Publications
Search form
Authorization
Login:
Password:
Register
Forgot your password?
Partners

Publications

Russian

Monographs

1. Krot, .. A Statistical Theory of Gravitating Body Formation in Extrasolar Systems/ A.M. Krot. Cambridge, Newcastle upon Tyne, etc.: Cambridge Scholars Publishing, 2021. 817p.  
2. Krot, A. M. A statistical theory of formation of gravitating cosmogonical bodies. Minsk: Bel. Navuka, 2012. 448 pp. [in Russian]. 
3. 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];  

 
4. Krot, A. M. Discrete models of dynamical systems based on polynomial algebra. Minsk: Navuka i tekhnika, 1990. 312 pp. [in Russian];  

   
5. Linkevich, A. D. Mathematical methods and models for investigation of neurodynamical mechanisms of cognitive processes / A. D. Linkevich; scientific editor prof. A. M. Krot. Minsk, Novopolotsk, 2001. 203 pp.  

       

Selected articles


  1. Krot, .. On the wave solutions of the generalized nonlinear Schrodinger-like equation of formation of a cosmogonical body / .. Krot // In the book Understanding the Schrodinger Equation: Some [Non]Linear Perspectives, Ch. 4. New York: Nova Science Publishers, 2020, pp. 93-133.

  2. Krot, .. Investigation of chaotic dynamics of Chuas circuit implemented by means of the matrix decomposition method / .. Krot, U.A. Sychou // Chaotic Modeling and Simulation (CMSIM). 2020. No.1. P. 55-73.

  3. Krot A. M., Pavlov S. I. Modeling and nonlinear analysis of chaotic wave processes in electrochemically active neuronal media based on matrix decomposition. Informatics, 2020, vol. 17, no. 3, pp. 7−24 (in Russian). https://doi.org/10.37661/1816-0301-2020-17-3-7-24

  4. Krot A.M.  An evolutionary model of chaotic wave processes in complex dynamical systems based on the matrix decomposition theory. Dopovd Naconal'no akadem nauk Ukrani=Reports of the National Academy of Sciences of Ukraine, 2019, no. 9, pp. 1219 (in Russian).

  5. Krot, A.M. Analysis of dynamical states of cosmogonical body formation based on the generalized nonlinear Schrodinger-like equation/ A.M. Krot // Chaotic Modeling and Simulation (CMSIM). 2019. Vol. 8, No.2 (April issue). P. 95-107.

  6. Krot A. M., Sychou U. A. A spectral analysis of chaotic oscillations in simulation model of Chuas circuit developed with use of matrix decomposition. Informatics, 2019, vol. 16, no. 1, pp. 723 (in Russian).

  7. Krot  A. M., Petrovich O. N., Rusetski I. S. Calculation algorithm of the trajectories of electrons in electrostatic and magnetostatic fields of electron-optical systems. Vests Natsyianal'nai akadem navuk Belarus. Seryia fzka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2019, vol. 55, no. 4, pp. 435444 (in Russian).

  8. Krot, A. M., Sychou U. A. The analysis of chaoticr egimes in Chuas circuit with smooth nonlinearity based on the matrix decomposition method. Vestsi Natsyyanalnai akademii navuk Belarusi. Seryya fizika-technichnych navuk =Proceedings of the National Academy of Sciences of Belarus. Physical-technical series, 2018, vol. 63, no. 4, pp. 501512 (in Russian)

  9. Krot, A.M. An explanation of stability of extrasolar systems based on the universal stellar law/ A.M. Krot // Chaotic Modeling and Simulation (CMSIM). 2018. Vol. 7, 4. P. 513-529.

  10. Krot, A.M. Derivation and investigation of the generalized nonlinear Schrödinger equation of cosmogonical body forming/ A.M. Krot // In the book Mathematical and Numerical Aspects of Dynamical System Analysis/ Ed. by J. Awrejcewicz et al. Łódź: ARSA Druk i Reklama, 2017, P. 277-288.

  11. Krot, A.M. Development of the generalized nonlinear Schrödinger equation of rotating cosmogonical body formation/ A.M. Krot // In the book "Complex Systems: Theory and Applications, Chapter 3. New York: Nova Science Publishers, 2017, pp.49-94.  

  12. 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).

  13. 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.

  14. Krot, A.M. Non-linear 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.

  15. Krot, A. M. A nonlinear Schrdinger-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.

  16. 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. New York: Nova science publishers 2012. P 201-264. 

  17. 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. 

  18. Krot, A.M. Bifurcation analysis of attractors of complex systems based on matrix decomposition theory. / .. Krot // Proc. of IEEE Intern. Conf. on Industrial Engineering and Management (IEEE IEM 2011), Zhengzhou, China, August 12-14, 2011.

  19. 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.

  20. Krot, A.M. On the principal difficulties and ways to their solution in the theory of gravitational condensation of infinitely distributed dust substance / .. Krot // Proc. of the 2007 IAG General Assembly in the book "Observing our Changing Earth", Vol.133 (Ed. by M.G. Sideris), Springer: Berlin, Heidelberg, 2009, pp. 283-292.

  21. Krot, A. M. A statistical approach to investigate the formation of the solar system / A. M. Krot // Chaos, Solitons and Fractals  2009. Vol. 41, No. 3. P. 1481-1500. (Elsevier Publ. Co., journal impact factor 3,12).

  22. 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.

  23. Dailyudenko, V. F. The spatio-temporal structure of nonlinear response of an active media in a self-organization system / V. F. Dailyudenko // Nonlinear Phenomena in Complex Systems  2009. Vol.12 No. 3. P. 251 266.

  24. Dailyudenko, V. F. Topological considerations of an attractor based on temporal locality along its phase trajectories / V. F. Dailyudenko  // Chaos, Solitons and Fractals  2008. Vol. 37 Issue 3 P. 876 - 893.

  25. Krot, A. M. The theory of matrix decomposition for development of nonlinear analysis of chaotic attractors of complex systems / A.M.Krot // Chaotic Modeling and Simulation International Conference (CHAOS 2008), Chania, Crete, Greece, June 3-6. Greece, 2008. P. 101.

  26. 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).

  27. Dailyudenko, V. F. The integrated and local estimations of instability for a class of autonomous delay systems / V. F. Dailyudenko // Chaos, Solitons and Fractals 2006. Vol. 30, No. 3. P. 759-768.

  28. Dailyudenko, V. F. Characteristic exponents for vector maps fr om the product of functional matrices and successive  orthogonalization of matrix sequences / V. F. Dailyudenko // Nonlinear Phenomena in Complex Systems 2004.  Vol.7, No. 1.  43 - 51 pp.

  29. Dailyudenko, V. F. Lyapunov exponents for complex systems with delayed feedback / V.F. Dailyudenko // Chaos, Solitons and Fractals 2003.   Vol. 17, No. 2-3.  473 484 pp.

  30. Dailyudenko, V. F. Reduced fractal analysis of the multidimensional attractor reconstructed fr om chaotic time series / V. F. Dailyudenko // Computational Science and Its Applications ICCSA 2003, Montreal, Canada, May, 2003 / Lecture Notes in Computer Sciences.  Part 1, vol. 2667, Springer  2003.  921-926 pp.

  31. 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.

  32. 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 (DSP2002), July 1-3 / Greece Santorini: 2002. Vol. 2. P. 959-962.

  33. 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 (DSP2002), July 1-3 / Greece Santorini: 2002. Vol. 2. P. 1001-1004.

  34. 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.

  35. 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

  36. 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. 

  37. 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.

  38. 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.

  39. 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.

  40. 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.

  41. 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.

  42. 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.

  43. Intelligent systems / NAS Belarus, Institute of technical cybernetics. A. M. Krot (scientific editor). Minsk,1998. 203 pp.

  44. 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. 

  45. 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.

  46. 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.  

  47. 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.

  48. 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. (Pergamon Press, journal impact factor  0,585).

  49. 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. (Plenum Publ. Co.,  journal impact factor  0,265).

  50. 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.

  51. Krot, A. M. A fast algorithm for calculating the inverse convolution for signal and image reconstruction / A. M. Krot, A. T. Kasko, H. B. Minervina // Comput. Maths Math. Phys. 1996. Vol. 36, No. 2. P. 269-277. (Pergamon Press,  journal impact factor  0,585).

  52. 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.).

  53. 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).

  54. 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. (Journal impact factor  0, 307).

  55. 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. (Scripta Technica, Inc., journal impact factor 0,359).

  56. 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. (Journal impact factor 0, 473).

  57. 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. (Pergamon Press,  journal impact factor  0, 585).

  58. 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. (Scripta Technica, Inc., journal impact factor 0,359).

  59. 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. (Scripta Technica, Inc., journal impact factor 0,359).

  60. 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. (Allerton Press, Inc., journal impact factor  0,137).

  61. 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. (Pergamon Press, journal impact factor 0,585).

  62. 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. (Scripta Technica, Inc., journal impact factor 0,359).

  63. 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. (Scripta Technica, Inc., journal impact factor 0, 359).

  64. 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. (Scripta Technica, Inc., journal impact factor 0,359).

  65. 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. (Scripta Technica, Inc., journal impact factor 0, 359).

  66. 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. (Scripta Technica, Inc., journal impact factor 0,359).