In many applications of tomography one is interested in finding the discontinuities of the unknown piecewise smooth function from the knowledge of the Radon transform of this function. For example, one could think about finding the boundaries of a crack in a solid, say aircraft wing or engine, or a rupture in a tissue in medical diagnostics. The aim of this paper is twofold. First, we want to s...

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that fold-Hopf singularities are O(h)-shifted and turned into fold-Neimark-Sacker points by one-step methods of order p. Then we analyze the effect of discretizations methods on the local bifurcation diagram near BogdanovTakens and fold-Hopf singularities. In particular we prove that the discre...

Wavelet transform is a powerful instrument in catching zero-dimensional singularities. Ridgelets are a powerful instrument in catching and representing monodimensional singularities in bidimensional space. In this paper we propose a hybrid video coder scheme using ridgelet transform for the first approximation of line-edge singularities in displaced frame difference images. We demonstrate the p...

ABSTRACT Finding singular configurations (singularities) of manipulators is obviously important, because these configurations are the ones where the instantaneous kinematics becomes indeterminate. In this paper, singularities of a three degree-of-freedom (DOF) fully parallel planar manipulator are analyzed with the aid of two Jacobian matrices which are expressed through instantaneous centers o...

A contact singularity is a normal singularity (V, 0) together with a holomorphic contact form η on V \ Sing V in a neighbourhood of 0, i.e. η∧(dη) r has no zero, where dim V = 2r + 1. The main result of this paper is that there are no isolated contact singularities.