Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schm\"udgen's theorem and results of positivity   This is a translation of a final paper. It contains proofs of some well-known
Positivstellens\"atze. The approach in this paper differs in two respects from
presentations in literature. We use the Stone-Weierstrass Theorem directly to
prove an inductive property, which makes the Kadison-Dubois Theorem superfluous
in our paper, and we also consider homogeneous and projective
Positivstellens\"atze. This leads us to a homogeneous version of Schm\"udgen's
theorem and a projective version of Putinar's theorem.

37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph