Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matlab program method of computing Carleman estimates and applications   In this paper, we introduce a Matlab program method to compute Carleman
estimate for the fourth order partial differential operator
$\gamma\partial_t+\partial_x^4\ (\gamma\in\mathbb{R})$. We obtain two kinds of
Carleman estimates with different weight functions, i.e. singular weight
function and regular weight function, respectively. Based on Carleman estimate
with singular weight function, one can obtain the known controllability and
observability results for the 1-d fourth order parabolic-type equation, while
based on Carleman estimate with regular weight function, one can deduce not
only the known result on conditional stability in the inverse problem of
half-order fractional diffusion equation, but also a new result on conditional
stability in the inverse problem of half-order fractional Schr\"odinger
equation.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci