Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Restrictions of Harmonic Functions on the Sierpinski Gasket to Segments   The restrictions of a harmonic function on the Sierpinski Gasket (SG) to the
segments in SG have been of some interest. We show that the sufficient
conditions for the monotonicity of these restrictions given by Dalrymple,
Strichartz and Vinson are also necessary. We then prove that the normal
derivative of a harmonic function on SG on the junction points of the contour
of a triangle in SG is always nonzero with at most a single exception.
  We finally give an explicit derivative computation for the restriction of a
harmonic function on SG to segments at specific points of the segments: The
derivative is zero at points dividing the segment in ratio 1:3. This shows that
the restriction of a harmonic function to a segment of SG has the following
curious property: The restriction has infinite derivatives on a dense set of
the segment (at junction points) and vanishing derivatives on another dense
set.

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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph