Software & Systems

The Editorial Board / Serov Valeriy Sergejevich

Serov V.S. was born on 4th of November 1952 in Pavlovo, Gorkovskaya obl., USSR.

Department of Mathematical Sciences, University of Oulu, Finland.

Associate professor of Moscow State University, Department of History.

EDUCATION

Sc.Dr., 1997, Moscow State University, Moscow, Russia. Thesis title: Some

problems of the spectral theory of the elliptic differential operators with singularities.

PhD, 1979, Moscow State University, Moscow, Russia. Thesis title: Absolute convergence of spectral expansions and fractional degrees of elliptic operators.

Diploma, Applied Mathematics, 1975, Moscow State University, Faculty of Computational

Mathematics and Cybernetics, Moscow, Russia.

TEACHING EXPERIENCE

1977–2002 Serov V.S. have been teaching at Moscow Lomonosov State University. Among the lectures courses are calculus, complex analysis, generalized functions, Fourier transforms, spectral theory of self–adjoint operators. The list of practical courses: calculus, analysis II, complex analysis, functional analysis.

2002–2009 Serov V.S. have been teaching at the University of Oulu three new courses:

"Fourier transform, distributions and applications to the Schrödinger operator", "Spectral theory for elliptic dierential operators" and "Introduction to partial dierential equations".

Serov V.S. have supervised 12 PhD and 12 Diploma works. In 1998 he was appointed the award of the Goerge Soros Honorary Docent. In 2002 he was accepted as the member of the Finnish Inverse Problems Society. Since 2006 Serov V.S. is a Senior Researcher of Finnish Centre of Excellence in Inverse Problems granted by Academy of Finland for the period 2006–2011.

Serov V.S. also has experience as a visiting professor in different universities in Greece, the USA, Germany, Spain, Finland, Sweden and Italy.

Among research interests:

1) Inverse Problems,

2) Spectral Theory,

3) Nonlinear Equations.

Since 1990 Serov V.S. participated in more than 80 International conferences, seminars and symposiums. His list of publications includes more than 110 items; among them, three textbooks.

http://www.mathnet.ru/php/person.phtml?option_lang=rus&personid=19088

REFERENCES

1. On a spectrum of the Schrödinger operator with Kato potential (with A.G. Razborov). Diff. Uravn. 2000, vol. 36 (5), pp. 689– 693.

2. About convergence of Fourier series on the eigenfunctions of Schrödinger operator with Kato potential. Matem. Zametki [Mathematical Notes]. 2000, vol. 67(5), pp. 755–763 (in Russ.)

3. Criteria for existence and stability of soliton solutions of the cubic–quintic nonlinear Schrödinger equation (with H.W. Schurmann). Physical Review E. 2000, vol. 62 (2), pp. 2821–2826.

4. Recovering singularities from backscattering in two dimensions (with P. Ola and L. Paivarinta). Comm.PDE. 2001, vol. 26 (3–4), pp. 697–715.

5. New mapping properties for the resolvent of the Laplacian and recovery of singularities of a multidimensional scattering potential (with L. Paivarinta). Inverse Problems. 2001, vol. 17 (5), pp. 1321–1326.

6. Some inverse problems for the Schrödinger operator with Kato potential (with A.G. Razborov and M.K. Sagyndykov). Ill–Posed and Inverse Problems. 2002, vol. 10 (4), pp. 395–411.

7. Solutions to the Helmholtz equation on the line describing guided waves in a nonlinear three–layer structure (with Yu.V. Shestopalov and H.W. Schurmann). Journ. of Physics A: Mathematical and General. 2002, vol. 35 (50), pp. 10789–10801.

8. Reflection and transmission of a plane TE–wave at a lossless nonlinear dielectric film (with Yu.V. Shestopalov and H.W. Schurmann). Physica D. 2001, vol. 158, pp. 197–215.

9. On the theory of TE polarized waves guided by a lossless nonlinear three–layer structure (with Yu.V. Shestopalov and H.W. Schurmann). Proc. Progress in Electromagnetic Research Symp. Osaka, Japan, 2001, p. 632.

10. An n–dimensional Borg–Levinson theorem for singular potentials (with L. Paivarinta). Adv. Appl. Math. 2002, vol. 29 (4), pp. 509–520.

11. Recovery of the singularities of a potential in two dimensional Schrödinger operator from fixed angle scattering data. Russian Math. Dokl. 2002, vol. 358 (2), pp. 160–162.

12. Some inverse problems for two dimensional Schrödinger operators with singular potential. Born approximation. Proc. int. conf. KROMSH'2001. 2002, Simpheropol's Univ. Press, pp. 24–30.

13. Waves in three–layer structures with Kerr–type nonlinearity and variable permittivity (with Yu.V. Shestopalov and H.W. Schurmann). Abstracts of int. conf. Math. Modeling of Wave Phenomena. Växjö, Sweden, 2002, pp. 22–23.

14. Integral equation approach to reflection and transmission of a plane TE–wave at a (linear/nonlinear) dielectric film with spatially varying permittivity (with H.W. Schurmann and E.D. Svetogorova). Journ. of Physics A: Mathematical and General. 2004, vol. 37 (9), pp. 3489–3500.

15. Waves in three–layer structures with Kerr–type nonlinearity and variable permittivity (with Yu.V. Shestopalov and H.W. Schurmann). Proc. of int. conf. Math. Modeling of Wave Phenomena. Växjö, Sweden, 2004, vol. 7, pp. 217–226.

16. Reconstruction of singularities in two dimensional Schrödinger operator with fixed energy (with A.D. Chernova). Inverse and Ill–posed Problems. 2004, vol. 12 (4), pp. 413–421.

17. Traveling wave solutions of a generalized modified Kadomtsev–Petviashvili equation (with H.W. Schurmann). Journ. of Math. Phys. 2004, vol. 45 (6), pp. 2181–2187.

18. New estimates of Green–Faddeev function and recovering of singularities in two dimensional

Schrödinger operator with fixed energy (with L. Paivarinta). Inverse Problems. 2005, vol. 21 (4), pp.1291–1301.

19. Integral equation approach to reflection and transmission of a plane TE–wave at a (linear, nonlinear, absorbing) dielectric film with spatially varying permittivity (with H.W. Schurmann and E.D. Svetogorova). PIERS 2004: electromagnetic research symposium. Pisa, 2004, vol. 2, pp. 121–124.

20. Weierstrass' solutions to certain nonlinear wave and evolution equations (with H.W. Schurmann). PIERS 2004: electromagnetic research symposium. Pisa, 2004, vol. 2, pp. 651–654.

21. Some inverse scattering problems for two–dimensional Schrödinger operator. Proc. of the 5th int. conf. on Inverse Problems in Engineering: Theory and Practice. Edited by D. Lesnic, Leeds Univ. Press, 2005, vol. 3, Leeds, UK.

22. Problems on theory of functions of complex variable with solutions (with T.A. Leontyeva and V.S. Panferov). Moscow, Mir, 2005, 360 p.

23. Inverse scattering problem for two–dimensional Schrödinger operator (with L. Paivarinta). Journ. Inverse and Ill–posed Problems. 2006, vol. 14 (3), pp. 295–305.

24. Some elliptic traveling wave solutions to the Novikov–Veselov equation (with H.W. Schurmann and J. Nickel). PIER. 2006, vol. 61, pp. 323–331.

25. Superposition in nonlinear wave and evolution equation (with H.W. Schurmann and J. Nickel). Int. Journ.of Theoretical Physics. 2006, vol. 45 (6), pp. 1057–1073.

26. Some elliptic traveling wave solutions to the Novikov–Veselov equation (with H.W. Schurmann and J. Nickel). Proc. PIERS. 2006, Cambridge/MA, USA, pp. 519–523.

27. Recovery of jumps and singularities of an unknown potential from limited data in dimension 1 (with M. Harju). Journ. of Physics A: Mathematical and General. 2006, vol. 39, pp. 4207–4217.

28. Fundamental solution and Fourier series in eigenfunctions of degenerate elliptic operator. Journ.of Mathematical Analysis and Applications. 2007, vol. 329 (1), pp. 132–144.

29. Reconstruction of discontinuities in one–dimensional nonlinear Schrödinger operator from limited data (with M. Harju). Inverse Problems. 2007, vol. 23 (2), pp. 493–506.

30. Recovery of jumps and singularities in the multidimensional Schrödinger operator from limited data (with L. Paivarinta). Inverse Problems and Imaging. 2007, vol. 1 (3), pp. 525–535.

31. Inverse Born approximation for the nonlinear two–dimensional Schrödinger operator. Inverse Problems. 2007, vol. 23 (3), pp. 1259–1270.

32. Partial recovery of the potentials in generalized nonlinear Schrödinger equation on the line (with M. Harju). Journ. of Mathematical Physics. 2007, vol. 48 (8), p.18.

33. On the theory of TM electromagnetic guided waves in a nonlinear three–layer structures (with H.W. Schurmann, Yu.V. Shestopalov and Yu.G. Smirnov). Proc. PIERS. Prague, Czech Republic, 2007, p. 140.

34. A uniqueness theorem and reconstruction of singularities for a two–dimensional nonlinear Schrödinger equation (with M. Harju). Nonlinearity. 2008, vol. 21, pp. 1323–1337.

35. Inverse Born approximation for the generalized nonlinear Schrödinger operator in two dimensions. Modern Physics Letters B (MPLB). 2008, vol. 22 (23), pp. 2257–2275.

36. Inverse Born approximation for the generalized nonlinear Schrödinger operator in two dimensions. Journ. of Physics: Conference Series. 2008, vol. 35, 012092.

37. Inverse fixed angle scattering and backscattering problems in two dimensions. Inverse Problems. 2008, vol. 24, 065002.

38. TM electromagnetic guided waves in a (Kerr-) nonlinear three–layer structure (with H.W. Schurmann and K.A. Yuskaeva). PIERS Proc. Moscow, Russia, 2009, pp. 364–369.

39. Integral equation approach to TM electromagnetic waves guided by a (linear/nonlinear) dielectric film with a spatially varying permittivity (with H.W. Schurmann and K.A. Yuskaeva). PIERS Proc. Moscow, Russia, 2009, pp. 1915–1919.

40. The fundamental solution and Fourier series in eigenfunctions of the magnetic Schrödinger operator. Journ. of Physics A: Mathematical and Theoretical. 2009, vol. 42, no. 22, 225205.

41. An inverse Born approximation for the general nonlinear Schrödinger operator on the line. Journ. of Physics A: Mathematical and Theoretical. 2009, vol. 42, no. 33, 332002.

42. A domain description and Green's function for elliptic differential operator with singular potential (with U. Kyllonen). Journ. of Mathematical Analysis and Applications. 2010, vol. 366, iss. 1, pp. 11–23.

43. Application of the Banach fixed–point theorem to the scattering problem at a nonlinear three–layer structure with absorption (with H.W. Schurmann and E.D. Svetogorova). Fixed Point Theory and Applications. 2010. Available at: http://www.fixedpointtheoryandapplications.com/content/2010/1/439682

44. Green's function and convergence of Fourier series for elliptic differential operators with potential from Kato space. Abstract and Applied Analysis. Submitted, 2010. Available at: http://www.hindawi.com/journals/aaa/2010/902638/

45. Inverse backscattering for the nonlinear Schrödinger operator in two dimensions (with J. Sandhu). Journ. Phys. A: Math. Theor. 2010, vol. 43, no. 32, 325206.

46. Inverse fixed energy scattering problem for the generalized nonlinear Schrödinger operator. Inverse Probl. 2012, vol. 28, no. 2.

47. Transmission eigenvalues for degenerate and singular cases. (with J. Sylvester). Inverse Probl. 2012, vol. 28, no. 6.

48. Inverse backscattering Born approximation for a two-dimensional magnetic Schrödinger operator. Inverse Probl. 2013, vol. 29, no. 7.

49. Inverse fixed angle scattering and backscattering for a nonlinear Schrödinger equation in 2D (with Fotopoulos G. and Harju M.). Inverse Probl. Imaging. 2013, vol. 7, no. 1, 183-197.

50. Transmission eigenvalues for non-regular cases. Commun. Math. Anal. 2013, vol. 14, no. 2, 129–142, (electronic only).

51. Inverse backscattering Born approximation for the magnetic Schrödinger equation in three dimensions. (with J.Sandhu) Math. Methods Appl. Sci. 2014, vol. 37, no. 2, pp. 265-269.