Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On semi-homogeneous maps of degree $k$   We study properties of continuous semi-homogeneous operators of degree $k$
via various functions (e.g. measures of noncompactness) on all bounded subsets
of a Banach space. We prove necessary and sufficient conditions for these
functions to vanish on the image of the unit ball under these operators. In
particular, we give criteriafor superposition operators to be improving and
criteria for the complete continuity of the Fr\'echet derivatives. The results
obtained can be applied in various areas of both pure and applied mathematics.

15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th