Photo of Dr Oleg Karpenkov

Dr Oleg Karpenkov Dr.

Lecturer in Pure Mathematics Mathematical Sciences

    Publications

    2021

    Continued Fraction approach to Gauss Reduction Theory (Journal article)

    Karpenkov, O. (n.d.). Continued Fraction approach to Gauss Reduction Theory. Retrieved from http://arxiv.org/abs/2107.02687v1

    On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups (Journal article)

    Karpenkov, O. (n.d.). On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups. Retrieved from http://arxiv.org/abs/2101.12707v1

    On a periodic Jacobi-Perron type algorithm (Journal article)

    Karpenkov, O. (n.d.). On a periodic Jacobi-Perron type algorithm. Retrieved from http://arxiv.org/abs/2101.12627v2

    Geometric criteria for realizability of tensegrities in higher dimensions (Journal article)

    Karpenkov, O., & Mueller, C. (2021). GEOMETRIC CRITERIA FOR REALIZABILITY OF TENSEGRITIES IN HIGHER DIMENSIONS. SIAM JOURNAL ON DISCRETE MATHEMATICS, 35(2), 637-660. doi:10.1137/19M1281903

    DOI: 10.1137/19M1281903

    The combinatorial geometry of stresses in frameworks (Journal article)

    Karpenkov, O. (n.d.). The combinatorial geometry of stresses in frameworks. Discrete and Computational Geometry: an international journal of mathematics and computer science. doi:10.1007/s00454-020-00234-8

    DOI: 10.1007/s00454-020-00234-8

    2020

    Equilibrium stressability of multidimensional frameworks (Journal article)

    Karpenkov, O., Müller, C., Panina, G., Servatius, B., Servatius, H., & Siersma, D. (n.d.). Equilibrium stressability of multidimensional frameworks. Retrieved from http://arxiv.org/abs/2009.05469v1

    Generalised Markov numbers (Journal article)

    Karpenkov, O., & van-Son, M. (2020). Generalised Markov numbers. Journal of Number Theory, 213, 16-66. doi:10.1016/j.jnt.2020.01.010

    DOI: 10.1016/j.jnt.2020.01.010

    2019

    Martin Integral Representation for Nonharmonic Functions and Discrete Co-Pizzetti Series (Journal article)

    Boiko, T., & Karpenkov, O. (2019). Martin Integral Representation for Nonharmonic Functions and Discrete Co-Pizzetti Series. MATHEMATICAL NOTES, 106(5-6), 659-673. doi:10.1134/S0001434619110014

    DOI: 10.1134/S0001434619110014

    The Sixth International Conference on Uniform Distribution Theory (UDT 2018) CIRM, Luminy, Marseilles, France, October 1–5, 2018. (Journal article)

    Nair, R., Karpenkov, O., & Verger-Gaugry, J. -L. (2019). The Sixth International Conference on Uniform Distribution Theory (UDT 2018) CIRM, Luminy, Marseilles, France, October 1–5, 2018.. Uniform Distribution Theory. doi:10.2478/UDT-2019–0009

    DOI: 10.2478/UDT-2019–0009

    Generalized Perron Identity for broken lines (Journal article)

    Karpenkov, O., & van-Son, M. (2019). Generalized Perron Identity for broken lines. Journal de Theorie des Nombres de Bordeaux, 31(1), 131-144. doi:10.5802/jtnb.1071

    DOI: 10.5802/jtnb.1071

    Generalized Perron Identity for broken lines (Journal article)

    Karpenkov, O., & Van-Son, M. (2019). Generalized Perron Identity for broken lines. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 31(1), 131-144. Retrieved from http://gateway.webofknowledge.com/

    Approximating reals by rationals of the form a/b^2 (Journal article)

    Karpenkov, O. (n.d.). Approximating reals by rationals of the form a/b^2. Retrieved from http://arxiv.org/abs/math/0610717v2

    Tensegrities on the space of generic functions (Journal article)

    Karpenkov, O. (n.d.). Tensegrities on the space of generic functions. Retrieved from http://arxiv.org/abs/1905.11262v1

    2018

    On Periodic Asymmetric Extrapolation (Journal article)

    Boiko, T., Karpenkov, O., & Rakhimberdiev, B. (2018). On Periodic Asymmetric Extrapolation. MATHEMATICAL NOTES, 104(5-6), 642-654. doi:10.1134/S0001434618110044

    DOI: 10.1134/S0001434618110044

    Geometric Conditions of Rigidity in Nongeneric settings (Chapter)

    Karpenkov, O. (2018). Geometric Conditions of Rigidity in Nongeneric settings. In J. Sidman, A. S. John, & M. Sitharam (Eds.), Handbook of Geometric Constraint Systems Principles. CRC Press.

    Open Problems on Configuration Spaces of Tensegrities (Journal article)

    Karpenkov, O. (2018). Open Problems on Configuration Spaces of Tensegrities. Arnold Mathematical Journal, 4(1), 19-25. doi:10.1007/s40598-018-0080-7

    DOI: 10.1007/s40598-018-0080-7

    2017

    Open problems in geometry of continued fractions (Journal article)

    Karpenkov, O. (n.d.). Open problems in geometry of continued fractions. Retrieved from http://arxiv.org/abs/1712.01450v1

    Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions (Journal article)

    Karpenkov, O., & Ustinov, A. (2017). Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions. Journal of Number Theory, 176, 375-419. doi:10.1016/j.jnt.2016.12.005

    DOI: 10.1016/j.jnt.2016.12.005

    ALEXEI BRONISLAVOVICH SOSSINSKY TURNS 80 (Journal article)

    Chernavski, A., Fuchs, D., Gussein-Zade, S., Ilyashenko, Y., Karpenkov, O., Kirillov, A., . . . Vassiliev, V. (2017). ALEXEI BRONISLAVOVICH SOSSINSKY TURNS 80. MOSCOW MATHEMATICAL JOURNAL, 17(3), 555-558. Retrieved from http://gateway.webofknowledge.com/

    2015

    Finite and infinitesimal flexibility of semidiscrete surfaces (Journal article)

    Karpenkov, O. (2015). Finite and infinitesimal flexibility of semidiscrete surfaces. Arnold Mathematical Journal, 1(04), 403-444. doi:10.1007/s40598-015-0025-3

    DOI: 10.1007/s40598-015-0025-3

    2014

    On offsets and curvatures for discrete and semidiscrete surfaces (Journal article)

    Karpenkov, O., & Wallner, J. (2014). On offsets and curvatures for discrete and semidiscrete surfaces. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 55(1), 207-228. doi:10.1007/s13366-013-0146-6

    DOI: 10.1007/s13366-013-0146-6

    2013

    Mean value property for nonharmonic functions (Journal article)

    Boiko, T., & Karpenkov, O. (n.d.). Mean value property for nonharmonic functions. Retrieved from http://arxiv.org/abs/1309.5040v1

    Euler elasticae in the plane and the Whitney--Graustein theorem (Journal article)

    Avvakumov, S., Karpenkov, O., & Sossinsky, A. (n.d.). Euler elasticae in the plane and the Whitney--Graustein theorem. doi:10.1134/S1061920813030011

    DOI: 10.1134/S1061920813030011

    Geometry of Continued Fractions (Book)

    Karpenkov, O. (2013). Geometry of Continued Fractions (Vol. 26). Heidelberg, Germany: Springer-Verlag GmbH.

    Multidimensional Gauss Reduction Theory for conjugacy classes of SL(n,Z) (Journal article)

    Karpenkov, O. (n.d.). Multidimensional Gauss Reduction Theory for conjugacy classes of SL(n,Z). Retrieved from http://arxiv.org/abs/0711.0830v3

    On stratifications for planar tensegrities with a small number of vertices (Journal article)

    Karpenkov, O., Schepers, J., & Servatius, B. (n.d.). On stratifications for planar tensegrities with a small number of vertices. Retrieved from http://arxiv.org/abs/1201.3557v1

    2012

    On Asymptotic Reducibility in SL(3,Z) (Journal article)

    Karpenkov, O. (n.d.). On Asymptotic Reducibility in SL(3,Z). Retrieved from http://arxiv.org/abs/1205.4166v1

    2011

    Energies of knot diagrams (Journal article)

    Karpenkov, O., & Sossinsky, A. (n.d.). Energies of knot diagrams. doi:10.1134/S1061920811030046

    DOI: 10.1134/S1061920811030046

    Continued fractions and the second Kepler law (Journal article)

    Karpenkov, O. (n.d.). Continued fractions and the second Kepler law. Retrieved from http://arxiv.org/abs/0911.2791v1

    2010

    Vladimir Igorevich Arnold (Journal article)

    Karpenkov, O. (n.d.). Vladimir Igorevich Arnold. Internat. Math. Nachrichten, 2010. Retrieved from http://arxiv.org/abs/1007.0688v1

    On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators (Journal article)

    Karpenkov, O. (n.d.). On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators. Retrieved from http://arxiv.org/abs/0708.1604v1

    On the flexibility of Kokotsakis meshes (Journal article)

    Karpenkov, O. (n.d.). On the flexibility of Kokotsakis meshes. Retrieved from http://arxiv.org/abs/0812.3050v1

    Rational approximation of the maximal commutative subgroups of GL(n,R) (Journal article)

    Karpenkov, O., & Vershik, A. (n.d.). Rational approximation of the maximal commutative subgroups of GL(n,R). Retrieved from http://arxiv.org/abs/0910.3482v1

    Geometry of configuration spaces of tensegrities (Journal article)

    Doray, F., Karpenkov, O., & Schepers, J. (n.d.). Geometry of configuration spaces of tensegrities. Retrieved from http://arxiv.org/abs/0806.4976v2

    2009

    Constructing multidimensional periodic continued fractions in the sense of Klein (Journal article)

    Karpenkov, O. (n.d.). Constructing multidimensional periodic continued fractions in the sense of Klein. Retrieved from http://arxiv.org/abs/math/0411031v3

    On irrational lattice angles (Journal article)

    Karpenkov, O. (2009). On irrational lattice angles. Functional Analysis and Other Mathematics, 2(2-4), 221-239. doi:10.1007/s11853-008-0029-9

    DOI: 10.1007/s11853-008-0029-9

    Bernoulli-Euler numbers and multiboundary singularities of type $B_n^l$ (Journal article)

    Karpenkov, O. (n.d.). Bernoulli-Euler numbers and multiboundary singularities of type $B_n^l$. Retrieved from http://arxiv.org/abs/0910.4046v1

    2008

    Elementary notions of lattice trigonometry (Journal article)

    Karpenkov, O. (n.d.). Elementary notions of lattice trigonometry. 2008. The second part in Funct. Anal. Other Math., 2, 2-4. Retrieved from http://arxiv.org/abs/math/0604129v3

    2007

    On examples of difference operators for $\{0,1\}$-valued functions over finite sets (Journal article)

    Karpenkov, O. (n.d.). On examples of difference operators for $\{0,1\}$-valued functions over finite sets. Functional Analysis and Other Mathematics,vol.1(2), pp.197-202, 2006. doi:10.1007/s11853-007-0010-z

    DOI: 10.1007/s11853-007-0010-z

    Classification of lattice-regular lattice convex polytopes (Journal article)

    Karpenkov, O. (n.d.). Classification of lattice-regular lattice convex polytopes. Functional Analysis and Other Mathematics, vol.1(1), pp.17-35, 2006. doi:10.1007/s11853-007-0002-z

    DOI: 10.1007/s11853-007-0002-z

    Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions (Journal article)

    Karpenkov, O. (n.d.). Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions. Monatshefte fuer Mathematik, 152, 217-249. Retrieved from http://arxiv.org/abs/math/0510482v2

    On invariant Mobius measure and Gauss-Kuzmin face distribution (Journal article)

    Karpenkov, O. (n.d.). On invariant Mobius measure and Gauss-Kuzmin face distribution. Proceedings of the Steklov Institute of Mathematics, vol.258, pp.74-86, 2007. Retrieved from http://arxiv.org/abs/math/0610042v2

    2006

    On existence and uniqueness conditions for an integer triangle with given angles (Journal article)

    Karpenkov, O. N. (2006). On existence and uniqueness conditions for an integer triangle with given angles. Russian Mathematical Surveys, 61(6), 1178-1179. doi:10.1070/rm2006v061n06abeh004374

    DOI: 10.1070/rm2006v061n06abeh004374

    Three examples of three-dimensional continued fractions in the sense of Klein (Journal article)

    Karpenkov, O. (n.d.). Three examples of three-dimensional continued fractions in the sense of Klein. C. R. Acad. Sci. Paris, Ser.I 343, pp.5-7, 2006. Retrieved from http://arxiv.org/abs/math/0601493v1

    Mobius energy of graphs (Journal article)

    Karpenkov, O. (n.d.). Mobius energy of graphs. Math. Notes, vol. 79(2006), no.1, pp.134--138.. Retrieved from http://arxiv.org/abs/math-ph/0509055v1

    2005

    'Classification of three-dimensional multistoried completely hollow convex marked pyramids' (Journal article)

    Karpenkov, O. (2005). 'Classification of three-dimensional multistoried completely hollow convex marked pyramids'. Russian Math. Surveys, 60(1), 165-166.

    2004

    On examples of two-dimensional periodic continued fractions (Journal article)

    Karpenkov, O. N. (n.d.). On examples of two-dimensional periodic continued fractions. Retrieved from http://arxiv.org/abs/math/0411054v1

    On two-dimensional continued fractions for the integer hyperbolic matrices with small norm (Journal article)

    Karpenkov, O. (n.d.). On two-dimensional continued fractions for the integer hyperbolic matrices with small norm. Uspekhi Mat. Nauk 59 (2004), no. 5(359), 149--150; translation in Russian Math. Surveys 59 (2004), no. 5, 959--960. doi:10.1070/RM2004v059n05ABEH000778

    DOI: 10.1070/RM2004v059n05ABEH000778

    On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities (Journal article)

    Karpenkov, O. (n.d.). On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities. Funktsional. Anal. i Prilozhen. 38 (2004), no. 2, 28--37, 95; translation in Funct. Anal. Appl. 38 (2004), no. 2, 102--110. doi:10.1023/B:FAIA.0000034040.08573.22

    DOI: 10.1023/B:FAIA.0000034040.08573.22

    2003

    Energy of a knot: variational principles; Mm-energy (Journal article)

    Karpenkov, O. N. (n.d.). Energy of a knot: variational principles; Mm-energy. Fund. Math. Today, 214-223. Retrieved from http://arxiv.org/abs/math/0411060v1

    'Energy of a knot: some new aspects' (Journal article)

    Karpenkov, O. (2003). 'Energy of a knot: some new aspects'. Fundamental mathematics today, 214-223.

    2002

    Combinatorics of multiboundary singularities B_n^l and Bernoulli-Euler numbers (Journal article)

    Karpenkov, O. (n.d.). Combinatorics of multiboundary singularities B_n^l and Bernoulli-Euler numbers. Funct. Anal. Appl. 36(2002), no 1, 78-81. Retrieved from http://arxiv.org/abs/math/0604024v1

    (Journal article)

    Karpenkov, O. N. (2002). Unknown Title. Functional Analysis and Its Applications, 36(1), 65-67. doi:10.1023/a:1014434318546

    DOI: 10.1023/a:1014434318546