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Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields

Małgorzata Stawiska — 2010

Commentationes Mathematicae

We study asymptotics of integrals of certain rational functions that depend on parameters in a field K of characteristic zero. We use formal power series to represent the integral and prove certain identities about coefficients of this series following from the generalized Vandermonde determinant expansion. Our result can be viewed as a parametric version of a classical theorem of Liouville. We also give some applications.

Notes on the book by Arthur Allen "The fantastic laboratory of Dr. Weigl".

Małgorzata Stawiska-Friedland — 2014

Antiquitates Mathematicae

This is a review of Arthur Allen's book "The fantastic laboratory of Dr. Weigl" about the lives and work of two Polish microbiologists Rudolf Weigl and Ludwik Fleck, in particular about their efforts in creating a vaccine against typhus and their fates during World War II. The remarks concern mainly the community of Polish mathematicians of the 1st half of the 20th century and its description by the author.

Some approximation problems in semi-algebraic geometry

Shmuel FriedlandMałgorzata Stawiska — 2015

Banach Center Publications

In this paper we deal with a best approximation of a vector with respect to a closed semi-algebraic set C in the space ℝⁿ endowed with a semi-algebraic norm ν. Under additional assumptions on ν we prove semi-algebraicity of the set of points of unique approximation and other sets associated with the distance to C. For C irreducible algebraic we study the critical point correspondence and introduce the ν-distance degree, generalizing the notion developed by other authors for the Euclidean norm. We...

Weighted pluripotential theory on compact Kähler manifolds

Maritza M. BrankerMałgorzata Stawiska — 2009

Annales Polonici Mathematici

We introduce a weighted version of the pluripotential theory on compact Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behavior under holomorphic maps. We also develop a homogeneous version of the weighted theory and establish a generalization of Siciak's H-principle.

Lelong classes on toric manifolds and a theorem of Siciak

Maritza M. BrankerMałgorzata Stawiska — 2012

Annales Polonici Mathematici

We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.

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