Zonotopes are a convenient abstract domain for the precise analysis of programs with numerical variables. Compared to the domain of convex polyhedra, it is less expensive and may easily handle non-linear assignments. However, the classical join operator of this abstract domain does not always preserve linear invariants, unlike the convex hull. We present a global join operator that preserves so...

We report on several abstract interpretation strategies that are designed to improve the performance of HyTech, a symbolic model checker for linear hybrid systems. We (1) simultaneously compute the target region from di erent directions, (2) conservatively approximate the target region by dropping constraints, and (3) iteratively re ne the approximation until su cient precision is obtained. We ...

0. Introduction. If (X,≤) is a partially ordered set and A ⊆ X, then the decreasing hull d(A) of A in X is defined to be d(A) = {x ∈ X : x ≤ a for some a ∈ A}. If the poset X is not understood from the context, we may write dX(A). A subset A ⊆ X is a decreasing set if A = d(A). The intersection or union of any collection of decreasing sets in X is again a decreasing set in X. The increasing hul...

We generalize Moore’s nonstandard proof of the Spectral theorem for bounded self-adjoint operators to case unbounded operators. The key step is use a definition hull an internally operator due Raab.

We denote the numerical range of the normal operator T by W (T). A characterization is given to the points inW (T) that lie on the boundary. The collection of such boundary points together with the interior of the the convex hull of the spectrum of T will then be the set W (T). Moreover, it is shown that such boundary points reveal a lot of information about the normal operator. For instance, s...

The group generated by the kinematic dynamo operator in the space of continuous divergence-free sections of the tangent bundle of a smooth manifold is studied. As shown in previous work, if the underlying Eulerian flow is aperiodic, then the spectrum of this group is obtained from the spectrum of its generator by exponentiation, but this result does not hold for flows with an open set of period...

The main purpose of this paper is to establish a new variant the Hildebrandt?s theorem for Weyl spectrum in separable Banach space. This asserts that convex hull an operator T equal intersection numerical spectra operators are similar T.

In this paper, we analyze the strength of split cuts in a lift-and-project framework. We first observe that the Lovász-Schrijver and Sherali-Adams lift-and-project operator hierarchies can be viewed as applying specific 0-1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts. More precisely, we define a new operator t...