- Spectral theory and eigenvalue approximation of operator-valued functions, pattern recognition methods in medical diagnostics, integrable dynamical systems, free boundary problems, mathematical modeling in biophysics.
RECENT TECHNICAL REPORTS (Center for Applied Mathematics and Statistics)
- REPORT 0203-4: Cancer diagnostic method based on pattern recognition of DNA changes in buccal epithelium in the pathology of the thyroid and mammary glands (with D. Klyushin, Yu. Petunin, N. Boroday, K. Ganina), 2003.
- REPORT 0102-16: Equations of interface dynamics for quasi-stationary Stefan problem (with V. Gafiychuck, A. Shnyr, and R. Zabrodsky), 2002.
- REPORT 0001-10: A variational method for eigenvalue problems nonolinearly dependent on the spectral parameter (with V. Slastikov), 2001.
- REPORT 0001-21: Computer-aided pattern recognition method for cytogenetic diagnosis of breast cancer and fibroadenomatosis (with Yu. Petunin, D. Klyushin, K. Ganina, N. Boroday), 2001.
- REPORT 9495-24: Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear systems.