Selected Publications

My papers on Google Scholar       My papers on arXiv

  1. Spectral Sections.
    arXiv:2008.04672 [math.SP], 36 pp.
  2. Self-adjoint local boundary problems on compact surfaces. II. Family index.
    To appear in the Journal of Noncommutative Geometry.
    arXiv:1809.04353 [math-ph], 46 pp.
  3. Self-adjoint local boundary problems on compact surfaces. I. Spectral flow.
    Journal of Geometric Analysis (2019).
    arXiv:1703.06105 [math.AP], 46 pp.
  4. The structure of the category of parabolic equations. I.
    CEUR Workshop Proceedings, 2016, Vol-1662, 121-133.
  5. The structure of the category of parabolic equations. II.
    CEUR Workshop Proceedings, 2016, Vol-1662, 134-147.
  6. Factorization of the Reaction-Diffusion Equation, the Wave Equation, and Other Equations.
    Proceedings of the Steklov Institute of Mathematics, 2014, Vol.287, Suppl. 1, S156-S166.
    (text in English, text in Russian)
  7. The spectral flow for Dirac operators on compact planar domains with local boundary conditions.
    Communications in Mathematical Physics, 2013, Vol.322(2), 385-414.
    arXiv:1108.0806 [math-ph]
  8. Homeomorphism criteria for the theory of grid generation.
    Zh. Vychisl. Mat. i Mat. Fiz., 52:5 (2012), 878–882 (in Russian);
    arXiv:1504.01087 [math.GT] (in English).
  9. (with M.I. Katsnelson)
    Zero-energy states in corrugated bilayer graphene.
    Physical Review B, 2008, Vol.77, No.20.
    arXiv:0802.1409 [cond-mat.mes-hall]
  10. Homeomorphism problems arising in the theory of grid generation.
    Proceedings of the Steklov Institute of Mathematics, 2008, Suppl.1, S165-S182.
    (see also text in Russian).
  11. On the existence of factor sets by external equivalence relations in IST.
    Siberian Mathematical Journal 43 (2002), no. 4, 708-713
    (see also text in Russian).
  12. External sets properties in IST. The Bulletin of Symbolic Logic. 8 (2002), Issue 1, 155-156.
  13. Heat equation on Riemann manifolds: morphisms and factorization to smaller dimension.
    Proceedings of Institute of Mathematics of NAS of Ukraine, 43 (2002), 194–200.
  14. On relative near-standardness in IST.
    Siberian Mathematical Journal 39 (1998), no. 3, 518-521
    (see also text in Russian).
  15. Modeling of solutions of the heat equation and of the Stefan problem with dimension decrease.
    Russian Acad. Sci. Docl. Math. 58 (1998), no.1, 88-90.
  16. (with L.D. Zabezhinskii, V.V. Prokhorov, M.N. Mil'shtein, S.G. Stakheev)
    Statement and personal-computer-aided realization of the conjugate problem of heat transfer in a power-technological boiler with a moving bed of dispersed heat-transfer agent.
    Journal of Engineering Physics and Thermophysics (1997) 70: 744.
  17. Self-similar solutions of the Stefan problem.
    Journal of Engineering Physics and Thermophysics (1992) 63: 1032.
  18. The shape of a growing dendrite.
    Journal of Engineering Physics and Thermophysics (1991) 61: 1394.