Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improved upper bound on the number of billiard ball collisions   We give a new upper bound $K_+$ on the number of totally elastic collisions
of $n$ hard spheres with equal radii and equal masses in $R^d$. Our bound
satisfies $\log K_+ \leq c(d) n \log n$.

37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio