http://hdl.handle.net/11716/5435 2026-04-09T11:47:33Z 2026-04-09T11:47:33Z Chmieliński, Jacek http://hdl.handle.net/11716/6845 2020-02-17T09:37:59Z 2007-01-01T00:00:00Z

11th International Conference on Functional Equations and Inequalities, Będlewo, September 17-23, 2006 Chmieliński, Jacek

2007-01-01T00:00:00Z Mityushev, Vladimir http://hdl.handle.net/11716/6844 2020-02-17T09:34:19Z 2007-01-01T00:00:00Z

Boundary value problem and functional equations for overlapping disks Mityushev, Vladimir We compare applications of the method of functional equations to boundary value problem for circular multiply connected domains and to circular polygons generated by overlapping disks. The second part of the paper is devoted rather to the statement of a problem than its resolution.

2007-01-01T00:00:00Z Híc, Pavel Pokorný, Milan http://hdl.handle.net/11716/6843 2023-05-16T15:37:12Z 2007-01-01T00:00:00Z

Randomly $C_n ∪ C_m$ graphs Híc, Pavel; Pokorný, Milan A graph G is said to be a randomly H graph if and only if any subgraph of G without isolated vertices, which is isomorphic to a subgraph of H, can be extended to a subgraph F of G such that F is isomorphic to H. In this paper the problem of randomly H graphs, where $H = C_n ∪ C_m, m ≠ n$, is discussed.

2007-01-01T00:00:00Z Syzdek, Wioletta http://hdl.handle.net/11716/6842 2023-05-16T15:39:55Z 2007-01-01T00:00:00Z

Submaximal Riemann-Roch expected curves and symplectic packing Syzdek, Wioletta We study Riemann–Roch expected curves on $P^1 × P^1$ in the context of the Nagata–Biran conjecture. This conjecture predicts that for a sufficiently large number of points multiple points Seshadri constants of an ample line bundle on algebraic surface are maximal. Biran gives an effective lower bound $N_0$ . We construct examples verifying to the effect that the assertions of the Nagata–Biran conjecture can not hold for small number of points. We discuss cases where our construction fails. We observe also that there exists a strong relation between Riemann–Roch expected curves on $P^1 × P^1$ and the symplectic packing problem. Biran relates the packing problem to the existence of solutions of certain Diophantine equations. We construct such solutions for any ample line bundle on $P^1 × P^1$ and a relatively small number of points. The solutions geometrically correspond to Riemann–Roch expected curves. Finally we discuss in how far the Biran number $N_0$ is optimal in the case of $P^1 × P^1$. In fact, we conjecture that it can be replaced by a lower number and we provide an evidence justifying this conjecture.

2007-01-01T00:00:00Z