Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The branch process of the cosmic strings   In the light of $\phi$-mapping method and the topological tensor current
theory, the topological structure and the topological quantization of
topological defects are obtained under the condition that Jacobian
$J(\phi/v)\neq0$. When $J(\phi/v)=0$, it is shown that there exists the crucial
case of branch process. Based on the implicit function theorem and the Taylor
expansion, the generation, annihilation and bifurcation of the linear defects
are detailed in the neighborhoods of the limit points and bifurcation points of
$\phi$-mapping, respectively.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph