Arcs, balls and spheres that cannot be attractors in $\mathbb {R}^3$

Aspherical manifolds that cannot be triangulated

Although Kirby and Siebenmann [13] showed that there are manifolds which do not admit PL structures, the possibility remained that all manifolds could be triangulated. In the late seventies Galewski and Stern [10] constructed a closed 5–manifold M 5 so that every n–manifold, with n 5, can be triangulated if and only if M 5 can be triangulated. Moreover, M 5 admits a triangulation if and only if...

Needle Variations that Cannot be Summed

A Category Test that Cannot be Manipulated∗

In Dekel and Feinberg (2004) we suggested a test for discovering whether a potential expert is informed of the distribution of a stochastic process. This category test requires predicting a “small”– category I – set of outcomes. In this paper we show that under the continuum hypothesis there is a category test that cannot be manipulated, i.e. such that no matter how the potential expert randomi...

Dissipative solitons that cannot be trapped.

We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states.

Common Tangents to Spheres in R3

We prove that four spheres in R3 have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.