http://hdl.handle.net/11089/2819 2026-04-04T17:29:23Z http://hdl.handle.net/11089/44503 Baire Category Lower Density Operators with Borel Values Balcerzak, Marek; Hejduk, Jacek; Wachowicz, Artur We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class &#928;<SUP>0</SUP><SUB>3</SUB> which is analogous to the measure case. We also introduce the notion of the Baire category density point of a subset with the Baire property of the Cantor space, and we prove that it generates a lower density operator with Borel values of class &#928;<SUP>0</SUP><SUB>3</SUB>. 2023-01-01T00:00:00Z http://hdl.handle.net/11089/40226 On the lattice of polynomials with integer coefficients: successive minima in L2 (0, 1) Banaszczyk, Wojciech 2020-01-01T00:00:00Z http://hdl.handle.net/11089/40065 Milnor Numbers of Deformations of Semi-Quasi-Homogeneous Plane Curve Singularities Michalska, Maria; Walewska, Justyna The aim of this paper is to show the possible Milnor numbers of deformations of semi-quasi-homogeneous isolated plane curve singularity f. Assuming that f is irreducible, one can write f=∑qα+pβ ≥ pqcαβ xαyβ where cp0c0q≠0, 2≤p<q and p, q are coprime. We show that as Milnor numbers of deformations of f one can attain all numbers from μ(f) to μ(f)−r(p−r), where q≡r(mod p). Moreover, we provide an algorithm which produces the desired deformations. 2019-01-01T00:00:00Z http://hdl.handle.net/11089/39819 An integral formula for Riemannian G-structures with applications to almost Hermitian and almost contact structures Niedziałomski, Kamil For a Riemannian G-structure, we compute the divergence of the vector field induced by the intrinsic torsion. Applying the Stokes theorem, we obtain the integral formula on a closed oriented Riemannian manifold, which we interpret in certain cases. We focus on almost Hermitian and almost contact metric structures. Mathematics Subject Classification 53C10 · 53C24 · 53C43 2019-01-01T00:00:00Z