We analyze properties of various square-free factorizations in greatest common divisor domains (GCD-domains) and domains satisfying the ascending chain condition for principal ideals (ACCP-domains).

Let X be a nonsingular quasi-projective complex algebraic variety and let E be an algebraic vector bundle on X of rank r ≥ 2. The pullback of E by the blowup of X at a suitably chosen nonsingular subvariety of X of codimension ...

Let F(X, Y ), G(X, Y ) be polynomials of degrees m, n > 0 respectively. We prove, that the set {(x, y) Є R² : F(x, y) = G(x, y) = 0} has at most mn connected components.

Kwantowa teoria decyzji statystycznych jest uogólnieniem klasycznej teorii decyzji statystycznych na struktury niekomutatywne. Spora część dotychczasowych wyników w tej teorii dotyczy struktur skończenie wymiarowych. Celem ...

Let X be an algebraic subset of Rⁿ, and ƒ: X → R a semialgebraic function. We prove that if ƒ is continuous rational on each curve C ⊂ X then: 1) ƒ is arc-analytic, 2) ƒ is continuous rational on X. As a consequence we ...

In this paper we present some new and old properties of divergences and divergence-free derivations.

Let k be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the Łojasiewicz exponent £ (a) of ...