We prove a generalization of the Poincaré-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the study of bounded homeomorphisms of the open annulus. We prove a fixed point theorem for bounded homeomorphisms and study the special case of those homeomorphis...

A famous theorem of Courcelle states that every problem that is definable in monadic second-order (mso) logic can be solved in linear time on input structures of bounded tree width. While Courcelle’s result is optimal from the algorithmic point of view, this thesis shows how to solve monadic secondorder definable decision, counting, and optimization problems on tree-widthbounded structures opti...

In order to solve domain equations over 1-bounded compact metric spaces, xed points of functors on categories of 1-bounded compact metric spaces are studied. Two categories of 1-bounded compact metric spaces are considered: KMS and KMS E. In both categories, objects are isomorphic if and only if they are isometric. As a consequence, provided that the operation of a domain equation can be extend...

Whether the clique-width of graphs in a certain class is bounded or not is an important question from an algorithmic point of view, since many problems that are NP-hard in general admit polynomial-time solutions when restricted to graphs of bounded clique-width. Over the last few years many classes of graphs have been shown to have bounded clique-width. For many, this parameter has been proved ...

A numerical evaluation of the discrete path integral for pure lattice gravity, with and without higher derivative terms, and using the lattice analog of the DeWitt gravitational measure, shows the existence of a well-behaved ground state for sufficiently strong gravity (G ~ Ge). Close to the continuous critical point separating the smooth from the rough phase of gravity, the critical exponents ...

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...