Lista publikacji
- Z. Szafraniec, On the division of functions of class C^r by real
analytic functions. Bull. Polish Acad. Sci. 30 (1982),
219-223.
- Z. Szafraniec, On the division of C^r-functions by real analytic
functions. Bull. Polish Acad. Sci. 30 (1982), 225-228.
- Z. Szafraniec, On the division of functions of class C^r by real
analytic functions. Bull. Soc. Math. France 113 (1985),
143-155.
- Z. Szafraniec, On the Euler characteristic of analytic and algebraic
sets. Topology 25 (1986), 411-414.
- Z. Szafraniec, On the topological invariants of germs of analytic
functions. Topology 26 (1987), 235-238.
- Z. Szafraniec, On the Euler characteristic of complex algebraic
varieties. Math. Annalen 280 (1988), 177-183.
- Z. Szafraniec, On the number of branches of a 1-dimensional
semianalytic set. Kodai Math. Journal 11 (1988), 78-85.
- Z. Szafraniec, On the Euler characteristic mod 2 of real projective
varieties. Math. Proc. Cambridge Phil. Soc. 104 (1988),
479-481.
- Z. Szafraniec, The Euler characteristic of algebraic complete
intersections. Jour. reine angew Math. 397 (1989), 194-201.
- Z. Szafraniec, On the Euler characteristic mod 2 of real projective
hypersurfaces. Bull. Polish Acad. Sci. 37 (1989), 103-107.
- Z. Szafraniec, On the number of singular points of a real projective
hypersurface. Math. Annalen 291 (1991), 487-496.
- Z. Szafraniec, Topological invariants of weighted homogeneous
polynomials. Glasgow Math. Journal 33 (1991), 241-245.
- Z. Szafraniec, On topological invariants of vector bundles. Ann.
Polonici Mathematici 56 (1992), 295-301.
- Z. Szafraniec, A formula for the number of branches of one-dimensional
semianalytic sets. Math. Proc. Cambridge Phil. Soc. 112 (1992),
527-534.
- Z. Szafraniec, Topological invariants of real analytic sets,
Rozprawy i Monografie 185, Wydawnictwo Uniwersytetu Gdanskiego,
1993.
- P. Dudziński, A. Łęcki, P. Nowak-Przygodzki, Z. Szafraniec. On the
topological invariance of the Milnor number mod 2. Topology 32
(1993), 573-576.
- 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.
- A. Łęcki, Z. Szafraniec, On bifurcation of periodic solutions for
analytic families of vector fields. Topological Methods in Nonlinear
Analysis 3 (1994), 396-374.
- Z. Szafraniec, A formula for the Euler characteristic of a real
algebraic manifold. Manuscripta Math. 85 (1994), 345-360.
- 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.
- 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.
- Z. Szafraniec, On the topological degree of real polynomial fields.
Glasgow Math. Journal 38 (1996), 221-231.
- M. Izydorek, S. Rybicki, Z. Szafraniec, A note on the
Poincare-Bendixson theorem. Kodai Math. Journal 19 (1996),
145-156.
- A. Parusiński, Z. Szafraniec, Algebraically constructible functions and
signs of polynomials. Manuscripta Math. 93 (1997), 443-456.
- 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.
- 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.
- Z. Szafraniec, Topological degree and quadratic forms. Journal of
Pure and Applied Algebra 141/3 (1999), 299-314.
- Z. Szafraniec, Fundamental class of real algebraic sets. Topology
and Its Applications 111 (2001), 217-225.
- Z. Szafraniec, On topological invariants of real analytic
singularities. Math. Proc. Cambridge Phil. Soc. 130 (2001),
13-24.
- A. Nowel, Z. Szafraniec, On trajectories of analytic gradient vector
fields. Journal of Diff. Equations 184 (2002), 215-223.
- Z. Szafraniec, Topological invariants of real Milnor fibres.
Manuscripta Math. 110 (2003) 2, 159-169.
- A. Nowel, Z. Szafraniec, On trajectories of analytic gradient vector
fields on analytic manifolds. Topological Methods in Nonlinear Analysis
25 (2005), 167-182 .
- A. Dzedzej, Z. Szafraniec, On families of trajectories of an analytic
gradient vector field. Ann. Polonici Mathematici 87 (2005), 99-109.
- A. Nowel, I. Karolkiewicz, Z. Szafraniec, Immersions of spheres and
algebraically constructible functions. Manuscripta Math. 128 (2009), 77-87.
- 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.
- A. Nowel, Z. Szafraniec, On the number of branches of real curve singularities.
Bull. London Math. Soc. 43 (2011), 1004-1020.
- 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
- I. Krzyżanowska, Z. Szafraniec, Polynomial mappings into a Stiefel manifold and immersions.
Houston Journal of Mathematics 40 (2014), 987-1006.
arXiv
- 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
- 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
- Z. Szafraniec, On bifurcations of cusps.
Journal of the Mathematical Society of Japan 71 (2019), 555-567,
DOI -10.2969/jmsj/79217921. Preprint:
arXiv
- Z. Szafraniec, On the family of trajectories of an analytic gradien
flow converging to a critical point.
arXiv
- 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