Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global {\L}ojasiewicz inequalities on comparing the rate of growth of
  polynomial functions   We present a global version of the {\L}ojasiewicz inequality on comparing the
rate of growth of two polynomial functions in the case the mapping defined by
these functions is (Newton) non-degenerate at infinity. In addition, we show
that the condition of non-degeneracy at infinity is generic in the sense that
it holds in an open and dense semi-algebraic set of the entire space of input
data.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph