Papers by Alexander Khrabrov

Research papers

• Khrabrov A. I. Comparison of some distances between sums of $\ell^p$ spaces. //
  Functional Analysis and Its Applications, Vol. 38, No. 1, P. 91--94, 2004.
  Russian version
• Khrabrov A. I. Estimates of distance between sum $\ell^p_n$-spaces, II. //
  Zapiski Nauchn. Semin. POMI. Vol. 303, 2003, P. 203--217.
  Russian version
• Khrabrov A. I. Distances between spaces with unconditional bases //
  Function theory and mathematical analysis. J. Math. Sci. (New York), Vol. 107, 2001, No 3, P. 3952--3962.
  Russian version     Preliminary english version
• Khrabrov A. I. Generalized volume ratios and the Banach--Mazur distance //
  Math. Notes, Vol. 70, No 6, 2001. P. 838--846.
  Russian version     Preliminary english version
• Khrabrov A. I. Extremal volume ratios for the sums of normed spaces //
  Function theory and partial differential equations. J. Math. Sci. (New York), Vol. 105, 2001, No 5, P. 2485--2494.
  Russian version     Preliminary english version
• Khrabrov A. I. Estimates of distances between the sums of spaces $\ell^p_n$ //
  Vestnik St. Petersburg Univ. Math. 2000, Vol. 33. No 3. P. 45--50.
  Russian version

Popular papers

• •à ¡à®¢ €. ˆ. Shapiro inequality (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2009. Nevsky Dialekt, St Petersburg, 2010, P. 130--158.
• Khrabrov A. I. Plank problem (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2009. Nevsky Dialekt, St Petersburg, 2009, P. 114--146.
• Khrabrov A. I. Linear algebra, polynomials and combinatorics (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2007. Nevsky Dialekt, St Petersburg, 2007, P. 131--152.
• Khrabrov A. I. Complex numbers and polynomials (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2006. Nevsky Dialekt, St Petersburg, 2006, P. 131--165.
• Khrabrov A. I. An elementary introduction to the majorization theory (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2000 - 2002. Nevsky Dialekt, St Petersburg, 2006, P. 382--423.
• Khrabrov A. I. Discrete harmonic functions (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2005. Nevsky Dialekt, St Petersburg, 2005, P. 112--145.
• Khrabrov A. I. Schweitzer inequality (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2005. Nevsky Dialekt, St Petersburg, 2005, P. 89--96.
  Russian version
• Khrabrov A. I. Dirichlet theorem and uniformly distributed sequences (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2004. Nevsky Dialekt, St Petersburg, 2004, P. 170--217.
• Khrabrov A. I. Grimm hypothesis. (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2004. Nevsky Dialekt, St Petersburg, 2004, P. 116--119.
  Russian version
• Khrabrov A. I. Periodic fractions. (Russian) //
  Computer instruments in the education, No 6, 2004.
  To the journal page
• Khrabrov A. I. Cauchy--Bunyakovsky inequality (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2003. Nevsky Dialekt, St Petersburg, 2003, P. 118--152.
  Russian version
• Khrabrov A. I. Extremal properties of Chebyshev polynomials (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2003. Nevsky Dialekt, St Petersburg, 2003, P. 113--118.
• Khrabrov A. I. Around mongolian inequality (Russian) //
  Matemat. prosv., Ser. 3, 2003, Vol. 7, P. 149--162.
  Russian version (zipped ps file)
  Russian version (zipped pdf file)
• Khrabrov A. I. Around mongolian inequality (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2002. Nevsky Dialekt, St Petersburg, 2002, P. 146--167.
  Russian version
• Khrabrov A. I. Chebyshev polynomials and recurrence relation (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2001.
  Izdat. St Petersburg State Univ., St Petersburg, 2001. P. 137--146.
  Russian version
  Reprinted at St Petersburg mathematical olympiad, 2000 — 2002.
  Nevsky Dialekt, St Petersburg, 2006, P. 349--359.
• Khrabrov A. I. Classical inequalities and its reversals (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 2000.
  Izdat. St Petersburg State Univ., St Petersburg, 2000. P. 96--106.
  Russian version
  Reprinted with correction and insertion at St Petersburg mathematical olympiad, 2000 — 2002.
  Nevsky Dialekt, St Petersburg, 2006, P. 424--439.
• Khrabrov A. I. Proofs of inequalities using quasilinearization method. (Russian) //
  Appendix to: St Petersburg mathematical olympiad, 1999.
  Izdat. St Petersburg State Univ., St Petersburg, 1999. P. 81--87.
  Russian version
  Reprinted at St Petersburg mathematical olympiad, 2000 — 2002.
  Nevsky Dialekt, St Petersburg, 2006, P. 374--381.
• Khrabrov A. I.
  Selected problems from mathematical olympiad (Russian)
  Russian version

Olympiad books

• Berlov S. L., Khrabrov A. I., Kokhas K. P., Ivanov S. V., Petrov F. V., Smirnov A. V.
  St Petersburg mathematical olympiad, 2010. (Russian)
  Nevsky Dialekt, St Petersburg, 2010. 160 pp.
• Khrabrov A. I., Kokhas K. P., Petrov F. V., Berlov S. L.
  St Petersburg mathematical olympiad, 2009. (Russian)
  Nevsky Dialekt, St Petersburg, 2009. 160 pp.
• Berlov S. L., Kokhas K. P., Khrabrov A. I., Ivanov S. V., Karpov D. V., Petrov F. V.
  St Petersburg mathematical olympiad, 2008. (Russian)
  Nevsky Dialekt, St Petersburg, 2008. 126 pp.
• Petrov F. V., Kokhas K. P., Berlov S. L., Khrabrov A. I., Bakharev F. L., Ivanov S. V.,
  Rostovsky D. A.
  St Petersburg mathematical olympiad, 2007. (Russian)
  Nevsky Dialekt, St Petersburg, 2007. 156 pp.
• Ivanov S. V., Kokhas K. P., Khrabrov A. I., Berlov S. L., Karpov D. V., Petrov F. V.
  St Petersburg mathematical olympiad, 2003 — 2005. (Russian)
  Nevsky Dialekt, St Petersburg, 2007. 574 pp.
• Khrabrov A. I., Ivanov S. V., Berlov S. L., Bakharev F. L., Karpov D. V., Kokhas K. P.,
  Petrov F. V.
  St Petersburg mathematical olympiad, 2006. (Russian)
  Nevsky Dialekt, St Petersburg, 2006. 190 pp.
• Kokhas K. P., Khrabrov A. I., Berlov S. L., Ivanov S. V., Karpov D. V., Petrov F. V.
  St Petersburg mathematical olympiad, 2000 — 2002. (Russian)
  Nevsky Dialekt, St Petersburg, 2006. 420 pp.
• Kokhas K. P., Khrabrov A. I., Berlov S. L., Ivanov S. V., Karpov D. V., Petrov F. V.
  St Petersburg mathematical olympiad, 2005. (Russian)
  Nevsky Dialekt, St Petersburg, 2005. 160 pp.
• Kokhas K. P., Khrabrov A. I., Berlov S. L., Ivanov S. V., Karpov D. V., Petrov F. V.
  St Petersburg mathematical olympiad, 2004. (Russian)
  Nevsky Dialekt, St Petersburg, 2004. 224 pp.
• Kokhas K. P., Ivanov S. V., Khrabrov A. I., Berlov S. L., Karpov D. V., Petrov F. V.
  St Petersburg mathematical olympiad, 2003. (Russian)
  Nevsky Dialekt, St Petersburg, 2003. 224 pp.
• Kokhas K. P., Ivanov S. V., Berlov S. L., Khrabrov A. I., Karpov D. V., Petrov F. V.
  St Petersburg mathematical olympiad, 2002. (Russian)
  Nevsky Dialekt, St Petersburg, 2002. 192 pp.
• Berlov S. L., Ivanov S. V., Karpov D. V., Kokhas K. P., Khrabrov A. I., Petrov F. V.
  St Petersburg mathematical olympiad, 2001. (Russian)
  Izdat. St Petersburg State Univ., St Petersburg, 2001. 146 pp.
• Berlov S. L., Ivanov S. V., Karpov D. V., Kokhas K. P., Khrabrov A. I., Petrov F. V.
  St Petersburg mathematical olympiad, 2000. (Russian)
  Izdat. St Petersburg State Univ., St Petersburg, 2000. 108 pp.
• Berlov S. L., Ivanov S. V., Karpov D. V., Kokhas K. P., Khrabrov A. I.
  St Petersburg mathematical olympiad, 1999. (Russian)
  Izdat. St Petersburg State Univ., St Petersburg, 1999. 88 pp.

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