Distance relays are used to protect EHV and HV Transmission lines. Over the past decades many algorithms have emerged for digital distance relays. These are based on the calculation of the transmission line impedance from the relaying to fault points. In this paper a novel method for digital distance relaying is proposed. In the method the tracking procedure is implemented. The method uses the ...

The Hausdorff distance, the Gromov-Hausdorff, the Fréchet and the natural pseudo-distances are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as infρ F (ρ) where F is a suitable functional and ρ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms...

Distance relays are used to protect EHV and HV Transmission lines. Over the past decades many algorithms have emerged for digital distance relays. These are based on the calculation of the transmission line impedance from the relaying to fault points. In this paper a novel method for digital distance relaying is proposed. In the method the tracking procedure is implemented. The method uses the ...

Euclidean geometry on a computer is concerned with the translation of geometric concepts into a discrete world in order to cope with the requirements of representation of abstract geometry on a computer. The basic constructs of digital geometry are digital lines, digital line segments and digitally convex sets. The aim of this paper is to review some approaches for such digital objects. It is s...

We describe homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological en-tropy and that they are actually semi-conjugeted to an algebraic homeomor-phism in the case when the entropy is positive.

Lehmer’s question is equivalent to one about generalized growth rates of Lefschetz numbers of iterated pseudo-Anosov surface homeomorphisms. One need consider only homeomorphisms that arise as monodromies of fibered knots in lens spaces L(n, 1), n > 0. Lehmer’s question for Perron polynomials is equivalent to one about generalized growth rates of words under injective free group endomorphisms.

— Let r > 1 be a real. In this paper, we study piecewise class P Cr circle homeomorphisms with irrational rotation numbers. We give characterizations for such homeomorphisms that are piecewise Cr conjugate to Cr diffeomorphisms. As a consequence, we obtain a criterion of piecewise Cr conjugacy to diophantine rotations. This characterization extends those obtained by Liousse for the PL circle ho...

Given any positive sequence {cn}n∈N, we construct orientation preserving homeomorphisms f : R → R such that Fix(f) = Per(f) = {0}, 0 is Lyapunov stable and lim sup |i(f ,0)| cm = ∞. We will use our results to discuss and to point out some strong di erences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.