Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new numerical method for inverse Laplace transforms used to obtain
  gluon distributions from the proton structure function   We recently derived a very accurate and fast new algorithm for numerically
inverting the Laplace transforms needed to obtain gluon distributions from the
proton structure function $F_2^{\gamma p}(x,Q^2)$. We numerically inverted the
function $g(s)$, $s$ being the variable in Laplace space, to $G(v)$, where $v$
is the variable in ordinary space. We have since discovered that the algorithm
does not work if $g(s)\rightarrow 0$ less rapidly than $1/s$ as
$s\rightarrow\infty$, e.g., as $1/s^\beta$ for $0<\beta<1$. In this note, we
derive a new numerical algorithm for such cases, which holds for all positive
and non-integer negative values of $\beta$. The new algorithm is {\em exact} if
the original function $G(v)$ is given by the product of a power $v^{\beta-1}$
and a polynomial in $v$. We test the algorithm numerically for very small
positive $\beta$, $\beta=10^{-6}$ obtaining numerical results that imitate the
Dirac delta function $\delta(v)$. We also devolve the published MSTW2008LO
gluon distribution at virtuality $Q^2=5$ GeV$^2$ down to the lower virtuality
$Q^2=1.69$ GeV$^2$. For devolution, $ \beta$ is negative, giving rise to
inverse Laplace transforms that are distributions and not proper functions.
This requires us to introduce the concept of Hadamard Finite Part integrals,
which we discuss in detail.

13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ