One, Two, Infinity

The Planning Spectrum - One, Two, Three, Infinity

Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula φ, which are the paths that are required to satisfy the formula. Two extreme cases are the universal interpretationA.φ, which requires that the formula be satisfied f...

Rational curves with one place at infinity

Let K be an algebraically closed field of characteristic zero. Given a polynomial f(x, y) ∈ K[x, y] with one place at infinity, we prove that either f is equivalent to a coordinate, or the family (fλ)λ∈K has at most two rational elements. When (fλ)λ∈K has two rational elements, we give a description of the singularities of these two elements.

Construction of Affine Plane Curves with One Place at Infinity

Can one detect a non-smooth null infinity?

It is shown that the precession of a gyroscope can be used to elucidate the nature of the smoothness of the null infinity of an asymptotically flat spacetime (describing an isolated body). A model for which the effects of precession in the non-smooth null infinity case are of order r ln r is proposed. By contrast, in the smooth version the effects are of order r. This difference should provide ...

Infinity-inner-products on A-infinity-algebras

In this paper the Hochschild-cochain-complex of an A∞-algebra A with values in an A∞-bimodule M over A and maps between them is defined. Then, an∞-inner-product on A is defined to be an A∞-bimodule-map between A and its dual A∗. There is a graph-complex associated to A∞-algebras with ∞-inner-product.