Signed Chord Length Distribution. I

Details Signed Chord Length Distribution. I Signed Chord Length Distribution. I

2007-11-29

arxiv.org/abs/0711.4734v3

Physics

Mathematical Physics

LaTeX2e, 24 pp, 18 fig (8 EPS files), part I (technicalities), v2: few corrections in equations and figures, v3: typos and boo

Scientific paper

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.

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