We study conditions involving the critical set of a regular polynomial endomorphism f∶ℂ2↦ℂ2 under which all complete external rays from infinity for f have well defined endpoints.
We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor D on a projective algebraic variety X to be attracting for a holomorphic map f:X → X.
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.
We present Kazimierz Żorawski's works on iteration - the first works on this topic by a Polish mathematician.
The text gives an account of two special sessions on the Joint Mathematics Meetings (San Antonio, Texas, USA) in January 2015, devoted to Polish mathematics.
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.
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...
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.
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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