Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dilation volumes of sets of finite perimeter   This paper analyzes the first order behavior (that is, the right sided
derivative) of the volume of the dilation $A\oplus tQ$ as $t$ converges to
zero. Here $A$ and $Q$ are subsets of $n$-dimensional Euclidean space, $A$ has
finite perimeter and $Q$ is finite. If $Q$ consists of two points only, $x$ and
$x+u$, say, this derivative coincides up to sign with the directional
derivative of the covariogram of $A$ in direction $u$. By known results for the
covariogram, this derivative can therefore be expressed by the cosine transform
of the surface area measure of $A$. We extend this result to finite sets $Q$
and use it to determine the derivative of the contact distribution function
with finite structuring element of a stationary random set at zero. The proofs
are based on approximation of the characteristic function of $A$ by smooth
functions of bounded variation and showing corresponding formulas for them.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat