Publications of Oleg Karpenkov

  1. Combinatorics of multiboundary singularities of the series Bl_n and the Bernoulli-Euler numbers.
    Funct. Anal. Appl. 36/1 (2002), 65-67, Russian version: Funkt. Anal. Prilozh. 36 (2002), 78-81. [Zbl], [MR], [doi], [arxiv:math/0604024].
  2. Energy of a knot: variational principles.
    Russ. J. Math. Phys. 9/3 (2002), 275-287. [Zbl], [MR].
  3. Energy of a knot: some new aspects.
    In Fundamental mathematics today, pages 214-223. Nezavis. Mosk. Univ., Moscow, 2003. [Zbl], [MR].
  4. On the triangulations of tori associated with two-dimensional continued fractions of cubic irrationalities.
    v Funct. Anal. Appl. 38/2 (2004), 102-110, Russian version: Funkt. Anal. Prilozh. 38 (2004), 28-37. [Zbl], [MR], [doi].
  5. On two-dimensional continued fractions of hyperbolic integer matrices with small norm.
    Russian Math. Surveys 59/5 (2004), 959-960. [Zbl], [MR], [doi].
  6. Classification of three-dimensional multistoried completely hollow convex marked pyramids.
    Russian Math. Surveys 60 (2005), 165-166. [Zbl], [MR], [doi].
  7. The Möbius energy of graphs.
    Math. Notes 79/1 (2006), 134-138, Russian version: Mat. Zametki 79 (2007), 146-149. [Zbl], [MR], [doi], [arxiv:math-ph/0509055].
  8. Classification of lattice-regular lattice convex polytopes.
    Funct. Anal. Other Math. 1/1 (2006), 17-35. [Zbl], [MR], [doi], [arxiv:math/0602193].
  9. Three examples of three-dimensional continued fractions in the sense of Klein.
    C. R. Math. Acad. Sci. Paris 343/1 (2006), 5-7. [Zbl], [MR], [doi], [arxiv:math/0601493].
  10. On a criterion for the existence and uniqueness of an integer triangle with given angles.
    Russian Math. Surveys 61/6 (2006), 1178-1179. [Zbl], [MR], [doi].
  11. On examples of difference operators for {0,1}-valued functions over finite sets.
    Funct. Anal. Other Math. 1/2 (2006), 175-180. [Zbl], [MR], [doi], [arxiv:math/0611940].
  12. Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions.
    Monatsh. Math. 152/3 (2007), 217-249. [Zbl], [MR], [doi], [arxiv:math/0510482].
  13. On an invariant Möbius measure and the Gauss-Kuz'min face distribution.
    Proc. Steklov Inst. 258 (2007), 74-86, Russian Version: Tr. Mat. Inst. Steklova 258 (2007), 79-92. [Zbl], [MR], [doi], [arxiv:math/0610042].
  14. Elementary notions of lattice trigonometry.
    Math. Scand. 102/2 (2008), 161-205. [Zbl], [MR].
  15. On irrational lattice angles.
    Funct. Anal. Other Math. 2/2-4 (2009), 221-239. [Zbl], [MR], [doi].
  16. Constructing multidimensional periodic continued fractions in the sense of Klein.
    Math. Comp. 78/267 (2009), 1687-1711. [MR], [doi], [arxiv:math/0411031].
  17. Bernoulli-Euler numbers and multiboundary singularities of type Bl_n.
    In Fundamental Mathematics in Works of Young Scientists, pages 43-54. Nezavis. Mosk. Univ., Moscow, 2009. [Russian].
  18. (With A. M. Vershik) Rational approximation of maximal commutative subgroups of GL(n,Bbb R).
    J. Fixed Point Theory Appl. 7/1 (2010), 241-263. [MR], [doi].
  19. On the flexibility of Kokotsakis meshes.
    Geom. Dedicata 147 (2010), 15-28. [MR], [doi].
  20. (With F. Doray and J. Schepers) Geometry of configuration spaces of tensegrities.
    Discrete Comput. Geom. 43/2 (2010), 436-466. [MR], [doi].
  21. On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators.
    Math. Notes 88/1-2 (2010), 28-38, Russian version: Mat. Zametki, 88(1), (2010), 30--42. [doi].
  22. Continued fractions and the second Kepler law.
    Manuscripta Matematica 134/1-2 (2011), 157-169. [MR], [doi].
  23. (With A. Sossinski) Energies of knot diagrams.
    Russian J. Math. Phys. 18/3 (2011), 306-317. [doi].

Other publications of Oleg Karpenkov

  1. Vladimir Igorevich Arnold, Internat. Math. Nachrichten (2010).
    [Photo]


    Pre-publications and E-prints of Oleg Karpenkov

    1. On Asymptotic Reducibility in SL(3,Z), abstract.
      http://arxiv.org/abs/1205.4166 , May 2012.
    2. Multidimensional Gauss Reduction Theory for conjugacy classes of SL(n,Z), abstract.
      http://arxiv.org/abs/0711.0830 , May 2012.
    3. Necessary flexibility conditions of semidiscrete surfaces, abstract.
      http://arxiv.org/abs/1004.2420 , October 2011.
    4. On examples of two-dimensional periodic continued fractions, abstract.
      Preprint n.2004-30, Cahiers du Ceremade, UMR 7534, Universite Paris-Dauphine, May 2004.
    5. On the coordinate vector fields of the Lyashko-Loojenga map (in Russian), abstract, 1999.
    [Photo]

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