منابع مشابه
Minkowski Content for Reachable Sets
In 1955, Martin Kneser showed that the Minkowski content of a compact p-rectifiable subset M of Rn is equal to its p-Hausdorff measure: lim t→0,t>0 Ln ` B(M, t) ́ α(n− p) tn−p = H(M). We extend his result to the reachable sets of a linear control system
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A geometric algebra of point sets in the complex plane is proposed, based on two fundamental operations: Minkowski sums and products. Although the (vector) Minkowski sum is widely known, the Minkowski product of two-dimensional sets (induced by the multiplication rule for complex numbers) has not previously attracted much attention. Many interesting applications, interpretations, and connection...
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A random iteration algorithm for graph-directed sets is defined and discussed. Similarly to the Barnsley-Elton’s theorem, it is shown that almost all sequences obtained by this algorithm reflect a probability measure which is invariant with respect to the system of contractions with probabilities.
متن کاملMinkowski product of convex sets and product numerical range
Let K1,K2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a ∈ K1, b ∈ K2}. We show that the set K1K2 is star-shaped if K1 is a line segment or a circular disk. Examples for K1 and K2 are given so that K1 and K2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product num...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1980
ISSN: 0024-3795
DOI: 10.1016/0024-3795(80)90246-3