4 citations · 5 across the 7 of their papers we have counts for
8 papers
On the effective reduction of an ideal
Tomasz Rodak, Adam Różycki, Stanisław Spodzieja
It is well known that in the Noetherian local ring with infinite residue field the reduction of $\mm$-primary ideal may be given in the form of a sufficiently general linear combin…
Effective Bertini theorem and formulas for multiplicity and the local Łojasiewicz exponent
Tomasz Rodak, Adam Różycki, Stanisław Spodzieja
The classical Bertini theorem on generic intersection of an algebraic set with hyperplanes states the following: \emph{Let X be a nonsingular closed subvariety of ,…
Effective Łojasiewicz gradient inequality and finite determinacy of non-isolated Nash function singularities
Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja
Let be a compact semialgebraic set and let be a nonzero Nash function. We give a Solernó and D'Acunto-Kurdyka type estimation of the exp…
Exponential convexifying of polynomials
Krzysztof Kurdyka, Katarzyna Kuta, Stanisław Spodzieja
Let be a convex closed and semialgebraic set and let be a polynomial positive on . We prove that there exists an exponent , such that for any…
A geometric model of an arbitrary differentially closed field of characteristic zero
Stanisław Spodzieja
We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. W…
Convexifying positive polynomials and sums of squares approximation
Krzysztof Kurdyka, Stanisław Spodzieja
We show that if a polynomial is nonnegative on a closed basic semialgebraic set , where $g…
Sufficiency of non-isolated singularities
Piotr Migus, Tomasz Rodak, Stanisław Spodzieja
We give, in terms of the Łojasiewicz inequality, a sufficient condition for -mappings germs of non-isolated singularity at zero to be isotopical.
Metric properties of semialgebraic mappings
Krzysztof Kurdyka, Stanisław Spodzieja, Anna Szlachcińska
We give an effective estimation from above for the local Łojasiewicz exponent for separation of semialgebraic sets and for a semialgebraic mapping on a closed semialgebraic set. We…