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Sums of squares and the Łojasiewicz exponent

2012/07/B/ST1/03293

Keywords

Descriptors

  • ST1_2: Algebra
  • ST1_4: Geometria algebraiczna i zespolona
  • ST1_8: Analiza

Panel

ST1 – Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution

Uniwersytet Łódzki, Wydział Matematyki i Informatyki

Voivodeship: łódzkie

Other projects carried out by the institution »

Principal investigator (from the host institution)

dr hab. Stanisław Spodzieja

Number of co-investigators in the project: 4

Call

OPUS 4 – announced on 2012-09-15

Amount awarded
211 440 PLN
Project start date
2013-07-08
Project end date
2017-07-07
Project duration
48 months (the same as in the proposal)
Project status
Project settled

Equipment purchased [PL]

  1. Komputer przenośny notebook wraz z oprogramowaniem. Cost: 5 000 PLN
  2. drukarka Brother.

Information in the final report

Publication in academic press/journals (21)

  1. Convexifying positive polynomials and sums of squares approximation

    Authors:
    Krzysztof Kurdyka, Stanisław Spodzieja
    Academic press:
    SIAM Journal on Optimization (SIOPT) (year: 2015, volume: 25, pages: 2512–2536), Publisher: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/140958165 – link to the publication

  2. Effective Łojasiewicz gradient inequality for generic Nash functions with isolated singularity

    Authors:
    Krzysztof Kurdyka, Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja
    Academic press:
    Bulletin de la Société des Sciences et des Lettres de Łódź. Série: Recherches sur les Déformations (year: 2016, volume: 66, pages: 47-64), Publisher: Łódzkie Towarzystwo Naukowe
    Status:
    Published

  3. Finite determinacy of non-isolated singularities

    Authors:
    Migus Piotr, Rodak Tomasz, Spodzieja Stanisław
    Academic press:
    Annales Polonici Mathematici (year: 2016, volume: 117, pages: 197–206), Publisher: Polish Acad. Sci. Inst. Math.
    Status:
    Published
    DOI:
    10.4064/ap3835-5-2016 – link to the publication

  4. On combinatorial criteria for non-degenerate singularities

    Authors:
    Szymon Brzostowski, Grzegorz Oleksik
    Academic press:
    Kodai Mathematical Journal (year: 2016, volume: 39, pages: 455–468), Publisher: Department of Mathematics, Tokyo Institute of Technology
    Status:
    Published

  5. Effective calculations of the multiplicity of polynomial mappings.

    Authors:
    Adam Różycki
    Academic press:
    Bulletin des Sciences Mathématiques (year: 2014, volume: 138, pages: 343-355), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.bulsci.2013.05.006 – link to the publication

  6. The jump of the Milnor number in the X9 singularity class.

    Authors:
    Szymon Brzostowski, Tadeusz Krasiński
    Academic press:
    Central European Journal of Mathematics (year: 2014, volume: 12, pages: 429-435), Publisher: Springer
    Status:
    Published
    DOI:
    10.2478/s11533-013-0351-4 – link to the publication

  7. Sum of squares and the Łojasiewicz exponent at infinity

    Authors:
    Krzysztof Kurdyka, Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja
    Academic press:
    Annales Polonici Mathematici (year: 2014, volume: 112, pages: 223-237), Publisher: INSTITUTE OF MATHEMATICS, POLISH ACADEMY OF SCIENCES
    Status:
    Published
    DOI:
    10.4064/ap112-3-2 – link to the publication

  8. Bifurcation values and stability of algebras of bounded polynomials.

    Authors:
    Krzysztof Kurdyka, Maria Michalska, Stanisław Spodzieja
    Academic press:
    Advances in Geometry (year: 2014, volume: 14, pages: 631-646), Publisher: De Gruyter
    Status:
    Published
    DOI:
    10.1515/advgeom-2014-0006, – link to the publication

  9. Curves testing boundedness of polynomials on subsets of the real plane

    Authors:
    Maria Michalska
    Academic press:
    Journal of Symbolic Computation (year: 2013, volume: 56, pages: 107-124), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jsc.2013.04.001 – link to the publication

  10. Cr-right equivalence of analytic functions

    Authors:
    Piotr Migus
    Academic press:
    Demonstratio Mathematica (year: 2015, volume: 48, pages: 46031), Publisher: De Gruyter
    Status:
    Published
    DOI:
    10.1515/dema-2015-0020 – link to the publication

  11. The Łojasiewicz exponent of semiquasihomogeneous singularities

    Authors:
    Szymon Brzostowski
    Academic press:
    Bulletin of the London Mathematical Society (year: 2015, volume: 47, pages: 848-852), Publisher: Cambridge University Press
    Status:
    Published
    DOI:
    10.1112/blms/bdv058 – link to the publication

  12. The Łojasiewicz exponent over a field of arbitrary characteristic

    Authors:
    Szymon Brzostowski, Tomasz Rodak
    Academic press:
    Revista Matemática Complutense (year: 2015, volume: 28, pages: 487–504), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s13163-014-0165-3 – link to the publication

  13. Reduction of a family of ideals

    Authors:
    Tomasz Rodak
    Academic press:
    Kodai Mathematical Journal (year: 2015, volume: 38, pages: 201-208), Publisher: Department of Mathematics, Tokyo Institute of Technology
    Status:
    Published
    DOI:
    link to the publication

  14. Extensions of real regular mappings and the Łojasiewicz exponent at infinity

    Authors:
    Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja
    Academic press:
    Bulletin des Sciences Mathématiques (year: 2013, volume: 137, pages: 718-729), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.bulsci.2013.03.005 – link to the publication

  15. Bifurcation values of C^{infty} functions

    Authors:
    Michał Klepczarek
    Academic press:
    Bulletin de la Société des Sciences et des Lettres de Łódź. Série: Recherches sur les Déformations (year: 2017, volume: 67, pages: 69{83), Publisher: Łódzkie Towarzystwo Naukowe
    Status:
    Published
    DOI:
    10.26485/0459-6854/2017/67.2/7 – link to the publication

  16. Effective calculation of the degree of * - covering

    Authors:
    Adam Różycki
    Academic press:
    Bulletin de la Société des Sciences et des Lettres de Łódź. Série: Recherches sur les Déformations (year: 2017, volume: 67, pages: 119–131), Publisher: Łódzkie Towarzystwo Naukowe
    Status:
    Published
    DOI:
    10.26485/0459-6854/2017/67.1/9 – link to the publication

  17. Local Cr-right equivalence of C(r+1) functions

    Authors:
    Migus Piotr
    Academic press:
    Glasgow Mathematical Journal (year: 2017, volume: 59, pages: 265–272), Publisher: Cambridge Univ. Press
    Status:
    Published
    DOI:
    10.1017/S0017089516000161 – link to the publication

  18. On the nondegenerate jumps of the Łojasiewicz exponent

    Authors:
    Oleksik Grzegorz
    Academic press:
    Bulletin de la Société des Sciences et des Lettres de Łódź. Série: Recherches sur les Déformations (year: 2015, volume: 65, pages: 46285), Publisher: Łódzkie Towarzystwo Naukowe
    Status:
    Published

  19. Positivstellensatz for homogeneous semialgebraic sets

    Authors:
    Aleksandra Gala-Jaskórzyńska, Krzysztof Kurdyka, Katarzyna Kuta, and Stanisław Spodzieja
    Academic press:
    Archiv der Mathematik (year: 2015, volume: 105, pages: 405–412), Publisher: September
    Status:
    Published
    DOI:
    10.1007/s00013-015-0822-x – link to the publication

  20. Metric properties of semialgebraic mappings

    Authors:
    Krzysztof Kurdyka, Stanisław Spodzieja, Anna Szlachcińska
    Academic press:
    Discrete & Computational Geometry (year: 2016, volume: 55, pages: 786-800), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00454-016-9776-4 – link to the publication

  21. Multiplicity and semicontinuity of the Łojasiewicz exponent

    Authors:
    Tomasz Rodak, Adam Różycki, Stanisław Spodzieja
    Academic press:
    Bulletin of the Polish Academy of Sciences. Mathematics (year: 2016, volume: 64, pages: 55-62), Publisher: Polish Acad. Sci. Inst. Math.
    Status:
    Published
    DOI:
    10.4064/ba8041-3-2016 – link to the publication

Book publications / chapters in book publications (2)

  1. Łojasiewicz exponent of overdetermined semialgebraic mappings

    Authors:
    Stanisław Spodzieja, Anna Szlachcińska
    Book:
    Analytic and Algebraic Geometry 2 (year: 2017, volume: 2, pages: 179–188), Publisher: Faculty of Mathematics and Computer Science. University of Łódź
    Status:
    Published

  2. On C0-sufficiency of jets

    Authors:
    Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja
    Book:
    Analytic and algebraic geometry (year: 2013, volume: 1, pages: 95-113), Publisher: Faculty of Mathematics and Computer Science. University of Łódź
    Status:
    Published

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