Displaying similar documents to “An upper estimation for the eigenfrequencies of vibrating Liapunoff bodies (first boundary value problem).”

On set covariance and three-point test sets

Jan Rataj (2004)

Czechoslovak Mathematical Journal

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The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of ℝ d is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives...

Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

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In some recent work, fractal curvatures C k f ( F ) and fractal curvature measures C k f ( F , · ) , k = 0 , ... , d , have been determined for all self-similar sets F in ℝ d , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent...