Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positivity of sums and integrals for higher order nabla-convex and
  completely monotonic functions   We extend the definitions of $\nabla-$convex and completely monotonic
functions for two variables. Some general identities of Popoviciu type for sum
$\sum \sum p_{ij} f(y_i, z_j)$ and integrals $\int P(y)f(y) dy$, $\int \int
P(y,z) f(y,z) dy \, dz$ are deduced. Using obtained identities, positivity of
these expressions are characterized for higher order $\nabla-$convex and
completely monotonic functions. Some applications in terms of generalized
Cauchy means and exponential convexity are given.

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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: stat