Curriculum Vitae
Ruben G. Airapetyan (Hayrapetyan)
Professor of Mathematics
Science & Mathematics Department
Kettering University, Flint, MI 48504-4898
Phone: (810) 762-78778 Fax : (810) 762-9796
Email: rhayrape@kettering.edu
EDUCATION:
Ph.D. in Applied Mathematics, Department of Mathematics, Kansas State University, Manhattan, Kansas, Thesis: Nonlinear problems and applications.
Ph.D. in Mathematics, Institute of Mathematics, Armenian Academy of Sciences, Yerevan, Armenia, Thesis: Mixed problems for hyperbolic equations and systems.
M.S. in Physics, Yerevan State University, Armenia.
RESEARCH INTERESTS:
Numerical methods for solving nonlinear and ill-posed problems; inverse problems of geophysics, quantum scattering, and the theory of ground penetrating radars; modeling and computer implementation of nonlinear dynamical processes related to chemical degradation of polymer additives in lubricants; partial differential equations, integral transforms.
TEACHING EXPERIENCE:
At Kettering University taught undergraduate courses: Calculus, Differential Equations and Laplace Transform, Boundary Value Problems, Intermediate Differential Equations, Matrix Algebra, Advanced Matrix Theory, Real Analysis, Complex Variables, Vector Analysis, Numerical Methods and Matrices, and Mathematical Modeling.
At Kansas State University taught undergraduate courses: College Algebra, Calculus, and Differential Equations.
At Moscow Institute of Electronics, Radio physics and Automatics taught undergraduate courses:
Calculus, Analytic Geometry, Linear Algebra, Differential Equations, Probability and Statistics.
At Yerevan State University taught graduate and undergraduate courses: Numerical Analysis, Programming, Optimization Theory, Partial Differential Equations, Asymptotic Methods; supervised undergraduate and graduate research projects.
Author of a textbook "Asymptotic Methods", Yerevan State University, Yerevan, 1990, 90 pp.
RESEARCH EXPERIENCE:
Conducted research in: applied mathematics, computational mathematics, theory of partial and ordinary differential equations, theory of special functions and integral transforms, theory of ill-posed and inverse problems, numerical analysis, micro-local analysis, integral geometry.
Have developed numerical methods and numerical algorithms, and have written numerical codes solving: nonlinear differential equations, inverse problems of geophysics and quantum scattering.
COMPUTER SKILLS: Programming in Fortran and Matlab.
EMPLOYMENT:
07/2005 – present, Professor, Science & Mathematics Department, Kettering
University, Flint, Michigan 48504.
07/2000 – 07/2005, Associate Professor, Science & Mathematics Department, Kettering
University, Flint, Michigan 48504.
08/1997 – 06/2000, Teaching Assistant, Department of Mathematics, Kansas State University,
Manhattan, Kansas 66506.
05/1998 – 08/1998, Researcher, Schlumberger-Doll Research, Ridgefield, CT.
02/1994 – 08/1997, Senior Researcher, Joint Institute for Nuclear Research in Dubna, Russia.
09/1994 - 08/1997, Professor, Moscow Institute of Electronics, Radio physics and Automatics,
Department of Physics and Mathematics, Dubna, Russia.
02/1988 - 01/1994, Associate Professor, Department of Mathematics, Yerevan State University,
Yerevan, Armenia.
02/1988 - 01/1994, Head of a scientific group, Center of Applied Mathematics, Yerevan State
University, Yerevan, Armenia.
01/1977 - 01/1988, Researcher, Institute of Mathematics, Armenian Academy of Science,
Yerevan, Armenia.
PROFESSIONAL ACTIVITIES:
Visiting:
Brigham Young University, Provo, UT, June-July, 2001;
Schlamberger-Doll Research, Ridgefield, Connecticut, May-August, 1998;
Technical University, Bergakademie Freiberg, Germany, April, 1997;
Potsdam University, Germany, March, 1997;
Oberwolfach Institute of Mathematics, Germany, Program: Research in Pairs, January, 1997;
International Center for Theoretical Physics, Trieste, Italy, July - September, 1995;
Banach International Mathematical Center, Warsaw, Poland, October, 1992;
Budapest University, Hungary, April, 1989.
Participation in the International Conferences:
Fourth ISAAC Congress, Toronto, Canada, August, 2003;
ASME/STLE International Tribology Conference & Exposition, Cancun, Mexico, 2002;
Third ISAAC Congress, Berlin, Germany, August, 2001;
SIAM Annual Meeting, San Diego, CA, July, 2001;
NetLander Scientific Symposium, Nantes, France;
International Conference on operator theory and its applications to scientific and industrial problems, Winnipeg, Canada, October, 1998;
Meeting of American Mathematical Society, Manhattan, KS, April 1998;
International Conference on inverse and ill-posed problems, Moscow, Russia, September, 1996;
International Conference on inverse and algebraic quantum scattering theory, Balatonfoldvar, Hungary, July, 1996;
International Conference on mathematical modeling and computational physics, Dubna, Russia, June, 1996;
Spring School on pseudo-differential calculus and index theory on singular and non-compact manifolds, Potsdam, Germany, February, 1996;
VII International Conference on Symmetry Methods in Physics, Dubna, Russia, June, 1995;
International Conference on differential equations and applied mathematics, Novosibirsk, Russia, September, 1980;
International Conference on differential equations and applied mathematics, Novosibirsk, Russia, August, 1975.
Grants: Kettering University grant 2000, RiP-program (research in pairs) at Oberwolfach, supported by the Deutsche Forschungsgemeinschaft and by the Volkswagenstiftung, 1997; RFFI (Russian Federation Fundamental Investigations), 1994-1997.
Awards: Kettering University Outstanding New Researcher Award, Kansas State University Hostinsky Award.
Reviewer for Mathematical Reviews.
Member of the American Mathematical Society and SIAM.
PUBLICATIONS:
1. Kinetics Approach to Modelling of Stress Induced Degradation of Formulated with Star Polymer Additives, STLE Tribology Transactions, v. 48, 2005, pp. 1-14 (coauthors I.I. Kudish, M.J. Covitch, and G.R. Hayrapetyan).
2. Kinetics of Stress- Induced Degradation of Star Polymers in Automotive Lubricants, STLE Tribology Transactions, 2004, (coauthors I.I. Kudish and M.J. Covitch).
3. Lubricants with Newtonian and non-Newtonian Rheologies and Their Degradation in Line Contacts", ASME Journal Of Tribology, V. 126, No. 1, pp. 112-124, (coauthor I.I. Kudish).
4. A New Approach to Modeling of Stress Induced Degradation of Formulated Lubricants and Their Behaviour in Lubricated Contacts, 2nd Tribology in Environmental Design International Conference, 2003, September 8-10, Bournemouth, UK, (coauthor I.I. Kudish).
5. Asymptotics of impedance in complex frequency domain and inverse problem of the theory of ground penetrating radars, Proceedings of the Third ISAAC Congress, Vol. 2, 2003, pp. 897-911, Berlin, Germany, (coauthor R.G. Alexandrian).
6. Modeling of line contacts with degrading lubricant, ASME Journal of Tribology, 2003, Vol. 125, No 3, pp. 513-522, (coauthor I.I. Kudish).
7. Modeling of Degradation of Polymer Additives in Lubricants Based on Kinetics of Scission and Viscosity Loss, STLE Tribology Transactions, V. 46, No. 1, 2003, pp. 1-11, (coauthors I.I. Kudish and M.J. Covitch).
10. Singularities of the Radon transform, Applicable Analysis, Vol. 79 (2001), N 3-4, pp. 351-379, (coauthor A.G. Ramm).
11. Propagation of smoothness for edge-degenerate wave equations, International Series of Numerical Mathematics, Vol. 140 (2001), pp. 11-18, (coauthor I. Witt ).
12. Isometric properties of the Hankel transformation in weighted in Sobolev spaces, Integral Transforms and Special Functions, 11 (2000), No.3, 201-224, (coauthor I. Witt ).
13. Dynamical systems and discrete methods for solving nonlinear ill-posed problems, Appl. Math. Rev., World Sci. Pub. Co., vol. 1, 2000, 491-536, (coauthor A.G. Ramm).
14. On a new statement of inverse problem of quantum scattering theory, Operator theory and its applications, Amer. Math. Soc., Providence RI, 2000, Fields Institute Comm., vol. 25, 2000, 95-110.
15. Continuous methods for solving nonlinear ill-posed problems, Operator theory and its applications, Amer. Math. Soc., Providence RI, 2000, Fields Institute Comm., vol. 25, 2000, 111-137, (coauthors A.G. Ramm and A.B. Smirnova).
16. Numerical inversion of the Laplace transform from real axis, J. of Math Analysis and Applications, 248 (2000), 572-587, (coauthor A.G. Ramm).
17. Nonlinear problems and applications, Ph.D. thesis, Kansas State University, 200, 131 pp.
18. Continuous Newton method and its modification, Applicable Analysis, 73 (1999), N 3-4, 463-484.
19. Example of two different potentials which have practically the same fixed-energy phase shifts, Phys. Letters A, 254 (1999), issue 3-4, 141-148, (coauthors A.G. Ramm and A.B. Smirnova).
20. Continuous analog of the Gauss-Newton method, Mathematical Models and Methods in Applied Sciences, 9 (1999), N 3, 463-474, (coauthors A.G. Ramm and A.B. Smirnova).
21. Numerical method for solving the inverse problem of quantum scattering theory, Lect. Notes in Physics, 488 (1997), 88-97, (coauthors I.V. Puzynin and E.P. Zhidkov).
22. Newtonian iterative scheme with simultaneous iterations of inverse derivative, Computer Physics Communications, 102 (1997), 97-108, (coauthor I.V. Puzynin).
23. Quantum motion on the three-dimensional sphere, Comm. of JINR, Dubna, E2-96-117, (1996), pp. 12, (coauthors Kh.H. Karayan, G.S. Pogosyan, A.N. Sissakyan, D.I. Zaslavsky).
24. Numerical method for solving the inverse problem of quantum scattering theory, Vestn.Mos.Un-ta., Ser.1, Matematika, Mekhanika, (1996), N 6, 38-40, (coauthor E.P. Zhidkov).
25. On regularizing numerical algorithms for solving the inverse problem of quantum scattering theory, Comm. of JINR, Dubna, P11-96-38, (1996), pp. 14, (coauthors J. Busha and E.P. Zhidkov).
26. Numerical method for solving the inverse scattering problem based on the asymptotic regularization, Mathematical modeling, 8 (1996), N 3, 33-48, (coauthors E.P. Zhidkov and R.L. Shakhbagyan).
27. Phenomenological investigation of baryon resonances, Turkish Journ. of Phys., 20 (1996), N 5, 465-476, (coauthors F.A. Gareev, G.S. Kazacha, Yu.L. Ratis, and E.A. Strokovsky).
28. Parametrix of the mixed problem for the wave equation with nonhomogeneous boundary conditions, Izv. Nats. Acad. Nauk Armenii Mat., 28 (1993), N 1, 82-88, English translation in Soviet Journal of Contemporary Mathematical Analysis, 28 (1993), N 1, (coauthor G.R. Alexandryan).
29. Parametrix of the mixed problem for the hyperbolic system of first order partial differential equations, Izv. Nats. Acad. Nauk Armenii Mat., 27 (1992), N 6, 1-27, English translation in Soviet Journal of Contemporary Mathematical Analysis, 27 (1992), N 6, (coauthor G.R. Alexandryan).
30. Fundamental solution of the model mixed problem with nonstrictly concave boundary, Izv. Acad. Nauk Armenii Mat., 26 (1991), N 4, 277-299, English translation in Soviet Journal of Contemporary Mathematical Analysis, 26 (1991), N 4.
31. On the problem of exact controllability of oscillating string, Sci.Notes of Yerevan State Univ., (1991), N 3, 15-20, (coauthor L.S. Kantardzhyan).
32. Plansherel's formula associated with admissible complex of straight lines in CPn, Izv. Acad. Nauk Armenii Mat., 23 (1988), N 5, 62-90, English translation in Soviet Journal of Contemporary Mathematical Analysis, 23 (1988), N 5, 463-488, (coauthors M.I. Graev, M.M. Graev, and G.R. Oganesyan).
33. Construction of weakly commuting extensions of operators and the problem of symmetrization of hyperbolic equations, Soviet Math. Dokl., 35 (1987), N 2, 439-443.
34. On the reduction of the Cauchy problem for a hyperbolic equation to symmetric systems, Izv. Acad. Nauk Armenii Mat., 21 (1986), N 1, 51-62, English translation in Soviet Journal of Contemporary Mathematical Analysis, 21 (1986), N 1.
35. Plansherel's theorem for an integral transformation, connected with a pair of Grassman manifolds, Izv. Acad. Nauk Armenii Mat., 19 (1984), N 6, 467-483, English translation in Soviet Journal of Contemporary Mathematical Analysis, 19 (1984), N 6, 53-69, (coauthors I.M. Gel'fand, M.I. Graev, G.R. Oganesyan).
36. Plansherel's theorem for an integral transformation associated with a complex of p-dimensional planes in Cn and CPn, Izv. Acad. Nauk Armenii Mat., 18 (1983), N 4, 271-282, English translation in Soviet Journal of Contemporary Mathematical Analysis, 18 (1983), N 4, 21-33, (coauthors M.I. Graev, M.M. Graev, and G.R. Oganesyan).
37. Plansherel's theorem for an integral transformation associated with a complex of p-dimensional planes in CPn, Soviet Math. Dokl., 27 (1983), N 1, 47-50, (coauthors M.I. Graev, M.M. Graev, and G.R. Oganesyan).
38. Plansherel's formula for the integral transformation associated with a complex of the straight lines intersected the algebraic curve in C3 and CP3, Dokl. Acad. Nauk Arm. SSR, 75 (1982), N 1, 9-15, (coauthors M.I. Graev, M.M. Graev, and G.R. Oganesyan).
39. On the well-posedness conditions for second order hyperbolic equations, in the book: Applications of the methods of function theory and functional analysis to the problems of the mathematical physics, Yerevan, 1982, 20-22.
40. On the well-posedness conditions for the mixed problem for hyperbolic systems, in the book: Well-posed boundary problems for nonclassic equations of the mathematical physics. Novosibirsk, 1981, 3-6.
41. Mixed problem for hyperbolic equations and systems, Ph.D. thesis, Institute of Mathematics, Armenian Acad. Sci.,Yerevan, 1981, 102 pp.
42. On the well-posedness conditions for the mixed problem for the strictly hyperbolic operator at the violation of the Lopatinsky condition, in the book: Partial Differential Equations. Trans. of Conf. on differential equations and applications, Novosibirsk, 1980, 3-8.
43. On a weak L2 - well posedness of the mixed problems for the hyperbolic systems, Dokl. Acad. Nauk Arm.SSR, 70 (1980), N 4, 205-211.
44. On the equivalent forms of the Lopatinsky condition for the hyperbolic equations, Dokl. Acad. Nauk Arm.SSR, 67 (1978), N 1, 18-24.
45. On a mixed problem for degenerating hyperbolic equations of second order at the violation of the uniform Lopatinsky condition, Dokl.Acad.Nauk Arm.SSR, 65 (1977),N1,3-9.
46. On a mixed problem for a hyperbolic equation of second order, Izv. Acad. Nauk Arm.SSR, ser. Matematika, 12 (1977), N 1, 32-45.
PRESENTED PAPERS: 1. Modeling of Degradation of Polymer Additives in Lubricants Based on Kinetics of Scission and Viscosity Loss", 2002 ASME/STLE International Tribology Conference & Exposition, Cancun, Mexico, October 2002, (coauthors I.I. Kudish, M.J. Covitch).
2. Modeling of Line Contacts with Degrading Lubricant, 2002, ASME/STLE International Tribology Conference & Exposition, Cancun, Mexico, October 2002, (coauthor I.I. Kudish).
3. Stress-Induced Degradation of Polymer Additives to Lubricants in Line Contacts", International Conference ASIATRIB, Cheju Island, Korea, October 21-24, 2002, (coauthor I.I. Kudish).
INVITED LECTURES: 1. “Layer Stripping in the Frequency Domain and the Inverse Problem of the Theory of Ground Penetrating Radars”, Colloquium of the Dept. of Mathematics and Statistics, Georgia State University, November 25, 2002, Atlanta, Georgia 2. “Geometric approach to parametrix of the mixed problems for hyperbolic systems”, Technical University, Bergakademie Freiberg, Germany, April, 1997
PAPERS SUBMITTED FOR PUBLICATION:
1. Kinetics approach to modeling of polymer additive degradation in lubricants, Proceedings of 3rd International Symposium on Tribology, Bejing, China, (coauthors I.I. Kudish and M.J. Covitch).
TEXTBOOK:
1. R.G. Airapetyan, Asymptotic methods, Yerevan State University, Yerevan, 1990.
PREPRINTS:
1. R.G. Airapetyan and I. Witt, Isometric properties of the Hankel transformation in weighted Sobolev spaces, Preprint 97/14, Potsdam University, 1997, 19 pp.
2. R.G. Airapetyan, E.P. Zhidkov, and R.L. Shakhbagyan, Numerical method for solving the inverse scattering problem based on the asymptotic regularization, Preprint P11-95-252, Joint Institute for Nuclear Research, Dubna, 1995, 16 pp.
3. R.G. Airapetyan, M.I. Graev, M.M. Graev, and G.R. Oganesyan, An integral of the normal curvature and Plancherel's formula in 3 – dimensional complex integral geometry, Preprint N 149, Keldysh Inst. of Appl. Math. Acad. Of Sci. USSR, Moscow, 1989, 27 pp.