Engibaryan Norayr Bagratovich

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Total publications: 30
Scientific articles: 30
Presentations: 6

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Doctor of physico-mathematical sciences (1979)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 12.11.1941
Keywords: integral and integral-differencial equations; functional analysis (factorization of operators etc.); mathematical physics (radiative transfer, kinetic theory of gases etc.); stochastic processes; multidimensional complex analysis; astrophysics.


The theory of nonlinear factorization equations (NFE) of integral and other linear operators was founded, including various applications. Generalized Volterian factorization problem for non-invertible integral operators was formulated and solved. A complete theory of Wiener–Hopf scalar and vector integral equations for conservative and supercritical (singular) cases was developed, using NFE. A theory of generalized Ambartsumian equation and Riccati-type operator equation was developed. A principal new approach to the solution of convolution-type integral equations on a finite interval was developed, including applications in radiative transfer (RT) theory. A structural theory for renewal equations (on the half-line and on the whole line) and Markov renewal equations was developed, including new-type limit and asymptotic theorems. For the first time the theory and solution methods for RT problems in spectral lines in general laws of non-coherent scattering, as well as - the mathematical theory of anisotrope scattering with summable indicatrix (including solution of Miln problem) was developed. The method of self-consisting optical depths (coming from Edington and V. Ambartsumian ideas) for exact solution of non-linear RT problems, was developed. Some factorization and other, methods to efficient numerical-analytical solution of RT problems and problems of kinetic theory of gases, was developed. The domains of normal convergence of multidimensional Loran series was constructed.


Graduated from Faculty of Mathematics and Mechanics of Yerevan State University in 1963 (department of math. analysis and theory of functions). Was Lenin scholarship holder. Ph. D. thesis was defended in 1968. D. Sci. thesis was defended in 1979. A list of my works contains more than 130nbsp;titles. Since 1971 I have led the research seminar on integral equations and mathematical physics; 35 years of teaching experience at Yerevan State University and other high schools; was head of some math. chairs; supervision of 16 Ph. D. and 5 D. Sci. thesis.

Member of a number local and international Scientific Boards.

Main publications:
  1. Engibaryan N. B., “Uravneniya v svertkakh, soderzhaschie singulyarnye veroyatnostnye raspredeleniya”, Izv. RAN, ser. matem., 60:2 (1996), 21–48  mathnet  mathscinet  zmath
  2. Engibaryan N. B., “Teoremy vosstanovleniya dlya sistemy integralnykh uravnenii”, Matem. cb., 189:12 (1998), 59–72  mathnet  mathscinet  zmath
  3. Engibaryan N. B., “Perenos izlucheniya v sfericheski simmetrichnoi srede”, Zhurn. vychisl. matem. i matem. fiz., 39:10 (1999), 1730–1739  mathscinet  zmath
  4. Yengibarian N. B., “Renewal equation on the whole line”, J. Stochastic Proc. Appl., 85 (2000), 237–247  crossref  mathscinet  zmath
  5. Engibaryan N. B., “Postanovka i reshenie nekotorykh zadach faktorizatsii integralnykh operatorov”, Matem. sb., 191:12 (2000), 61–76  mathnet  mathscinet  zmath
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. A discrete model for nonlinear problems of Radiation Transfer: principle of invariance and factorization
N. B. Engibaryan
Matem. Mod., 27:5 (2015),  127–136
2. Approximate solution of Wiener–Hopf integral equations and its discrete counterparts
A. G. Barseghyan, N. B. Engibaryan
Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015),  836–845
3. Transport equations
N. B. Engibaryan, A. G. Barseghyan
TMF, 180:2 (2014),  206–216
4. Solvability of an integrodifferential equation arising in the nonlocal interaction of waves
N. B. Engibaryan, A. Kh. Khachatryan
Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014),  834–844
5. Differential equations where the derivative is taken with respect to a measure
N. B. Engibaryan
Mat. Sb., 202:2 (2011),  93–106
6. Random walks and mixtures of Gamma-distributions
N. B. Engibaryan, A. Barseghyan
Teor. Veroyatnost. i Primenen., 55:3 (2010),  571–577
7. On the factorization of integral operators on spaces of summable functions
N. B. Engibaryan
Izv. RAN. Ser. Mat., 73:5 (2009),  67–82
8. Integro-differential equation of non-local wave interaction
N. B. Engibaryan, A. Kh. Khachatryan
Mat. Sb., 198:6 (2007),  89–106
9. On the fixed points of monotonic operators in the critical case
N. B. Engibaryan
Izv. RAN. Ser. Mat., 70:5 (2006),  79–96
10. On nonlinear theory dynamics of dilute gas
N. B. Engibaryan, A. Kh. Khachatryan
Matem. Mod., 16:1 (2004),  67–74
11. A renewal equation in a multidimensional space
N. B. Engibaryan
Teor. Veroyatnost. i Primenen., 49:4 (2004),  779–785
12. Asymptotic and structural theorems for the Markov renewal equation
N. B. Engibaryan
Teor. Veroyatnost. i Primenen., 48:1 (2003),  62–77
13. Conservative systems of integral convolution equations on the half-line and the entire line
N. B. Engibaryan
Mat. Sb., 193:6 (2002),  61–82
14. Setting and solving several factorization problems for integral operators
N. B. Engibaryan
Mat. Sb., 191:12 (2000),  61–76
15. Exact linearization of the sliding problem for a dilute gas in the Bhatnagar–Gross–Krook model
N. B. Engibaryan, A. Kh. Khachatryan
TMF, 125:2 (2000),  339–342
16. Renewal equations on the semi-axis
N. B. Engibaryan
Izv. RAN. Ser. Mat., 63:1 (1999),  61–76
17. Radiative transfer in a spherically symmetric medium
N. B. Engibaryan
Zh. Vychisl. Mat. Mat. Fiz., 39:10 (1999),  1730–1739
18. Renewal theorems for a system of integral equations
N. B. Engibaryan
Mat. Sb., 189:12 (1998),  59–72
19. Some convolution-type integral equations in kinetic theory
N. B. Engibaryan, A. Kh. Khachatryan
Zh. Vychisl. Mat. Mat. Fiz., 38:3 (1998),  466–482
20. Convolution equations containing singular probability distributions
N. B. Engibaryan
Izv. RAN. Ser. Mat., 60:2 (1996),  21–48
21. Convolution equation with a completely monotonic kernel on the half-line
N. B. Engibaryan, B. N. Enginbarian
Mat. Sb., 187:10 (1996),  53–72
22. Some factorization problems for integral operators of convolution type
N. B. Engibaryan, L. G. Arabadzhyan
Differ. Uravn., 26:8 (1990),  1442–1452
23. A class of integral renewal equations
N. B. Engibaryan, A. A. Pogosyan
Mat. Zametki, 47:6 (1990),  23–30
24. The solution of one class of convolution-type integral equations
R. S. Vardanyan, N. B. Engibaryan
Zh. Vychisl. Mat. Mat. Fiz., 29:9 (1989),  1291–1300
25. Convolution equations and nonlinear functional equations
L. G. Arabadzhyan, N. B. Engibaryan
Itogi Nauki i Tekhn. Ser. Mat. Anal., 22 (1984),  175–244
26. Systems of Wiener–Hopf integral equations, and nonlinear factorization equations
N. B. Engibaryan, L. G. Arabadzhyan
Mat. Sb. (N.S.), 124(166):2(6) (1984),  189–216
27. Linear algebraic systems with Toeplitz matrices
N. B. Engibaryan, M. A. Mnatsakanyan
Zh. Vychisl. Mat. Mat. Fiz., 17:5 (1977),  1102–1116
28. An integral equation with a difference kernel
N. B. Engibaryan, M. A. Mnatsakanyan
Mat. Zametki, 19:6 (1976),  927–932
29. Integral equations on the half-line with difference kernels and nonlinear functional equatons
N. B. Engibaryan, A. A. Arutyunyan
Mat. Sb. (N.S.), 97(139):1(5) (1975),  35–58

Presentations in Math-Net.Ru
1. Методы решения уравнений свертки
N. B. Engibaryan
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
February 27, 2014 11:00
2. Об уравнениях переноса
N. B. Engibaryan
Conference "Mathematical Physics. Vladimirov-90" dedicated to the 90th anniversary of academician V. S. Vladimirov
November 13, 2013 13:00   
3. On vector integral convolution equations
N. B. Engibaryan
Complex analysis and mathematical physics
September 17, 2012 16:00
4. Nonuniform semigroups and pseudo-reversible processes in transport theory
N. B. Yengibaryan
International Conference "Irreversibility Problem in Classical and Quantum Dynamical Systems"
December 8, 2011 11:30   
5. On Markov chains with a countable set of states
N. B. Engibaryan
Second Russian-Armenian Workshop on Mathematical Physics, Complex Analysis and Related Topics
October 9, 2008 10:45   
6. Вопросы общей теории факторизации линейных операторов в банаховых пространствах
N. B. Engibaryan
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
October 18, 2007 11:00

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