The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tesselation of its universal covering, the hyperbolic space H. The tesselation is analysed with tools from hyperbolic crystallography. Actions on H of groups/subgroups are identified for SU(1, 1), for a hyperbolic C...

This paper presents a complete solution to an extended H = control problem for a generalized plant comprising a physical system cascaded with weights containing poles in the closed right half-plane. Necessary and su$cient conditions for a solution to exist are obtained which guarantee closed-loop stability of the physical system and controller as well as achieving the H = norm constraint on the...

The H∞ control problem for linear discrete-time descriptor systems which are of high index and possibly non-regular is considered. The goal is to compute a descriptor feedback such that the closed loop system is stable, causal, and H∞ norm bounded by a prescibed real number. In a recent solution of this problem, where causality is established by a preliminary feedback and where stability and H∞...

Let H be an abstract group and let C be a variety of finite groups (i.e., a class of finite groups closed under taking subgroups, quotients and finite direct products); for example the variety of all finite p-groups, for a fixed prime p. Consider the smallest topology on H such that all the homomorphism H −→ C from H to any group C ∈ C (endowed with the discrete topology) is continuous. We refe...

The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tesselation of its universal covering, the hyperbolic space H. The tesselation is analysed with tools from hyperbolic crystallography. Actions on H of groups/subgroups are identified for SU(1, 1), for a hyperbolic C...

We use convergence theory as the framework for studying Hclosed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space are pretopological notions. Additionally, we define a version of H-closedness for pretopological spaces and investigate the properties of such a space.

In this note we propose a new way of constructing compact 7-manifolds with a closed G 2-structure. As a result we find a first example of a closed G 2-structure on S 3 × S 4. We also prove that any integral closed G 2-structure on a compact 7-manifold M 7 can be obtained by embedding M 7 to a universal space (W 3(80+8.C 3 8) , h). MSC: 53C10, 53C42 Key words: closed G 2-structures, submanifolds...

It is shown that the so-called \pure" mixed H 2 =H 1 optimization problem does not have a \good" solution. More precisely, a class of non-singular \pure" mixed H 2 =H 1 optimization problems (minimization of an L 2-norm subject to a Youla parameterization and an L 1 constraint) is considered. It is shown that, whenever the L 1 constraint is not redundant, the optimal controller has innnite orde...