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    Recently Submitted Papers

  1. "Numerical Solution of an Inverse Problem in Size-Structured Population Dynamics." Joint with B. Perthame and M. Doumic.
  2. "Towards a Generalization of Dupire's Equation for Several Assets." Joint with P. Amster and P. de Napoli.

  3. Papers Published or Accepted in Refereed Journals

  4. "Bi-Hamiltonian Aspects of a  Matrix Harry Dym Hierarchy." Journal of Mathematical Physics (2008). Joint with L. Fontanelli, P. Lorenzoni and M. Pedroni.
  5. "Iterative Regularization Methods for a Discrete Inverse Problem in MRI." Cubo. A Mathematical Journal. Vol. 10. N. 8. (2008) pp 135-144. Joint with A. Leitão.
  6. "On the Inverse Problem for a Size-Structured Population Model." Inverse Problems 23 (2007) pp 1037-1052. Joint with B. Perthame. 
  7. "Mathematical Modelling and Parameter Estimation of the Serra da Mesa Basin." Mathematical and Computer Modelling (2008). IN PRESS. Joint with C. Mocenni, E. Sparacino, and A. Vicino. 
  8. "On the Asymptotics of Fast Mean-Reversion Stochastic Volatility Models." Joint with M. O. Souza. Accepted for publication in International Journal of Theoretical and Applied Finance
  9. "On the Inverse Doping Profile Problems for the Voltage-Current Map." Inverse Problems 22 (2006) pp 1071-1088. Joint with A. Leitão and P. Markowich.
  10. "Huygens' Principle for Hyperbolic Operators and Integrable Hierarchies."  Physica D. Volume 213, pp. 231-245, (2006). Joint with F. Chalub.
  11. "Huygens' Principle, Dirac Operators, and Rational Solutions of the AKNS Hierarchy." Mathematical Physics, Analysis and Geometry. Volume 8, Number 3, pp 187-210, (2005). Joint with F.Chalub.
  12. "Matrix Bispectrality and Huygens' Principle for Dirac Operators." Contemporary Mathematics. Vol. 362. pp 89-112, (2004). Joint with F. Chalub.
  13. "Three-Dimensional Reconstruction by Chahine's Method from Electron Microscopic Projections Corrupted by Instrumental Aberrations." Inverse Problems.   Vol. 19, Number 4, pp 933-950, (2003). Joint with R. Marabini, C.O.S. Sorzano, and G. T. Herman.
  14. "On the Inverse Problem for Scattering of Electromagnetic Radiation by a Periodic Structure."   Studies in Applied Mathematics. Vol. 111, Number 2, pp 115--165, (2003). Joint with L. O. Castellano Pérez.
  15. "On the Bi-Hamiltonian Theory for the Harry Dym Equation." Theoretical and Mathematical Physics. Vol. 133, Number 2, pp. 1583--1595, (2002). Joint with M. Pedroni and V. Sciacca.
  16. "Bundle Bispectrality for Matrix Differential Equations." Integral Equations and Operator Theory. Vol. 41, pp. 472--496, (2001). Joint with A. L. Sakhnovich.
  17. "Tangent Graeffe Iteration." Numerische Mathematik. Vol. 89, No. 4, pp. 749-782 (2001). Joint with G. Malajovich.
  18. "On the Geometry of Graeffe Iteration." Journal of Complexity. Vol. 17, No. 3, pp. 541-573 (2001). Joint with G. Malajovich.
  19. "Convexity for the Diffuse Tomography Model"  Inverse Problems. Vol. 7,  pp 729 - 738 (2001). Joint with B.F.Svaiter.
  20. "On Huygens' Principle for Dirac Operators and Nonlinear Evolution Equations." Journal of Nonlinear Mathematical Physics. Vol. 8, Supplement, pp 62-68 (2001). Joint with F. Chalub.
  21. "A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability."Regular and Chaotic Dynamics. No. 1, Vol. 5, pp 33-52, (2000). Joint with G. Falqui, F. Magri and M. Pedroni.
  22. "Rational Solutions of the Master Symmetries of the KdV Equation"Communications in Mathematical Physics. Vol. 211, No. 1, pp 85-109, (2000). Joint with D.S.Valerio Silva.
  23. "An Elementary Approach to the Polynomial Tau Functions of the KP Hierarchy "Theoretical and Mathematical Physics. Vol. 122, No. 1, pp. 23-36, (2000). Joint with G. Falqui, F. Magri and M. Pedroni.
  24. "Geodesic Flows on Diffeomorphisms of the Circle, Grassmannians, and the Geometry of the Periodic KdV Equation."Advances in Theoretical and Mathematical Physics. Vol. 3, No.4, pp 1027 --1092, (1999). Joint with M. Schonbek and A. Todorov.
  25. " Darboux Transformations, Darboux Coverings, and Rational Reductions of the KP Hierarchy "Matemática Contemporânea. Vol. 15, pp 45-65, (1998). Joint with P. Casati, G. Falqui, F. Magri and M. Pedroni.
  26. "Bihamiltonian Formalism and the Darboux-Crum Method . Part I: From the KP to mKP Hierarchy" Inverse Problems. Vol. 13 No. 3, pp 755-780, (1997). Joint with F. Magri.
  27. "On the Geometry of Darboux Transformations for the KP Hierarchy and Its Connection with Discrete KP" Communications in Mathematical Physics. Vol. 188, No. 2, pp 305-326, (1997). Joint with F. Magri and M. Pedroni.
  28. "A Fast and Stable Algorithm for Splitting Polynomials." Computers and Mathematics with Applications. Vol. 33, No. 3, pp.1-23, (1997). Joint with G. Malajovich.
  29. "Rational Solutions of Nonlinear Evolution Equations, Vertex Operators and Bispectrality." Journal of Differential Equations 97:1, (1992), 71-98
  30. "On a Zero Curvature Problem Related to the ZS-AKNS Operator." Journal of Mathematical Physics, 33:11, (1992), 3666 - 3675.
  31. "On the Polynomial tau-functions for the KP Hierarchy and the Bispectral Property." Letters in Mathematical Physics, 24:1, (1992), 41 - 48.
  32. "Diffuse Tomography: Computational Aspects of the Isotropic Case." Inverse Problems, 8:3, (1992), 421-433, Joint with F. A. Grünbaum.
  33. "An Inverse Problem for a Model of Scattered and Diffused Radiation." F. A. Grünbaum e G. A. Latham. Proceedings of the Centre for Mathematics and Its Applications, Australian National University, 31, (1992), 69-81
  34. "Differential Equations in the Spectral Parameter, Darboux Transformations and a Hierarchy of Master Symmetries for KdV" Joint with F. Magri. Communications in Mathematical Physics, 141:2, (1991), 329 - 351.
  35. "Image Reconstruction of the Interior of Bodies that Diffuse Radiation." Science, # 248, (1990), 990-993, J. R. Singer et al. (click here for a list of references to this paper)
  36. "Differential Equations in the Spectral Parameter for Matrix Differential Operators." Physica D Nonlinear Phenomena 43:2-3, (1990), 269-287

  37.  

    Books

  38. "An Introduction to Inverse Problems; Examples, Methods, and Questions." Minicourse at the 22nd Brazilian Mathematics Colloquium. IMPA, 1999.
  39. " Topics on Wave Propagation and Huygens' Principle." Minicourse at the 21st Brazilian Mathematics Colloquium. IMPA, 1997.
  40. Chapters of Books

  41. " Inverse Problems for Semiconductors: Models and Methods." Joint with A. Leitão and P. Markowich. Inverse Problems for Semiconductors: Models and Methods.. In: Carlo Cercignani; Ester Gabetta. (Org.). Transport Phenomena and Kinetic Theory. Applications to Gases, Semiconductors, Photons, and Biological Systems. Basel: Birkhauser, 2006.
  42. "Imaging of Media that Diffuse and Scatter Radiation." F. A. Grünbaum et al., Radar and Sonar, Part 2, IMA Volumes in Mathematics and its Applications Volume 39, pp 57-70.

  43.  

    Papers at Conference Proceedings

     
  44. "Multiple Scale Asymptotics of Fast Mean Reversion Stochastic Volatility Models." Proceedings of the Third Brazilian Confererence: on Statistical Modelling in Insurance and Finance. Sao Paulo : Institute of Mathematics and Statistics, USP. pp. 248-253. (2007). Joint with M. O. Souza.
  45. "Asymptotic Behavior of Stochastic Volatility Models." Proceedings of the Second Brazilian Confererence: on Statistical Modelling in Insurance and Finance. Sao Paulo : Institute of Mathematics and Statistics, USP. pp. 222-227. (2005). Joint with M. O. Souza.
  46. "Inverse Problems in Finance: A Short Survey on Calibration Techniques." Proceedings of the Second Brazilian Conference on Statistical Modelling in Insurance and Finance. pp. 64-76 (2005).
  47. "Integrable Systems, Huygens' Principle, and Dirac Operators." Proceedings of the Workshop Nonlinearity, Integrability and all That. Twenty Years after NEEDS '79 pp 89-96, (2000). Joint with F. Chalub.
  48. " The Bispectral Problem, Rational Solutions of the Master Symmetry Flows, and Bihamiltonian Systems" CRM Proc. Lecture Notes, 14, Amer. Math. Soc., Providence, RI, (1998), 139-155.
  49. "An Algorithm for Deinterleaving Pulse Trains Using the Fast Wavelet Transform" Proceedings of the Brazilian Symposium of Telecommunications (Recife 1997) Joint with M.A.Grivet, R. Tavora, and E.L.Pinto.
  50. "Diffuse Tomography." Joint with F. A. Grünbaum. "Proceedings of the Meeting on Physiological Imaging, Spectroscopy, and Early Detection, Los Angeles, Jan. 1993, " SPIE Proceedings, 1887, (1993), 263-270.
  51. "Diffuse Tomography." Joint with F. A. Grünbaum et al. `Proceedings of the Laser Spectroscopy Symposium of the S.P.I.E. Los Angeles Meeting Jan. 1991." Progress in Biomedical Optics,1431, (1991), 232-238
  52. "An Oscillation Theorem for a Hill's Type Equation" Joint with L. R. Sinay, 17° Seminário Brasileiro de Análise, (1983), pp 95-100.
  53. Editorial Committees of Books

  54. Sixth Workshop on Partial Differential Equations. Part II. Papers from the Workshop on Partial Differential Equations: Theory, Computation, and Applications held in Rio de Janeiro, July 19--23, 1999. Edited by Hermano Frid, Jorge Hounie, Rafael Iório, Dan Marchesin, André Nachbin and Jorge Zubelli. Mat. Contemp. {19} (2000). Sociedade Brasileira de Matemática, Rio de Janeiro, 1999. pp. i--viii and 1--202.
  55. Sixth Workshop on Partial Differential Equations. Part I. Papers from the Workshop on Partial Differential Equations: Theory, Computation, and Applications held in Rio de Janeiro, July 19--23, 1999. Edited by Rafael Iório, Dan Marchesin, André Nachbin and Jorge Zubelli. Mat. Contemp. 18 (2000).  Sociedade Brasileira de Matemática, Rio de Janeiro, 1999. pp. i--viii and 1--207. 
  56. Fifth Workshop on Partial Differential Equations. Papers from the Workshop on Partial Differential Equations: Theory, Computation, and Applications held in Rio de Janeiro, July 14--18, 1997. Edited by Paulo Cordaro, Dan Marchesin, André Nachbin and Jorge P. Zubelli. Mat. Contemp. 15 (1998).  Sociedade Brasileira de Matemática, Rio de Janeiro, 1998. pp. i--viii and 1--312.
  57. Fourth Workshop on Partial Differential Equations. Part II. Papers from the Workshop on Partial Differential Equations: Theory, Computation, and Applications held in Rio de Janeiro, July 17--21, 1995. Edited by Rafael Iório, Dan Marchesin, André Nachbin and Jorge Zubelli. Mat. Contemp. 11 (1996). Sociedade Brasileira de Matemática, Rio de Janeiro, 1996. pp. i--vi and 1--190.
  58. Fourth Workshop on Partial Differential Equations. Part I. Papers from the Workshop on Partial Differential Equations: Theory, Computation, and Applications held in Rio de Janeiro, July 17--21, 1995. Edited by Rafael Iório, Dan Marchesin, André Nachbin and Jorge Zubelli. Mat. Contemp. 10 (1996).  Sociedade Brasileira de Matemática, Rio de Janeiro, 1996. pp. i--vi and 1--180.
  59. General Audience Papers

  60. "Sólitons: Na Crista da Onda por mais de 100 Anos." Revista Matemática Universitária. Vol. 30, pp 44--62, (2001). Joint with F. Chalub.
  61. "Sólitons: Na Crista da Onda por mais de 100 Anos." Boletim da Sociedade Portuguesa Matemática . Vol. 51, pp 3--24, (2004). Joint with F. Chalub. Reprinted version of the previous paper.