Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Sums of squares and the Łojasiewicz exponent

2012/07/B/ST1/03293

Keywords:

Real field polynomial sum of squares Positivstellensatz semialgebraic set Łojasiewicz exponent

Descriptors:

  • ST1_2: Algebra
  • ST1_4: Algebraic and complex geometry
  • ST1_8: Analysis

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

woj. 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 (Y-m-d): 2013-07-08

Project end date (Y-m-d): 2017-07-07

Project duration:: 48 months (the same as in the proposal)

Project status: Project settled

Equipment purchased [PL]

  1. drukarka Brother.
  2. Komputer przenośny notebook wraz z oprogramowaniem (5 000 PLN)

Information in the final report

  • Publication in academic press/journals (25)
  • Book publications / chapters in book publications (2)
  1. Bifurcation values and stability of algebras of bounded polynomials.
    Authors:
    Krzysztof Kurdyka, Maria Michalska, Stanisław Spodzieja
    Academic press:
    Advances in Geometry (rok: 2014, tom: 14, strony: 631-646), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.1515/advgeom-2014-0006, - link to the publication
  2. Convexifying positive polynomials and sums of squares approximation
    Authors:
    Krzysztof Kurdyka, Stanisław Spodzieja
    Academic press:
    SIAM Journal on Optimization (SIOPT) (rok: 2015, tom: 25, strony: 2512–2536), Wydawca: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/140958165 - link to the publication
  3. Cr-right equivalence of analytic functions
    Authors:
    Piotr Migus
    Academic press:
    Demonstratio Mathematica (rok: 2015, tom: 48, strony: 45300), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.1515/dema-2015-0020 - link to the publication
  4. Finite determinacy of non-isolated singularities
    Authors:
    Migus Piotr, Rodak Tomasz, Spodzieja Stanisław
    Academic press:
    Annales Polonici Mathematici (rok: 2016, tom: 117, strony: 197–206), Wydawca: Polish Acad. Sci. Inst. Math.
    Status:
    Published
    DOI:
    10.4064/ap3835-5-2016 - link to the publication
  5. Reduction of a family of ideals
    Authors:
    Tomasz Rodak
    Academic press:
    Kodai Mathematical Journal (rok: 2015, tom: 38, strony: 201-208), Wydawca: Department of Mathematics, Tokyo Institute of Technology
    Status:
    Published
    DOI:
    brak - 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 (rok: 2014, tom: 12, strony: 429-435), Wydawca: Springer
    Status:
    Published
    DOI:
    10.2478/s11533-013-0351-4 - link to the publication
  7. The Łojasiewicz exponent over a field of arbitrary characteristic
    Authors:
    Szymon Brzostowski, Tomasz Rodak
    Academic press:
    Revista Matemática Complutense (rok: 2015, tom: 28, strony: 487–504), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s13163-014-0165-3 - link to the publication
  8. Curves testing boundedness of polynomials on subsets of the real plane
    Authors:
    Maria Michalska
    Academic press:
    Journal of Symbolic Computation (rok: 2013, tom: 56, strony: 107-124), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jsc.2013.04.001 - link to the publication
  9. Local Cr-right equivalence of C(r+1) functions
    Authors:
    Migus Piotr
    Academic press:
    Glasgow Mathematical Journal (rok: 2017, tom: 59, strony: 265–272), Wydawca: Cambridge Univ. Press
    Status:
    Published
    DOI:
    10.1017/S0017089516000161 - link to the publication
  10. Arnold's problem on monotonicity of the Newton number for surface singularities
    Authors:
    Szymon Brzostowski, Tadeusz Krasiński, Justyna Walewska
    Academic press:
    Journal of the Mathematical Society of Japan (rok: 2017, tom: -, strony: 14 pp), Wydawca: Mathematical Society of Japan
    Status:
    Submitted
    DOI:
    brak - link to the publication
  11. 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 (rok: 2013, tom: 137, strony: 718-729), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.bulsci.2013.03.005 - link to the publication
  12. Metric properties of semialgebraic mappings
    Authors:
    Krzysztof Kurdyka, Stanisław Spodzieja, Anna Szlachcińska
    Academic press:
    Discrete & Computational Geometry (rok: 2016, tom: 55, strony: 786-800), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00454-016-9776-4 - link to the publication
  13. Positivstellensatz for homogeneous semialgebraic sets
    Authors:
    Aleksandra Gala-Jaskórzyńska, Krzysztof Kurdyka, Katarzyna Kuta, and Stanisław Spodzieja
    Academic press:
    Archiv der Mathematik (rok: 2015, tom: 105, strony: 405–412), Wydawca: September
    Status:
    Published
    DOI:
    10.1007/s00013-015-0822-x - link to the publication
  14. Sum of squares and the Łojasiewicz exponent at infinity
    Authors:
    Krzysztof Kurdyka, Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja
    Academic press:
    Annales Polonici Mathematici (rok: 2014, tom: 112, strony: 223-237), Wydawca: INSTITUTE OF MATHEMATICS, POLISH ACADEMY OF SCIENCES
    Status:
    Published
    DOI:
    10.4064/ap112-3-2 - link to the publication
  15. The Łojasiewicz exponent of semiquasihomogeneous singularities
    Authors:
    Szymon Brzostowski
    Academic press:
    Bulletin of the London Mathematical Society (rok: 2015, tom: 47, strony: 848-852), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1112/blms/bdv058 - link to the publication
  16. 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 (rok: 2017, tom: 67, strony: 69{83), Wydawca: Łódzkie Towarzystwo Naukowe
    Status:
    Published
    DOI:
    10.26485/0459-6854/2017/67.2/7 - link to the publication
  17. 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 (rok: 2017, tom: 67, strony: 119–131), Wydawca: Łódzkie Towarzystwo Naukowe
    Status:
    Published
    DOI:
    10.26485/0459-6854/2017/67.1/9 - link to the publication
  18. Effective calculations of the multiplicity of polynomial mappings.
    Authors:
    Adam Różycki
    Academic press:
    Bulletin des Sciences Mathématiques (rok: 2014, tom: 138, strony: 343-355), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.bulsci.2013.05.006 - link to the publication
  19. 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 (rok: 2016, tom: 66, strony: 47-64), Wydawca: Łódzkie Towarzystwo Naukowe
    Status:
    Published
    DOI:
    brak - link to the publication
  20. On combinatorial criteria for non-degenerate singularities
    Authors:
    Szymon Brzostowski, Grzegorz Oleksik
    Academic press:
    Kodai Mathematical Journal (rok: 2016, tom: 39, strony: 455–468), Wydawca: Department of Mathematics, Tokyo Institute of Technology
    Status:
    Published
    DOI:
    brak - link to the publication
  21. 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 (rok: 2015, tom: 65, strony: 45555), Wydawca: Łódzkie Towarzystwo Naukowe
    Status:
    Published
    DOI:
    brak - link to the publication
  22. A geometric model of an arbitrary differentially closed field of characteristic zero
    Authors:
    Stanisław Spodzieja
    Academic press:
    Transactions of the American Mathematical Society (rok: 2017, tom: --, strony: 26 pp), Wydawca: American Mathematical Society
    Status:
    Submitted
    DOI:
    brak - link to the publication
  23. Milnor numbers in deformations of homogeneous singularities
    Authors:
    Szymon Brzostowski, Tadeusz Krasiński, Justyna Walewska
    Academic press:
    Bulletin des Sciences Mathématiques (), Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  24. Multiplicity and semicontinuity of the Łojasiewicz exponent
    Authors:
    Tomasz Rodak, Adam Różycki, Stanisław Spodzieja
    Academic press:
    Bulletin of the Polish Academy of Sciences. Mathematics (rok: 2016, tom: 64, strony: 55-62), Wydawca: Polish Acad. Sci. Inst. Math.
    Status:
    Published
    DOI:
    10.4064/ba8041-3-2016 - link to the publication
  25. A formula for the local Łojasiewicz exponent
    Authors:
    Adam Różycki, Stanisław Spodzieja
    Academic press:
    Bulletin des Sciences Mathématiques (), Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  1. Łojasiewicz exponent of overdetermined semialgebraic mappings
    Authors:
    Stanisław Spodzieja, Anna Szlachcińska
    Book:
    Analytic and Algebraic Geometry 2 (rok: 2017, tom: 2, strony: 179–188), Wydawca: 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 (rok: 2013, tom: 1, strony: 95-113), Wydawca: Faculty of Mathematics and Computer Science. University of Łódź
    Status:
    Published
    DOI:
    link to the publication

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