Search results for " Mathematics"
showing 10 items of 10797 documents
"Table 38" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for $m_{\Phi}=600$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 34" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for $m_{\Phi}=100$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 27" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for $m_{\Phi}=600$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 28" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for $m_{\Phi}=1000$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 26" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for $m_{\Phi}=400$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 39" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for $m_{\Phi}=1000$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 25" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for $m_{\Phi}=200$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 29" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for all Stealth SUSY benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 40" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for all Stealth SUSY benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
A numerical property of Hilbert functions and lex segment ideals
2017
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the Osequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called fractal functions, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.