Engibaryan, Norayr Bagratovich

Statistics Math-Net.Ru
Total publications: 39
Scientific articles: 39
Presentations: 7

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Abstract pages:14998
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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. N. B. Engibaryan, “On the factorization of matrix and operator Wiener–Hopf integral equations”, Izv. RAN. Ser. Mat., 82:2 (2018),  33–42  mathnet  mathscinet  elib; Izv. Math., 82:2 (2018), 273–282  isi  scopus
2. N. B. Engibaryan, “A discrete model for nonlinear problems of Radiation Transfer: principle of invariance and factorization”, Matem. Mod., 27:5 (2015),  127–136  mathnet  elib
3. A. G. Barseghyan, N. B. Engibaryan, “Approximate solution of Wiener–Hopf integral equations and its discrete counterparts”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015),  836–845  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 55:5 (2015), 834–843  isi  scopus
4. N. B. Engibaryan, A. G. Barseghyan, “Transport equations”, TMF, 180:2 (2014),  206–216  mathnet  mathscinet  elib; Theoret. and Math. Phys., 180:2 (2014), 932–941  isi  scopus
5. N. B. Engibaryan, A. Kh. Khachatryan, “Solvability of an integrodifferential equation arising in the nonlocal interaction of waves”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014),  834–844  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 54:5 (2014), 834–844  isi  elib  scopus
6. N. B. Engibaryan, “Differential equations where the derivative is taken with respect to a measure”, Mat. Sb., 202:2 (2011),  93–106  mathnet  mathscinet  zmath  elib; Sb. Math., 202:2 (2011), 243–256  isi  scopus
7. N. B. Engibaryan, A. Barseghyan, “Random walks and mixtures of Gamma-distributions”, Teor. Veroyatnost. i Primenen., 55:3 (2010),  571–577  mathnet  mathscinet; Theory Probab. Appl., 55:3 (2011), 528–535  isi  scopus
8. N. B. Engibaryan, “On the factorization of integral operators on spaces of summable functions”, Izv. RAN. Ser. Mat., 73:5 (2009),  67–82  mathnet  mathscinet  zmath  elib; Izv. Math., 73:5 (2009), 921–937  isi  scopus
9. N. B. Engibaryan, A. Kh. Khachatryan, “Integro-differential equation of non-local wave interaction”, Mat. Sb., 198:6 (2007),  89–106  mathnet  mathscinet  zmath  elib; Sb. Math., 198:6 (2007), 839–855  isi  scopus
10. N. B. Engibaryan, “On the fixed points of monotonic operators in the critical case”, Izv. RAN. Ser. Mat., 70:5 (2006),  79–96  mathnet  mathscinet  zmath  elib; Izv. Math., 70:5 (2006), 931–947  isi  elib  scopus
11. N. B. Engibaryan, A. Kh. Khachatryan, “On nonlinear theory dynamics of dilute gas”, Matem. Mod., 16:1 (2004),  67–74  mathnet  mathscinet  zmath
12. N. B. Engibaryan, “A renewal equation in a multidimensional space”, Teor. Veroyatnost. i Primenen., 49:4 (2004),  779–785  mathnet  mathscinet  zmath; Theory Probab. Appl., 49:4 (2005), 737–744  isi
13. N. B. Engibaryan, “Asymptotic and structural theorems for the Markov renewal equation”, Teor. Veroyatnost. i Primenen., 48:1 (2003),  62–77  mathnet  mathscinet  zmath; Theory Probab. Appl., 48:1 (2004), 80–92  isi
14. N. B. Engibaryan, “Conservative systems of integral convolution equations on the half-line and the entire line”, Mat. Sb., 193:6 (2002),  61–82  mathnet  mathscinet  zmath; Sb. Math., 193:6 (2002), 847–867  isi  scopus
15. N. B. Engibaryan, “Setting and solving several factorization problems for integral operators”, Mat. Sb., 191:12 (2000),  61–76  mathnet  mathscinet  zmath; Sb. Math., 191:12 (2000), 1809–1825  isi  scopus
16. N. B. Engibaryan, A. Kh. Khachatryan, “Exact linearization of the sliding problem for a dilute gas in the Bhatnagar–Gross–Krook model”, TMF, 125:2 (2000),  339–342  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 125:2 (2000), 1589–1592  isi
17. N. B. Engibaryan, “Renewal equations on the semi-axis”, Izv. RAN. Ser. Mat., 63:1 (1999),  61–76  mathnet  mathscinet  zmath; Izv. Math., 63:1 (1999), 57–71  isi  scopus
18. N. B. Engibaryan, “Radiative transfer in a spherically symmetric medium”, Zh. Vychisl. Mat. Mat. Fiz., 39:10 (1999),  1730–1739  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 39:10 (1999), 1660–1669
19. N. B. Engibaryan, “Renewal theorems for a system of integral equations”, Mat. Sb., 189:12 (1998),  59–72  mathnet  mathscinet  zmath; Sb. Math., 189:12 (1998), 1795–1808  isi  scopus
20. N. B. Engibaryan, A. Kh. Khachatryan, “Some convolution-type integral equations in kinetic theory”, Zh. Vychisl. Mat. Mat. Fiz., 38:3 (1998),  466–482  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 38:3 (1998), 452–467
21. N. B. Engibaryan, “Convolution equations containing singular probability distributions”, Izv. RAN. Ser. Mat., 60:2 (1996),  21–48  mathnet  mathscinet  zmath; Izv. Math., 60:2 (1996), 249–280  scopus
22. N. B. Engibaryan, B. N. Enginbarian, “Convolution equation with a completely monotonic kernel on the half-line”, Mat. Sb., 187:10 (1996),  53–72  mathnet  mathscinet  zmath; Sb. Math., 187:10 (1996), 1465–1485  isi  scopus
23. N. B. Engibaryan, L. G. Arabadzhyan, “Some factorization problems for integral operators of convolution type”, Differ. Uravn., 26:8 (1990),  1442–1452  mathnet  mathscinet  zmath; Differ. Equ., 26:8 (1990), 1069–1078
24. N. B. Engibaryan, A. A. Pogosyan, “A class of integral renewal equations”, Mat. Zametki, 47:6 (1990),  23–30  mathnet  mathscinet  zmath; Math. Notes, 47:6 (1990), 540–546  isi
25. R. S. Vardanyan, N. B. Engibaryan, “The solution of one class of convolution-type integral equations”, Zh. Vychisl. Mat. Mat. Fiz., 29:9 (1989),  1291–1300  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 29:5 (1989), 20–27
26. N. B. Engibaryan, È. A. Melkonyan, “On the method of discrete ordinates”, Dokl. Akad. Nauk SSSR, 292:2 (1987),  322–326  mathnet  mathscinet
27. L. G. Arabadzhyan, N. B. Engibaryan, “Factorization of Wiener-Hopf multiple integral operators”, Dokl. Akad. Nauk SSSR, 291:1 (1986),  11–14  mathnet  mathscinet  zmath
28. L. G. Arabadzhyan, N. B. Engibaryan, “Convolution equations and nonlinear functional equations”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 22 (1984),  175–244  mathnet  mathscinet  zmath; J. Soviet Math., 36:6 (1987), 745–791
29. N. B. Engibaryan, L. G. Arabadzhyan, “Systems of Wiener–Hopf integral equations, and nonlinear factorization equations”, Mat. Sb. (N.S.), 124(166):2(6) (1984),  189–216  mathnet  mathscinet  zmath; Math. USSR-Sb., 52:1 (1985), 181–208
30. N. B. Engibaryan, M. G. Muradyan, “Linear differential equations and Riccati equations”, Dokl. Akad. Nauk SSSR, 235:2 (1977),  263–265  mathnet  mathscinet  zmath
31. N. B. Engibaryan, M. A. Mnatsakanyan, “Linear algebraic systems with Toeplitz matrices”, Zh. Vychisl. Mat. Mat. Fiz., 17:5 (1977),  1102–1116  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 17:5 (1977), 3–17
32. N. B. Engibaryan, “Some factorization theorems for integral operators”, Dokl. Akad. Nauk SSSR, 230:5 (1976),  1021–1024  mathnet  mathscinet  zmath
33. N. B. Engibaryan, M. A. Mnatsakanyan, “An integral equation with a difference kernel”, Mat. Zametki, 19:6 (1976),  927–932  mathnet  mathscinet  zmath; Math. Notes, 19:6 (1976), 541–544
34. N. B. Engibaryan, A. A. Arutyunyan, “Integral equations on the half-line with difference kernels and nonlinear functional equatons”, Mat. Sb. (N.S.), 97(139):1(5) (1975),  35–58  mathnet  mathscinet  zmath; Math. USSR-Sb., 26:1 (1975), 31–54
35. N. B. Engibaryan, M. A. Mnatsakanyan, “Linear transfer problems”, Dokl. Akad. Nauk SSSR, 217:3 (1974),  533–535  mathnet  mathscinet
36. N. B. Engibaryan, M. A. Mnatsakanyan, “On solutions of dual integral equations”, Dokl. Akad. Nauk SSSR, 210:5 (1973),  1014–1017  mathnet  mathscinet  zmath
37. N. B. Engibaryan, A. A. Arutyunyan, “On Wiener–Hopf equations”, Dokl. Akad. Nauk SSSR, 209:2 (1973),  275–278  mathnet  mathscinet  zmath
38. N. B. Engibaryan, M. A. Mnatsakanyan, “On the factorization of integral operators”, Dokl. Akad. Nauk SSSR, 206:4 (1972),  792–795  mathnet  mathscinet  zmath
39. N. B. Engibaryan, “On the factorization of symmetric integral operators”, Dokl. Akad. Nauk SSSR, 203:1 (1972),  19–21  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. The inverse problem of diffuse transmission in transport theory
N. B. Engibaryan
Internaional conference «Modern Mathematical Physics. Vladimirov-95»
November 14, 2018 14:30   
2. Методы решения уравнений свертки
N. B. Engibaryan
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
February 27, 2014 11:00
3. 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   
4. On vector integral convolution equations
N. B. Engibaryan
Complex analysis and mathematical physics
September 17, 2012 16:00
5. 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   
6. 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   
7. 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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