Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The weighted difference substitutions and Nonnegativity Decision of
  Forms   In this paper, we study the weighted difference substitutions from
geometrical views. First, we give the geometric meanings of the weighted
difference substitutions, and introduce the concept of convergence of the
sequence of substitution sets. Then it is proven that the sequence of the
successive weighted difference substitution sets is convergent. Based on the
convergence of the sequence of the successive weighted difference sets, a new,
simpler method to prove that if the form F is positive definite on T_n, then
the sequence of sets {SDS^m(F)} is positively terminating is presented, which
is different from the one given in [11]. That is, we can decide the
nonnegativity of a positive definite form by successively running the weighted
difference substitutions finite times. Finally, an algorithm for deciding an
indefinite form with a counter-example is obtained, and some examples are
listed by using the obtained algorithm.

26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int