Garnik A. Karapetyan

Garnik A. Karapetyan
Native name Armenian: Գառնիկ Ալբերտի Կարապետյան
Born (1958-02-03) February 3, 1958
Gyumri, Armenia
Nationality Armenia
Education Mathematician, Doctor of Physico-mathematical sciences, Professor
Alma mater Yerevan State University
Awards Anania Shirakatsi medal
Scientific career
Fields
Mathematical analysis, Differential equations, Mathematical physics
Institutions Department of Mathematics and Mathematical Modeling, Institute of Mathematics and High Technology, Russian-Armenian University

Garnik A. Karapetyan (Armenian: Գառնիկ Ալբերտի Կարապետյան, born February 3, 1958, Gyumri, Armenia) is an Armenian scientist and mathematician. His main research is in the fields of mathematical analysis, differential equations and mathematical physics. He is currently a professor of mathematics at Russian-Armenian University and chairs the Department of Mathematics and Mathematical Modeling.

Biography

Born on February 3, 1958, Gyumri.

1975–1980 – BSc, Faculty of Mechanics and Mathematics, Yerevan State University (YSU). Graduation with distinction.

October, 1980 – April, 1983 – PhD, Department of Differential Equations and Functional Analysis, Faculty of Mechanics and Mathematics, YSU.

1983 – Early defense of PhD thesis. Assistant at the Department of Numerical Analysis, Faculty of Applied Mathematics, YSU.

1987 – Obtained the academic rank of docent (associate professor) at the Department of Mathematics and Mathematical Modeling, YSU.

1990–1994 – Deputy dean of the Faculty of Informatics and Applied Mathematics, YSU.

1992 – Acting dean of the Faculty of Informatics and Applied Mathematics, YSU.

1994–2000 – Scientific Secretary of the Faculty of Informatics and Applied Mathematics, YSU.

1997–1999 – Chairman of the Mathematics Olympiad Committee of Armenia.

2002–Present – Head of the Department of Mathematics and Mathematical Modeling, Russian-Armenian (Slavonic) State University (RAU).

January, 2007 – Doctoral thesis defense at the Specialized Council in Mathematics, YSU.

2008 – Obtained the academic rank of professor at the Department of Mathematics and Mathematical Modeling, RAU.

2008 – Conferred the title of Distinguished Professor of RAU.

2008 – Obtained the recognition (nostrification) of diploma certifying the degree conferment of Doctor of Physico-mathematical Sciences in the Russian Federation and the academic rank of Professor of the Russian Federation.

2008–Present – Member of the Scientific Council of RAU and Dissertation Council in Mathematics of the Republic of Armenia.

2015–Present – Deputy director of the Institute of Mathematics and High Technology, RAU.

2015–Present – Director of the Applied Mathematics and Informatics program, RAU.

2017 – Awarded with the Medal of Anania Shirakatsi.[1]

Scientific activity

Main scientific papers are dedicated to differential equations, elliptic and hypoelliptic equations, the study of the properties of functions in different multianisotropic spaces, integral representations and embedding theorems for functions in multianisotropic spaces.

Books

  • Ghazaryan H.G, Hovhannisyan A.H, Harutyunyan T.N, Karapetyan G.A., Ordinary Differential Equations (textbook). Yerevan։ "Zangak-97", 2002. 320 pages.
  • Ghazaryan H.G, Hovhannisyan A.H, Mamikonyan F.H., Karapetyan G.A., Ordinary Differential Equations (problem book). Yerevan։ "Zangak-97", 1988. 184 pages.
  • Karapetyan G.A., Yeghiazaryan V.S., 300 RAU Entrance Exam Tests in Mathematics. Yerevan։ RAU Publishing House, 2006. 304 pages.
  • Karapetyan G.A., Aghekyan G.V., Harutyunyan K.V., Hayrapetyan S.R., Algebra (mathematics manual for university applicants). Yerevan։ RAU Publishing House, 2007. 388 pages.
  • Karapetyan G.A., Aghekyan G.V., Aramyan R.H, Dashtoyan L.L., Hayrapetyan S.R., RAU Entrance Exam Tests in Mathematics. Yerevan։ RAU Publishing House, 2008. 120 pages.
  • Karapetyan G.A., Melkonyan A.A., Mikilyan M.A., Differential Equations with Examples and Problems (problem book). Yerevan։ RAU Publishing House, 2009. 235 pages.
  • Karapetyan G.A., Margaryan V.N., Hayrapetyan S.R., Practice in Mathematical Analysis (problem book). Yerevan։ RAU Publishing House, 2010. 310 pages.
  • Karapetyan G.A., Hayrapetyan S.R., Mathematical Analysis with Examples and Problems (problem book). Yerevan։ RAU Publishing House, 2014. 417 pages.

Publications in scientific journals

  • Ghazaryan H.G., Karapetyan G.A., Convergence of Galerkin approximations to the solution of the Dirichlet problem // DAN SSSR, vol. 264, №2, 1982, pp. 291–294.
  • Karapetyan G.A., Existence and solution behavior of one class of hypoelliptic equations // DAN Аrm. SSR, vol. 74, №5, 1982, pp. 202–07.
  • Karapetyan G.A., Solution of -elliptic equations in the half-space // DAN Аrm. SSR, vol. 75, №15, 1982, pp. 200–204.
  • Karapetyan G.A., Theorems of Liouville and Phragmén–Lindelöf type for general regular equations // Izv. AN. Arm. SSR, ser. Math. 17, №6, 1982, pp. 473–496.
  • Hakobyan G.O., Karapetyan G.A., Estimates in Hölder spaces for solving quasi-elliptic equations // Mol. Nauch. Rab., YSU, 2 (38), 1982, pp. 47–59.
  • Hakobyan G.O., Karapetyan G.A., Estimates of Schauder type for solving semi-elliptic equations with constant coefficients // Inter. Collection, ser. Math., №2, 1984, pp. 5–13.
  • Karapetyan G.A., Existence and uniqueness of the solution of the Dirichlet problem for hypoelliptic equations in unbounded domains // Proceedings of YSU, 151, №2, 1982, pp. 3–12.
  • Karapetyan G.A., On the behavior of one class of hypoelliptic equations in unbounded domains // Mol. Nauch. Rab., YSU, 2 (36), 1982, pp. 5–13.
  • Karapetyan G.A., Solution of semi-elliptic equations in the half-space // Tr. MIAN SSSR, vol. 170, 1984, pp. 119–138.
  • Ghazaryan. H.G., Karapetyan G.A., On the convergence of Galerkin approximations to the solution of the Dirichlet problem // Mathematical Collection, 124 (166), 1984, №3 (7), pp. 291–306.
  • Karapetyan G.A., The Galerkin method for one general class of hypoelliptic equations // Inter. Collection, ser. Math., №4, 1986, pp. 93–107.
  • Karapetyan G.A., Arakelyan M.Z., Theorems of Liouville and Phragmén–Lindelöf type for semi-elliptic equations with general initial conditions // Inter. Collection, ser. Math., №4, 1986, pp. 81–93.
  • Karapetyan G.A., On one class of degenerate regular equations in the half-space // Izv. AN Аrm. SSR, ser. Math., 21, 1986, №5, pp. 472–487.
  • Karapetyan G.A., Quasilinear boundary value problems for regular equations in unbounded domains // Izv.AN. SSR, ser. Math., 23, 1988, №1, pp. 22–38.
  • Karapetyan G.A., Smooth dependence on the parameter of the solution of regular equations // Proceedings of YSU, 8, 1988, pp. 21–29.
  • Karapetyan G.A., On the stabilization at infinity to a polynomial of solutions for one class of regular equations // Tr. MIAN SSSR, 187, 1989, pp. 116–129.
  • Karapetyan G.A., On the stabilization at infinity to a polynomial of solutions for one class of hypoelliptic equations // Fourth conference on differential equations and applications, Rousse 89, Bulgaria, pp. 144.
  • Karapetyan G.A., Regular equations depending on a parameter // Izv. AN. SSR, vol. 25, 1990, №2, pp. 192–202.
  • Karapetyan G.A., Inner estimates for semi-elliptic equations with small parameter // Dif. Eq. andFunc. Analysis, 1993, Yerevan, pp. 100–105.
  • Karapetyan G.A., Petrosyan A.G., Solution of degenerate semi-elliptic equations in the half-space // Proceedings of YSU, №1, 1998, pp. 13–22.
  • Karapetyan G.A., Sardaryan V.T., Krmzyan A.P., Eigenvalue problem for self-adjointhypoelliptic operators // Proceedings of the NAS of Armenia, ser. Math., vol. 34, №2, 1999, pp. 37–58.
  • Karapetyan G.A., Dallakyan G.V., Approximation of the solutions of semi-elliptic equations in R^n // Proceedings of the NAS of Armenia, ser. Math., vol. 34, № 4, 1999, pp. 31–43.
  • Karapetyan G.A., Multiplicative inequalities of Gagliardo–Nirenberg type for WpN spaces // ”Issledovano v Rossii”. /zhurnal.ape.relarn.ru/articles/2004, pp. 634–644.
  • Karapetyan G.A., The smooth dependence on parameter of solutions of regular equations // Transactions of A. Razmadze Mathematical Institute, 2005, v.137, pp. 6–15.
  • Karapetyan G.A., Galiardo — Nirenberg general inequalities for multianisotrop spaces // Transactions of A. Razmadze Mathematical Institute, 2006, v.142. pp. 8–18.
  • Karapetyan G.A., Darbinyan A.A., Index of the semi-elliptic operator with variable coefficients of special type // Collection of Scientific Articles. Annual Conference (28 November – 2 December 2006). Physical, mathematical and natural sciences. Yerevan. RAU, 20–24, 2007.
  • Karapetyan G.A., Darbinyan A.A., On the index of the semi-elliptic operator in R^n // Proceedings of the NAS of Armenia. Math.,vol.42, №5, 33–50,2007. (Englishtranslation; J. of Contemporary Math. Analysis).
  • Karapetyan G.A., Darbinyan A.A., Index of the semi-elliptic operator with constant coefficients in a domain // Collection of Scientific Articles. Annual Conference (3–7 December 2007). Physical, mathematical and natural sciences. Yerevan. RAU, 45–53, 2008.
  • Karapetyan G.A., Darbinyan A.A., Noethericity of the regular operator with constant coefficients in a domain // Proceedings of A. Razmadze Mathematical Institute, Tbilisi, vol.146, 57 – 66, 2008.
  • Karapetyan G.A., Darbinyan A.A., Noethericity of the semi-ellliptic operator with constant coefficients in a domain // Proceedings of YSU, №.3,16 – 24.2008.
  • Karapetyan G.A., Darbinyan A.A., Noethericity of the regular operator with constant coefficients in R^n // Scientific conference dedicated to the 80thanniversary of the academician Sergey Mergelyan. (20–21 May 2008). pp. 27–28. Theses.
  • Tananyan H.G., Karapetyan G.A., Degenerate semi-elliptic equations with constant coefficients in the half-space // Collection of Scientific Articles. Annual Conference (5–10 December 2008). Physical, mathematical and natural sciences. Yerevan. RAU, 27–30, 2008.
  • Tananyan H.G., Karapetyan G.A., Degeneration of Semielliptic Equations with Constant Coefficients in Rectangular Parallelepipeds // Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) Vol. 45, Number 2 (2010), 82–93.
  • Karapetyan G.A., Darbinyan A.A., Index of the regular operator with constant coefficients in a domain // 3rd Russian-Armenian Conference on Mathematical Physics, Complex Analysis and Related Topics, 91–94, 2010.
  • Tananyan H.G., Karapetyan G.A., The small parameter method for regular hypoelliptic equations with variable coefficients in the half-space // 3rd Russian-Armenian Conference on Mathematical Physics, Complex Analysis and Related Topics, Yerevan, 2010, pp. 95–99.
  • Tananyan H.G., Karapetyan G.A., The Application of Newton’s diagram method in the method of small parameter for regular hypoelliptic equations in the half-space // Collection of Scientific Articles. Annual Conference (6–10 December 2010). Physical, mathematical and natural sciences. Yerevan. RAU, 106–112, 2011.
  • Tananyan H.G., Karapetyan G.A., The Small Parameter Method for Linear Differential Regular Equations in Unbounded Domains // Proceeding of the ISAAC Conference. Moscow, August 22–27, 2011.
  • Karapetyan G.A., Darbinyan A.A., Index of the semi-elliptic operator with variable coefficients // Collection of Scientific Articles. 6th Annual Conference (5–9 December 2011). Physical, mathematical and natural sciences. Yerevan. RAU, 5–11, 2011
  • Tananyan H.G., Karapetyan G.A., The small parameter method for the approximation of the eigenvalues of hypoelliptic operators in the half-space // Collection of Scientific Articles. 6th Annual Conference (5–9 December 2011). Physical, mathematical and natural sciences. Yerevan. RAU, 43–51, 2011
  • Tananyan H.G., Karapetyan G.A., The small parameter method for regular linear differential equations on unbounded domains // Math. Journal, ISSN, 2077-9878, v. 4, № 1, 2013.
  • Karapetyan G.A., Integral representation through the hypoelliptic operator // 9th Annual Conference, RAU, pp. 5–11, 2–6 December 2014.
  • Karapetyan G.A., On the stabilization at infinity to a polynomial of solutions of regular equations. Theory of operators and its applications // International Conference, Rostov-on-Don, 25.04.15 – 29.04.15.
  • Karapetyan G.A., Integral representation through the differentiation operator and embedding theorems for multianisotropic spaces // International Conference Harmonic Analysis and Approximations, VI, Tsaghkadzor, Armenia, pp. 46–48, 12–18 September 2015.
  • Karapetyan G.A., Saribekyan N.S., Spectral stability of higher order semi-elliptic operators // Proceedings of the NAS of Armenia, Math., vol. 51, №1, pp. 21–37, 2016.
  • Karapetyan G.A., Integral Representations of Functions and Embedding Theorems for Multianisotropic Spaces on the Plane with One Anisotropy Vertex // Journal of Contemporary Mathematical Analysis, 2016, Vol. 51, No. 6, pp. 269—281.
  • Karapetyan G.A., Arakelyan M.K., Estimation of multianisotropic kernels and its application to the embedding theorems // AMU, Annual Session 2016, Dedicated to the 110th Anniversary of Artashes Shahinyan, Yerevan, pp. 68–69, 31.05.16 – 02.06.16.
  • Karapetyan G.A., Petrosyan H.A., Embedding theorems for the n-dimensional multianisotropic spaces with two points of anisotropicity // AMU, Annual Session 2016, Dedicated to the 110th Anniversary of Artashes Shahinyan, Yerevan, pp. 70–71, 31.05.16 – 02.06.16.
  • Karapetyan G.A., Integral representation of functions and embedding theorems for multianisotropic spaces for the three-dimensional case // Eurasian Mathematical Journal, ISSN, v.7, n.4, (2016), 19–39.
  • Karapetyan G.A., Arakelyan M.K., Estimation of multianisotropic kernels and their application to the embedding theorems // Transactions of A. Razmadze Mathematical Institute 171, (2017), 48–56.
  • Karapetyan G.A., Integral representation and embedding theorems for n-dimensional multianisotropic spaces with one vertex of anisotropicity // Siberian Mathematical Journal, v.58, n.3, 445–460, 2017.
  • Karapetyan G.A., Petrosyan H.A., Embedding theorems for multianisotropic spaces with two vertices of anisotropicity // Proceedings of the YSU, Physics & Mathematics, 2017, Volume 51, Issue 1, Pages 29–37.
  • Karapetyan G.A., Petrosyan H.A., About the solvability of regular hypoelliptic equations in R^n // AMU, Annual Session 2017, Yerevan, pp. 40–42, 29.05.17 – 31.05.17.
  • Karapetyan G.A., An Integral Representation and Embedding Theorems in the Plane for Multianisotropic Spaces // Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2017, Vol. 52, No. 6, pp. 261—269.

Notes

  1. ↑ G.A. Karapetyan awarded with the Medal of Anania Shirakatsi

References

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