Search results for "multiplication"
showing 10 items of 83 documents
The positioning system of the ANTARES Neutrino Telescope
2012
The ANTARES neutrino telescope, located 40km off the coast of Toulon in the Mediterranean Sea at a mooring depth of about 2475m, consists of twelve detection lines equipped typically with 25 storeys. Every storey carries three optical modules that detect Cherenkov light induced by charged secondary particles (typically muons) coming from neutrino interactions. As these lines are flexible structures fixed to the sea bed and held taut by a buoy, sea currents cause the lines to move and the storeys to rotate. The knowledge of the position of the optical modules with a precision better than 10cm is essential for a good reconstruction of particle tracks. In this paper the ANTARES positioning sys…
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.
On some dual frames multipliers with at most countable spectra
2021
A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the spectra of some dual frames multipliers giving, in particular, conditions to be at most countable. The contribution extends the results available in literature about the spectra of Bessel multipliers with symbol decaying to zero and of multipliers of dual Riesz bases.
Star-product approach to quantum field theory: The free scalar field
1990
The star-quantization of the free scalar field is developed by introducing an integral representation of the normal star-product. A formal connection between the Feynman path integral in the holomorphic representation and the star-exponential is established for the interacting scalar fields.
Ionization and scintillation response of high-pressure xenon gas to alpha particles
2013
High-pressure xenon gas is an attractive detection medium for a variety of applications in fundamental and applied physics. In this paper we study the ionization and scintillation detection properties of xenon gas at 10 bar pressure. For this purpose, we use a source of alpha particles in the NEXT-DEMO time projection chamber, the large scale prototype of the NEXT-100 neutrinoless double beta decay experiment, in three different drift electric field configurations. We measure the ionization electron drift velocity and longitudinal diffusion, and compare our results to expectations based on available electron scattering cross sections on pure xenon. In addition, two types of measurements add…
On Determinants of Integrable Operators with Shifts
2013
Integrable integral operator can be studied by means of a matrix Riemann--Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Riemann--Hilbert problem becomes operator valued and this complicates strongly the analysis. In this note, we show how to circumvent, in a very simple way, the use of such a setting while still being able to characterize the large-$x$ asymptotic behavior of the determinant associated with the operator.
Explicit form of the time operator of a gaussian stationary process
2004
We present the time operator theory in the framework of stationary stochastic processes. The main results of the paper is the derivation of the time operator acting on the Fock space associated with a discrete time gaussian stationary process.
An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications
2020
Author's accepted manuscript. This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Bergelson, V., Knutson, I. J. H. & Son, Y. (2020). An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications. International Mathematics Research Notices, 2021(19), 14965-15018 is available online at: https://academic.oup.com/imrn/article/2021/19/14965/5775499 and https://doi.org/10.1093/imrn/rnaa035. Generalized polynomials are mappings obtained from the conventional polynomials by the use of the operations of addition and multiplication and taking th…
Algebrability of the set of hypercyclic vectors for backward shift operators
2020
Abstract We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Frechet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case, we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.
The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves
2017
Abstract Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g > 7 .