Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Multiple Frequency Power Density Measurements   We shall give a priori conditions on the illuminations $\phi_i$ such that the
solutions to the Helmholtz equation $-div(a \nabla u^i)-k q u^i=0$ in \Omega,
$u^i=\phi_i$ on $\partial\Omega$, and their gradients satisfy certain non-zero
and linear independence properties inside the domain \Omega, provided that a
finite number of frequencies k are chosen in a fixed range. These conditions
are independent of the coefficients, in contrast to the illuminations
classically constructed by means of complex geometric optics solutions. This
theory finds applications in several hybrid problems, where unknown parameters
have to be imaged from internal power density measurements. As an example, we
discuss the microwave imaging by ultrasound deformation technique, for which we
prove new reconstruction formulae.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
1
The categories of this paper are: cs
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph