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The object is an elliptical galaxy ad z=0.901 which is also associated with an ISO detection in the supplementary catalog. | The object is an elliptical galaxy at z=0.901 which is also associated with an ISO detection in the supplementary catalog. |
Ol the remaining 8 variable nuclei. one (2-860.0) is associated with a mid-IR detection and another (3-948.0) is within ~2” of a 1.4GlILIZ radio source. | Of the remaining 8 variable nuclei, one ) is associated with a mid-IR detection and another ) is within $\sim$ $\arcsec$ of a 1.4GHz radio source. |
The other 6 are not associated with anv of the multi-wavelength survevs discussed here. | The other 6 are not associated with any of the multi-wavelength surveys discussed here. |
Overall. (7/16) of our variable galaxy nuclei have X-ray counterparts from the 2Ms Chandra survey (or excluding the two matches with greatest positional offsets). | Overall, (7/16) of our variable galaxy nuclei have X-ray counterparts from the 2Ms Chandra survey (or excluding the two matches with greatest positional offsets). |
Optical variables make up of the X-ray sources. | Optical variables make up of the X-ray sources. |
Of the brightest X-ray sources (full-band. [ας >2.4x ! eves/s) five out of nine (56%.)) are associated with optical variables. | Of the brightest X-ray sources (full-band flux $\geq$ $\times$ $^{-16}$ ergs/s) five out of nine ) are associated with optical variables. |
Lf we assume that the observed optical variability indicates the presence of an AGN. this is an important check on the nature of the A-ray emilling source and could potentially help discriminate between low-Iuminosi(y X-ray emitting AGN and other X-ray. emitting phenomena such as supernova remnants or X-ray binaries. | If we assume that the observed optical variability indicates the presence of an AGN, this is an important check on the nature of the X-ray emitting source and could potentially help discriminate between low-luminosity X-ray emitting AGN and other X-ray emitting phenomena such as supernova remnants or X-ray binaries. |
There does not appear to be a relation between photon index and the detection of optical variability. | There does not appear to be a relation between photon index and the detection of optical variability. |
Five of the eight X-ray sources in the IDF with enough signal to determine photon indices are optical variables. | Five of the eight X-ray sources in the HDF with enough signal to determine photon indices are optical variables. |
The N-rav/optical variables nake up two of the softer X-ray sources and three of the harder sources in (his small sample. | The X-ray/optical variables make up two of the softer X-ray sources and three of the harder sources in this small sample. |
Seven of our 16 variables are associated with mid-IR detections (446)) and five (3154)) wave radio emission at L4GlILIz. | Seven of our 16 variables are associated with mid-IR detections ) and five ) have radio emission at 1.4GHz. |
Variable galaxies make up of the detected sources a Ίσμηι. | Variable galaxies make up of the detected sources at $\micron$. |
This is comparable to the portion of the mid-IR integrated light attributed to AGN based on the correlation of mid-IR. sources with Chandra sources (Elbaz 1999). | This is comparable to the portion of the mid-IR integrated light attributed to AGN based on the correlation of mid-IR sources with Chandra sources (Elbaz 1999). |
Finally. we have compared our results with two photometric studies (o identify QSOs in the IDF on the basis of multi-band colors. | Finally, we have compared our results with two photometric studies to identify QSOs in the HDF on the basis of multi-band colors. |
Jarvis MacAlpine (1998) identified 12 high redshift (223.5) QSO candidates. | Jarvis MacAlpine (1998) identified 12 high redshift $>$ 3.5) QSO candidates. |
Eleven of these sources were included in our variability survey but none showed significant variability amplitudes. having a median σ of ~0.6. | Eleven of these sources were included in our variability survey but none showed significant variability amplitudes, having a median $\sigma$ of $\sim$ 0.6. |
Dased on structure functions for AGN/QSOs (Trevese 1994: Hook 1994: Hawkins 2002) and taking into account. time-dilation effects. (At,..,=At/(1+z)). the average magnitude change expected in our survey lor high-z QSOs is ~0.10.2 magnitudes. | Based on structure functions for AGN/QSOs (Trevese 1994; Hook 1994; Hawkins 2002) and taking into account time-dilation effects $\Delta$ $_{rest}$ $\Delta$ t/(1+z)), the average magnitude change expected in our survey for high-z QSOs is $\sim$ 0.1–0.2 magnitudes. |
Even sources dominated by an AGN component. as expected for these color-selected candidates. would be difficult to detect above the 36 sienilicance threshold due to their faint apparent magnitudes (V,,2:21.7). | Even sources dominated by an AGN component, as expected for these color-selected candidates, would be difficult to detect above the $\sigma$ significance threshold due to their faint apparent magnitudes $_{nuc}$$\gea$ 27.7). |
Nonetheless. an average magnitude change of only 70.05 is significantly less (han the 0.10.2 average magnitude change predicted from QSO structure Iunctions. | Nonetheless, an average magnitude change of only $\sim$ 0.05 is significantly less than the 0.1–0.2 average magnitude change predicted from QSO structure functions. |
Conti (1999) also identily 20 compact sources having QSO-like colors and morphologies with estimated. redshifts between ze1 and 5.5. | Conti (1999) also identify 20 compact sources having QSO-like colors and morphologies with estimated redshifts between $\sim$ 1 and 5.5. |
The nuclear magnitudes [or these objects | The nuclear magnitudes for these objects |
where the scattering augle ος. is given by Eqn. 9.. | where the scattering angle $\theta_{sc}$ is given by Eqn. \ref{eq:angles}. |
The inteeration hits over ϐ also differ from those euiploved by MALO. | The integration limits over $\theta$ also differ from those employed by MM10. |
Note. too. the kinematic restriction onu the scattering angle 0, imaiposed by Equ. 7: | Note, too, the kinematic restriction on the scattering angle $\theta_{sc}$ imposed by Eqn. \ref{eq:cond}: |
We have calculated ICS spectra nuuericallv/ sine Equ. 11.. | We have calculated ICS spectra numerically using Eqn. \ref{eq:isoe_urel}. . |
The photon enissivitv spectrum (photons cm? stosr | fy is obtained bv integration over the electron aud. photon euergv distributions with suitable jiorinalization. | The photon emissivity spectrum (photons $^{-3}$ $^{-1}$ $^{-1}$ $^{-1}$ ) is obtained by integration over the electron and photon energy distributions with suitable normalization. |
For the purposes of conrparison. we use he same parameters as MMIO: the iucideut photons are asstuned to be plhotospleric. with an οπσον ej=2 ον and a muuber density ».=10072 m.. the clectron sinctic euergv is assuned to have a power-law fori. fi)-—t51). | For the purposes of comparison, we use the same parameters as MM10: the incident photons are assumed to be photospheric, with an energy $\epsilon_1=2$ eV and a number density $n_\gamma=10^{12}$ $^{-3}$; the electron kinetic energy is assumed to have a power-law form, $f(\gamma)\sim (\gamma-1)^{-\delta}$. |
Tu Fig. | In Fig. |
3aa. we show the ICS photou spectra resulting from an electron distribution extending o 100 MeV. with a spectral index à= 3. viewed with angeles ranging from A=0 (disk center) to A=27/3 (over-the-limh). | \ref{fig:aic_mnm}a a, we show the ICS photon spectra resulting from an electron distribution extending to 100 MeV with a spectral index $\delta=3$ , viewed with angles ranging from $\lambda=0$ (disk center) to $\lambda=2\pi/3$ (over-the-limb). |
The results are normalized such that no)=1 electron cmP with an enerev >0.5 MeV (5» 2). | The results are normalized such that $n_e(\gamma)=1$ electron $^{-3}$ with an energy $>\!0.5$ MeV $\gamma>2$ ). |
Fig. | Fig. |
3bb shows the ICS spectra from electron distributions with different values of the spectral index ὃ, for a source on the solar limb (A= 7/2). | \ref{fig:aic_mnm}b b shows the ICS spectra from electron distributions with different values of the spectral index $\delta$, for a source on the solar limb $\lambda=\pi/2$ ). |
We find that the calculated INR spectra have a photo- spectral iudex of a~(0|1)/2. as expected for tle ultra-relativistic case(?7).. simular to those obtained by MALO (their Fie. | We find that the calculated HXR spectra have a photon spectral index of $\alpha\simeq(\delta+1)/2$, as expected for the ultra-relativistic case, similar to those obtained by MM10 (their Fig. |
2 and Fie. | 2 and Fig. |
D). | 4). |
However. our photon Huxes are more two than orders of miaguitude lower hau those reported by MMIO. | However, our photon fluxes are more two than orders of magnitude lower than those reported by MM10. |
They are similar in order of maguitude to the fully-isotropic case calculated roni Equ. | They are similar in order of magnitude to the fully-isotropic case calculated from Eqn. |
5 as nüsht be expected(7). | \ref{eq:jones} as might be expected. |
We πα, noreover. that the difference iu the INR photon spectra calculated for different viewing augles A lie within au order of magnitude of cach other. iu contrast to the aree range of values reported by MBMIO which span nore than two orders of magnitude. | We find, moreover, that the difference in the HXR photon spectra calculated for different viewing angles $\lambda$ lie within an order of magnitude of each other, in contrast to the large range of values reported by MM10 which span more than two orders of magnitude. |
Iu practice. the ceuter-to-linh variation of an ICS source would be uodi&ed bv the contribution of Compton backscatter of ICS IIXR. photons on photospheric electrons in the 100 keV cnerey range. an effect that we do not include. | In practice, the center-to-limb variation of an ICS source would be modified by the contribution of Compton backscatter of ICS HXR photons on photospheric electrons in the $-$ 100 keV energy range, an effect that we do not include. |
Note that the high οποιον cutoff of the photon spectra depends on viewing angle because the πιαπα cuereies from up-scattering are achieved for largest scattering aneles. | Note that the high energy cutoff of the photon spectrum depends on viewing angle because the maximum energies from up-scattering are achieved for largest scattering angles. |
Finally. the high-cucrey cutoff of the up-scattered photons frou different electron power-law cuerey distributions are independent of the spectral iudex ὃν while those reported by MMIO vary significantly with à. | Finally, the high-energy cutoff of the up-scattered photons from different electron power-law energy distributions are independent of the spectral index $\delta$, while those reported by MM10 vary significantly with $\delta$. |
We conclude that our results for ICS in the Hnüt of ultra-relativistie electron energies are consistent witli expectations. | We conclude that our results for ICS in the limit of ultra-relativistic electron energies are consistent with expectations. |
We attribute the differences between the calculations reported here and those reported by MMIO to an error made in the expression for the photon cluissivity in the latter publication. | We attribute the differences between the calculations reported here and those reported by MM10 to an error made in the expression for the photon emissivity in the latter publication. |
We now explore ICS for cases iu which the electrous are rot necessarily highlv relativistic. | We now explore ICS for cases in which the electrons are not necessarily highly relativistic. |
Solar fares produce copious EUV aud SXR photons. | Solar flares produce copious EUV and SXR photons. |
These may be up-scattered to TINR or οταν cuereies by electrous with ar lower cucreies than generally considered by previous reatinents of ICS. | These may be up-scattered to HXR or $\gamma$ -ray energies by electrons with far lower energies than generally considered by previous treatments of ICS. |
For example. au eq=1 keV SAR ioton can be upescattered to és7I7?e=16100 keV for clectrous with =25. | For example, an $\epsilon_1=1$ keV SXR photon can be up-scattered to $\epsilon_{\rm max}\approx 4\gamma^2\epsilon_1=16-100$ keV for electrons with $\gamma=2-5$. |
While the ioton nuniber deusitv of EUV/SXR. photons is much sualler (CE10*105 7) than the muuber deusitv 6| photosphlieric photons (71012 3) we note that. eiven power-law. or simular. distributious iuferred for electron energev distributions during solar flares. the uunber of nüldlv relativistic electrons produced bv a solar flare far out-amuuber those at ultra-relativistic iergies. | While the photon number density of EUV/SXR photons is much smaller $\lesssim 10^7 - 10^8$ $^{-3}$ ) than the number density of photospheric photons $\sim 10^{12}$ $^{-3}$ ) we note that, given power-law, or similar, distributions inferred for electron energy distributions during solar flares, the number of mildly relativistic electrons produced by a solar flare far out-number those at ultra-relativistic energies. |
The product of the photon number density il the electron uniuber deusifv nen, may therefore not differ substantially between the ultra-relativistic aud nmildlv relativistic cases. | The product of the photon number density and the electron number density $n_\gamma n_e$ may therefore not differ substantially between the ultra-relativistic and mildly relativistic cases. |
Tn considering ICS on wildly relativistic electrons. however, we can no longer exploit the approximations possible for the case of ultra-relativistie electrons and we nmst instead use the ecucral expression. | In considering ICS on mildly relativistic electrons, however, we can no longer exploit the approximations possible for the case of ultra-relativistic electrons and we must instead use the general expression. |
Consider an electron distribution expressed im separable form as f5.0)=N.FE.(G)QUOOΕλlr for an isotropic distribution. where Jv. is a normalization factor toeusure the integral over the electron energv distributionresults iu the total nuuber deusitv of fast clectrons. | Consider an electron distribution expressed in separable form as $f_e(\gamma,\Omega)=K_e F_e(\gamma)Q_e(\Omega_e)=K_e F_e(\gamma)/4\pi$ for an isotropic distribution, where $K_e$ is a normalization factor toensure the integral over the electron energy distributionresults in the total number density of fast electrons. |
The eeneral expression for the ICS Cluission rate for photous with a direction O. ou au isotropic electron distribution is given by | The general expression for the ICS emission rate for photons with a direction $\Omega_\gamma$ on an isotropic electron distribution is given by |
it was constructed so as to reproduce recent results of microscopic diagranunatic calculations (based on Brueckner theory) of infinite uniform nuclear matter with two- as well as three-body forces. | it was constructed so as to reproduce recent results of microscopic diagrammatic calculations (based on Brueckner theory) of infinite uniform nuclear matter with two- as well as three-body forces. |
In. particular. this effective force not only fits well the cnerev per nucleon in svnunetric ancl asvoimetric nuclear matter. but fits also the nucleon cllective masses for cillerent asvmmetries and cdilferent densities which directly determine the entrainment cocllicients as previously cisceussed. | In particular, this effective force not only fits well the energy per nucleon in symmetric and asymmetric nuclear matter, but fits also the nucleon effective masses for different asymmetries and different densities which directly determine the entrainment coefficients as previously discussed. |
Nevertheless. the SLy forces. which were constrained to reproduce some properties of finite nuclei (apart from the other constraints that we imposed) would be preferable if. not onky the liquid core but also the crust lavers would have to be described with the same underlving microscopic Hamiltonian. | Nevertheless, the SLy forces, which were constrained to reproduce some properties of finite nuclei (apart from the other constraints that we imposed) would be preferable if not only the liquid core but also the crust layers would have to be described with the same underlying microscopic Hamiltonian. |
Besides the equation of state of neutron star matter with the force SLy4 has been tabulated and. widely applied(?).. | Besides the equation of state of neutron star matter with the force SLy4 has been tabulated and widely applied\citep{haensel-04}. |
For comparison. we have also considered the parametrization NRAPR (7). since it was adjusted: on the realistic equation of state of 2.. | For comparison, we have also considered the parametrization NRAPR \citep{steiner-05} since it was adjusted on the realistic equation of state of \citet{akmal-98}. |
Nevertheless this force leads to a ferromagnetic instability at rather low density p2po. | Nevertheless this force leads to a ferromagnetic instability at rather low density $\rho \lesssim 2 \rho_0$. |
The parameters of the forces and the associated. B-cocllicients introduced in Section δι,are given in Tables 1. ancl 2 respectively. | The parameters of the forces and the associated B-coefficients introduced in Section \ref{sect.micro}, ,are given in Tables \ref{table.forces.parameters} and \ref{table.forces.Bcoef} respectively. |
The nuclear matter properties predicted by these forces are summarized in Table 3.. | The nuclear matter properties predicted by these forces are summarized in Table \ref{table.forces.properties}. |
Figure 1. shows the binding energy per particle in uniform infinite neutron matter defined by E=Cy[ns.0]/n,—mc. | Figure \ref{fig:eos_pnm}
shows the binding energy per particle in uniform infinite neutron matter defined by $E/A=U_{\rm N}\{n_n,0\}/n_n -m c^2$. |
Let us stress that the LNS force was fitted to the latest results of many body calculations with two- and three-body forces. while the forces of the Lyon eroup were adjusted to reproduce an older neutron matter equation of state based on variational methods. | Let us stress that the LNS force was fitted to the latest results of many body calculations with two- and three-body forces, while the forces of the Lyon group were adjusted to reproduce an older neutron matter equation of state based on variational methods. |
Figures 3.. 4. and 5. show the equilibrium composition of cold neutron star matter. composed. of neutrons. protons. electrons. ancl muons. obtained by solving Eqs. (80)). (88)) | Figures \ref{fig:SLy4_core}, \ref{fig:LNS_core} and \ref{fig:NRAPR_core} show the equilibrium composition of cold neutron star matter, composed of neutrons, protons, electrons and muons, obtained by solving Eqs. \ref{eq.neutrality}) ), \ref{eq.beta.equi}) ) |
and (89)). | and\ref{eq.beta.equi2}) ). |
The figures show the electron. muon and. proton fractions. defined respectively by ni fan. num,∕ and δνfr. as a function of the mass-energyNf density p=Cue. which is | The figures show the electron, muon and proton fractions, defined respectively by $n_e/n_{\rm b}$ , $n_\mu/n_{\rm b}$ and $n_p/n_{\rm b}$ as a function of the mass-energy density $\rho=U_{\rm ins}/c^2$ , which is |
have been vounger bv Alog(Aec/vr)0.20.4. depending on the age range considered (larger olfsets result for vounger ages]. | have been younger by $\Delta
\log({\rm Age / yr}) \sim 0.2-0.4$, depending on the age range considered (larger offsets result for younger ages). |
In the previous section we noted a significant. svstematic cllect between the age dillerences of 1103. on the one hand. and those of both the OGLE-LE team ancl our own redeterminations on the other. | In the previous section we noted a significant systematic effect between the age differences of H03 on the one hand, and those of both the OGLE-II team and our own redeterminations on the other. |
H03 converted the Starburst99 Johnson (Vo22) colour to the Cousins svstem. | H03 converted the Starburst99 Johnson $(V-R)$ colour to the Cousins system. |
As we showed in de Cirijs et al. ( | As we showed in de Grijs et al. ( |
2005: their figs. | 2005; their figs. |
10 and 11). filter. conversions may be. responsible for. significant dillerences in the resulting age determinations. | 10 and 11), filter conversions may be responsible for significant differences in the resulting age determinations. |
In order Oo investigate the possibility of this οσοι plaving a role or these data. we carefully analysed the properties of he original and converted svstenis. used. | In order to investigate the possibility of this effect playing a role for these data, we carefully analysed the properties of the original and converted systems used. |
Massey. (2002) calibrated his photometry using the Landolt (1992) standard stars. so that his photometry should. be analysed: using he filter set. used to obtain the standard-star photometry. | Massey (2002) calibrated his photometry using the Landolt (1992) standard stars, so that his photometry should be analysed using the filter set used to obtain the standard-star photometry. |
Vhe Landolt. (1992). filter curves are very. close to. the ilter transmission. curves used by Lloltzman et al. ( | The Landolt (1992) filter curves are very close to the filter transmission curves used by Holtzman et al. ( |
1995). who also kindly supplied us with the original. unpublished Landolt KWPNO curves (J. Holtzman. priv. | 1995), who also kindly supplied us with the original, unpublished Landolt KPNO curves (J. Holtzman, priv. |
comm.). | comm.). |
For completeness. we will therefore assess the dilferences in the resulting ages for our LMC cluster sample based on using the "standard" Johnson-Cousins system (as done ον L103). the curves used by Lloltzman et al. ( | For completeness, we will therefore assess the differences in the resulting ages for our LMC cluster sample based on using the “standard” Johnson-Cousins system (as done by H03), the curves used by Holtzman et al. ( |
1995). and the original IXDPNO curves used by Landolt (1992). | 1995), and the original KPNO curves used by Landolt (1992). |
The results. of this are. shown in Fig. 2. | The results of this are shown in Fig. \ref{cffilters.fig}. |
Lig. | Fig. |
2cc shows that the filter transmission curves used bv Loltzman et al. ( | \ref{cffilters.fig}c c shows that the filter transmission curves used by Holtzman et al. ( |
1995). and. Landolt (1992). respectively. indeed vield. relatively similar age estimates. | 1995) and Landolt (1992), respectively, indeed yield relatively similar age estimates. |
The most important comparison figure is displaved in panel b. however. | The most important comparison figure is displayed in panel b, however. |
The systematic trend seen here mimics that seen in Figs. | The systematic trend seen here mimics that seen in Figs. |
laa and c. in the sense that if one uses the Johnson-Cousins filter system (even if based. on the appropriate conversion equations) instead. of the native Lanclolt KPNO system. one will obtain lower ages than expected. at. the voung-age end of the age range covered by our LAIC cluster sample. ancl vice versa. | \ref{lmccf.fig}a a and c, in the sense that if one uses the Johnson-Cousins filter system (even if based on the appropriate conversion equations) instead of the native Landolt KPNO system, one will obtain lower ages than expected at the young-age end of the age range covered by our LMC cluster sample, and vice versa. |
To provide further evidence for this scenario. we applied a simple linear regression to the data points in Fig. | To provide further evidence for this scenario, we applied a simple linear regression to the data points in Fig. |
2cc (shown by the dotted line). and applied the resulting equation as a first-order correction to HO3's age determinations in both Figs. | \ref{cffilters.fig}c c (shown by the dotted line), and applied the resulting equation as a first-order correction to H03's age determinations in both Figs. |
laa and c. The resulting. corrected. age comparison is shown in Fig. | \ref{lmccf.fig}a a and c. The resulting, corrected age comparison is shown in Fig. |
2dd. while the numerical values are once again included in Fable 1.. | \ref{cffilters.fig}d d, while the numerical values are once again included in Table \ref{regression.tab}. |
Ht thus appears that the systematic dillerences in LMC cluster ages between the LI03 results and those of OGLIZ-LE and ourselves are indeed caused by their conversions of the photometry to a different filter svstem. | It thus appears that the systematic differences in LMC cluster ages between the H03 results and those of OGLE-II and ourselves are indeed caused by their conversions of the photometry to a different filter system. |
1n the discussion of our results. we have thus far assumed a fixed metallicity of Z=0.008 and a fixed extinction of £(BV)—0.10 mag (assuming the Calzetti attenuation law) for all of our sample clusters. | In the discussion of our results, we have thus far assumed a fixed metallicity of $Z=0.008$ and a fixed extinction of $E(B-V)=0.10$ mag (assuming the Calzetti attenuation law) for all of our sample clusters. |
The XnalvSIZD. tool has been developed to also provide independent information on a clusters metallicity ancl extinction. provided that a significant number of cata points defining the SED are available to match the number of free parameters (cl. | The AnalySED tool has been developed to also provide independent information on a cluster's metallicity and extinction, provided that a significant number of data points defining the SED are available to match the number of free parameters (cf. |
cle CGrijs et al. | de Grijs et al. |
2003c.d: Anders et al. | 2003c,d; Anders et al. |
2004). | 2004). |
''herefore. we have also reanalysed the LMC. cluster photometry assuming (i) variable metallicity and (21)20.0 mae. (1) Z=0.008 ancl variable extinction. and (iii) variable extinction and metallicity. the results of which are shown in Figs. | Therefore, we have also reanalysed the LMC cluster photometry assuming (i) variable metallicity and $E(B-V)=0.10$ mag, (ii) $Z=0.008$ and variable extinction, and (iii) variable extinction and metallicity, the results of which are shown in Figs. |
3aa. b and c. respectively. | \ref{internal.fig}a a, b and c, respectively. |
From close scrutiny of these panels. it appears that the age-metallicity degeneracy is least important.semple: this implies that the assumption of Z=0.008 adopted. by 1103. OGLE-L and. ourselves in the previous sections is a reasonable approximation of the average LMC cluster metallicity. | From close scrutiny of these panels, it appears that the age-metallicity degeneracy is least important; this implies that the assumption of $Z=0.008$ adopted by H03, OGLE-II and ourselves in the previous sections is a reasonable approximation of the average LMC cluster metallicity. |
We also note that adopting Z=0.008 as a reasonable approximation for the average cluster metallicity is supported. αἲ least for clusters vounger than ~3d Car by a number of spectroscopic studies based on individual ‘luster stars (see. e.g. Olszewski et al. | We also note that adopting $Z=0.008$ as a reasonable approximation for the average cluster metallicity is supported – at least for clusters younger than $\sim 3$ Gyr – by a number of spectroscopic studies based on individual cluster stars (see, e.g., Olszewski et al. |
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