Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper semismooth functions and the subdifferential determination
  property   In this paper, an upper semismooth function is defined to be a lower
semicontinuous function whose radial subderivative satisfies a mild directional
upper semicontinuity property. Examples of upper semismooth functions are the
proper lower semicontinuous convex functions, the lower-C$^1$ functions, the
regular directionally Lipschitz functions, the Mifflin semismooth functions,
the Thibault-Zagrodny directionally stable functions. It is shown that the
radial subderivative of such functions can be recovered from any
subdifferential of the function. It is also shown that these functions are
subdifferentially determined, in the sense that if two functions have the same
subdifferential and one of the functions is upper semismooth, then the two
functions are equal up to an additive constant.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs