This paper presents SinguLab, a graphical user interface for the singularity analysis of parallel robots. The algorithm is based on Grassmann-Cayley algebra. The proposed tool is interactive and introduces the designer to the singularity analysis performed by this method, showing all the stages along the procedure and eventually showing the solution algebraically and graphically, allowing as we...

Abstract In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc elements such as unphysical matter. The same effects are shown to lead to a resolution of the Schwarzschild singularity. The resulting quantum extension of space-time is likely to have signific...

In families of polynomial functions one may encounter “singularity exchange at infinity” when singular points escape from the space and produce “virtual” singularities of the limit polynomial, which have themselves an influence on the topology. The total quantity of singularity involved in this phenomenon may not be conserved. Inspite of the fact that some of the ingredients do not behave well ...

Recently there has been growing interest in asymptotically anti–de Sitter ~AdS! black holes, motivated by the discovery of the Bañados-Teitelboim-Zanelli ~BTZ! black hole @1# in general relativity ~for reviews see @2,3#! and by the so-called AdS-CFT ~conformal field theory! speculation in string theory @4#. Very recently, Pretorius and Choptuik presented results of fully nonlinear numerical sim...

This is a report on my ongoing joint work with Martin Kalck. The recollement generated by a projective module is described. Application to singularity categories is discussed.

A singularity-robust trajectory generator is presented which, given a prescribed manipulator path and corresponding kinematic solution, computes a feasible trajectory in the presence of kinematic singularities. The resulting trajectory is close to minimum time, subject to individual bounds on joint velocities and accelerations, and follows the path with precision. The algorithm has complexity O...