1,720,984 research outputs found
An algorithm for reconstructing a convex polygon from its covariogram
Full text linkThe covariogram of a convex body gives the volume of the intersections of with its translates . Matheron conjectured in 1986 that the covariogram determines, up to translations and reflections, a convex body. Recently, Averkov and Bianchi proved Matheron's conjecture for arbitrary planar convex bodies. In this work, the authors give a new algorithm for reconstructing a convex polygon given its covariogram. This algorithm simplifies another one given in [M. Schmitt, in Mathematical morphology in image processing, 151--169, Dekker, New York, 1993]
Approximation from the Exterior of Caratheodory Multifunctions
Full text linkWe approximate a globally measurable multifunction F(t,x) which takes compact values in a euclidean space by means of a decreasing sequence of globally measurable multifunctions F_n(t,x) which are locally lipschitzian with respect to x, in the following cases: F(t,\cdot) is upper semicontinuous and takes connected values, or F(t,\cdot) is continuous
Approximation from the Exterior of Multifunctions with Connected Values
No full textWe approximate an upper semicontinuous multifunction F from a metric space T into the compact, connected subsets of a euclidean space by means of a decreasing sequence ofmultifunctions which are locally lipschitzean with respect to theHausdorff distance
Approximation from the Exterior of a Multifunction with connected Values Defined on an Interval
No full textWe approximate an upper semicontinuous multifunction F(t) from the interval [0,1] into the compact, connected subsets of a euclidean space by means of a decreasing sequence of multifunctions which are lipschitzian with respect to the Hausdorff distance
Some Results about Relaxation of Integral Functionals
No full textWe give a representation formula for the integrand of the relaxed functional of the integral of the Calculus of Variations, in the case in which it is defined on vector functions of a real variable
Hybrid stabilization of planar linear systems with one-dimensional outputs
No full textWe consider a linear control system x'=Ax+Bu with output y=Cx, where x is two-dimensional, u,y are one-dimensional, and give necessary and sufficient conditions in order that it can be stabilized by a hybrid, linear feedback, where the action of the "switch" just depends on the sign of y. We also show, on these conditions, that the use of two control functions is enough for getting the goal
The sum of squared distances under a diameter constraint, in arbitrary dimension
No full textIt has been conjectured by H. S. Witsenhausen that the maximum M(d,n) of over all sets X consistingof n points in the d-dimensional Euclidean space with unit diameter is attained if and only if the points of X are distributed as evenly as possible among the vertices of a regular d-dimensional simplex of edge-length 1. In this paper the authors give a proof of this conjecture
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