Signed Chord Length Distribution. I

Abstract

In this paper is discussed an application of signed measures (charges) to description of segment and chord length distributions in nonconvex bodies. The signed distribution may naturally appears due to definition via derivatives of nonnegative autocorrelation function simply related with distances distribution between pairs of points in the body. In the work is suggested constructive geometrical interpretation of such derivatives and illustrated appearance of "positive" and "negative" elements similar with usual Hanh-Jordan decomposition in measure theory. The construction is also close related with applications of Dirac method of chords.

LaTeX2e, 24 pp, 18 fig (8 EPS files), part I (technicalities), v2: few corrections in equations and figures, v3: typos and bookmarks, for version in Russian, 25 pp, PDF and DjVu, see http://friedmann.objectis.net/Members/vlasov/hordes

References in corpus (2)

• Averaged residence times of stochastic motions in bounded domains
• Some questions of Monte-Carlo modeling on nontrivial bundles

Cited by in corpus (1)

• Extension of Dirac's chord method to the case of a nonconvex set by use of quasi-probability distributions