2004, Studia Mathematica 4

Oriented angles in affine space

Thu, 01 Jan 2004 00:00:00 GMT

Oriented angles in affine space Waliszewski, Włodzimierz The concept of a smooth oriented angle in an arbitrary affine space is introduced. This concept is based on a kinematics concept of a run. Also, a concept of an oriented angle in such a space is considered. Next, it is shown that the adequacy of these concepts holds if and only if the affine space, in question, is of dimension 2 or 1.

Seshadri fibrations on algebraic surfaces

Thu, 01 Jan 2004 00:00:00 GMT

Seshadri fibrations on algebraic surfaces Szemberg, Tomasz; Tutaj-Gasińska, Halszka We show that small Seshadri constants in a general point of a surface have strong geometrical implications, the surface is fibered by curves computing the Seshadri constant. We give a sharp bound in terms of the selfintersection of the given ample line bundle and discuss some examples.

Seshadri constants of unisecant line bundles on ruled surfaces

Thu, 01 Jan 2004 00:00:00 GMT

Seshadri constants of unisecant line bundles on ruled surfaces Syzdek, Wioletta The aim of this paper is to show that for any ruled surface $X$ with a unisecant polarization $L ≡ C_0 + μ_0f$ the Seshadri constant of $L$ at every point of $X$ is equal $1$.

Local analytic solutions of a functional equation

Thu, 01 Jan 2004 00:00:00 GMT

Local analytic solutions of a functional equation Smajdor, Andrzej; Smajdor, Wilhelmina All analytic solutions of the functional equation \[|f(r exp(iθ))|^2 + |f(1)|^2 = |f(r)|^2 + |f(exp(iθ))|^2\] in the annulus \[P := {z ∈ C : 1 − ε < |z| < 1 + ε}\] and in the domain \[D := {z = re^{iθ} ∈ C : 1 − ε < r < 1 + ε , θ ∈ (−δ, δ)},\] are found