Selected published research and research accepted for publication

All papers except 1, 7-10, 15, 23, 29, 34 , 38 and 39 are single - authored by Marianna A.Shubov.

  1. "Asymptotic distribution of eigenfrequencies for a coupled Euler-Bernoulli and Timoshenko beam model"; NASA Technical Publication NASA/CR - 2003 - 212022; November 2003. (NASA Dryden Center) (jointly with C.A. Peterson); (78 pages in print).
     

  2. "Flutter phenomenon and its mathematical analysis", Part I (Flutter of helicopter, propeller, and turbine blades; flutter of hard disk drives, and transmission lines), (39 manuscript pages), an invited survey paper for Journal of Aerospace Engineering; to appear.
     

  3. "Flutter phenomenon and its mathematical analysis",Part II (Flutter of long-span suspension bridges and flutter of tubes conveying fluids-biomedical setting), (34 manuscript pages); an invited survey paper for Journal of Aerospace Engineering; to appear.
     

  4. "Flutter phenomenon and its mathematical analysis", Part III (Flutter problem in aeroelasticity), (42 manuscript pages); an invited survey paper for Journal of Aerospace Engineering to appear.
     

  5. "Bending-torsion vibration model with two-end energy dissipation", (25 manuscript pages), Applied Mathematics and Computation; to appear.
     

  6. "Spectral properties of the generalized resolvent operator for aircraft wing model in subsonic air flow", In book: Advances in Dynamics and Control, Ed. S.Sivasundaram, (Volume in a series "Nonlinear Problems in Aviation, Aerospace, Aeronautics, and Astronautics); to appear.
     

  7. "Asymptotic and spectral properties of the operator-valued functions generated by aircraft wing model, (jointly with A. V. Balakrishnan), Mathematical Methods for the Applied Sciences, 27, (2004), p.329-362.
     

  8. "Spectral properties of nonselfadjoint operators generated by coupled Euler-Bernoulli and Timoshenko beam model", (jointly with A.V. Balakrishnan and C.A. Peterson); Zeitschrift für Angewandte Mathematik und Mechanik, (ZAMM); 84, (2), (2004), (23 journal pages).
     

  9. "Asymptotic and spectral results for nonselfadjoint operators generated by coupled Euler-Bernoulli and Timoshenko beam model", (jointly with A.V.. Balakrishnan, C.A. Peterson, and C.A. Martin). In the Book: "Semigroup of operators: Theory and Application", Eds. C.Kubrusly and N.Levan, (2002), p.15-31.
     

  10. "Asymptotic analysis of coupled Euler-Bernoulli and Timoshenko beam model," (jointly with C. Peterson). Accepted to Mathematische Nachrischten.
     

  11. "Spectral properties of the generalized resolvent operator for an aircraft wing model in subsonic airflow"; (24 manuscript pages); Accepted to:  Advances in Dynamics and Control (volume in a series "Nonlinear Systems in Aviation, Aerospace, Aeronautics, and Astronautics".
     

  12. "Asymptotic and spectral analysis of Timoshenko beam model",     Mathematische Nachrichten,  241, (2002). p. 125-162.
     

  13.  "Asymptotic and spectral analysis of nonselfadjoint operators generated by a filament with a critical value of a boundary parameter".  Accepted to Mathematical Methods in the Applied Sciences, 26, (2002), p.213-245.
     

  14. "Asymptotic analysis of aircraft wing model in subsonic air flow", IMA Journal on Applied Mathematics, 66, (2001), p.319-356.
     

  15.  "Asymptotic behavior of aeroelastic modes for aircraft wing model    in  subsonic air flow", (jointly with A.V.. Balakrishnan), to appear in: Proceedings of the Royal Society: Mathematical, Physical and Engineering Sciences.
     

  16. "Asymptotic representations for root vectors of nonselfadjoint operators and pencils generated by aircraft wing model",   Journal of Mathematical Analysis and its Applications, 260, (2001), p. 341-366.
     

  17. "Riesz Basis property of root vectors of nonselfadjoint operators generated by aircraft wing model in subsonic air flow",  Mathematical Methods for Applied Sciences, 23, (2000), p. 1585-1615.
     

  18. "Asymptotics of aeroelastic modes and the basis property of mode shapes for aircraft wing model", an invited paper in Special Issue on Control of Structural and Dynamical Systems of the Journal of Franklin Institute, 338. (2/3), (2001)  p.171-185.
     

  19. "Asymptotic and spectral analysis of aircraft wing model in subsonic air flow",  in :Eds.  G.Cagnol, M.P.Polis, J.-P.Zolesio;  Cambridge, UK, (2001), p.397-414.
     

  20. "Exact controllability of Timoshenko beam",  IMA Journal of Mathematical Control and Information, 17, (2000), p.375-395.
     

  21. "Transformation operators for class of damped hyperbolic equations", Asymptotic Analysis, 24, (2000), p.183-208/
     

  22. "Geometric properties of root vectors for the equation of nonhomogeneous damped string.  Transformation operators method",  Applicable Analysis,  77, (1-2), (2001),  p. 97-123.
     

  23. "Asymptotics of eigenfrequencies and eigenmodes of nonhomogeneous inextensible filament loaded at one end"  (jointly with B.P.Belinskiy and C.F.Martin).  to appear in:  Mathematical Methods in the Applied Sciences, 24, (15), (2001), p.1139-1167.
     

  24. "Riesz basis property of generalized eigenvectors of radial damped wave equation," Advances in Differential Equations, 5 , (4-6), (2000), p.623-656.
     

  25. "Nonselfadjoint spectral operators and their application to control theory," in: Volterra Equations and Applications, Eds. C.Corduneanu and I.W. Sandberg, Gordon and Breach Sci. Publ., (2000), p. 457-464.
     

  26. "Nonhomogeneous damped string:  Riesz basis property of root vectors via Transformation Operators Method,"  in:  Semigroups of Operators:  Theory and Applications,  Ed. A.V.Balakrishnan; Birkhauser, (2000),  p.287-295.
     

  27. "Spectral operators generated by Timoshenko beam model", System and Control Letters, 38, (4-5), (1999),  p.249-258.
     

  28. "The Riesz basis property of the system of the root vectors of nonhomogenous damped string. Transformation operators method",  Methods of Analysis and Applications, 8, (4), (1999), p.571-592.
     

  29. "Boundary and distributed controllability of the damped wave equation. Reduction of control time", (jointly with C.F. Martin) Journal of Mathematical Analysis and Applications, 240, (1999), p.16-36.
     

  30. "Timoshenko beam model: Spectral Properties and Control," Proceedings of the Workshop on Dynamics and Control  "Complex Dynamics Process  Incomplete Information.", Germany, (1999), p.140-152.
     

  31. "Asymptotics of spectra and eigenfunctions for nonselfadjoint operators generated by radial nonhomogeneous damped wave equations,''  Asymptotic Analysis, 16, (1998), p.245-272.
     

  32. "Exact boundary and distributed controllability of radial damped wave equation,'' Journal de Mathematiques Pures et Appliquees., 77 , (1998) , p.415-437.
     

  33. "Spectral decomposition method for damped string. Reduction of control time,''  Applicable Analysis, 68, (1998) , p.241-259.
     

  34. "On controllability of elastic string with viscous damping", (jointly with B.Belinskiy, J.Dauer, C.Martin), Numerical Functional Analysis and Optimization, 19 ,(3-4), (1998), p.227-255.
     

  35. "Spectral operators generated by 3-dimensional damped wave equation and their application to control theory,'' Spectral and Scattering theory (ed .A.G. Ramm), Plenum Press, New York ,(1998),  p.177-188.
     

  36. "Nonselfadjoint operators generated by the equation of nonhomogeneous damped string,"  Transactions of American Math. Society , Vol.  349, (1997) , p.4481-4499.
     

  37. "Spectral operators generated by damped hyperbolic equations,'' Integral Eqs. and Operator Theory, 28 (1997), p.358-372.
     

  38. "Unique controllability of damped wave equation,'' (jointly with C. Martin}, J. Dauer, B. Belinskiy), SIAM Journal on Control and Optimization, Vol. 35 (5), (1997), p.1773-1789.
     

  39. "Nonselfadjoint operators and controllability of damped string",  (jointly with C. Martin, J. Dauer, and B. Belinskii), Proc. of 36th IEEE Conf. Decision and Control, San Diego, CA, (1997), p.515-520.
     

  40. "Exact controllability of nonhomogeneous radial damped wave equation.'' Refereed Proceedings of 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Berlin, August 1997; Vol. 5 (1997), p.215-220.
     

  41. "Basis property of eigenfunctions of nonselfadjoint operator pencils generated by equation of nonhomogeneous damped string,'' Integral Eqs. and Operator Theory, 25 (1996), p.289-328.
     

  42. "Asymptotics of resonances and eigenvalues for nonhomogeneous damped string.'' Asymptotic Analysis, 13 (1996), p.31-78.
     

  43. "Asymptotics of resonances and geometry of resonance states in the scattering of acoustic waves by inhomogeneity of density,'' Differential and Integral Eqs., 8 (3) (1995), p.1073-1115.
     

  44. "Stark quantum defect for high Rydberg states of three-dimensional Schrodinger operator with screened Coulomb potential,'' Il Nuovo Cimento , 110B (1995), p.1057-1092.
     

  45. "Asymptotic behavior of the quantum defect as a function of an angular momentum,'' Differential and Integral Eqs., 8 (8) (1995), p.1885-1910.
     

  46. "Low-energy chain of resonances for the three-dimensional Schrodinger operator with nearly Coulomb potential,'' Journal of Differential Equations , 114 (1994), p.1-31.
     

  47. "High-energy asymptotics of resonances for three-dimensional Schrodinger operator with screened Coulomb potential,'' Journal of Mathematical Physics , 35 (2), (1994), p.656-679.
     

  48. "Resonance selection principle and low-energy resonances for a radial Schrodinger operator with nearly Coulomb potential.'' Journal of Math. Analysis and Applications, 181 (1994), p.600-625.
     

  49. "Geometry of resonance poles for three-dimensional Schrodinger operator with nearly Coulomb potential,'' Trends and Developments in Ordinary Differential Equations, Editors Y. Alavi and Po-Fang Hsieh, World Scientific Publishing Co. (1994), p.315-325.
     

  50. "Asymptotics of the discrete spectrum for a radial Schrodinger equation with nearly Coulomb potential,'' Integral Eq. and Operator Theory, 14 (1991), p.586-608.
     

  51. "Certain class of unconditional bases in Hilbert space and its application to functional model and scattering theory,'' Integral Equations and Operator Theory, 13 (1990), p.750-770.
     

  52. "Construction of eigenfunctions of the discrete spectrum and principle for selecting eigenvalues for a radial Schrodinger operator with nearly Coulomb potential,'' Theoretical and Mathematical Physics, 76 (1988), p.379-392.
     

  53. "Nearness of the Riesz bases to orthonormal bases in Hilbert space,'' Journal of Soviet Mathematics, 27 (1984),p.2673-2677.
     

  54. "The serial structure of resonances of the three-dimensional Schrodinger operator,'' Proceedings of the Steklov Institute of Mathematics, 159 (1984), p.197-217.
     

  55. "The resonance selection principle for the three-dimensional Schrodinger operator,'' Proceedings of the Steklov Institute of Mathematics, 159 (1984), p.181-195.
     

  56. "Resonances in the scattering of acoustical waves by a spherical inhomogeneity of the density,'' American Math. Soc. Transl., (2) 115 (1980), p.143-164.
     

  57. "Construction of resonance states for the three-dimensional Schrodinger operator,'' Problems of Mathematical Physics, 9, Leningrad University, (1979), p.145-180 (Russian).
     

  58. "Nonphysical sheet for the string equation,'' Journal of Soviet Mathematics, 10 (1978), p.918-933.
     

  59. "Resonances in the scattering of acoustic waves by a spherical inhomogeneity of the density." Soviet Mathematical Doklady, 15(4), (1974), p.1131-1134.

Papers that are submitted

 1*."Riesz spectral operators generated by coupled Euler --Bernoulli and Timoshenko beam model   with two-end energy dissipation.", Submitted to advances in Applied Mathematics.

 2*."Riesz basis property of mode shapes for an aircraft wing model (subsonic case)"; (54 manuscript pages) Submitted to IMA Journal of Applied Mathematics.

 
3*."Numerical instability in spectral approximations for a nonhomogeneous damped string," (jointly with A. Balogh), (35 manuscript pages); Submitted to Numerical Functional Analysis and Optimization.


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