The purpose of this paper is twofold. First, we provide a short review and summarize results on the robustness of controllability and stabilizability for finite dimensional control problems. We discuss the computation of system radii which provide a measure of robustness. Second, we consider systems which arise as finite difference and finite element approximations to control systems defined by...

To determine the (k, l)-radius of a graph we have to find a set L of l vertices, such that the maximum k-distance of a set K, where |K| = k and L ⊆ K, attains the minimum value in a graph. This notion generalizes the radius, diameter and k-diameter. In this contribution the (k, l)-radius of the wheel Wn is determined for all possible values of parameters k and l.

Charge radii of all magnesium isotopes in the sd shell have been measured, revealing evolution of the nuclear shape throughout two prominent regions of assumed deformation centered on (24)Mg and (32)Mg. A striking correspondence is found between the nuclear charge radius and the neutron shell structure. The importance of cluster configurations towards N=8 and collectivity near N=20 is discussed...

We introduce three natural and well-defined generalizations of maximal Poisson-disk sampling. The first is to decouple the disk-free (inhibition) radius from the maximality (coverage) radius. Selecting a smaller inhibition radius than the coverage radius yields samples which mix advantages of Poisson-disk and uniform-random samplings. The second generalization yields hierarchical samplings, by ...

We consider the problem of computing the outer-radii of point sets. In this problem, we are given integers n, d, k where k ≤ d, and a set P of n points in R. The goal is to compute the outer k-radius of P , denoted by Rk(P ), which is the minimum, over all (d − k)-dimensional flats F , of maxp∈P d(p, F ), where d(p, F ) is the Euclidean distance between the point p and flat F . Computing the ra...

The covering radius of a code is the least r such that the set of balls of radius r around codewords covers the entire ambient space. We introduce a generalization of the notion of covering radius. The m-covering radius of a code is the least radius such that the set of balls of the radius covers all m-tuples of elements in the ambient space. We investigate basic properties of m-covering radii....

In a series of papers [12], [13], [14] based on ideas introduced by Soardi andWoess [17] and Salvatori [15], we have developed tools to compute the norms and/or spectral radii of Markov operators that are invariant under the left action of a group when the action is either transitive or almost transitive (i.e has a compact factor space). In [12], [13], we where concerned with countable homogene...

We extend the isotonic analysis for Wicksell's problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in astronomy. The main result is a version of the Kiefer–Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate n −1 log n faster than n −2/3 log n. The main result is useful ...

The best constraints on dark halo properties of elliptical galaxies come from large radii; however, observations at these radii are difficult due to the faint stellar light and/or sparse kinematic tracers (i.e., globular clusters, planetary nebulae). We present line-of-sight stellar velocity distributions of elliptical galaxy NGC 821 obtained to approximately 100 (over 2 effective radii) with l...