Search results for "Delta functions"
showing 2 items of 2 documents
Multiplication of distributions in any dimension: Applications to δ-function and its derivatives
2009
In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here, mainly motivated by some engineering applications in the analysis of the structures, we propose a different definition of multiplication of distributions which can be easily extended to any spatial dimension. In particular we prove that with this new definition delta functions and their derivatives can still be multiplied.
Search for Subsolar-Mass Ultracompact Binaries in Advanced LIGO's First Observing Run
2018
We present the first Advanced LIGO and Advanced Virgo search for ultracompact binary systems with component masses between 0.2 $M_\odot$ - 1.0 $M_\odot$ using data taken between September 12, 2015 and January 19, 2016. We find no viable gravitational wave candidates. Our null result constrains the coalescence rate of monochromatic (delta function) distributions of non-spinning (0.2 $M_\odot$, 0.2 $M_\odot$) ultracompact binaries to be less than $1.0 \times 10^6 \text{Gpc}^{-3} \text{yr}^{-1}$ and the coalescence rate of a similar distribution of (1.0 $M_\odot$, 1.0 $M_\odot$) ultracompact binaries to be less than $1.9 \times 10^4 \text{Gpc}^{-3} \text{yr}^{-1}$ (at 90 percent confidence). N…