Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted Means of B-Splines, Positivity of Divided Differences, and
  Complete Homogeneous Symmetric Polynomials   We employ the fact certain divided differences can be written as weighted
means of B-splines and hence are positive. These divided differences include
the complete homogeneous symmetric polynomials of even degree $2p$, the
positivity of which is a classical result by D. B. Hunter. We extend Hunter's
result to complete homogeneous symmetric polynomials of fractional degree,
which are defined via Jacobi's bialternant formula. We show in particular that
these polynomials have positive real part for real degrees $\mu$ with
$|\mu-2p|< 1/2$. We also prove a positivity criterion for linear combinations
of the classical complete homogeneous symmetric polynomials and a sufficient
criterion for the positivity of linear combinations of products of such
polynomials.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg