida: 2000. – Vol. 4056. – P. 482-489.
54. Krot, A. M. On approach to speech recognition using nonlinear signal decomposition into Volterra-Wiener functional series / A. M. Krot, P. P. Tkachova // Proc. of the 10th Mediterranean Electrotechnical Conference (Melecon 2000), May 29-31 / Cyprus – 2000. – Vol. 2. – P. 522-525.
55. Krot, A. M. Chaotic dynamic methods based on decomposition of vector functions in vector-matrix series into state-space / A. M. Krot // Proc. of the 10th Mediterranean Electrotechnical Conference (Melecon 2000), May 29-31 / Cyprus – 2000. – Vol. 2. – P. 643-646.
56. Krot, A. M. Biomedical signal processing based on estimation of minimal dimension embedding of chaotic attractor / A. M. Krot, H. B. Minervina // Proc. of the 10th Mediterranean Electrotechnical Conference (Melecon 2000), May 29-31 / Cyprus – 2000. – Vol. 2. – P. 733-736.
57. Krot, A. M. Nonlinear dynamics method based on locally-topological analysis of phase trajectories / A. M. Krot, H. B. Minervina // Proc. of the 4rd World Conf. on: Circuits, Systems, Communications and Computers (IEEE/WSES) CSCC'2000, Vouliagmeni, July 10-15 / Greece – Athens: 2000. – P. 4771-4774.
58. Krot, A. M. The model of slow-gravitating spheroidal body based on statistical approach / A. M. Krot // Proc. of the 2nd World Conf. on: Mathematics&Computers in Physics(MCP'2000), Vouliagmeni, July 10-15 / Greece – Athens: 2000. – P. 5181-5188.
59. Krot, A. M. Nonlinear signal decomposition into functional series for speech recognition: a new approach / A. M. Krot, P. P. Tkachova, B. A. Goncharov // Proc. of X European Signal Processing Conf. (EUSIPCO-2000), 5-8 September / Finland – Tampere: 2000. – Vol. 3. – P. 1285-1288.
60. Krot, A. M. The decomposition of vector functions in vector-matrix series into state-space of nonlinear dynamic system / A. M. Krot // Proc. of X European Signal Processing Conf. (EUSIPCO-2000), 5-8 September / Finland – Tampere: 2000. – Vol. 3. – P. 2453-2456.
61. Krot, A. M. Using linear and nonlinear decompositions in state-space for calculating minimal dimension embedding of chaotic attractor / A. M. Krot, H. B. Minervina // Proc. of X European Signal Processing Conf. (EUSIPCO-2000), 5-8 September / Finland – Tampere: 2000. – Vol. 3. – P. 1613-1616.
62. Krot, A. M. Matrix decompositions of vector functions and shift operators on the trajectories of a nonlinear dynamical system / A. M. Krot // Nonlinear Phenomena in Complex Systems. – 2001. – Vol. 4, No. 2. – P. 106-115.
63. Krot, A. M. Gravidynamical equations for a weakly graviting spheroidal body / A. M. Krot // Proc. of SPIE 15thAnnual Intern. Symposium on Aerospace / Defense Sensing, Simulation, and Controls (AeroSense), 16-20 April / USA –Orlando, Florida: 2001. – Vol. 4394. – P. 1271-1282.
64. Krot, A. M. On algorithm for phoneme speech recognition using nonlinear signal decomposition / A. M. Krot, P. P. Tkachova, H. B. Minervina // Proc. of the 8th IEEE Intern. Conference on Electronics, Circuits and Systems (ICECS 2001), 2-5 September / Malta: 2001. – P. 1251-1254.
65. Krot, A. M. Minimal attractor embedding estimation based on matrix decomposition for analysis of dynamical systems / A. M. Krot, H. B. Minervina // Nonlinear Phenomena in Complex Systems. –2002. – Vol. 5, No. 2. – P.161-172.
66. Krot, A. M. New approach to speech signal recognition using nonlinear signal decomposition by measuring Wiener kernels / A. M. Krot, P. P. Tkachova, B. A. Goncharov // Smart Engineering System Design. – 2002. – Vol. 4 – P. 265-276.
67. Krot, A. M. Analysis of nonlinear signals based on estimating minimal attractor embedding dimension / A. M. Krot, H. B. Minervina // Proc. of 14th Intern. Conference on Digital Signal Processing (DSP’2002), July 1-3 / Greece – Santorini: 2002. – Vol. 2. – P. 1001-1004.
68. Krot, A. M. Application of expansion into matrix series to analysis of attractors of complex nonlinear dynamical systems / A. M Krot // Proc. of 14th Intern. Conference on Digital Signal Processing (DSP’2002), July 1-3 / Greece – Santorini: 2002. – Vol. 2. – P. 959-962.
69. Krot, A. M. Development of gravidynamical equations for a weakly gravitating body in the vicinity of absolute zero temperature / A. M. Krot // Proc. of 53rd Intern. Astronautical Congress (IAC) - The 2nd World Space Congress (WSC-2002), October 10-19 / USA – Houston, Texas: 2002. – P. 1-11.
70. Krot, A. M. Restoration of dynamical systems attractors and estimation of their geometric characteristics into state-space / A. M. Krot, H. B. Minervina // In: Lecture Notes in Computer Sciences, (Computational Science and Its Applications–ICCSA 2003, May, 2003), Springer / Canada – Montreal: 2003. – Vol. 2667, part 1. – P. 407-416.
71. Krot, A. M. Investigation of geometric shapes of hydrodynamic structures for identification of dynamical states of convective liquid / A. M. Krot, P. P. Tkachova // In: Lecture Notes in Computer Sciences, (Computational Science and Its Applications – ICCSA 2003, May, 2003), Springer / Canada – Montreal: 2003. – Vol. 2667, part 1. – P. 398-406.
72. Krot, A. M. The equations of movement of rotating and gravitating spheroidal body / A. M. Krot // Proc. of 54 Intern. Astronautical Congress (IAC), September 29-October 3 / Germany – Bremen: Preprint IAC-03-J.1.08, 2003. – P. 1-11.
73. Krot, A. M. Estimating the medical state on the basis of characteristics attractor in the reconstructed state-space fr om electrocardiosignals / A. M. Krot, H. B. Minervina // Proc. of 54 Intern. Astronautical Congress (IAC), September 29-October 3 / Germany – Bremen: Preprint IAC-03-J.1.08, 2003. – P. 1-7.
74. Krot, A. M. The development of model for boundary layers past a concave wall with usage of nonlinear dynamics methods / A. M. Krot, V. A. Baldin. H. B. Minervina // Advances in Space Research. – 2006. – Vol. 37, No. 3. – P. 501-506. (Elsevier Publ. Co., journal impact factor – 1,409).
75. Krot, A. M. The attractor model for finite length Görtler whirlwinds / A. M. Krot, V. A. Baldin, H. B. Minervina // Electromagnetic Waves and Electronics Systems. – 2006. – Vol. 11, ¹ 2-3 – P. 33-40.
76. Krot, A. M. A Models of forming planets and distribution of planetary distances and orbits in the solar system based on the statistical theory of spheroidal bodies / A. M. Krot // Chapter in the book “Solar system: structure, formation and exploration” / USA – New York: Nova science publishers, 2012. – P. 201-264.
77. Krot, A. M. Nonlinear analysis of the Hopfield network dynamical states using matrix decomposition theory / A. M. Krot, R. A. Prakapovich // Chaotic modeling and simulation. – 2013. – Vol. 1. – P. 133-146.
78. Krot, A. M. On the principal difficulties and ways to their solution in the theory of gravitational condensation of infinitely distributed dust substance / A. M. Krot / Proc. of the 2007 IAG General Assembly in the book “Observing our Changing Earth” (Ed. by M.G. Sideris), Springer / Germany – Berlin, Heidelberg: 2009. – Vol.133. – P. 283-292.
79. Krot, A. M. The development of matrix decomposition theory for nonlinear analysis of chaotic attractors of complex systems and signals / A. M. Krot // Proc. of IEEE 16th International Conference on Digital Signal Processing (DSP 2009), July 5-7 / Greece – Thira, Santorini: 2009.
80. Krot, A. M. A statistical approach to investigate the formation of the solar system / A. M. Krot // Chaos, Solitons and Fractals. – 2009. – Vol. 41, ¹ 3. – P. 1481-1500. (Elsevier Publ. Co., journal impact factor – 3,12).
81. Krot, A. M. Self-organization processes in a slow-flowing gravitational compressible cosmological body / A. M. Krot // Selected papers of the CHAOS-2008 International Conference in the book "Topics on Chaotic Systems", World Scientific / Ed. by C.H. Skiadas, I. Dimotikalis, C. Skiadas – Singapore, New Jersey, London, Hong Kong: 2009. – P. 190-198.
82. Krot, A. M. A quantum mechanical approach to description of initial gravitational interactions based on the statistical theory of spheroidal bodies / A. M. Krot // Nonlinear Sci. Lett. A. – 2010. – Vol. 1, No. 4 – P. 329-369.
83. Krot, A. M. Bifurcation analysis of attractors of complex systems based on matrix decomposition theory / A. M. Krot // Proc. of IEEE Intern. Conf. on Industrial Engineering and Management (IEEE IEM 2011), August 12-14 / China – Zhengzhou: 2011.
84. Krot, A. M. A nonlinear Schrödinger-like equation in the statistical theory of spheroidal bodies / A. M. Krot // Chaotic Modeling and Simulation (CMSIM) – 2012. – Vol. 2, No.1. – P. 67-80.
85. Krot, A. M. A nonlinear Schrödinger-like equation in the statistical theory of formation of cosmological bodies / A. M. Krot // Chapter in the book “Chaos and Complexity Research Compendium” / USA – New York: Nova Science Publishers, 2013. – Vol. 3. – P. 93-112.
86. Krot, A. M. On the universal stellar law for extrasolar systems / A. M. Krot // Planetary and Space Science – 2014. – Vol. 101C. – P. 12-26. (Elsevier Publ. Co., journal impact factor – 1,942).
