http://hdl.handle.net/11716/5433 2026-04-30T03:06:02Z http://hdl.handle.net/11716/6139 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. 2004-01-01T00:00:00Z http://hdl.handle.net/11716/6138 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. 2004-01-01T00:00:00Z http://hdl.handle.net/11716/6137 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 $1$. 2004-01-01T00:00:00Z http://hdl.handle.net/11716/6136 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 2004-01-01T00:00:00Z