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The light eurve of the 1993 April observation of Mrk 478 is taken directly from (1996). | The light curve of the 1993 April observation of Mrk 478 is taken directly from \cite{mcs96}. |
. Because part of the observation was perlormed with the source on the boresight position and part with the source off-axis. corrections had to be applied for the dilference in effective area to produce a continuous light curve. | Because part of the observation was performed with the source on the boresight position and part with the source off-axis, corrections had to be applied for the difference in effective area to produce a continuous light curve. |
This procedure was described in Marshalletal.(1996). | This procedure was described in \cite{mcs96}. |
. That paper also showed how the spectral energy distribution of Alrk 478 peaks in the EUV. | That paper also showed how the spectral energy distribution of Mrk 478 peaks in the EUV. |
The oobservation of 1Η 0419.577 was the second longest in (is compilation. 26 davs. | The observation of 1H 0419–577 was the second longest in this compilation, 26 days. |
Its periodogram. shown in Figure 9.. has a peak at 5.8 davs. | Its periodogram, shown in Figure \ref{ps3}, has a peak at 5.8 days. |
Similar to (he case of Ton S130. there may be weaker signals at other frequencies. | Similar to the case of Ton S180, there may be weaker signals at other frequencies. |
Interestingly. 1I 0419577 does not appear to sulfer as much [rom the red noise that dominates4711.. Ton S180. and other Sevfert ealaxies at low frequencies: (hus (he feature al 5.8 days is more prominent. | Interestingly, 1H 0419–577 does not appear to suffer as much from the red noise that dominates, Ton S180, and other Seyfert galaxies at low frequencies; thus the feature at 5.8 days is more prominent. |
It is not clear what is responsible lor this qualitatively different behavior. or indeed if il is a persistent property of the power spectrum of the source. | It is not clear what is responsible for this qualitatively different behavior, or indeed if it is a persistent property of the power spectrum of the source. |
It is possible that the 5.3 day signal simplyis (he red-noise behavior of this object. as the observation only spans %4.5 eveles of that period. | It is possible that the 5.8 day signal simply the red-noise behavior of this object, as the observation only spans $\approx 4.5$ cycles of that period. |
This light curve of 111 0419577 was published without any analvsis or interpretation in à paper about the serenclipitous discovery of à new AM Ier star only 4 from the Sevfert ealaxy in (his observation (Ilalpernetal.1998). | This light curve of 1H 0419–577 was published without any analysis or interpretation in a paper about the serendipitous discovery of a new AM Her star only $4^{\prime}$ from the Seyfert galaxy in this observation \citep{hlm98}. |
. The latter paper illustrated that ecan reliably discover periods. | The latter paper illustrated that can reliably discover periods. |
In the case of the AM Ler star. the period of 85.821 minutes was unambieuous despite its proximitv to the satellite orbit period (96.4 minutes) because the observation was so long. | In the case of the AM Her star, the period of 85.821 minutes was unambiguous despite its proximity to the satellite orbit period (96.4 minutes) because the observation was so long. |
This may be the only oobservation in which new periods were discovered. | This may be the only observation in which new periods were discovered. |
The variability amplitucle of Chis higbh-Iuminosity QSO is small on short (me scales. | The variability amplitude of this high-luminosity QSO is small on short time scales. |
Note that one observation in 1994 June was badly compromised by placement of the source on a "dead spot in the DS microchannel plate that had been created by an earlier observation | Note that one observation in 1994 June was badly compromised by placement of the source on a “dead spot” in the DS microchannel plate that had been created by an earlier observation |
Data in columns (2). (3). (6). were taken from the electronic version. dated 15th. May 1997. of Llarris 96 conipilation. | Data in columns (2), (3), (6), were taken from the electronic version dated 15th May 1997 of Harris 96 compilation. |
For 11. galactic σος we found new distance measurements from the Llipparcos observations. | For 11 galactic gc's we found new distance measurements from the Hipparcos observations. |
hey are shown in Table 2.. | They are shown in Table \ref{hip.gcMW}. |
In Table. 2.. one can [ind in columns: (1) NGC name. (2) Hipparcos distance modulus measurements with reference number. (3) average of Llipparcos distance modulus measurements. (4) absolute V. magnitude. [roni llarris 97. (5) calculated. absolute V. magnitude using Llippareos data. see section 3.2.2 (6) an asterix if the available velocity dispersion comes from individual star spectra. | In Table \ref{hip.gcMW}, one can find in columns: (1) NGC name, (2) Hipparcos distance modulus measurements with reference number, (3) average of Hipparcos distance modulus measurements, (4) absolute V magnitude from Harris 97, (5) calculated absolute V magnitude using Hipparcos data, see section 3.2, (6) an asterix if the available velocity dispersion comes from individual star spectra. |
In Table 3. we present the cata concerning 29 &c's of M31 with a published. measurement of their velocity cüspersion. | In Table \ref{M31} we present the data concerning 29 gc's of M31 with a published measurement of their velocity dispersion. |
Columns of Table 3. correspond to: (1) Name from Sargent et al. | Columns of Table \ref{M31} correspond to: (1) Name from Sargent et al. |
77. (2) apparent V. magnitude. (3) radial. velocity. (4) all velocity dispersion measurements with reference. (5) mean velocity dispersion. as used. for the caleulations in this paper. | 77, (2) apparent V magnitude, (3) radial velocity, (4) all velocity dispersion measurements with reference, (5) mean velocity dispersion as used for the calculations in this paper. |
Velocity dispersion measurements are taken from Djorgovski et al. | Velocity dispersion measurements are taken from Djorgovski et al. |
97. Dubath and Crillmair 97. Dubath et al. | 97, Dubath and Grillmair 97, Dubath et al. |
97. Peterson SS. | 97, Peterson 88. |
All apparent magnitudes and mean racial velocities come from Lluchra et al. | All apparent magnitudes and mean radial velocities come from Huchra et al. |
91. | 91. |
Using the 56 galactic σος with a measured. velocity dispersion. we performed a mean linear regression. assuming the errors are both on the absolute magnitudes and on the loga's. We obtain with one cluster (NGC 2419) rejected. at 30: the direct linear regression (assuming lareer errors on dispersions than on absolute magnitudes) gives: with r=O0.81. r being the Pearson correlation factor. and a dispersion around the EJ relation of Disp-0.68. | Using the 56 galactic gc's with a measured velocity dispersion, we performed a mean linear regression, assuming the errors are both on the absolute magnitudes and on the $log \sigma 's.$ We obtain with one cluster (NGC 2419) rejected at $3 \sigma$: the direct linear regression (assuming larger errors on dispersions than on absolute magnitudes) gives: with r=0.81, r being the Pearson correlation factor, and a dispersion around the FJ relation of Disp=0.68. |
Considering that a globular cluster is constituted. by some hundreds of thousands of stars. we chose for a second analvsis to eliminate the velocity dispersion data originating from the measurements of singular star radial velocities. | Considering that a globular cluster is constituted by some hundreds of thousands of stars, we chose for a second analysis to eliminate the velocity dispersion data originating from the measurements of singular star radial velocities. |
As a matter of fact this kind of observations involve at the worst around 10 stars and at the best around. 150. stars. | As a matter of fact this kind of observations involve at the worst around 10 stars and at the best around 150 stars. |
The selection of the stars lor observation strategy involves choosing bright stars or periferic ones. | The selection of the stars for observation strategy involves choosing bright stars or periferic ones. |
The selection criteria for the observation of those stars will obviously alfect. the measurement by adding biases such as the Malniquist Eliminating σον with a velocity dispersion. measured [rom individual. stars spectra. ancl keeping only the measurements obtained. [rom integrated. light. spectra. we obtained a subsample of 31 gc's. | The selection criteria for the observation of those stars will obviously affect the measurement by adding biases such as the Malmquist Eliminating gc's with a velocity dispersion measured from individual stars spectra and keeping only the measurements obtained from integrated light spectra, we obtained a subsample of 31 gc's. |
We performed a mean linear regression. and obtained with no cluster rejected at 39: the direct linear regression gives: with r-0.71. r being the Pearson correlation factor. ancl a dispersion around the EJ relation of Disp=0.73. | We performed a mean linear regression, and obtained with no cluster rejected at $3 \sigma$: the direct linear regression gives: with r=0.71, r being the Pearson correlation factor, and a dispersion around the FJ relation of Disp=0.73. |
οne can see on Figure 1 t10 mean IJLJ relatrelations for ththe 56 σος obtained with all measurements (dashed line) and with only velocity dispersions (31 ec’s) measured. from an integrated light spectrum (solid Line). | One can see on Figure \ref{FJ1} the mean FJ relations for the 56 gc's obtained with all measurements (dashed line) and with only velocity dispersions (31 gc's) measured from an integrated light spectrum (solid line). |
Excluding the 7 σος calibrated by Hipparcos. the direct regression on the 24 remaining &c's gives. with no rejection with r=0.71. and Disp=0.75. | Excluding the 7 gc's calibrated by Hipparcos, the direct regression on the 24 remaining gc's gives, with no rejection: with r=0.71, and Disp=0.75. |
For 11 gcs with à new distance determination obtained by Llipparcos. we can re-caleulate their absolute magnitude. | For 11 gc's with a new distance determination obtained by Hipparcos, we can re-calculate their absolute magnitude. |
Ln order to take into account the same extinction Correction as in Harris 97 on the apparent magnitudes. we recaleulated the absolute magnitude in V using: | In order to take into account the same extinction correction as in Harris 97 on the apparent magnitudes, we recalculated the absolute magnitude in V using: |
with Fies. | with Figs. |
3. ΟΕ where it can be seen that the ronunant eucrev thermalizes more rapidly with increasing f/. | \ref{fig:fig3} (b,d,f), where it can be seen that the remnant energy thermalizes more rapidly with increasing $f'$. |
This )oliasiour arises from the fact that mass loading reduces he rate at which the recunuaut expands at carly times. as it causes more braking iu the ejecta and seuds the reverse shock back throueli it more quickly. | This behaviour arises from the fact that mass loading reduces the rate at which the remnant expands at early times, as it causes more braking in the ejecta and sends the reverse shock back through it more quickly. |
Iu coutrast. we rote that ΑΕΕ is csseutially coustant when amass loading occurs by livdrvodvuamic ablation (Paper D. | In contrast, we note that $M_{\rm FE}$ is essentially constant when mass loading occurs by hydrodynamic ablation (Paper I). |
Since the. nass loading is esseutiallv saturated iu both formmlatious at this stage. these differences arise from the fact that in his paper we also mass load in the shocked ejecta (unlike in Paper D. which has the effect ofincreasing itspressure. | Since the mass loading is essentially saturated in both formulations at this stage, these differences arise from the fact that in this paper we also mass load in the shocked ejecta (unlike in Paper I), which has the effect of increasing itspressure. |
In Fig. | In Fig. |
8 we show the radius at the cud of the ree-expansion stage. ΠΕ. as a function of my and f. | \ref{fig:fig7} we show the radius at the end of the free-expansion stage, $R_{\rm FE}$ , as a function of $n_{0}$ and $f'$. |
We derive an appropriate analytical approximation for the depeudence of Rpr on ny aud f/ bv following the same procedure as iu Sec. | We derive an appropriate analytical approximation for the dependence of $R_{\rm FE}$ on $n_{0}$ and $f'$ by following the same procedure as in Sec. |
L1 of Paper 1. The agreeineut between the simulations and the analytical approximation is generally $ood. although the latter svstematically muacderestimates Reg at lich values of f (as was also fone in Paper L where an explanation for this is given). | 4.1 of Paper I. The agreement between the simulations and the analytical approximation is generally good, although the latter systematically underestimates $R_{\rm FE}$ at high values of $f'$ (as was also found in Paper I, where an explanation for this is given). |
For future purposes. however. we are more concerned witli accurate estimates for Rost. the radius at the eud of the Quasi-Sedov-Tavlor phase. | For future purposes, however, we are more concerned with accurate estimates for $R_{\rm QST}$, the radius at the end of the Quasi-Sedov-Taylor phase. |
We note that the much higher values of f£ which we consider in this paperlead to a greater range in Ree at a given ny. | We note that the much higher values of $f$ which we consider in this paperlead to a greater range in $R_{\rm FE}$ at a given $n_{0}$ . |
decretion disk. or outwards in a viscous accreting disk. | decretion disk, or outwards in a viscous accreting disk. |
This can be seen only with the use of the 2D1D algorithin. that permits both an accurate 2D computation of the planet-cdisk iteraction aud the 1D computation of the elobal disk evolution. | This can be seen only with the use of the 2D1D algorithm, that permits both an accurate 2D computation of the planet-disk interaction and the 1D computation of the global disk evolution. |
The elobal disk evolution also matters for the type III regime. | The global disk evolution also matters for the type III regime. |
The outer edge of the 1D exid is located at61 AU from the stay. as prescribed by Desch (2007). | The outer edge of the 1D grid is located at$61$ AU from the star, as prescribed by \citet{Desch2007}. |
.. The imuer edge is located arbitrarily at 0.2 AU. | The inner edge is located arbitrarily at $0.2$ AU. |
The inuer and outer edees of the 1D exid are open. allowing eas to flow out of the eid. | The inner and outer edges of the 1D grid are open, allowing gas to flow out of the grid. |
The rugs of the evid are logarithimicallvtributed: ór£r is constant through the two erids. | The rings of the grid are logarithmically: $\delta r/r$ is constant through the two grids. |
The cells of the 2D erid aresquared: àrfr= 0. | The cells of the 2D grid are: $\delta r/r=\delta \theta$ . |
The 2D erid extends from 1 or 1.6 to 23.5 AU. covering the planets region. | The 2D grid extends from $1$ or $1.6$ to $23.5$ AU, covering the planets region. |
Iu the computation of the force of the disk ou the planets. a part of their ΕΠΗ sphere is excluded. | In the computation of the force of the disk on the planets, a part of their Hill sphere is excluded. |
To perform this. we calculate iu the code the vector force E, using the following:: where G is the eravitatioual coustaut. A, the nass of the planet. dS is the surface of the considered cell. sis the vector from the planet o the center of the cell s is its leneth. aud si=Vs?|εἰ ds the smoothed distance to the auet. | To perform this, we calculate in the code the vector force $\vec{F}_p$ using the following: where $G$ is the gravitational constant, $M_p$ the mass of the planet, ${\rm d}{\cal S}$ is the surface of the considered cell, $\vec{s}$ is the vector from the planet to the center of the cell, $s$ is its length, and $s'=\sqrt{s^2+\epsilon^2}$ is the smoothed distance to the planet. |
The sunoothing leusth € is 0.6ry. where ry is the Tall radius of the planet. | The smoothing length $\epsilon$ is $0.6\,r_H$, where $r_H$ is the Hill radius of the planet. |
The term f(s) is our filter used. to exclude the neighborhood of he planet eiveu :: Tt is a inooth increasing function from 0 at s= Qtolwhens>x. through 0.1 when s—0.17 ry. 1/2 when s= O.6ry. and 0.9 when s=0.73rg (seeFigure2ofCridactal.2008). | The term $f(s)$ is our filter used to exclude the neighborhood of the planet given : It is a smooth increasing function from 0 at $s=0$ to $1$ when $s\to\infty$, through $0.1$ when $s=0.47\,r_H$ , $1/2$ when $s=0.6\,r_H$ , and $0.9$ when $s=0.73\,r_H$ \citep[see Figure~2
of][]{Crida-etal-2008}. |
. The Soli Nebula fouud by Desch(2007). las the folowing properties. | The Solar Nebula found by \citet{Desch2007} has the following properties. |
Asstmine that Jupiter formed at 5.15 AU. Saturn at 8.158 AU. Uranus at 11.2 AU and Neptune at 11.5 AU. the eas density shouldbe:: This is about 10 times more dense than the Tavashi(1981) nebula at 5 AU. and 6.1 times nore dense at LO AU. and 3 times more dense at 30 AU. | Assuming that Jupiter formed at $5.45$ AU, Saturn at $8.18$ AU, Uranus at $14.2$ AU and Neptune at $11.5$ AU, the gas density should: This is about 10 times more dense than the \citet{Hayashi1981} nebula at 5 AU, and 6.4 times more dense at 10 AU, and 3 times more dense at 30 AU. |
The steep density slope makes the disk a decretion disk. viscously spreading outwards. fed w the internal parts. | The steep density slope makes the disk a decretion disk, viscously spreading outwards, fed by the internal parts. |
The steady state profile ound by Desch(2007) has a slightly different shape. but we use the power law for couvenience. | The steady state profile found by \citet{Desch2007} has a slightly different shape, but we use the power law for convenience. |
The two profiles are alinost identical in the giant auets region. | The two profiles are almost identical in the giant planets region. |
The outer edge of the disk is fouud o be located at G1 AU from the star. | The outer edge of the disk is found to be located at $61$ AU from the star. |
The temperature is 150(7/1AU).&298IN, which corresponds to an aspect ratio of The viscosity is eiven bv an e prescription (Shakura&Suuvaev1973).. with a=L«10I | The temperature is $150(r/1 {\rm AU})^{-0.429}\,K$, which corresponds to an aspect ratio of The viscosity is given by an $\alpha$ prescription \citep{Shakura-Sunyaev-1973}, with $\alpha =
4\times 10^{-4}$. |
With these characteristics. the disk profile relmaius almost unchanged for nearly 10 τήπολι: vears. Which leaves time foratmosphere. | With these characteristics, the disk profile remains almost unchanged for nearly 10 millions years, which leaves time for. |
However. this also leaves time to migrate. | However, this also leaves time to migrate. |
Iun our simulations. the planets are initially ocated ou circular orbits at the position. from which the Desch(2007) disk is derived (sec above). | In our simulations, the planets are initially located on circular orbits at the position from which the \citet{Desch2007} disk is derived (see above). |
The planets masses are grown smoothly youn 0 to their present masses over 30 vears at the vceinming of the simulation. | The planets masses are grown smoothly from 0 to their present masses over $30$ years at the beginning of the simulation. |
The plauets are not accreting gas from the disk. | The planets are not accreting gas from the disk. |
During the first 100 orbits of Jupiter (1271 voars). the planets do not feel the disk potential. and therefore dout mierate. | During the first 100 orbits of Jupiter (1274 years), the planets do not feel the disk potential, and therefore don't migrate. |
During this time. the planets lanuch a wale. open a gap. perturb the disk. | During this time, the planets launch a wake, open a gap, perturb the disk. |
are released under theinfluence of the disk. aud start their migration. | are released under theinfluence of the disk, and start their migration. |
The aspect ratio is S.l at the location of Jupiter. and 9.1% at the location ofSaturn. | The aspect ratio is $8.1\%$ at the location of Jupiter, and $9.1\%$ at the location ofSaturn. |
The Reynolds muuber -Ον is Acos107 at the location of Jupiter. aud3.02«410? at the location of Saturn. | The Reynolds number $\mathcal{R}=r^2\Omega/\nu$ is $3.8\times10^5$ at the location of Jupiter, and$3.02\times10^5$ at the location of Saturn. |
Denoting P=3lu24qR2n | Denoting $\mathcal{P}=\frac{3}{4}\frac{H}{r_H}+\frac{50}{q\mathcal{R}}$ , |
The progenitors of core collapse supernovae (CC SNe) are massive stars. either single or in binary systems. that complete exothermic nuclear burning. up to the development of an tron core that cannot be supported by any further nuclear fusion reactions or by electron degeneracy pressure. | The progenitors of core collapse supernovae (CC SNe) are massive stars, either single or in binary systems, that complete exothermic nuclear burning, up to the development of an iron core that cannot be supported by any further nuclear fusion reactions or by electron degeneracy pressure. |
The subsequent collapse of the iron core results in the formation of a compact object. a neutron star or a black hole. accompanied by the high-velocity ejection of a large fraction of the progenitor mass. | The subsequent collapse of the iron core results in the formation of a compact object, a neutron star or a black hole, accompanied by the high-velocity ejection of a large fraction of the progenitor mass. |
The SNe ejecta sweep. compress and heat the interstellar medium. and release the heavy elements which are produced during the progenitor evolution and in the explosion itself. | The SNe ejecta sweep, compress and heat the interstellar medium, and release the heavy elements which are produced during the progenitor evolution and in the explosion itself. |
This can further trigger subsequent star formation process (e.g.?).. hence having a profound effect on galaxy evolution. | This can further trigger subsequent star formation process \cite[e.g.][]{McKee1977}, hence having a profound effect on galaxy evolution. |
Due to the short lifetime of their progenitor stars. the rate of occurrence of CC SNe closely follows the current star formation rate (SER) in a stellar system. | Due to the short lifetime of their progenitor stars, the rate of occurrence of CC SNe closely follows the current star formation rate (SFR) in a stellar system. |
The evolution of the CC SN rate with redshift is a probe of the SF history (SFH) and allows us to constrain the chemical enrichment of the galaxies and the effect of energy/momentum feedback. | The evolution of the CC SN rate with redshift is a probe of the SF history (SFH) and allows us to constrain the chemical enrichment of the galaxies and the effect of energy/momentum feedback. |
Poor statistics is a major limiting factor for using the CC SN rate as a tracer of the SFR. | Poor statistics is a major limiting factor for using the CC SN rate as a tracer of the SFR. |
At low redshift the difficulty is in sampling large enough volumes of the local Universe to ensure significant statistics (e.g.2).. | At low redshift the difficulty is in sampling large enough volumes of the local Universe to ensure significant statistics \cite[e.g.][]{Kennicutt1984}. |
While at high redshift the difficulty lies in detecting and typing complete samples of intrinsically faint SNe (???).. | While at high redshift the difficulty lies in detecting and typing complete samples of intrinsically faint SNe \citep{Botticella2008,Bazin2009,Li2010}. |
Moreover some fraction of CC SNe are missed by optical searches. since they are embedded in dusty spiral arms or galaxy nuclet. | Moreover some fraction of CC SNe are missed by optical searches, since they are embedded in dusty spiral arms or galaxy nuclei. |
This fraction may change with redshift. if the amount of dust in galaxies evolves with time. | This fraction may change with redshift, if the amount of dust in galaxies evolves with time. |
Progress in using CC SN rates as SFR tracers requires accurate measurements of rates at various cosmic epochs and in different environments. | Progress in using CC SN rates as SFR tracers requires accurate measurements of rates at various cosmic epochs and in different environments. |
Furthermore it requires a meaningful comparison with other SFR diagnostics to verify its reliability and to analyse its main limitations. | Furthermore it requires a meaningful comparison with other SFR diagnostics to verify its reliability and to analyse its main limitations. |
The CC SN rate is also a powerful tool to investigate the nature of SN progenitor stars and to test stellar evolutionary models. | The CC SN rate is also a powerful tool to investigate the nature of SN progenitor stars and to test stellar evolutionary models. |
Different sub-types of CC SNe have been identified on the basis of their spectroscopic and photometric properties and a possible sequence has been proposed on the basis of the progenitor mass loss history with the most massive stars losing the largest fraction of their initial mass (?).. | Different sub-types of CC SNe have been identified on the basis of their spectroscopic and photometric properties and a possible sequence has been proposed on the basis of the progenitor mass loss history with the most massive stars losing the largest fraction of their initial mass \citep{Heger2003}. |
However. this simple scheme where only the mass loss drives the evolution of massive stars cannot easily explain the variety of observational properties showed by CC SNe of the same sub-type and the relative numbers of different sub-types (?).. | However, this simple scheme where only the mass loss drives the evolution of massive stars cannot easily explain the variety of observational properties showed by CC SNe of the same sub-type and the relative numbers of different sub-types \citep{2009ARA&A..47...63S}. |
In particular. two important outstanding Issues are: the minimum mass of a star that leads to à CC SN (in a single or binary system): and what is the mass range of progenitor stars of different CC SN sub-types. | In particular, two important outstanding issues are: the minimum mass of a star that leads to a CC SN (in a single or binary system); and what is the mass range of progenitor stars of different CC SN sub-types. |
It is possible to constrain the mass range of stars that produce CC SNe by comparing the CC SN rate expected for a given SER and the observed one in the same galaxy sample or in the same volume. | It is possible to constrain the mass range of stars that produce CC SNe by comparing the CC SN rate expected for a given SFR and the observed one in the same galaxy sample or in the same volume. |
In this paper we exploit a complete. multi-wavelength dataset collected for a volume-limited sample of nearby galaxies to compare different SFR diagnostics with the CC SN rate. | In this paper we exploit a complete, multi-wavelength dataset collected for a volume-limited sample of nearby galaxies to compare different SFR diagnostics with the CC SN rate. |
This provides a method to constrain the cutoff mass for CC SN progenitors by exploiting the SFR as traced by Ultraviolet (UV) and emission. | This provides a method to constrain the cutoff mass for CC SN progenitors by exploiting the SFR as traced by Ultraviolet (UV) and emission. |
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