XXV. mezinárodní kolokvium o regionálních vědách

Title in English: 25th International Colloquium on Regional Sciences: Conference proceedings The conference proceedings consists of papers presented at the 25th International Colloquium on Regional Sciences that was organized by Department of Regional Economics and Administration FEA MU. It contains 57 articles arranged by topic. The individual articles deal with e.g. socioeconomic disparities among regions, regional policy, territory attractiveness, tourism, or regional public administration

Integrals and variational multipliers of second-order ordinary differential equations

summary:Summary: Here, a relation between integrals and variational multipliers of a system of second-order ordinary differential equations is studied. A simple necessary and sufficient local condition for the existence of a multiplier is given

Lagrange functions generating Poisson manifolds of geodesic arcs

summary:Let $X$ a smooth finite-dimensional manifold and $W_\Gamma(X)$ the manifold of geodesic arcs of a symmetric linear connection $\Gamma$ on $X$. In a previous paper [Differential Geometry and Applications (Brno, 1995) 603-610 (1996; Zbl 0859.58011)] the author introduces and studies the Poisson manifolds of geodesic arcs, i.e. manifolds of geodesic arcs equipped with certain Poisson structure. In this paper the author obtains necessary and sufficient conditions for that a given Lagrange function generates a Poisson manifold of geodesic arcs. These conditions are formulated in terms of tangent Frobenius algebras