Lista publikacji






  1. Z. Szafraniec, On the division of functions of class C^r by real analytic functions. Bull. Polish Acad. Sci. 30 (1982), 219-223.

  2. Z. Szafraniec, On the division of C^r-functions by real analytic functions. Bull. Polish Acad. Sci. 30 (1982), 225-228.

  3. Z. Szafraniec, On the division of functions of class C^r by real analytic functions. Bull. Soc. Math. France 113 (1985), 143-155.

  4. Z. Szafraniec, On the Euler characteristic of analytic and algebraic sets. Topology 25 (1986), 411-414.

  5. Z. Szafraniec, On the topological invariants of germs of analytic functions. Topology 26 (1987), 235-238.

  6. Z. Szafraniec, On the Euler characteristic of complex algebraic varieties. Math. Annalen 280 (1988), 177-183.

  7. Z. Szafraniec, On the number of branches of a 1-dimensional semianalytic set. Kodai Math. Journal 11 (1988), 78-85.

  8. Z. Szafraniec, On the Euler characteristic mod 2 of real projective varieties. Math. Proc. Cambridge Phil. Soc. 104 (1988), 479-481.

  9. Z. Szafraniec, The Euler characteristic of algebraic complete intersections. Jour. reine angew Math. 397 (1989), 194-201.

  10. Z. Szafraniec, On the Euler characteristic mod 2 of real projective hypersurfaces. Bull. Polish Acad. Sci. 37 (1989), 103-107.

  11. Z. Szafraniec, On the number of singular points of a real projective hypersurface. Math. Annalen 291 (1991), 487-496.

  12. Z. Szafraniec, Topological invariants of weighted homogeneous polynomials. Glasgow Math. Journal 33 (1991), 241-245.

  13. Z. Szafraniec, On topological invariants of vector bundles. Ann. Polonici Mathematici 56 (1992), 295-301.

  14. Z. Szafraniec, A formula for the number of branches of one-dimensional semianalytic sets. Math. Proc. Cambridge Phil. Soc. 112 (1992), 527-534.

  15. Z. Szafraniec, Topological invariants of real analytic sets, Rozprawy i Monografie 185, Wydawnictwo Uniwersytetu Gdanskiego, 1993.

  16. P. Dudziński, A. Łęcki, P. Nowak-Przygodzki, Z. Szafraniec. On the topological invariance of the Milnor number mod 2. Topology 32 (1993), 573-576.

  17. A. Łęcki, Z. Szafraniec, Applications of the Eisenbud&Levine's theorem to real algebraic geometry. Computational Algebraic Geometry Progr. in Math. 109, Birkhauser 1993, pp. 177-184.

  18. A. Łęcki, Z. Szafraniec, On bifurcation of periodic solutions for analytic families of vector fields. Topological Methods in Nonlinear Analysis 3 (1994), 396-374.

  19. Z. Szafraniec, A formula for the Euler characteristic of a real algebraic manifold. Manuscripta Math. 85 (1994), 345-360.

  20. E. Becker, J.-P. Cardinal, M.-F. Roy, Z. Szafraniec, Multivariate Bezoutians, Kronecker symbol and Eisenbud&Levine formula. Proceedings of MEGA 94 Conference. Progr. in Math. 143, Birkhauser 1996, pp. 79-104.

  21. A. Łęcki, Z. Szafraniec, An algebraic method for calculating the topological degree. Topology in Nonlinear Analysis, Banach Center Publications 35, Polish Academy of Sciences, Warszawa 1996, pp. 73-83.

  22. Z. Szafraniec, On the topological degree of real polynomial fields. Glasgow Math. Journal 38 (1996), 221-231.

  23. M. Izydorek, S. Rybicki, Z. Szafraniec, A note on the Poincare-Bendixson theorem. Kodai Math. Journal 19 (1996), 145-156.

  24. A. Parusiński, Z. Szafraniec, Algebraically constructible functions and signs of polynomials. Manuscripta Math. 93 (1997), 443-456.

  25. Z. Szafraniec, Some congruence for the topological degree for families of polynomial mappings. Topological Methods in Nonlinear Analysis, Gdansk Scientific Society, Gdansk 1997, pp.43-48.

  26. A. Parusiński, Z. Szafraniec, On the Euler characteristic of fibres of real polynomial maps. Singularities Symposium - Lojasiewicz 70, Banach Center Publications 44, Polish Academy of Sciences, Warszawa 1998, pp. 175-182.

  27. Z. Szafraniec, Topological degree and quadratic forms. Journal of Pure and Applied Algebra 141/3 (1999), 299-314.

  28. Z. Szafraniec, Fundamental class of real algebraic sets. Topology and Its Applications 111 (2001), 217-225.

  29. Z. Szafraniec, On topological invariants of real analytic singularities. Math. Proc. Cambridge Phil. Soc. 130 (2001), 13-24.

  30. A. Nowel, Z. Szafraniec, On trajectories of analytic gradient vector fields. Journal of Diff. Equations 184 (2002), 215-223.

  31. Z. Szafraniec, Topological invariants of real Milnor fibres. Manuscripta Math. 110 (2003) 2, 159-169.

  32. A. Nowel, Z. Szafraniec, On trajectories of analytic gradient vector fields on analytic manifolds. Topological Methods in Nonlinear Analysis 25 (2005), 167-182 .

  33. A. Dzedzej, Z. Szafraniec, On families of trajectories of an analytic gradient vector field. Ann. Polonici Mathematici 87 (2005), 99-109.

  34. A. Nowel, I. Karolkiewicz, Z. Szafraniec, Immersions of spheres and algebraically constructible functions. Manuscripta Math. 128 (2009), 77-87.

  35. A. Nowel, I. Karolkiewicz, Z. Szafraniec, An algebraic formula for the intersection number of a polynomial immersion. Journal of Pure and Applied Algebra 214 (2010), 269-280.

  36. A. Nowel, Z. Szafraniec, On the number of branches of real curve singularities. Bull. London Math. Soc. 43 (2011), 1004-1020.

  37. I. Krzyżanowska, Z. Szafraniec, On polynomial mappings from the plane to the plane. Journal of the Mathematical Society of Japan 66 (2014), 805-818. arXiv

  38. I. Krzyżanowska, Z. Szafraniec, Polynomial mappings into a Stiefel manifold and immersions. Houston Journal of Mathematics 40 (2014), 987-1006. arXiv

  39. J. Bobowik, Z. Szafraniec, Counting signed swallowtails of polynomial selfmaps of R^3. Manuscripta Math. 151 (2016), 209-221. DOI - 10.1007/s00229-016-0832-4. Preprint: Mappings from R^3 to R^3 and signs of swallowtails. arXiv

  40. Z. Szafraniec, Counting indices of critical points of rank two of polynomial selfmaps of R^4. Journal of Pure and Applied Algebra 221 (2017), 1449-1457, DOI - 10.1016/j.jpaa.2016.10.004. Preprint: arXiv

  41. Z. Szafraniec, On bifurcations of cusps. Journal of the Mathematical Society of Japan 71 (2019), 555-567, DOI -10.2969/jmsj/79217921. Preprint: arXiv

  42. Z. Szafraniec, On the family of trajectories of an analytic gradien flow converging to a critical point. arXiv

  43. Z. Szafraniec, On the stable set of an analytic gradient flow. Journal of Mathematical Analysis and Applications 503 (2021), 125321, DOI -10.1016/j.jmaa.2021.125321. Preprint: arXiv