Parallel manipulators which are singular with respect to the Schönflies motion group X(a) are called Schönflies-singular, or more precisely X(a)-singular, where a denotes the direction of the rotary axis. A special class of such manipulators are architecturally singular ones because they are singular with respect to any Schönflies group. Another remarkable set of Schönfliessingular planar paral...

We consider the quadratic family of complex maps given by qc(z) = z 2 + c where c is the center of a hyperbolic component in the Mandelbrot set. Then, we introduce a singular perturbation on the corresponding bounded superattracting cycle by adding one pole to each point in the cycle. When c = −1 the Julia set of q−1 is the well known basilica and the perturbed map is given by fλ(z) = z 2 − 1 +...

We show that the set of singular holomorphic foliations on projective spaces with split tangent sheaf and good singular set is open in the space of holomorphic foliations. We also give a cohomological criterion for the rigidity of holomorphic foliations induced by group actions and prove the existence of rigid codimension one foliations of degree n − 1 on P for every n ≥ 3.

The aim of this note is to investigate the size of the singular set of a general class of free interface problems. We show porosity of the singular set, obtaining as a corollary that both its Hausdorff and Minkowski dimensions are strictly smaller than n− 1.

It is well known that on every compact 3-manifold there is a C flow displaying a singular-hyperbolic isolated set which has no periodic orbits [BDV], [M1]. By contrast, in this paper we prove that every singular-hyperbolic attracting set of a C flow on a compact 3manifold has a periodic orbit. 2000 Math. Subj. Class. Primary: 37D30; Secondary: 37D45.

An S-type singular value inclusion set for rectangular tensors is given. Based on the set, new upper and lower bounds for the largest singular value of nonnegative rectangular tensors are obtained and proved to be sharper than some existing results. Numerical examples are given to verify the theoretical results.