16 research outputs found
Data-flow Analysis of Programs with Associative Arrays
Dynamic programming languages, such as PHP, JavaScript, and Python, provide
built-in data structures including associative arrays and objects with similar
semantics-object properties can be created at run-time and accessed via
arbitrary expressions. While a high level of security and safety of
applications written in these languages can be of a particular importance
(consider a web application storing sensitive data and providing its
functionality worldwide), dynamic data structures pose significant challenges
for data-flow analysis making traditional static verification methods both
unsound and imprecise. In this paper, we propose a sound and precise approach
for value and points-to analysis of programs with associative arrays-like data
structures, upon which data-flow analyses can be built. We implemented our
approach in a web-application domain-in an analyzer of PHP code.Comment: In Proceedings ESSS 2014, arXiv:1405.055
Black hole encircled by a thin disk: fully relativistic solution
We give a full metric describing the gravitational field of a static and
axisymmetric thin disk without radial pressure encircling a Schwarzschild black
hole. The disk density profiles are astrophysically realistic, stretching from
the horizon to radial infinity, yet falling off quickly at both these
locations. The metric functions are expressed as finite series of Legendre
polynomials. Main advantages of the solution are that (i) the disks have no
edges, so their fields are everywhere regular (outside the horizon), and that
(ii) all non-trivial metric functions are provided analytically and in closed
forms. We examine and illustrate basic properties of the black-hole -- disk
space-times.Comment: 14 page
Relativistic disks by Appell-ring convolutions
We present a new method for generating the gravitational field of thin disks
within the Weyl class of static and axially symmetric spacetimes. Such a
gravitational field is described by two metric functions: one satisfies the
Laplace equation and represents the gravitational potential, while the other is
determined by line integration. We show how to obtain analytic thin-disk
solutions by convolving a certain weight function -- an Abel transformation of
the physical surface-density profile -- with the Appell-ring potential. We thus
re-derive several known thin-disk solutions while, in some cases, completing
the metric by explicitly computing the second metric function. Additionally, we
obtain the total gravitational field of several superpositions of a disk with
the Schwarzschild black hole. While the superposition problem is simple
(linear) for the potential, it is mostly not such for the second metric
function. However, in particular cases, both metric functions of the
superposition can be found explicitly. Finally, we discuss a simpler procedure
which yields the potentials of power-law-density disks we studied recently.Comment: 20 pages, 4 figures, supplemental material is provided in the
ancillary Mathematica notebook "holeyMorganMorganDisks.nb" and the MX file
"holeyMorganMorganDisks.mx