Generalized O(n) -gradients for connections on Lie algebroids are derived.

We recall Labatie's effective method of solving polynomial equations with two unknowns by using the Euclidean algorithm.

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 ...