In this note, we use a reduction by Cornaz and Jost from the graph (max-)coloring problem to the maximum (weighted) stable set problem in order to characterize new graph classes where the graph coloring problem and the more general max-coloring problem can be solved in polynomial time.

Dies ist eine Internet-Sonderausgabe des Aufsatzes „Language-specific encoding in multilingual corpora: Requirements and solutions“ von Jost Gippert (1999). Sie sollte nicht zitiert werden. Zitate sind der Originalausgabe in Multilinguale Corpora: Codierung, Strukturierung, Analyse. 11. Jahrestagung der Gesellschaft für Linguistische Datenverarbeitung (ed. J. Gippert / P. Olivier), Praha 1999, ...

For the Schrr odinger operator on the half line we prove the following results: the mapping from real compactly supported potentials to the associated Jost functions (in some class of entire functions) is one-to-one and onto. Moreover, we prove that such potential is uniquely determined by its bound states and resonances.

We derive estimates of the Hessian of two smooth functions defined on Grassmannian manifold. Based on it, we can derive curvature estimates for minimal submanifolds in Euclidean space via Gauss map as [24]. In this way, the result for Bernstein type theorem done by Jost and the first author could be improved.

In this paper, we systematically investigate the nonlocal Hirota equation with nonzero boundary conditions via Riemann–Hilbert method and multi-layer physics-informed neural networks algorithm. Starting from Lax pair of equation, first give out Jost function, scattering matrix, their symmetry asymptotic behavior. Then, problem are constructed precise formulae N-double poles solutions N-simple w...